Friday, April 9, 2021

What is mathematics about?

I commend to you James Franklin’s latest article “Mathematics as a Science of Nonabstract Reality: Aristotelian Realist Philosophies of Mathematics.”  It’s a helpful brief survey of different ways that an Aristotelian alternative to Platonist and nominalist approaches to mathematics might be developed.  (Franklin explores these issues in greater depth in his book An Aristotelian Realist Philosophy of Mathematics.) 

Franklin approaches the dispute between these three views, and between alternative ways of spelling out the Aristotelian view, by way of the question: What is mathematics about?  The Platonist says that it is about a realm of abstract objects distinct from both the world of concrete material things and the human mind.  The nominalist says that it is not really about anything, since mathematical entities are in no way real.  The Aristotelian approach rejects nominalism and agrees with Platonism that mathematical entities are real.  But it disagrees with the Platonist about the location of these entities.  They are, for the Aristotelian, properties of concrete particular things themselves, rather than denizens of a Platonic “third realm.”

But exactly what sort of properties of concrete particular things?  Franklin suggests that different views which can plausibly all be characterized as broadly “Aristotelian” have proposed different properties as the ones mathematics is paradigmatically concerned about.  Some say that mathematics is fundamentally about the study of quantity; some say it is fundamentally about relations; some say it is about structure; and some say it is about patterns. 

Franklin discusses all of these possibilities and notes that, arguably, the study of relations and the study of structure more or less amount to the same thing.  The difference would be that the former starts with the elements of a structure and then works up to an account of how the relations between them give rise to a larger whole, whereas the latter starts with the whole and then works down to the relations between the elements.  The study of pattern might also be seen as the study of certain kinds of relations or certain kinds of structure.  So, these approaches to understanding what mathematics is about might, in Franklin’s view, plausibly be unified.  They can, in particular, be accommodated to the view that mathematics is about the study of the structural features of concrete reality.

What cannot be so easily assimilated to this approach, in Franklin’s view, is quantity.  For certain quantitative phenomena, though they have structural features, are not entirely reducible to structure.  (He gives size as an example.)  Hence Franklin thinks that there currently exists no entirely unified Aristotelian approach to the question of what mathematics is about.  We have to say that it is the science of quantity and structure (as he does in the subtitle to his book).

Varieties of realism

Franklin also has something to say about the main objections to Aristotelian philosophy of mathematics.  Now, in order to understand these objections and his responses to them, as well as the Aristotelian approach itself, it seems to me useful to compare the dispute in philosophy of mathematics to the more general dispute between parallel views about the problem of universals.  Recall that nominalism holds that universals like triangularity, humanness, etc. are mere fictions, whereas realism holds that they are real, something the human mind discovers rather than invents.  But there are several alternative ways of spelling out realism.

Platonic realism holds that universals are not only real, but exist in a “third realm” over and above both the world of concrete material things and any mind.  Aristotelian realism holds that universals are real, but denies that there is any such third realm.  Rather, it takes triangularity, humanness, etc. to exist only either in particular individual triangles, human beings, etc., or in minds which entertain these universals in abstraction from the particular individuals.

A third view, sometimes called Scholastic realism, can be interpreted as a kind of middle ground position between Platonic and Aristotelian realism.  Like Aristotelian realism, it denies that there is any “third realm” distinct from both the material world and all minds.  But like Platonic realism, it holds that universals are to be located first and foremost somewhere distinct from both the material world and finite minds – namely, in the infinite mind of God, where they function as the archetypes according to which God creates the world of concrete things.

You could think of Scholastic realism as “Aristotelianizing” Plato by bringing the realm of the Forms into a mind, namely the divine mind, thereby eliminating the third realm.  Or you could think of it as “Platonizing” Aristotle by making the divine mind function in something like the way the realm of the Forms does in Platonism.  Because it rejects the third realm and adheres to the Aristotelian twofold divide between the material world and minds, I tend to think of Scholastic realism as essentially a variation on Aristotelian realism.  But it is a dramatic enough modification that it is useful to have the separate label for it.

Now, applying these distinctions to the philosophy of mathematics, the mathematical Platonism Franklin is talking about obviously corresponds to Platonic realism about universals, and the mathematical nominalism he is talking about obviously corresponds to nominalism about universals. 

The Aristotelian philosophies of mathematics he describes correspond, naturally, to Aristotelian realism about universals.  But Aristotelian realism about universals, as I’ve said, takes universals to exist in two ways, even though it rules out the third realm of the Platonist.  They exist in concrete particulars themselves, but also in the intellects that abstract them from the particulars.  And it is the latter fact that opens the door to developing Aristotelian realism in a Scholastic realist direction.  The divine mind, qua mind, is technically not a Platonic third realm, and thus stays within the letter of Aristotelian realism.  But it nevertheless functions much like Plato’s third realm does.  In particular, it gives the Scholastic realist a way of dealing with phenomena that Aristotelian realism has a problem with, such as uninstantiated universals. 

For example, consider extinct animals like velociraptors.  After they died out, the universal velociraptor was no longer instantiated, and before human beings discovered its remains, no human mind entertained that universal.  So, during the long interval between extinction and discovery, the universal could be found neither in the world of concrete material things nor in human minds.  But what was true about the essence and properties of velociraptors did not change during that time.  What could have grounded that fact?  The Scholastic realist would answer that the universal still existed in the divine intellect.  (For exposition and defense of Scholastic realism, see chapter 3 of Five Proofs of the Existence of God.)

If you are a realist about mathematics, then, but reject Plato’s “third realm,” then there are two other realms where you might try to locate mathematical entities: in the world of concrete material objects, or in minds (including, in principle, the divine mind).  What, in Five Proofs, I label the Augustinian proof for God’s existence emphasizes the latter realm, and Scholastic realism is in that tradition.  Franklin instead emphasizes the former realm.  Naturally, one can also take mathematical entities to exist in both realms.  But one is likely to put greater emphasis on one rather than the other depending on which mathematical entities one takes to be most central to mathematics.

Franklin points out that Aristotelian realists about mathematics tend to focus on physically realizable and perceivable mathematical properties like symmetry and ratio, whereas arguments for Platonic realism often focus instead on higher infinities, the perfection of geometrical idealizations, and the like.  This different focus is, I think, also reflected in the different ways that Aristotelian realism itself might be developed.  If your emphasis is on showing how mathematics can be accommodated to an Aristotelian epistemology, you’ll probably focus more on the sorts of mathematical properties Franklin does, and on finding ways to locate mathematical properties in general in concrete material reality.  If instead your emphasis is on showing how the strongest points in favor of Platonism (infinities, geometrical perfection, etc.) can be accommodated within a broadly Aristotelian metaphysics, you’re more likely to be willing to take Aristotelian realism in a Scholastic realist direction (unless you prefer to add a dash of instrumentalism to your realism – see below). 

Naturally, the former route is also a more promising one if, when doing philosophy of mathematics, you want to avoid having to appeal to inevitably controversial theological premises, defense of which would require getting into matters far removed from mathematics itself.  Scholastic realism is a more natural option to consider when you’re approaching mathematics from the point of view of debates in natural theology.  (Cf. my review in First Things of William Lane Craig’s book God Over All: Divine Aseity and the Challenge of Platonism.)

Objections to Aristotelianism

Franklin addresses three main objections to Aristotelian philosophy of mathematics.  The first is to hold that the Aristotelian approach is undermined by Frege’s famous critique in The Foundations of Arithmetic of John Stuart Mill’s empiricist account of arithmetic.  Now, in a post on Frege and Mill from some time back, I noted that while it is controversial whether Frege was fair to Mill himself, his criticisms were effective against the crude position often attributed to Mill.  Franklin points out that they are not effective against a more sophisticated position than the one often attributed to Mill.

The second main objection to Aristotelianism is that higher infinities, and even huge finite numbers, are not plausibly instantiated in the physical world.  Here Franklin proposes two possible replies.  The first is to point out that this objection would prove too much insofar as it would, if effective, undermine natural science no less than an Aristotelian interpretation of mathematics.  For example, what Newtonian physics tells us about mass, distance, and force applies to values too large to be instantiated in the physical world, as well as to values that are instantiated.  Computational chemistry studies merely possible compounds.  And so on.  In other words, natural science studies uninstantiated universals.  If this is OK for science, why not for mathematics interpreted in an Aristotelian way?

The trouble with this response, though, as Franklin realizes, is that it just raises the question of exactly what the metaphysical status is of uninstantiated universals, whether those studied by mathematics or those studied by natural science.  Now, Franklin makes the perfectly reasonable point that an Aristotelian needn’t be a realist across the board.  One could take some mathematical entities to be real, but others to be merely useful fictions.  You have to go case by case.  But this is more plausible in some cases than in others, and Franklin allows that what he calls a “quasi-Platonist” account of some mathematical entities may be necessary.

Here, it seems to me, is a case where Aristotelian realism stands in need of development in a Scholastic realist direction.  The same can be said of the consideration raised by the third main objection to Aristotelianism considered by Franklin, which is that some mathematical entities (e.g. perfect circles and other geometrical entities) are idealizations that are never found perfectly realized in the physical world.  In response, Franklin points out that what applied mathematics strictly needs are only the approximations that are found in the physical world.  But this seems to me to miss the point.  For there are objective truths about the idealizations no less than there are about the approximations, and these cannot be grounded in what is actually there in the physical world.  As with infinities, Scholastic realism is able to deal with these in a way that an Aristotelian realism that avoids going in a theological direction is not.

Related reading:

Frege on what mathematics isn’t

The access problem for mathematical Platonism

Review of Craig’s God Over All: Divine Aseity and the Challenge of Platonism

Rucker’s Mindscape

David Foster Wallace on abstraction

Frege on objectivity

202 comments:

  1. It seems noteworthy to me that the notion of a universal of velociraptor _cannot_ be instantiated, because, there being no living or perfectly-preserved specimens, the term is necessarily inadequately defined. Is that an argument that favors Arist. Realism?

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    1. the notion of a universal of velociraptor cannot be instantiated because it is a hollywood fiction. created by PEDO hollywood to support the obvious LIE of evolutionism which no faithful catholic, or anyone with proper education, would ever take seriously.. That a blog proporting to be from a "traditionalist catholic" perspective would accept the kind of "Modernism" unequivocally condemned by Saint Pope Pius X, and would feel the need to insert such a falacious reference to please its fake "catholic", Novus Ordite consumers, is a sad sign of our times.

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    2. Simon,

      I write an article on the philosophy of mathematics, and your lunatic takeaway is that I am a modernist-evolutionist-abettor-of-Hollywood-pedophiles. Who let you out of your cell and gave you access to a computer?

      The internet never ceases to be a strange and depressing place, and daily to provide confirmation of the doctrine of original sin.

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    3. How on earth can there be a universal for a species of creature when the term 'species' is ill defined and non-essentialist?

      Biological evoiution proceeds through the changing frequency distribution of genes in a population over time. If we start at point X in time with a particular population of creatures, which we are inclined to say are members of the same species ( because of genetic, anatomical and behavioural similarities, and the fact that they can interbreed ), then a very long time later ( at time Y say ) sufficient changes will have accrued that we would say that a different species had evolved. However, this would be a human act of decision and labelling. All that is happening between times X and Y is that the frequency distribution of genes in the population is changing.

      So let us take a particular species like 'Triceratops' , 'Bald eagle' or indeed 'velociraptor'. Since there will be an evolutionary continuum from the far past and different progenitors to these 'species', and indeed continuum into a very different far future, how can we possibly sensibly speak of the universals 'Triceratops', 'Bald eagle' or 'Velocitaptor'?

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    4. Yet another kickass heavy-metal essay. Exemplary, Ed.

      Keep going, King.

      By the way, Kai Nielsen passed away on Wednesday the 7th. I'll be posting my letter to him a couple of years ago. All his talk in his writings about non-evasiveness, yet he didn't live that text. Yet I still maintain that he's the greatest thinker of all time and will be remembered as The Man Who Saved Theism, in spite of his notorious atheism.

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    5. Machine

      You.claim that Nielson is the greatest thinker of all time and will be remembered as The Man Who Saved Theism, although he was an atheist. Well, perhaps you have had astounding insights which have escaped us lesser mortals, but you will understand that on first encounter these sound like unhinged claims. In a very few sentences , could you point to your reasons for making these claims please? 'King' Ed has not found it necessary to keep abreast of Nielson's work , such is his estimation of its importance.

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    6. What is with this particular post and the unusually-high concentration of lunatics, trolls and sp3rgs?

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    7. Ed doesn't need to because he's read Nielsen and my numerous previous comments about the subject on this blog. Unlike lazy anonymous you.

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    8. Marchog 3.32PM

      It is unkind and uncharitable of you to portray machinephilosophy like that, before he has had the opportunity to defend his odd comments.

      machinephilosophy 3.32PM

      I thought my post was perfectly reasonable. You could at least have provided references to your 'numerous previous comments' ( are you certain that Feser has read them all? ) if you were not willing to provide a concise summery here, instead of requiring me to develop psychic powers.

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    9. How on earth can there be a universal for a species of creature when the term 'species' is ill defined and non-essentialist?

      Biological evoiution proceeds through the changing frequency distribution of genes in a population over time.


      Unknown, even granting the historical assertion about the gradual alterations of populations, this historical proposition cannot DISPROVE the existence of "species" in the Aristotelian sense. Effectively, all that you have managed to do is claim that the terms we have - triceratops, bald eagles, etc - are merely (sometimes) useful terms, i.e. one of the versions of nominalism. It does nothing to PROVE that nominalism is correct and none of the philosophies (like Platonism or any of the Aristotelian philosophies) that hold out for "forms" is correct.

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    10. Tony

      I am thinking Unknown is likely channeling the traditional Cladist definition of species not the Aristotelian.

      It's like Gnus who confuse Aristotle's Motion/Motus with Newton's Momentum and comically claim Newton has "refuted" the first way or something?

      Why is everyday always a terminology fight with a Gnu?

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    11. Tony 5.15PM

      I was not batting for any particular general theory of universals, just raising a problem as I saw it with using the term in the case of a biologically non-essentialist concept like 'species', something you have done absolutely nothing to address.

      Of course biological evolution proceeds at population level. Within a 'species' there will be genetic diversity, and it is natural selection, acting on individuals within populations which breed together over time, that shifts the frequency distribution of genes in these populations and so drives biological evolution. That is all very standard.

      Coming back to our Tricerotops, if we could ressurect a female of this 'species' from a fossil, then stand it in a time sequenced line with biological mothers going back many millions of years, and biological daughters going forewards for many millioms more, you would have a procession with creatures at the beginning and end of which you would never think to label 'triceratops', and which could not interbreed with the mate of the original one, yet at no point in the procession will there have been any kind of discontinious transition. So if the concept 'triceratops' ( like 'Bald eagle' , or any other biological species) does not have essential content, how can there be a universal for it?

      Ya'kov 8.35pm

      More of your usual insults and obscuranticism , with your talk of 'Gnus', 'channeling' and terminological confusion. Be away with you troll!

      On a more general note, I once pointed out that Thomism had a clear problem with using everyday terminology ( eg species, evil, momentum, perverted ) in a manner very diffetent to that used by ordinary people , for which I was rewarded with a barrage of protest as ( among other things ), did this not happend in physics too ( eg velocity, power flavour, charm )? The difference of course is that Thomism is an extremely minor philosophical current struggling to get a fair hearing ( whereas physics is, er, rather well established ), so your terminological problem should matter greatly to you.

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    12. @Unknown

      >More of your usual insults and obscuranticism , with your talk of 'Gnus', 'channeling' and terminological confusion. Be away with you troll!

      But you are using the Cladist definition of species not the Aristotelian. You are confused. It is your own fault you don't understand the proper Terms of Art. Also I note in yer back pedaling response to Tony you are now, as is yer want, pretending you meant something other than what you said and trying to change the subject.

      Which is what you do.

      >I once pointed out that Thomism had a clear problem with using everyday terminology ( eg species, evil, momentum, perverted ) in a manner very diffetent to that used by ordinary people.

      There is no problem. That is no excuse for not using the proper terms of Art for Thomism here on a blog dedicated to Thomism or learning about them. Popular understandings of some common terms are not an excuse to ignore learning about proper terms of Art and "species" has a specific definition in Scholastic Thought. Go look it up.

      Or you can continue to cry when people call you out on yer ignorance rather then own it humbly and do better.

      > for which I was rewarded with a barrage of protest as ( among other things ), did this not happend in physics too ( eg velocity, power flavour, charm )?

      Except when a Thomist talks about Motion we are talking about Motus aka "a potency being put into act by something already in act".

      It has nothing to do with Newton & physics and BTW Newton's momentum can be modeled that way.

      What you didn't know that?

      >The difference of course is that Thomism is an extremely minor philosophical current struggling to get a fair hearing ( whereas physics is, er, rather well established ), so your terminological problem should matter greatly to you.

      Yer not an expert in philosophy. You don't know what is major or minor. Stop blowing smoke.

      Also common sense this is a blog full of Thomists whose definitions applies. Also popular ignorance is not an excuse. There are many popular notions that are false for example "Man evolved from Gorillas". No, that is false "Man and modern Primates are presumed to have a common ancestor". There that is better.

      See proper terms of art in evolutionary science not popular notions. Works quite well.

      This is a Blog where they discuss Scholastic Philosophy. Why don't you actually try contributing to that discussion instead of boring the wee shite out of the rest of us with yer base and childish ridicule?

      Unknown yer not interested in philosophy by yer own admission. What is it you said below to BalancedTryteOperators?

      First you called metaphysical deliberations meaningless and drivel. Then when asked why you are here (a philosophy blog which discusses Metaphysics) you answer "There have been many discussions about the behaviour of the Trump regime or some leftists in the US for example, or the efficacy or otherwise of public policy as regards covid-19."

      All subjects about politics. Not philosophy!

      You validate everything I say about you. You have nothing to contribute here. Go too the comboxs over at Breitbart or Newsmax and pick a fight with a Trump supporter. You will have a ball.

      But here bring with the philosophy or get lost.

      Unknown why can't you learn philosophy? Why can't pick a nice Atheist friendly metaphysical view and defend it? Why can't you formulate philosophical defeaters for Scholastic philosophical concepts?

      You might actually not be boring if you did. I know I would like you a whole lot better.

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    13. Yakov 12.13AM

      Another interminable deranged rant from Mr Yakov . Completely unhelpfull. Hope someone had the heart pills ready for you after that one, or probably more aptly the antipsychotics.

      Have you noticed that not one of your fellow travellers in metaphysics and theology behaves remotely like you? That is because they have judgement, perspective and self control, qualities which are evidently absent in you.

      How on earth was my response to Tony a case of back pedalling, claimimg I said something different from what I actually did and an exercise in concealment? I am completely baffled. As for the contention that my genuine puzzlement as conveyed in my original post is due to a terminological confusion, if that is so, the helpfull thing to do would be to explicate it instead of demanding that someone become an expert in Thomism before daring to comment on this blog, or at least to spend forever checking that everyday words that they might encounter are not in fact being used as specialized technical terms. In any case, if the word 'species ' has a specialised meanining in Thomism , that hardly precludes me from asking how the notion of a universal can be applied to a non-essentialist notion such as a biologucal species, which you people often do. I belive that my original post followed one which asked about making sense of universals in the case of a long extinct but presently undiscovered kind of dinosaur for example.

      You have anger and self control issues Mr Yakov, but I am guessing that you already knew that.

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    14. Mr Yakov

      As a PS, please stop assuming that any 'Unknown' you encounter and take exception to is me - many 'Unknowns' crop up and post on this blog. Much of the time I really do not know what you are rambling on about. One example is your reference to my confusions about the Thomistic conception of 'motion' in your post above. But that is another terminological infelicity which evidently causes you endless problems to add to the list.

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    15. Unknown, an essentialist conception of species is perfectly compatible with modern evolutionary theory. Indeed, the most plausible explanation for why biological organisms form distinct "clusters" we can recognize as "species", as opposed to a continuum of forms, is simply because it reflects the fact that species are the combinations of alleles/genotypes that "work" in a given environmental context. That is, they occupy adaptive peaks in the fitness landscape to use the technical terminology. And these peaks are discrete/discontinuous, hence "species" are real entities reflecting a real phenomenon.
      When species evolve, allele frequencies are moving to another fitness peak, usually because the environemental conditions are changing.
      Species are real discrete biological phenomena, despite the evolutionary process being a continuous temporal one.

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    16. Jonatan Blais 5.54AM

      What we take to be individual species are a good approximation to a discrete biological phenomenon at a point in time ( though hardly perfectly so , as some different species can interbreed),
      but not so over time , as the evolutionary process is a continuous one which will extend into the future. What can therefore constitutes the universal of a species , bearing in mind that God has awareness of all future conditions? There just arn't any essential species to have a universal of, or is there a different universal for a population of organisms in each second of evolutionary time? And how could there be a universal for an extinct creature like a tricerotops? I mean, at what precice moment of prehistory did the authentic triceratops exist?

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    17. Unknown, I'm afraid you misinterpreted evolutionary biology. It is not surprinsing since it reflects a common and widespread misconception willfully fed to the general public to buttress the naturalistic assumptions of most popular science writers and communicators.

      Evolutionary theory is based on population genetics, a heavily mathematized field in which evolution is modeled as a random walk through a multivariate function called a fitness landscape whose peaks represent genotypic/phenotypic "solutions" to this function.

      Natural selection is the algorithm that explores this function and actualizes some of the potential genotypic/phenotypic solutions. What we call "species" are these possible viable solutions and their essences are represented in the language of biology by the genotypes/phenotypes defining their respective peaks.

      For any given environmental conditions x, there are a finite number of viable solutions y, thus a finite number of possible species. These solutions are true universally. Because of the constraints imposed by physics (e.g. pH, temperature, pressure, etc...), only a finite number of environmental conditions are compatible with life. Again, the whole ensemble is finite, not infinite, and computable in principle if not in practice. Therefore, "species" represent a truly universal category. The fact that at any given time, the species being actualized varies is completely irrelevant to the universality of these solutions and their essences. Potential hybrids are equally irrelevant to the question.

      The fact that modern biology, by nature an informational and algorithmic phenomenon, remains best explained by an aristotelian hylemorphic metaphysics and cannot be reduced to physics, greatly bothered mid 20th century biologists like e.g. Ernst Meyer and Jacques Monod. No satisfying solution has yet been found for the naturalists (Robert Koons has made several interesting points about that, but there are another even more fundamental one based on the languinstic property of the genetic code that could be developped).

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    18. @Unknown

      So basically pretending to be two people is sick and proves me right. Yer here to troll and not intelligently discuss the issues.

      You are basically dishonest. I don't for a second believe there are many unknowns. If there are then you lot have a moral obligation to differentiate yerselfs. Pick a unique handle and stick with it.

      Anyway I am right. You are using a cladist definition of species not a scholastic one.

      Yer confusing terms just like you are trying to confuse by pretending to be multiple people.

      Grow up buddy. Learn some philosophy and oh BTW. Isn't this "off topic"? What does this all have to do with various theories of realism and Math?

      Could you do some reading and address the issue. You might actually become a proper Philosophical Atheist which could only make you interesting. Instead of all this....

      (Why do I get the feeling this guy is just Stardusty posting on another name? It could be Paps? I wouldn't put it past either of them).

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    19. Son of Yakov 11.21AM

      Yet another installment of War and Peace, this time with Yako displaying paranoia by claiming that I am StarDusty posting under another name, or maybe 'Paps'! You really have lost it now wacko Yacko - hope your missis has the antipsychotics handy.

      Jonatan Blais 10.45AM

      Thank you for that full and erudite reply, but I remain unconvinced.

      The frequency distribution of allelles in a population will vary over time, randomly by genetic drift and directedly because of natural selection. Sometimes there will be relative stasis over time , sometimes gradual shifts over a long period, and sometimes very rapid change, depending on the circumstances. But evolution is always gradual and Darwinian, even when changes are relatively rapid as compared to the average rate, and we just do not get instantanrous transitions. Given that this is so, it is just not possible to say that species X say emerged at a particular point in time and ceased to exist at another ( unless there was an extinction event ) - this is a matter of humans making a labelling decision with the very limited information available in the fossil record. Even if a genotypic and so phenotypic shift is very rapid as these things go, it will still be very slow indeed when judged on a human time scale. So I still think that the notion of a species ( other than instantaneously , at a point in time ) is vague, and a consequence of not seeing the continuous nature of evolution and so.the non-essentialism among the organismal forms in the biological world.

      Although there is much consensus among mathematical evolutionary bioligists, punctuated equillibrium, with its rapid transitions between peaks of the fitness landscape ( which would in any case be extraordinarily slow by ordinary standards ) is not a consensus view, and I think that most evolutionary biologists would be surprised to learn that modern biology is best explained by an Aristotelian, hylomorphic meraphysics.

      I

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    20. "The frequency distribution of allelles in a population will vary over time, randomly by genetic drift and directedly because of natural selection. Sometimes there will be relative stasis over time , sometimes gradual shifts over a long period, and sometimes very rapid change, depending on the circumstances. But evolution is always gradual and Darwinian, even when changes are relatively rapid as compared to the average rate, and we just do not get instantanrous transitions."

      Nothing I said require any particular tempo in evolution. For example, I think (like most contemporary biologists) that Gould's punctuated equilibrium is mostly wrong. But that's irrevelant.

      "it is just not possible to say that species X say emerged at a particular point in time and ceased to exist at another ( unless there was an extinction event ) - this is a matter of humans making a labelling decision with the very limited information available in the fossil record."

      Again, this is irrelevant. The adaptive peaks are what represent what we call species and as long as the environmental conditions remain the same, these peaks remain the same. At any given time, gene pools are either at or "en route" toward these peaks. But the peaks are stable as long as the environment is stable. Our labelling reflect the fitness landscape, even if the various population gene pools are not always all at the top of their respective peak. The reproductive isolation mechanisms that evolve during the process of speciation, themselves relfect the need to ensure that gene pools are indeed discontinous and discrete to reflect the discretness of the landscape.

      "...I think that most evolutionary biologists would be surprised to learn that modern biology is best explained by an Aristotelian, hylomorphic meraphysics."

      That's because most evolutionary biologists (and I'm one of them), like most scientists in general, know virtually nothing about philosophy and are usually quite bad at interpreting the philosophical implications even of their own science. Most assume uncritically that naturalism is true without ever really thinking about it. However, some evolutionary biologists (like Mayr and Monod) were aware of the formidable problem posed by the inherent teleology in biology for the project of reducing biology to physics. As I said, we're still waiting for a solution...

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    21. Jonatan Blais

      When a population is moving - genetically speaking - from one adaptive peak to another, the shift from one island of stability to the next may take a very long time indeed. Are you saying that the term species is ill defined and so inapplicable during this transition? Also, how do you know that present populations of many organisms that are generally condidered to be species are not in this transitional phase and so not at stable adaptive peaks?

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    22. Unknown

      What I'm saying is that when we talk about species, we talk about co-adapted gene complexes that reflect a real discontinuity in nature. The fact that in some cases, populations are in transit toward an adaptive peak that they haven't reach yet doesn't change the fact that these populations are aiming at a target so to speak. For example, a cryptic lizard species that evolved skin colours and skin tags to mimic certain tree trunks and the lichen it harbours may not have yet reach the optimum resemblance that its genome and its biology could allow, but this cryptic strategy is still an essential part of what defines that species’ essence.

      Reproductive isolation mechanisms, that define most of the species we commonly think about under the biological species concept, exist to protect the integrity of gene pools, so they can reach these peaks. When things change, it is the shape of the landscape that changes. Such change in the fitness function means that populations will track these changes and reproductive barriers will insure they retain their genetic integrity along their path toward a new peak if they survive extinction.

      The way to reconcile the “scientific image” given by evolutionary theory and the manifest image (to use Sellar’s terminology) is, as always not trivial, but we must remember that this is what the theory looks like at the moment. It may change in the future. Indeed, how population can cross adaptive valleys is an unresolved issue in biology. But philosophically, the fact remains that when we talk about species, we refer to a real universal biological phenomenon: there exists a finite number of discrete/discontinuous adaptive peaks for life on earth and so a finite number of potentially successful genotypes/phenotypes actualizing these potentialities.

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  2. I am waiting with baited breath for either Mike Flynn or Grodriguez to show up and say something really cool and interesting in support of this post.

    If they do then Christmas come early.

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    1. Mike Flynn is enduring a familial crisis and is engaging here only to distract his mind from darker thoughts.

      1. Regarding the reality of mathematical objects: In physics it is important to distinguish between things and heaps. The former have essence; the latter do not. That is, a tricerotops may be a thing (ouisia, substantia) but a sand dune is not. It is a mereological sum of things. But before we respond that a tricerotops is also a sum of tissues, we note that in a thing the parts act as part of the thing and not as things in themselves. None of the sand grains in a dune function as the hands or feet or stomach of the dune. They each act independently as a sand grain. The dune has no more thinginess than a traffic snarl on a highway.
      2. A thing may have fuzzy boundaries without losing its thinginess. "The existence of dawn and duck does not invalidate the distinction between night and day." Night and day are not things, but the analogy can be used. So, Barney the triceratops is a thing and thus has an essence: a form in virtue of which it can be called a triceratops. But is the species of triceratops a thing or a heap?
      3. Considered across time, does the fuzziness of the emergence of triceratops and its passing away invalidate the existence of triceratops? (Always recognizing that by modern hair-splitting, we can actually recognize multiple species of triceratops over time and space.)
      4. Does all that mean that the 'origin of species' lies in human perception?

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    2. TheOFloinn 7.45AM

      To your unanswered questions 3 and 4 I would answer yes and yes. The discrete existance of an entity 'triceratops' and the coming to be of new discrete species are human fictions, a way of looking at the biological world that simply does not acknowledge its evolutionary continuity and falsely imports essentialism into it.

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    3. Mike, sorry to hear that. Prayers for you and yours.

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    4. God be with you Mike Cheers.

      Spot on analysis btw.

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  3. Would it be accurate alternatively to refer to the position known as Scholastic realism as Neoplatonic realism? Didn't Plotinus achieve a synthesis of sorts between Platonism and Aristotelianism by locating the Forms in the Intellect that emanates from the One?

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    1. The idea came way before Plotinus, actually: https://journals.openedition.org/etudesplatoniciennes/448

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  4. What exactly is the nature of quantity in reality? Quantity is a uniquely material property, and it doesn't seem reducible to just a limitation of existence - quantity has its own definition and formal structure or content, we coherently speak of things having more quantity than something else (say bigger in size, mass, length, etc), and so from this it seems that quantity is a real type of being.

    But if it's a real type of being, not just a lack or limitation, then why do higher actualities lack it? Why isn't God quantitative, for example? If quantity is a real type of being with its own nature, then how is it rooted in God who is supposed to be pure act?

    Does quantity in some way reflect God? If so, how?

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    1. Quantity is not limited to physical things; for example, you can count angels if there are any, or virtues. More here https://www.google.com.au/books/edition/Neo_Aristotelian_Perspectives_in_Metaphy/2QBgAwAAQBAJ?q=&gbpv=1#f=false

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    2. I guess I'm talking dimensive quantity specifically, as Aquinas denies angels have that.

      So if dimensive quantity seems like a real type of being, then the questions above are still interesting: Why do higher actualities lack dimensive quantity? How is it rooted in God and how does it reflect Him?

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    3. Hey JoeD

      I would think Ed would agree with Aristotle and Kant that it's a basic concept already assumed in all thinking. Specifically, it's already assumed in our use of the singular and plural in any statement or question we pose.

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    4. @machinephilosophy,

      How would it relate to God though? Why isn't an angel quantitative, or God?

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    5. Unless I'm missing he point of your question I would say that quantity is necessary, even in the binary is/is not. "an" is a singular indefinite article, "angel" is a singular noun. Our God is one. Unity(singularity)/plurality is already built into language and thought. There's a bivalence in polar concepts, true/false, and so on.

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    6. I guess I'm talking dimensive quantity specifically, as Aquinas denies angels have that.

      So if dimensive quantity seems like a real type of being, then the questions above are still interesting: Why do higher actualities lack dimensive quantity? How is it rooted in God and how does it reflect Him?


      But JoeD, clearly dimensive quantity is an aspect of "being" only to the extent that the entity is material being. And clearly having a material aspect, i.e. that which distinguishes and separates individuals of the same nature, can only apply to SOME sorts of being, not to all. It is manifestly inapplicable to God, since it is a feature of divinity to be simple and unique, so there cannot be several with his nature. That is to say: to be extended, and thus to be material, is PER SE already to be limited.

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    7. Does the space of colors have "dimensive" quantity? I would say so, in that there's continuous variation from red through orange to yellow. But colors are not material beings (though no doubt only material beings have them).

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    8. James Franklin 7.14PM

      There is a continuum of wavelengths across the visible part of the electromagnetic spectrum, but not of colours. On the contrary, the transitions are rather sudden, but there is variation between individuals, especially as regards the location of the cut off at the short wavelength end.

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    9. @Tony,

      But in that case isn't quantity (and secondary matter in general) still a positive reality rather than limitation? If so, why do higher actualities lack the positive actuality of quantity?

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  5. @grodrigues,

    Quick question about math: I've read that while the Axiom of Choice provides us with the most examples of nonmeasurable sets (NMS), their existence is also provable using weaker axioms such as BPI or Hahn-Banach.

    But as Pruss points out: "But a lot of these AC-ish results have no intuitive plausibility over and beyond AC. The only reason I have to think BPI or HB are true is that I have reason to think AC is true--because it just seems true--and AC entails them. If I thought AC were false, I would have no reason to think BPI and HB are true."

    "Dependent Choice (DC), and Choice for families of two-element sets (AC2), may be different--they may have intuitive plausibility over and beyond that of full AC."


    Is this true? If one rejects the AC would this also weigh against the weaker BPI and HM because they approach AC?

    Some more options are presented here: https://math.stackexchange.com/questions/133999/can-one-construct-a-non-measurable-set-without-axiom-of-choice

    "Non-measurable sets can be generated by free ultrafilters over N too, which as remarked is a strictly weaker assumption that the axiom of choice. If there are ℵ1 many real numbers and DC holds then there is an non-measurable set as well, which implies that ZF+DC(ℵ1) also implies the existence of non-measurable sets of real numbers - however this is not enough to imply the existence of free ultrafilters over the natural numbers!"

    "Several other ways to generate non-measurable sets of real numbers:"

    "3) The existence of a Hamel basis for R over Q"



    Do these other options - about DC with aleph 1 and Hamel basis - also prove nonmeasurable sets?

    And if one wants to reject nonmeasurable sets completely, what mathematical possibilities or principles would need to be rejected in order to end up without NMS?

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    1. Also, here's an article on transcending the universe V of math and going into even greater infinities: https://mathoverflow.net/questions/100981/ultrainfinitism-or-a-step-beyond-the-transfinite

      Quote: ""Now, let us be brave and say: what about breaking through into the trans-transfinite? What about , for instance, starting from V itself and state that its size is some hyperinfinte number, say ℵ0,1 ?"

      "(SIDE NOTE ON NOTATION: The standard aleph series would now be ℵ0,0 , ℵ1,0, .... The second subindex controls the degree of hyperfiniteness, much like degrees of unsolvability. I could have put it on top, but then it would cause troubles with cardinal exponentiations )."

      "Wait, I hear you say loud and clear. Are you crazy? Don't you know that there is NO SET X such that X=V? Don't you know that there is no max ordinal? Yes, ladies and gentlemen, I do know it. But I do reply: and so what? The objection is exactly the same as the one of the finitists vis-a'-vis ω. Someone has broken through the finite, so why not the transfinite? There is no set, but who said that it must be a set? In fact, start with a pairs of transitive countable models of ZFC, M0 and M1, with M0≤M1, of different tallness (the ordinal height of the first being strictly smaller than the height of the second). From the point of view of M0, IT is the full universe of sets, and the ideal ordinals of M1 some unimaginable higher level of infinity. Of course, say you, M0 does not see M1."

      "True, but we do. And -I think- nothing prevents us from formalizing their reciprocal relation as some new theory of sets (the elements of M0) and classes (the elements of M1). Note that here all sets are classes, but not viceversa. Also, being more reckless, we could generalize the above by stipulating an entire chain of ascending hyper-infinities, and perhaps enrich ZFC with an axiom that says that for each model there is a cofinal (in V) ascending chain of taller models, the Cofinal Tallness Axiom...."


      Here are some comments about whether V contains all sets:

      "In an (I hope) temporary bout of megalomania, I answer as follows. What you and Cantor and others regard as the absolute infinite, V, is really only a level Vκ of the cumulative hierarchy, corresponding to an inaccessible cardinal κ below which there are cardinals that are, in the sense of Vκ (but not in the sense of my whole universe), large in all the ways you mentioned. My universe has lots of far larger cardinals, including larger κ′'s that share the properties I just stated for κ. All these hyper-transfinite things, which the rest of humanity can't see, make me feel wonderful, until I realize that my hyper-universe does't seem to have any essentially new properties, compared with your tiny Vκ; indeed, my universe seems to be adequately described by ZFC plus the axiom () that there is a proper class of inaccessible cardinals μ each of which is the supremum of the smaller cardinals that satisfy, in Vμ, the large-cardinal axiom I0 (or whatever is currently at the top of the large-cardinal chart). My () is a bit stronger than I0, but not enough stronger to impress any set-theorists. So I guess I'll go take the medication to cure my megalomania, and rejoin the rest of the world in ZFC plus (not entirely specified) large cardinals."

      "To summarize: The intuitive idea of V is that it contains all the sets. If the cumulative hierarchy can be continued hyper-transfinitely beyond your V, then your V isn't the genuine V."


      So my question is: Can all of math be contained in something like V or a hyper-hyper class? Or can infinite recursion go on forever?

      I've also heard it said that the cardinality of all possible propositions is so great the concept of cardinality doesn't apply to it. So is the realm of propositions the greatest realm there is, or are there some things greater than that?

      Do you happen to know enough to be able to answer this in some way?

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    2. There's an intersting new paper on realism about the higher infinities by Rupert McCallum, Intrinsic justifications for large-cardinal axioms, in Philosophia Mathematica, https://academic.oup.com/philmat/advance-article-abstract/doi/10.1093/philmat/nkaa038/6210985

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    3. @JoeD:

      This is off-topic, so we should not clutter the combox with what is in essence a two-person private conversation. I will answer the questions to the best of my ability in a textual dump and leave it at that.

      "Is this true? If one rejects the AC would this also weigh against the weaker BPI and HM because they approach AC?"

      I am not sure what you are asking here, since Pruss is talking about "intuitive plausibility" which is not a mathematical concept. For what it's worth, I think Pruss is right. "Intuitive plausibility" is finicky; there is a running joke, attributed to J. Bona I think, that goes like: "The Axiom of Choice is obviously true, the Well-ordering theorem obviously false and who can tell about Zorn’s lemma?" I heartily concur with the sentiment (especially that AC is obviously true), but all statements are equivalent...

      "Do these other options - about DC with aleph 1 and Hamel basis - also prove nonmeasurable sets?"

      Yes. The fact that every linear space is free is equivalent to AC but the fact that R over Q is free (or has a Hamel basis) is weaker than AC. It is a result of Pawlikowsi (of the 1990's if memory does not betray me), that HB (the Hahn-Banach theorem) over ZF + DC is enough to prove Banach-Tarski but HB is provable with BPI which is stricly weaker than AC. I do not know about the DC + "there are aleph_1 reals" although I do note that the latter is the Continuum Hypothesis (or something very close to it -- would have to check it), which is even more problematic than AC.

      "And if one wants to reject nonmeasurable sets completely, what mathematical possibilities or principles would need to be rejected in order to end up without NMS?"

      We already had this discussion, and as I said then, I do not think there are any problems, philosophical or otherwise, with the mathematical statement "there is a non-measurable set". If you do want to reject them, you must reject every principle that entails their existence. AC is an umbrella, but below it there is a plethora of weaker principles, and these do not form a consistency strength chain but are rather a forest, so things get complicated. Rubin and Rubin is the standard monograph on the topic; Herrlich's book is also good. While DC is enough to say, do most analysis it is not quite enough. To illustrate, you can hardly do functional analysis without HB; for *separable* spaces, HB is provable in ZF + DC. Are separable spaces enough for the mathematical applications? Complicated to answer. As soon as you need spaces of operators, spaces of continuous functions on non-metrizable spaces, most C-star algebras, etc. you leave the realm of separability. And the subjects themselves, independently of their would-be applications, are perfectly legitimate mathematics.

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    4. (continue)

      "So my question is: Can all of math be contained in something like V or a hyper-hyper class? Or can infinite recursion go on forever?"

      Most mathematicians do not peek beyond the first few stages of the cumulative hierarchy, so most standard mathematics can be formalized in a fraction of the universe of sets, using say, subsystems of second order arithmetic a la reverse mathematics. Beyond that, most mathematics can be formalized in ZFC. "Most" is not all though. Goedel's incompleteness theorems impose limits on "one formalization to rule them all". The question of the extent -- both in "depth" and "width" -- of the universe of sets is itself a mathematical question. In category theory, you tend to talk about "all" objects of this or that type, which goes beyond ZFC. In my opinion, the best way to approach the matter is still not found, but things get technical here and after all, what do I know?

      "I've also heard it said that the cardinality of all possible propositions is so great the concept of cardinality doesn't apply to it."

      I do not understand this. First, when I think of propositions I think of a quotient of statements in a language and the latter is a countable set, so the set of propositions is countable. But maybe they are thinking of a different thing. The statement "so great the concept of cardinality doesn't apply to it" can mean different things. It could simply mean that the class in question is not a proper set but a class, and thus there are no cardinals in the universe to measure it. For example, maybe what you read had in mind the identification of propositions in first order predicate calculus with subsets of a set, and then naively, it follows that every proposition is identified with a subset of the universe V of sets, and thus lives in 2^V which is obviously not an element of V. So what we have is a (proper) class, not a set, which just happens to be have grown too large to be a member of the respectable sets and be measurable with cardinals in V.

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    5. @grodrigues, Thanks for the input!

      One final question about Pruss comments though is this: Is it accurate to say that if one thought AC were false, one would also not have much reason to think BPI or HB are true, or would undermine a lot of the plausibility behind them?

      And from this what I gather is that if we rejected BPI, HB and even free R-over-Q, then though that would certainly be a possible move to make it would likely impoverish the current mathematical landscape and bring limitations on what we could do, correct?

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    6. @JoeD:

      "Is it accurate to say that if one thought AC were false, one would also not have much reason to think BPI or HB are true, or would undermine a lot of the plausibility behind them?"

      With the caveat that we are talking about plausibility, that is my understanding of what Pruss is saying, and I agree with him.

      "And from this what I gather is that if we rejected BPI, HB and even free R-over-Q, then though that would certainly be a possible move to make it would likely impoverish the current mathematical landscape and bring limitations on what we could do, correct?"

      Right -- not "likely" but "provably so". How much can it be recovered or worked around is subject of current, intense research (buzzwords like "topos theory" are what you should be looking at).

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    7. @grodrigues, Understood. Also, is free R-over-Q a type of AC-ish thing like HB and BPI, or is it distinct from Choice-ish principles?

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    8. I do not understand this. First, when I think of propositions I think of a quotient of statements in a language and the latter is a countable set, so the set of propositions is countable.

      I used to think just this against having higher-than-countably many propositions. But what about the possibility of analogical and equivocal meanings to terms? Arguably, there COULD be any number of shades of meaning to each term, which would have the effect of making therefore any number of distinguishable propositions from the same basic N words. However, also arguably, it would take ACTUAL acts of finite intelligences in language-making to generate such distinct meanings, and those acts would never be more than countable.

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    9. @JoeD:

      "Also, is free R-over-Q a type of AC-ish thing like HB and BPI, or is it distinct from Choice-ish principles?"

      Depends on how you define "a type of AC-ish thing". A reasonable criteria is an existential statement that requires some choice principle to prove. In that sense, the answer is yes. Note that as I said above, the fact that every linear space (over any field whatsoever) is free is equivalent to AC.

      @Tony:

      "But what about the possibility of analogical and equivocal meanings to terms? Arguably, there COULD be any number of shades of meaning to each term, which would have the effect of making therefore any number of distinguishable propositions from the same basic N words."

      You would need at the very least an uncountable number of meanings, which strikes me as implausible. But with analogical meanings we are leaving the realm of mathematics as currently practiced.

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    10. @grodrigues,

      1) About propositions, even if we take univocal propositions it strikes me as plausible to say there are at least uncountably many propositions, if not even more.

      This is because for every possible object of thought there needs to be a proposition about it, and so for every individual member of the Real line there needs to be a proposition stating whether it's necessary or true.

      But the real line is uncountable, so the cardinality of propositions must be at least uncountable because propositions must apply to every number and member of the Real line, including those that can't be countably added.

      2) I've also read that the cardinality of all functions (both arbitrary and not) is greater than that of the real numbers. Assuming the continuum hypothesis this would make the functions Aleph-2.

      Either way, would this mean that functions are even more uncountable than the real numbers?

      And what category of mathematical objects would have a greater cardinality than even the functions, if such has been discovered?

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  6. Thank you for the post Prof. Feser. This is some what related given that he did engage a lot with the Thomistic-Aristotelian tradition but I'm wondering if you heard recently about the death of Kai Nielsen? It was confirmed by the University of Calgary and the Daily Nous just yesterday:

    https://dailynous.com/2021/04/09/kai-nielsen-1926-2021/?fbclid=IwAR2NH7IXTIFvzjixs-iyaO6o7z3Be6eVHC8iCc7NKCcEj9TnkWpKgWZ3a6c

    I remember you had mentioned him as the “go-to” guy on issues of morality and religion." in your post where you discuss your conversion story from Atheism to Theism. Like Smith and Sobel, I was wondering if you'd write a brief-tribute to him as well, considering that he was definitely a sophisticated/philosophical Atheist?

    A brief question I had is that on your brief tribute to Sobel, you had written that "serious philosophical atheists seem very thin on the ground indeed". With Smith and Nielsen now passing away, I'm wondering which Atheist philosophers now left do you still consider serious thinkers. Are Graham Oppy and Paul Draper the only ones left now?

    Secondly, I know you've done a series of "Adventures into Old Atheism", but I'd really love to see what you think of sophisticated and formidable Atheists in analytic philosophy like Mackie, Sobel, Smith, Gale, Draper, William Rowe, Stephen Maitzen, Adolf Grunbaum, Evan Fales, J.L. Schellenberg, Nicholas Everitt, Michael Martin, Michael Tooley, Robin Le Poidevin and many more etc. Which of these did you feel provided the most formidable critiques of Theism? Do you agree with Robert Koons that "Logic and Theism" is the best book defending Atheism, or would that title go to Oppy's "Arguing About Gods"? Just some general thoughts on sophisticated Atheism and where you think it is headed post Nielsen and Smith's deaths would be very much appreciated. I think your experience in the discipline and engagement with top Atheist philosophers makes you equipped to provide a unique perspective here.

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    1. Hello Ben,

      What I meant by that remark is merely that some of Nielsen's essays on religion and ethics had an influence on me early in my atheist days. But frankly, I haven't thought much about his work in years. I don't find those particular arguments all that impressive now, and while he's certainly much better than Dawkins and Co., I wouldn't put him in the same class as Mackie, Oppy, Smith, or Sobel.

      Re: the other people you name, while they're all smart people who are also much more impressive than Dawkins and Co., I'm not sure why it would be worthwhile for me to do a series of posts on them. For one thing, they are not as well-known or influential as Nietzsche, Marx, and other stars in the "Adventures in the Old Atheism" series. For another, most of them don't actually have much of interest to say about the classical (Neo-Platonic, Aristotelian, and Scholastic) tradition -- which, as you know, is in my view where the serious debate is to be had. If an atheist writes a formidable book criticizing Plantinga, Swinburne, Alston, William James, Paley, Reformed epistemology, the kalam argument, Intelligent Design, etc., well, it's all well and good for someone to respond, but I'm not terribly interested in doing so myself, since I don't favor those approaches anyway.

      Anyway, this is off-topic!

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  7. "So, during the long interval between extinction and discovery, the universal could be found neither in the world of concrete material things nor in human minds."

    Couldn't we say that it was instantiated in the fossils? (however poorly)

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  8. Ed gives an excellent account of what I wrote about Aristotelian philosophy of mathematics, and also explains well how it differs from Scholastic Realism. Many thanks.

    It's reasonable to say that Scholastic Realism has some advantage with uninstantiated universals, as it provides, so to speak, somewhere to "put them" (viz, the mind of God). The strict Aristotelian does have a problem providing an alternative account - I tried it in "Uninstantiated properties and semi-Platonist Aristotelianism," Review of Metaphysics 2015, but it's hard to say how convincing that is.

    However I think Scholastic Realism shares one problem with Platonism (though not some others). Any "blueprint" theory, whether the blueprints are abstract Forms or divine ideas, tends to overlook that the real things share something over and above their copying the blueprint, and indeed, it's the other way round since what they have in common is what makes them all copies of the blueprint. For example, red things have something about them (or humans share worth) intrinsically. For comparison, if you built coffee percolators from blueprints and then threw the blueprints away, that wouldn't affect their ability to make coffee all the same way, due to their intrinsic causal powers. While you can't throw away Forms or divine Ideas, that doesn't affect the extrinsic nature of their relation to the things in this world, which share intrinsic properties (as the Aristotelian realist holds).

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    1. Hello Jim, I think we're in agreement. In particular, I agree that the natures of things must be in the things themselves, and that things can't be seen as mere shadows or reflections of natures that really exist only elsewhere (whether in Plato's third realm or in a divine intellect). Thus, rejecting Platonism and embracing Aristotle's insight can't be merely a matter of rejecting a third realm while locating natures merely in minds, even the divine mind. It must also involve recognizing that the natures are in the things themselves.

      I didn't make this clear in the original post, so I thank you for prodding a clarification.

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    2. @Ed Feser,

      Would the same analysis apply to a thing's act of existence? Because I recall that while Aquinas denies the Platonic option for forms, he affirms it for being.

      And though it can be said our being participates in God's being in some way, is existence also really inside the things themselves, or is it just a mere shadow or reflection of God's being?

      Would the existence of things be Platonised in this fashion, or would it also be in the things themselves as well just like natures?

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  9. There seems to be an almost physicalist grounding to some of this article. One argument I have against both the nominalist and Aristotelean foundations for maths is that it seems implausible that it could be used in physics in the way it is to predict completely new things that have never been seen.

    I would also argue that the distinction between Platonic realism and Scholastic realism here sounds like a misunderstanding of Platonism? Presumably the scholastic realism was an attempt to integrate Augustine with the likes of;

    “ Ideas are certain original forms of things, their archetypes, permanent and incommunicable, which are contained in the Divine intelligence. And though they neither begin to be nor cease, yet upon them are patterned the manifold things of the world that come into being and pass away. ”

    Is this any different really than neoplatonism? To suggest Platonism is talking about “a third realm”, rather than the divine ideas of the One, which shape the forms that compromise the universe, seems like an unnecessary distinction. Also, the idea of these as separate realms where the universals are disconnected from the particulars seems to miss the hierarchical structure where the latter sit within the former. You can over abstract to the point you get disconnected from the reality. When a mathematician or a physicist some new or clearer understanding of things, they are reaching into the world of universals through intuition or imagination. There is a reality to the universals that is tangible in the forms they shape, which as Paul says is one of the ways god reveals himself to us. But as a microcosm of god, there is also a way in which we can occasionally ‘reach through the veil’.

    This diagram is a simple way in which you could represent things that could sit in either Platonism or Scholasticism (it’s a first draft and needs work, but should describe the general principle)

    https://i.imgur.com/t1DzVwm.jpg

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    1. I think there is a similar confusion of Plato where people think he is a dualist between form and matter. If you think of his analogy of the cave, the representations that we call the physical world are the shadows on the back of the cave. He doesn’t claim the shadows as having some independent reality from the forms, they are literally an image of the reality. There is not two separate things, just the form and how it is represented to the senses. This is exactly what quantum physics indicates, the physical properties only have substance as part of an interaction between forms. The physical properties have no independent existence.

      It’s also what happens when you look in a mirror, the image may show you something of the reality inside you, sad eyes or a smile, but the reality of your form is far more than the image it presents to the senses,

      Just to confuse things, I think we are two forms entwined like a double helix. One is the evolved form from the dust of the earth, the other more directly god breathed. They are not separate substances, but separate spirit forms in a unity that is the soul. They are our higher and lower natures, but both together are represented by the body. There is a kind of dualism, maybe even represented in some way by the two hemispheres of the brain, but there is no substance dualism.

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    2. "One argument I have against both the nominalist and Aristotelean foundations for maths is that it seems implausible that it could be used in physics in the way it is to predict completely new things that have never been seen."

      On Aristotle view it seems than that is not much of a problem, for when we do physics we are really interacting with real features of the universe(thought only some of these). Our mathematics come from reality, so it should be capable of describing reality if we know how to use it.

      About Plato, i agree that the guy likely did not believe on what is normally atributed to him, specially seeing how early is the notion of the forms being God ideas:https://journals.openedition.org/etudesplatoniciennes/448

      A very important detail there is that the scene from the Timaeus where the Demiurge start to shape matter to become like the forms is read as a alegory by people close to Plato himself. He also seems to me to reject the naive view of platonism for something more theological on the Parmenides, but i failed to understand that one before, so i'm probably wrong.

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    3. Interesting thanks.

      I personally think it’s worth fixing the language, and distinguishing between unchanging divine ideas, and the dynamic forms they shape to comprise the universe. This way the forms are Kant’s “thing in itself” or Aquinas’s forms, and things don’t get as confused as they seem to in that article.

      Just as Augustine and Aquinas knew that the universe had a start from scripture, there are many other areas where scripture fills in gaps that human intellect even now cannot discern itself. Obviously revelation is far more important than helping us to tidy up our poor understandings, but it’s something that Plato didn’t have (the NT at least).

      We also of course have the benefit of the likes of quantum mechanics, although in some ways this just helps refute the errors of physicalists. As Heisenberg observed;

      “ I think that modern physics has definitely decided in favor of Plato. In fact the smallest units of matter are not physical objects in the ordinary sense; they are forms, ideas which can be expressed unambiguously only in mathematical language.”

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    4. I believe that it is traditional to separate God ideas and the organization of things on the universe(the forms), Philo analogy of the architect seems pretty good in illustrating it.

      Also, i don't think i get the comparison between Kant and Aquinas here. I believe that Kant "thing in itself" is more of a negative concept, for to him our intellect is worthless when dealing with the non-empirical reality(which to Kant could not even be shown to exist or not).

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    5. Yes fair point, but you do find “ideas” and “forms” used almost interchangeably by some. If we keep “ideas” for the universals, the archetypal ‘templates’, and “forms” for the dynamic particulars that flow from these and are represented as matter when they interact with each other, then I think that can help avoid confusion.

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    6. Yea, that is a good way to be less confusing. But i remember what you call form usually being called "essence" or "nature", that is how i usually say it too, so i don't see the confusion happening much.

      Delete
    7. Yes my philosophy is a bit simplistic, and I don’t find either any of the frameworks very intuitive. I have been thinking that it doesn’t seem as if divine ideas are really like blueprints that directly ‘generate’ forms, so there is a stage in between where you get various types of an idea, and in a way you could say that essence is the type of form.

      But yes you’re right that the confusion problem is with me, as I’m probably the only one who understands what I’m talking about :)

      Delete
    8. It happens :)

      You sounds a bit more platonic, i admit that i have a harder time following this type, but it does interest. I won't call it simplistic, but it does look like you have some work to do to by the way that you talk about it.

      While platonists are harder to get, it is a interesting aproach and it does have a lot of rigor and beauty at the same time. Maybe more mystical christians like St. Augustine and St. Bonaventure would help?

      Delete
    9. Yes both Augustine and Bonaventure make more sense to me than some of Aristotelian aspects of Aquinas, and obviously far better than ‘raw’ Plato. I also understand why the Palamites have the “energies” for god’s immanence, but not sure if it’s really necessary or meaningful to include them in an ontological framework.

      One way or another, a kind of platonic idealism best describes what seems self evident to me following my journey through atheism and eastern religions, and finally to catholicism. It also matches my understanding of what physics is telling us best, although I’m sure Dr Fesser (and maybe yourself) will disagree :). What I haven’t been able to find is an updated christian ontology that fits, Whitehead, Barfield, Steiner etc go too far away from what we can know through reason or scripture IMO, without addressing the fundamental ontological picture. The German idealists seem to generally confuse the substance of the universe with god. Until I find something that fits better, I think you’re right that Augustine and Bonaventure may well be the best guides to help me fit it all together, and perhaps some Böhme etc

      Delete
  10. It's not called nominalism it's called formalism: the belief that mathematics is a game of symbols and nothing more.

    ReplyDelete
  11. Hi Ed, a question regarding the third objection to Aristotelian realism. you said:

    "The same can be said of the consideration raised by the third main objection to Aristotelianism considered by Franklin, which is that some mathematical entities (e.g. perfect circles and other geometrical entities) are idealizations that are never found perfectly realized in the physical world. In response, Franklin points out that what applied mathematics strictly needs are only the approximations that are found in the physical world. But this seems to me to miss the point. For there are objective truths about the idealizations no less than there are about the approximations, and these cannot be grounded in what is actually there in the physical world."

    the Avicennian response to this objection is that such entities do in fact exist perfectly in the physical world, but as objects cognized by the estimative faculty. so the fact that one can't literally see something as perfectly circular is no reason for saying it isn't actually so - for such circularity isn't an object of vision in the first place, but rather the estimative capacity of the soul. (compare this to someone who says that 'hostility' doesn't exist in the physical world (e.g., in this wolf) because it isn't detectable by one of the five external senses).

    so Avicennian(-Aristotelian) realism deals with the objection, but without going in a theological direction. what do you think of it?

    pax.

    ReplyDelete
    Replies
    1. Meaningless , time wasting drivel, like metaphysical deliberations in general.

      Delete
    2. @Unknown if you think all metaphysics is nonsense, then WHY are you on this blog?

      Here's hoping Dr. Feser personally helps you find different blogs that aren't "meaningless, time-wasting drivel."

      Delete
    3. TBO 9.58AM

      Plenty of stuff appears on this blog which is not metaphysical BalancedTryteOperators, or at least not entirly so. There have been many discussions about the behaviour of the Trump regime or some leftists in the US for example, or the efficacy or otherwise of public policy as regards covid-19. So your comment does not hit home at all.

      As regards the 'Avicennian response' stated in the post by Sinawi, it was a right old word salad. Sounds profound, but wtf did it mean?

      There are brilliant people studying metaphysical issues in leading universities across the planet ( eg the nature of universals ), and coming to absolutely no consensus at all, nor is there any prospect of achieving one. Of course, religious believers will carefullyr mould their metaphysics to their theology, so giving it even more credence in their minds, even though both are completely made up.

      Delete
    4. >@Unknown if you think all metaphysics is nonsense, then WHY are you on this blog?

      I think he is here because his Grinder app is down or something?

      Awe wee lamb.

      Delete
    5. Can do both, no problem, you homophobic asshole. So you continue your personal tradition of representing your fellow Catholics in the worst possible ways, with the most prejudiced of insults and quips. Why did they put up with you on here?

      Delete
    6. Guys, cut it out. Any more of this childish pissing match stuff from either of you or anyone else will be deleted.

      Delete
    7. @Feser

      Unknown is nothing more than an anti-Philosophy Gnu Atheist leftist type. He is not here to debate.

      He is here to mock. He is basically Papalinton only dumber. He has nothing intelligent to say and he can't formulate a philosophical defeater to save his life. He is obsessed with left wing politics and injects it into everything.

      I don't apologize for mocking him. He deserves to be mocked. He is dumber than Jerry Coyne.

      I am on your side. I always have been. He isn't here to debate or discuss philosophy. Will he take up a defense of strong realism or anti-Realism? Well he defend Hume? No because he doesn't understand philosophy only the talking points of media matters.

      It is getting old.

      Delete
    8. @Unknown

      I have no respect for guys like you. I have great respect for Atheists and non-believers who know philosophy and argue their non-belief philosophically. Who defend their own metaphysics with philosophical arguments and attempt philosophical defeaters for the views that are contrary. I have encountered few of them but those who I do encounter I relish.

      But twats like you I nor respect at all. The only book on atheism you read was likely from Dawkins and nor Jack Smart or Graham Oppy.

      Yer like the Young Earth Creationist with a 5th graders understanding of science who stumbles into a den of college biology students or higher and begins mocking evolution and taunts how women dina give birth to wee monkeys or similar shite like that.

      So far yer on that level. Yer atheism/non-belief doesn't offend me. Yer creepy statements about my children's bottoms doesn't offend me. Yer left wing politics doesn't offend me. Yer anti-Trump obsession doesn't offend me (he is gone move on). Being English doesn't offend me.

      Nay it is yer anti-Intellectualism & anti-Philosophy that is offensive. If you don't understand philosophy or metaphysics then go read a book. Heck there are a host of Atheist ones ye could read. I am sure Dr. Feser could recommend on.

      But enough of the anti-intellectual anti-philosophy fundamentalism.

      It is so boring and it is nor gonna convince anybody anymore then me quoting a dozen KJV verses on a Richard Dawkin forum will convert the locals.

      Stop being boring will ya?

      Delete
    9. Metaphysics is the last refuge for theology and religious belief. But as we become more philosophically adept it is apparent that metaphysics itself is increasingly becoming a highly problematic conception in itself. From the Stanford Encyclopaedia of Philosophy:

      "The topics “the first causes of things” and “unchanging things”—have continued to interest metaphysicians, though they are not now seen as having any important connection with the topic “being as such”. The first three of Aquinas's Five Ways are metaphysical arguments on any conception of metaphysics. Additionally the thesis that there are no first causes and the thesis that there are no things that do not change count as metaphysical theses, for in the current conception of metaphysics, the denial of a metaphysical thesis is a metaphysical thesis. No post-Medieval philosopher would say anything like this:

      'I study the first causes of things, and am therefore a metaphysician. My colleague Dr McZed denies that there are any first causes and is therefore not a metaphysician; she is rather, an anti-metaphysician. In her view, metaphysics is a science with a non-existent subject-matter, like astrology.'

      This feature of the contemporary conception of metaphysics is nicely illustrated by a statement of Sartre's:

      'I do not think myself any less a metaphysician in denying the existence of God than Leibniz was in affirming it. (1949: 139)"


      A reliance on an 'old' notion of what constitutes metaphysics simply poses more questions than answers about its epistemic grounding.

      Delete
    10. Yes Paps you can cut/paste a small part of section 2.1 Being As Such, First Causes, Unchanging Things of a broad article on Metaphysics from an online philosophy dictionary.

      The entire article is found here BTW. For people who care about context over proof text.

      https://plato.stanford.edu/entries/metaphysics/


      Good for you! Aren't you special!

      But can you rationally argue & defend any of the conclusions which are not argued here but merely summarized for breviary or defend yer anti-metaphysics thesis? Are you taking the strong anti-Metaphysics position or the weak one? Do you even know the difference or did you not read beyond section 2.1?

      Do you know if these views presuppose Realism or Conceptionalism or Nominalism?

      Can you argue them or do you just do cut/paste?

      I note one of the authors of the article is Peter van Inwagen. An Analytic Philosopher, & past President of the Society of Christian philosophers and a Critic of Atheism.

      Opps!

      The other is Meghan Sullivan a philosopher at Notre Dame who teaches a course called "God and the Good Life".

      Here is the Trailer.
      https://www.youtube.com/watch?v=NMFF0m4FxqQ&t=164s&ab_channel=PhiLifeTeam

      BTW what about the Pro Metaphysical view? Do you know how to formulate defeaters for it or do you just copy/paste?

      Geez man since the days when Crude and I used to make fun of you over at the Dangerous Idea blog you haven't changed at all.

      That is not a compliment BTW.....

      Next to Unknown yer the laziest fecking Atheist here and most philosophically incompetent.

      Geez man would it kill you to learn actual philosophy?

      Feser is right. Quote"The internet never ceases to be a strange and depressing place, and daily to provide confirmation of the doctrine of original sin."

      I would add "Against stupidity even the gods themselves contend in vain."

      Why do I bother?

      Delete
    11. This comment has been removed by the author.

      Delete
    12. additional:

      The wee Kangaroo writes:

      >Metaphysics is the last refuge for theology and religious belief.
      But as we become more philosophically adept it is apparent that metaphysics itself is increasingly becoming a highly problematic conception in itself.

      Yet the article you proof text from was written by two philosophers who are apparent theists? One a known critic of Atheism?

      Opps again!

      We get it Paps. Reductionist Materialism is a metaphysical view. As is skepticism and Positivism and Logical Positivism. Care to I don't know adopt one and defend on of those views while actually formulating a defeater for Thomism's metaphysics?

      Would it kill you or are you merely comfortable in yer non belief and don't wish to tax yerself? Not even to become a better more thoughtful Atheist?

      I don't get this breed of anti-Philosophy lolcow lowbrow Gnus? They are worst than Simon the obvious YEC nutter who posted above accusing Feser of "modernism".

      Delete
    13. This is all I am going to say to you lot till you actually address the topic.

      Now bugger off!

      Delete
    14. @Feser

      BTW just to show I am nor here to bitch at the local Gnus but discuss the topic I have a question if you want to answer it.

      Scholastic realism-"like Platonic realism, it holds that universals are to be located first and foremost somewhere distinct from both the material world and finite minds – namely, in the infinite mind of God, where they function as the archetypes according to which God creates the world of concrete things."

      My question is is that a reference to the Archetypal Idea?

      My wife explained this concept to me decades ago when we where young & the children had not yet came so she took a few courses in theology.

      God has an archetypal idea of Ed Feser in his mind of how He would conceve of the perfect Edward Feser as he should become in the World to Come or had he existed in an unfallen word.

      God has an idea of what the Archangel Lucifer would be had he not abused his free will and fell? It is an idea in the divine mind that is a perfect reflection of what his creations should ideally be?

      Ever heard of this?

      Delete
    15. PROFESSOR FESER

      I would like to draw your attention to Son of Yak'ov's extraordinary outburst at 4.55pm and 5.19PM, followed by others.

      After you specifically instructed us to cease our hostilities and dial things down, he immediately launched into his bizarre rants. The fellow is unstable, obnoxious and abusive, and conflating me with every other 'Unknown' he has ever taken exception to in the history of this blog. I am very happy to abide by your instructions , but this 'Son of Yalov' really does need reigning in'. He is clearly unhinhed.

      Delete
    16. @Unknown

      You know if you actually would learn about Philosophy and Metaphysics even the Atheist versions and learned how to argue philosophical defeaters you might actually be...well..interesting.

      Instead by yer own admission to BalancedTryteOperators you claim Metaphysics is "meaningless drivel" and you only want to to talk about the "many discussions about the behaviour of the Trump regime or some leftists in the US for example, or the efficacy or otherwise of public policy as regards covid-19."END

      Which is about politics and not about philosophy or metaphysics. Which is boring.

      Dude go to a political blog and have at it with the locals. I'm not stopping you but if yer gonna post here could you at least learn some philosophy?

      Snearing isn't gonna make me an Atheist anytime soon buddy or a wee leftist. Only a good philosophical argument has a chance.

      If I disbelieve I am not going to be some come lolcow Gnu (like some of us). I would want to be a Graham Oppy or Sorbel or you know somebody intelligent. Not a wee Gnu scrub.

      So would it kill you to go learn philosophy?

      Would it?

      Delete
    17. BTW Unknown do you have anything to say about the topic of Realism and Mathematics? Anything about Platonic or Aristotelian or Scholastic Realism in Mathematics?

      Or do you want to waste time talking about Trump and or yer anti-metaphysics metaphysics(which btw as per that article Papalinton cited above from the two Theistic philosophers) I would like to know if you advocate a stong anti-metaphysics metaphysical view or a weak one?

      Also I recall Tony pointed out yer objections to the use of the term "species" isn't a defeater to Realism nor a defense of nominalism.

      Try arguing philosophy old boy. You might actually like it. You might actually become a worthy opponent to Classical Theism instead of all....this.....

      Delete
    18. Anything else to add Mr Y? Talk about a complete meltdown.

      Delete
    19. Good on ya, Son of Ya'Kov. The occasional outburst is very Catholic. The enemy is usually an ankle biter. He respects this like nothing else.

      Delete
    20. I think Ya'Kov is making some really good points here. Just keep it civil.

      Delete
    21. Cervantes and Daniel

      Keep it civil? Have you read some of the stuff that this bloke writes - in novellas?? Civil is not a word in his dictionary i'm afraid. Our negative interaction on this thread began when he suggested that I was here because my Grinder app had broken down, which - though not gay myself - I do not take as a personal insult , but was clearly intended as one, emerging as it did from the sewer of his homophobic mind. It was also no doubt intended to raise a laugh from his fans , who are generally hardly likely to be discerning and respectful in this area. Don't you have anything to say about that, let alone about his endless venting immediately after Feser had effectively told is both to cut it out?

      You know, it is a very easy thing to deal with someone you think disruptive or a troll - do not feed them! Yakov is so psychologically unsophisticated and gauche, not to mention unstable,that he cannot comprehend this never mind implement it. Why are you both too unprincipled and cowardly to properly reign him in?

      Cervantes - arn't you the troll long ago labelled as such and banned by Professor Feser?

      Delete
    22. Ed has given his warning. I imagine it has to do with his tone and his grinder comment. But he also included you in the warning. I would suggest you keep the personal attacks to a minimum. Also comments like this are not going to win you any friends here ( not that it seems you are here to make friends at all)

      "Meaningless , time wasting drivel, like metaphysical deliberations in general."

      Yakov's posts after Ed's warning have been faily focused on attacking your comment here.

      Delete
    23. Being anti-metaphysics has been the desperate strategy employed by atheists since Hume.
      Being anti-metaphysics is essentially being anti-thinking. It is being anti-intellectual.
      Of course, this position is both self-defeating and an admission of defeat at the same time.
      When you know you don't have any good argument to defeat a certain metaphysical view, i.e. theism, you try to discredit metaphysics itself... which is self-defeating... This was Hume's attitude which has remain the main attitude among atheists since then and has transformed our culture into the anti-intellecual barbarism it has become.

      Delete
    24. Daniel

      No , I am not here to win friends, and the notion from Cervantees that I will respect an outburst more than anything else is ludicrous.

      Yes, his posts following Professor Feser's injunction have been FAIRLY focussed on the comment you quote - which I did elaborate upon subsequently - so I suppose that is saying something. He was quite unapogetic about his previous behaviour though, calling me a twat and a 'wee Gnu scrub' among other things , as well as completely misunderstanding and misrepresenting a perfectly valid post of mine and my rejoinder to Tony's response.
      You can only see this output as beng reasonable because of its contrast with his usual mode of delivery.

      As for my aversion to metaphysics, it stems from my observation that people tend to select their positions to shore up their theology, but where this is not true, they pick ones that intuitively appeal to them, then indefinitely too and fro with others with different selections, there being absolutely no prospect of resolution. As such they often seem like ideological positions, held for ultimately non-intellectual reasons. When I look at the issue of universals for example, it seems intuitively obvious to me that they are abstractions from really existing physical objects, and have no independent existance of their own( it is a source of great wonderment to me that others can place them in a non spaciotemporal
      Platonic realm, or a disembodied divine mind ). Now if I looked more closely at all the reasons for and against this approach I would almost certainly stick with and defend it as it fits with my wider conceptions of how the world works, and ditto with nominalists, Platonists etc. Metaphysics just seems to me to be a game where people expend a great deal of energy and hot air justifying positions that they were always going to hold anyway, with absolutely no way of ultimately settling the disagreements.

      Do you think that I am misrepresenting things here?

      Delete
    25. Unknown,

      Yer basically a troll. Either that or you are the stupidest person here. Or both!

      This is a philosophy blog. Argue philosophy or feck off! It can be any philosophy or metaphysics. Make yer case for metaphysical naturalism if you like. Or reductionist materialism? Or make the case for a metaphysics of anti-realism? Nominalism? If you can make the case for Nominalism then lets have or do you wish to bore the shite out of us discussing Donald Trump?

      Geez man stop being a crybaby ponce and do some philosophy. I am not seeing it.

      Geez you couldn't even read my mathematics link.

      What is the fecking point of you ladd?

      > Platonists etc. Metaphysics just seems to me to be a game where people expend a great deal of energy and hot air justifying positions that they were always going to hold anyway.

      Spoken like a moron who hasn't picked up a book on philosophy in his life. Yer as pathetic as the YEC with the 5th grader's understanding of biology arguing with the college evolutionist who still thinks his "Women dina give birth to monkeys" argument brillant.

      Go learn some philosophy or show yerself to be the troll that you are!

      It is not an unreasonable request! This is a philosophy blog!

      Delete
    26. Yako

      Have you considered consulting a councillor , if not a psychiatrist? Your abusive outbursts become ever more astonishing, despite instructions from Feser himself to desist.

      The thing is, you have no doubt been posting on here for many years, have probably interacted a lot with the other leading contributors , who see you as an internet mate or colleague, and you obviously 'bat for their side'metaphysically speaking. These are the reasons why they will not clearly call you out for your unstable behaviour , though Daniel did make a doomed appeal for you to be civil.

      Let me make the situation quite explicit then, as others will not. You are an obnoxious, unstable turd, with little impulse control, and numerous signs of psychological derangement, such as frequently flipping between alternate personalities, and a compulsive need to produce interminable diatribes against a victim that you have singled out. You are also so psychologically inept and gauche that you have no inkling that to be rid of someone you find objectionable, the best thing to do is ignore them completely, not to repeatedly interact with them and provoke them, picking at them like an itchy sore. You are surely a most absurd figure Son of Jakoff, a truely ludicrous turd.

      Delete
    27. @Unknown,

      Now that I am back from Mass I can focus on yer nonsense more closely.

      Forget civility ya pounce! I prefer an honest insult to a phony courtesy! The later may have been perfected by the English but the former is preferred by the Scots. The former is at least honest unlike yer performance to date. The later is patronizing and makes me wish to projectile vomit.


      >my aversion to metaphysics, it stems from my observation that people tend to select their positions to shore up their theology,

      Which has nothing to do with the actual arguments themselves for a particular metaphysical position. This is as boring as some idiot lolcow "theist" who waxes eloquent about Stalin's abusive Father or Marx's overly Calvinistic Father or (insert relevant Atheist who had daddy issues) to "explain" his Atheism.

      Well so much pop psychology doesn't do anything useful but beg the question! It presupposes God exists or that the Atheists in question didn't have good reason (to them) for becoming Atheists. It doesn't deal with arguments. Ergo it is boring.

      It is just as tedious when wee English Atheists pounces like yer self bore me with yer pop psychology about believers needing a crutch or something. It is the same stupid argumentative fallacy that begs the question like "Atheists have daddy" issues nonsense.

      Geez from my readings it appear Richard Dawkins got on well with his dad and Feser nor Flew seem to be longing for some Cosmic emotional support when they flipped from Atheist to Theist.

      Mackie, Oppy, Smith, or Sobel. The three Atheist philosophers Feser respects. Why don't you get off yer arse and read them? Then come back here with their arguments?

      That would be far more interesting then hearing you kvetch about how tedious metaphysics is or yer sad question begging believe metaphysics is some crutch for diluted.

      So are the metaphysical positions advocated by Mackie, Oppy, Smith, or Sobel just shore ups for their non-belief? I would NEVER disrespect them with such trip!

      Unknown if yer not really a troll. If you really are sincere then get off yer arse and go learn some philosophy and Atheist Metaphysics.

      Otherwise take yer shite to some wee Creationist blog and have at it with the lolcow Theists. We are Classical Theists here. Bring a sophisticated rational philosophical argument or go slum with the plebs.

      This is a philosophy blog. It is nor an unreasonable request you learn some philosophy.

      You can start by critiquing realism or explaining how one can be a realist and not a Classic Theist. Do something interesting!

      Please!

      Delete
    28. Yako

      Never seen anyone loose it in such a protracted manner on-line before. Your melt down.is spectacular.

      Delete
    29. "I have no intention of initiating an interaction with Yakov again," 10:59AM

      What is the time stamp of that post? 12:19PM?

      Dude keep your promises. It is a bad look when you don't.
      Now take care of yerself.

      Delete
    30. Daniel

      Referring back to my post of April 11 at 6.23AM

      My inquiry to you regarding my general worries about the metaphysical enterprise was a genuine one, and I would welcome your reply. It is of course a meta question, concerning our inability to reach anything like a metaphysical consensus. This makes me wonder if there is something dubious about the entire project.

      I have actually just ordered two books from Amazon, which deal with the topic of universals , so that I can really swat up on the debate and take a more informed view about it - 'Universals' by JP Moreland, and 'A Survey of Metaphysics' by Lowe. Now I am very sure what will happen here. I already have a basic grasp of the territory, and am pretty sure in which general theoretical direction I will go. Having learned many of the arguments, I will deploy them against detractors, but when I encounter people whose rejoinders cause me problems, I will hardly concede the argument, but go away and research how others have replied, then continue the defence. And on it will go. But isn't this how metaphysical disputation almost always goes , especially if one of the disputants has a theological axe to grind, in which case it begins to look as though ones adoption of metaphysical positions is driven and maintained by non-cognitive factors such as commitmebt and belief.

      Some time ago I read 'What is this thing called Metaphysics' by Peter Van Inwaagen, a wonderfully honest and rather ideosyncrstic work, abd in a final chapter he considers the question of why we are, as a species, so very bad at metaphysics, as indicated by our inability to reach any kind of consensus about any metaphysical question. He considers the question from a variety of angles, but in the end still finds it puzxling. And this is a leading academic metaphysician!

      Delete
    31. Yakov imagines he has a defeater on the issue of my stance on metaphysics. He imagines that having noted that 2 apparent theists wrote the Stanford article in its Encyclopaedia of Philosophy destroys my argument on metaphysics. Now I know Peter van Inwagen is a theist, the other I don't know nor concerned to know. Little does Yakov understand if a known philosopher, and a theist to boot, acknowledges great problems with the concept of metaphysics in establishing the 'truth' of things, that alone strengthens my argument formidably and challenges Yakov/Feser's notion of the epistemic reality of metaphysics as an explanatory model. Both Van Wagen and Feser can't be right.

      Of course it must be pointed out that van Inwagen is an Episcopalian. And Episcopalians describe themselves as "Protestant, yet Catholic". But I guess Yakov will seek any refuge in a storm given his philosophical smarts.

      I think metaphysics has largely proven to be a 'cake-fight' unless and until it is grounded in the physical. As I noted earlier and elsewhere, metaphysics must supervene the physical, it must be grounded in its physical corollary and not be divorced from it, unhinged, to waft out on its own. Otherwise you end up with all manner of nonsense, disembodied spirits, Jewish laser rays starting California's forest fires from outer space, walking on water, an omni-spirit agent standing outside of time and space but capable of entering into them at will, you name it.

      Now I know it would be a miracle to win the lottery even with purchasing a ticket in that draw given the stupendous odds of your number coming up. But to win the lottery without even buying a ticket? That's the kind of metaphysical miracle that the religious faithful, like Yakov/Feser wants you to buy into. What am I missing here from an epistemological let alone ontological perspective?

      Delete
    32. @Paps

      It is sad you never moved beyond low brow fundamentalism to anything more intellectually rigorous.

      >Yakov imagines he has a defeater on the issue of my stance on metaphysics.

      Your anti-metaphysics is itself a metaphysical view and it false by its own standard. It is that simple and you remain an irrational Atheist when you could be a rational one.

      Vague reference to a part of a part of a llarticle designed to give an overview on the meaning of the term "metaphysics" isn't the same as giving an argument against the concept itself. Also having read the whole article I don't see where Van Wagen is arguing Metaphysics is useless or at odds with Feser?

      He is clearly arguing for the democracy of the term. Which I support. A reductionist materialist view of reality is a metaphysical view just an essentialist or Thomist or mechanist view are metaphysical views.

      The case then becomes which view is the more consistent and coherent? Make yer argument.
      Considering yer lackluster performance historically I won't hold my breath.

      His article shows the term has grown past its exclusive use by Aristotle to encompass later philosophies and I don't dispute that & I would very much doubt Dr. Feser would either.

      Funny how you missed that and read only what you wanted to see? Talk about confirmation bias.

      >I think metaphysics has largely proven to be a 'cake-fight' unless and until it is grounded in the physical.

      Which proves you still haven't learned anything. As one of the opening maxums of Thomism and Aristotle is ""Whatever is in our intellect must have previously been in the senses."

      Opps!

      Quite while yer ahead Paps or go read the list of Atheist philosopher I recommended so you might actually become interesting.

      Unknown sees to me doing it with his last two posts. Get with the program Kangaroo boi.

      Delete
    33. “As for my aversion to metaphysics, it stems from my observation that people tend to select their positions to shore up their theology, but where this is not true, they pick ones that intuitively appeal to them, then indefinitely too and fro with others with different selections, there being absolutely no prospect of resolution. As such they often seem like ideological positions, held for ultimately non-intellectual reasons."

      As Talmid said elsewhere, this appears to be true of a variety of other human endeavors, such as politics, sports teams and so on. I would suggest that no one makes decisions on purely intellectual grounds. The closest we get to certainty is in the STEM subjects. But even here, there are areas of debate where controversy can occur, such as the metaphysical status of mathematics. Or whether biology is ultimately reducible to chemistry, and chemistry to physics. And yes, some of these metaphysical debates play into apologetic rationally based arguments for the existence or non existence of God. But do you chuck out the entire enterprise of metaphysics because some of its ideas leads to conclusions you don’t like? Or do you try to understand them on their own terms and be as objective as possible?

      I personally believe that metaphysics can ground a rational belief in the existence of God, but this belief does not equate to revealed religion or produce faith, even though it can help to ground faith. Accepting a first mover, first cause, grounding necessity for all existence, formal principle of all things, and a final cause of all things can all be accepted on Aristotelian grounds, but not lead to faith. Anthony Flue is an example of a life long atheist who accepted Aristotle’s god but rejected the Christian God.

      “When I look at the issue of universals for example, it seems intuitively obvious to me that they are abstractions from really existing physical objects, and have no independent existence of their own( it is a source of great wonderment to me that others can place them in a non spaciotemporal Platonic realm, or a disembodied divine mind ). “

      Agreed. This is a basic premise of Aristotle. The universals are not in some third realm. They are particularized in things and universalized in abstractions in human minds. Aquinas uses this Aristotelian concept to argue for the existence of God in the fourth way, and posits that God is the ultimate source of all intelligibility in creation based on the transcendentals. These are the most general of all universals, such as being and truth. So he takes this truth that you see as intuitively obvious, and he builds on it to argue for the existence of God. All five of his proofs work this way.

      Delete
    34. “Now if I looked more closely at all the reasons for and against this approach I would almost certainly stick with and defend it as it fits with my wider conceptions of how the world works, and ditto with nominalists, Platonists etc. Metaphysics just seems to me to be a game where people expend a great deal of energy and hot air justifying positions that they were always going to hold anyway, with absolutely no way of ultimately settling the disagreements.

      Do you think that I am misrepresenting things here?”

      So I think you need to grant your own bias and preference here and try your best to at least understand the opposing positions, and not let your hatred of your opponent’s world view lead you to disparage their positions a priori. For example, when watching your favorite football team (soccer) you will obviously be cheering on your own side, but if your opponent scores a great point, you can at least admire their skill, even though you morn the loss of the point for your team.

      I think it is also good to remember that people sometimes convert from atheism or agnosticism to theism (and vice versa of course). Its not like this never happens. Often times conversions have philosophical touch points, but more often than not, those touch points tend to be deeply personal as well.

      Finally, I think everyone engages in metaphysical speculation, even though they don't often realize they are doing so explicitely. When an Atheist says we are just star dust, that statement includes a swath of metaphysical assumptions. Are theists just supposed to lay down their metaphysical guns and let the Atheist walk all over them? Of course not. They will marshal arguments to show that the Atheist is committed to a form of materialism that is by no means a certainty. They will poke holes in his statement. They will try to convince others that the statement is, although true in some respects, false in others.

      Delete
    35. DANIEL 6.38AM


      Thank you for your thoughts Daniel, though of course nothing that you said begins to account for why nothing like metaphysical consensus is seen in any area even among intelligent, philosophically well informed people. I would suggest that people start off with positions that appeal to them for some reason ( cultural, theological or whatever ), and that in defending them they become a member of a metaphysical tribe, and typically remain within it. There are few absolute defeaters in this area, and it is always possible to reject a premise which an opponent holds dear. Yes, people do occasionally change metaphysical or theological perspectives , but not often, and when this happens it is generally for deeply personal affective reasons as you say, not for intellectual ones born of fancy arguments.

      Of course I do not think that metaphysical statements are literally meaningless ( that would be a metaphysical position in itself, and I have no difficulty in seeing many metaphysical statements as intelligable and meaningful ), but I do think that our inability to achieve anything like consensus positions demonstrates that non-cognitive factors are deeply at work here. Of course, every side in any metaphysical dispute will see itself as clearly the correct one, while opponents are intellectually or philosophically wanting or defective in some way.

      I will certainly take a step back in my coming reading about the problem of universals, and try to give positions that do not immediately recommend themselves to me the fairest hearing. But I am only being honest in reporting how things seem to me now, and I think it almost certain that my eventual position will be to an extent independent of the arguments, as they will be nowhere near compelling enough to force the selection of any position, and those that locate universals outside of material reality ( in a non-spatiotemporal Platonic realm for example ) are unlikely to strike me as the best ones.

      Delete
  12. Can fictionalism account for mathematical notions?

    ReplyDelete
    Replies
    1. Anonymous

      I personally do not know nearly enough about the matter to answer 'yes' with firm conviction, but many philosophers of mathematics think so, or at least that it is the least problematic conception of them available. But as a general point I would say always go with the least metaphysically extravagant perspective first in philosophy and try your best to make it work, or you risk importing all manner of nonsense and delusion into your world view. So please read up on fictionalism in the philosophy of mathematics ( actually, there are numerous varieties ) and accounts which root it in the physical world, and try to make these work, before being beguiled by Platonism or theological conceptions, which will bring a great deal of metaphysical baggage with them.

      Delete
    2. Although I disagree with some of Plato's conclusions, I think his analogy of the cave is a good one. Sometimes reality is such that our existing worldview will blind us to the deeper realities. And what would appear to be extravagant baggage from one point in your journey towards a deeper understanding, can become the least metaphysically extravagant perspective at another point.

      Delete
  13. Interesting post about the philosophy of mathematics. I'm wondering what's the ontological status of 1/0? I'm not sure how to square that with the Aristotelian or Scholastic approach.

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    Replies
    1. Well answer me this how do you count the number of cars in a parking lot using Imaginary Numbers? What is the ontological status of 3i?

      One cannot be divided by Zero because Zero is nothing so there is nothing to divide it.

      As to the ontological status I might think these concepts are beings of reason or conceptual ideas not representations of concrete real things.

      Delete
    2. 1/0 doesn't exist in any version of the philosophy of mathematics. Division by zero isn't defined. It doesn't matter what you think mathematical objects are, because 1/0 isn't one.

      Delete
    3. I can use real numbers to count cars in the parking lot. Even Zero if the lot is empty but can I use negative numbers or imaginary ones? No I can't.

      I like what Michael Brazier says above "1/0 is not a mathematical object". Sort of reminds me of people who ask "Who created God?". Which given my Classic Theist presuppositions sounds like "Who created the Uncreated?" or "What is North of the North Pole?" Or "What is Up from Up?".

      The questions are word games and without proper and agreed upon definitions we are all just talking past each other & or talking giberish.

      I note some claimed 1/0 = Infinity and others say that cannot be so and the best I can make of the argument against it with my non-Mathematical mind is it treats Zero as if it was somehow a type of 1 which is a contradiction since it wouldn't be Zero then?

      Also Infinity isn't a real number either and Zero isn't actually counting anything it is just saying there is nothing there to count.

      Interesting....

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    4. If 'zero was a kind of 1' how do you figure that 1/0 = infinity?

      The way you should think about this is that 1/x goes to infinity as x approaches zero. This is an example of a limit. As x gets smaller and smaller so does 1/x get larger and larger. That is why you will often read that 1/0 = infinity. Of course 1/0 is actually undefined but in the limit, 1/0 = infinity.

      Delete
    5. >If 'zero was a kind of 1' how do you figure that 1/0 = infinity?

      If 1/0 =r were a real number, then r⋅0=1, but this is impossible for any r. See division by zero for more details.

      Or better yet see this link.

      https://brilliant.org/wiki/what-is-1-0/

      It also apparently contains a refutation of the argument from Calculus you cite in yer post as well.

      Anyway I'll leave this to Grodriguez or Mike Flynn.

      I don't know enough to comment with any authority.

      Delete
    6. I found much of your post incomprehensible.

      1/x tends to infinity as x tends to zero. So 1/0 is sometimes loosely taken to be infinity, but ofcourse , as x goes to zero it never quite gets there, so we should say that 1/x is undefined but thatinfinity is its limit as x tends to zero.

      What is so difficult to understand about that?

      Delete
    7. Hello,

      Thank you all for the comments. I suppose if 1/0 then it does not exist. However, as Unknown mentions, if we apply the calculus approach then lim x-> 0 1/x = infinity (One can use a Real Analysis method to prove this). Philosophically, would this get thornier? Is it just conceptual?

      Delete
    8. Mysterious Brony

      I like your tag, and am curious as to why you chose it. Is 'Brony' your real name, or a character that I am unfamiliar with? I am thinking of adopting one myself, as I am often confused with other 'Unknowns' on these threads, but the selection is not a straighforward process!

      Delete
    9. @Unknown,

      Well, to give you a few hints, Mysterious Brony likes to see sparkles at twilight, and his favorite pies are pink. And Applejack is the best alcoholic beverage there is.

      Delete
    10. I quoted from the link I provided. If you don't understand then clearly you didn't read it.

      Delete
    11. JoeD 7.22AM

      Sorry JoeD, no idea what you sre talking about!

      Are you sure that he is not a Bronie, but misspelt?

      Son of Y 7.22AM

      It is possible to prove all manner of absurdities if you take 1/0 to be defined. It is not, as I explained.


      Delete
    12. Hello,

      As JoeD hinted, Brony is a term for males who like the show My Little Pony: Friendship is Magic. Admittedly, I like the show but not as much as I used to. I used this tag in the old Classical Theism forum. I decided to use it again because of familiarity. Maybe some of the guys from the old Classical Theism forum will recognize me.

      Delete
    13. Hi Mysterious Brony

      Well, that's nice, and a little unusual, but not in a bad sense - I like ideosyncracy in people. Never heard of the show myself, so i'll look it up on YouTube.

      I admire your openess, as I would have thought that being into such a program might leave you exposed to ridicule by neanderthals, such as can occasionally be found on conservative sites like this.

      Delete
    14. >It is possible to prove all manner of absurdities if you take 1/0 to be defined. It is not, as I explained.

      I never said it was and I dina care either way.

      I provided a link.
      https://brilliant.org/wiki/what-is-1-0/

      If you didn't read it then we are not on the same page.

      Division by Zero is impossible like claiming God can somehow make 2+2=5. I can equally divide 10 cookies among 10 people at 1 cookie each. Or 5 people 2 each. But I cannot divide 10 cookies equally with zero/no people as that is absurd.

      Delete
    15. Son of Yakov 10.41AM

      That is why I have repeatedly stated that 1/0 is undefined imbecile.

      Delete
    16. I didn't dispute it was undefined. You prove yerself a troll.

      Delete
  14. One cannot be divided by Zero because Zero is nothing so there is nothing to divide the One.

    ReplyDelete
  15. Son of Ya'Kov and Unknown,

    I have zero time to read through your comments and decide which are sufficiently substantive to keep and which to delete, to decide which insults were provoked and reasonable and which are just childish, to determine who is primarily at fault, etc. All I know is that you are crapping up my combox.

    So, unless you want me just to delete all of your posts from here on out, grow the hell up already. If one of you throws out another insult, I hope the other will have the self-control just to ignore it. Neither of you is exactly churning out high quality polemic anyway.

    ReplyDelete
    Replies
    1. I would be for deleting them all. I think that would be best for all. I will not back down to a bully and Unknown is a bully. You don't have to take my side. But since I advocate actually arguing the post I would accept for the good of all you delete both of us.

      BTW Unknown has claimed more than one poster is using the monker "Unknown" and that I am confusing them.

      Well I checked all the profiles of unknown. They are all the same.

      https://www.blogger.com/profile/12542926199146156167

      He lies. I do not sir. It is yer blog do what you will.

      Delete
    2. Yakov 11.34AM

      I have not claimed that multiple Unknowns are posting on this thread, but that multiple ones post generally, and that you lump all the ones you take exception to as me, for example someone recently who was confused about the Thomistic meaning of the term motion.

      You would really love to.
      have everything deleted wouldn't you, to erase the record of your behaviour. Let it all stay I say.

      Delete
    3. >I have not claimed that multiple Unknowns are posting on this thread, but that multiple ones post generally,

      A distinction without a difference.

      >I have no intention of initiating an interaction with Yakov again,

      Well that is that promise broken. I simply don't believe you. You don't keep yer word.

      Also I didn't threaten the blog master.

      "If you delete on my posts in the shamefully unjusr manner threatened, I will make it a personal hobby of mine to crap up.your combox for the next ten years."

      Yer words sir for all to see.....

      Delete
  16. FESER 10.43AM

    Your lack of interest in the justice of the situation does not surprise me, Yakov began this with a homophobic comment about Grinder, and immediately after your injunction to us both to cease our 'childish pissing match' he proceeded to churn out acres of abuse. Your lack of interest in what has transpired shames you.

    I have no intention of initiating an interaction with Yakov again, but you cannot expect me to allow abuse to pass while you ignore it. If you delete on my posts in the shamefully unjusr manner threatened, I will make it a personal hobby of mine to crap up.your combox for the next ten years.

    ReplyDelete
  17. Son on Ya'kov,

    Sure, from the little I've read, I see that he's said many stupid and jerk-like things. I fail to see how that entails that Grindr jokes, posting "wee lamb" every 20 minutes, etc. does not count as crapping up the combox.

    Unknown,

    Lighten up. This is a combox exchange, for goodness' sake, not a human rights trial at the Hague. So I'd be a fool to have enough interest in "the justice of the situation" to want to read through all this stuff and try to pick the gnat shit out of the pepper. Certainly I'd have to have more time to waste on this than I actually do.

    Both of you, just cut it out from here on out. That's all I'm going to say and all I care to say.

    ReplyDelete
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    1. Prof Feser

      From this moment on I will simply ignore Son of Yakov's existance, regardless of what he has to say against me. I will be magnanimous. But you must be aware that the fellow is completely off his rocker, so I would appeal to you that if you catch him "in action" so to speak, you intervene to stop him. I am quite certain that I can do as I promise, but equally certain that it will only be a matter of a very short time before he attacks me again. We will see.

      Happy Easter to you Professor Feser!

      Delete
    2. @Prof Feser

      >Sure, from the little I've read, I see that he's said many stupid and jerk-like things.

      I rest my case. I wish these Gnus would just pick up Mackie, Oppy, Smith, or Sobel, read them carefully and have at it with us. I wouldn't say a bad word to them.

      But the "metaphysics/philosophy is bad" meme is just tedious. All the Gnus use it because their Atheism is unsophisticated. Like YEC Fundie Christianity is to Thomism & Classical Theism in general.


      >I fail to see how that entails that Grindr jokes, posting "wee lamb" every 20 minutes, etc. does not count as crapping up the combox.

      Fair enough. But I will continue to mock this "anti-Philosophy" & anti-metaphysics fundamentalism with your permission?

      I will try to be subtle and not use base name calling or imputations of the poster's private sexual proclivities..

      But comparing this low brow mentality to YEC Fundie Christianity is spot on you must agree? (stole it from you).

      Cheers boss.

      Delete
    3. Does Yakov have a firearm licence? Very concerning.

      Delete
    4. @Paps

      I have a better question. Do you have an actual rational argument to make other than yer boring "Oh Philosophy is bad! Metaphysics is woo! SCIENCE! Good Heavens Ms Sakamoto your beautiful!"?

      Because you haven't changed Paps old boy. You still haven't read any Atheist philosophers and you cannot make a single philosophical argument against Natural Theology arguments to save yer life.

      Get with the program buddy! Make an argument or go kiss a Kangaroo down there.

      Mackie, Oppy, Smith, or Sobel, why haven't you read them? Or are you going to bore us all to death with Loftus' recycled anti-YEC fundie polemics?

      Geez man. Yer lack of progress in life is just sad.

      Now go do yer reading. I got my eye on you buddy.

      Delete
    5. Oh No. Philosophy is good. Really good. It is when philosophy is misappropriated to perpetuate religious nonsense that it fails to drag itself from the miasma of the past. I draw your attention to this testimony from the Stanford Encyclopaedia of Philosophy:

      "The rise of [the new] science progressively undermines not only the ancient geocentric conception of the cosmos, but also the set of presuppositions that had served to constrain and guide philosophical inquiry in the earlier times. The dramatic success of the new science in explaining the natural world promotes philosophy from a handmaiden of theology, constrained by its purposes and methods, to an independent force with the power and authority to challenge the old and construct the new, in the realms both of theory and practice, on the basis of its own principles."

      Not to acknowledge the momentous progress of a different and exponentially more powerful explanatory model than the rather dilapidated theology/religion as a basis on which to ground philosophical thought today is simply an exercise in ground-hog day, an exercise in theosophy, the art of sophistry rather than bona fide philosophy.


      Delete
    6. @Paps

      So you beg the question by a priori dismissing religion because some metaphysical & philosophical arguments lead us to conclusions that are positive for religion.

      This is like denying the evidence for that silly Big Bang theory formulated by that Priest Fr. Lemaître because it shows our Cosmos having a beginning. We can't have that! So we should ignore it and close our eyes chanting "The Steady State Theory is still true! The Steady State Theory is still true!".

      Paps you should your bias not your critical thinking skills which are non-existent at this point.

      >I draw your attention to this testimony from the Stanford Encyclopaedia

      Proof texting is not argument son. The Standford Encyclopaedia is not the KJV you quote at some YEC Baptist.

      Yer positivism is tedious pal as is your sophistry. I mean "God is immaterial & nothingness is immaterial"...that is the best you got?

      Nothingness is immaterial because there is nothing there. There is a complete lack of anything ergo that would include the material as well as the immaterial.

      God is Being itself which by definiiton cannot be nothing. Geez read a book Paps...

      >Not to acknowledge the momentous progress of a different and exponentially more powerful explanatory model than the rather dilapidated theology/religion

      Geocentracism is an archaic scientific view not a religious one son. We are back to yer Galileo fallacy. As I recall Crude and I dispatched that long ago with you.....

      Delete
  18. BTW claiming "metaphysical deliberations are meaningless" is an irrational anti-intellectual claim.

    First the view itself is a metaphysical claim thus it is meaningless by its own standard and second it is not the same as disagreeing with a particular metaphysical position and formulating a philosophical defeater for it & or arguing for a contrary metaphysical view (like naturalism, nominalism, anti-realism etc).

    For example Sinawi April 10, 2021 at 7:29 AM made an excellent observation that Avicennian(-Aristotelian) realism deals with the objection:
    i.e.that some mathematical entities (e.g. perfect circles and other geometrical entities) are idealizations that are never found perfectly realized in the physical world. , but without going in a theological direction.

    I found that interesting. Granted I don't deny the existence of the Divine Intellect which holds archetypal ideas of the things God will actually create. But is it really needed to justify realism in mathematics beyond Aristole?

    Anybody have anything to contribute?

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    Replies
    1. Hi Son of Ya'Kov

      "BTW claiming "metaphysical deliberations are meaningless" is an irrational anti-intellectual claim.

      First the view itself is a metaphysical claim thus it is meaningless by its own standard and second it is not the same as disagreeing with a particular metaphysical position and formulating a philosophical defeater for it & or arguing for a contrary metaphysical view (like naturalism, nominalism, anti-realism etc)."

      I couldn't agree more ! As I said earlier, it is self-defeating and a cop out for not being able to refute other metaphysical views.

      Delete
    2. I also founded the Unknown original post hilarious because before attacking metaphysics he clearly says that politics are a valid theme for discussion when:

      1. Politics does depend a lot on metaphysics.

      2. Political discussions have the same problems that he pointed out on metaphysical ones, except that on politics they are turned up to eleven.

      But when i arrived his silly quote war with Son had alread begun, so i did not want to be a part of it.

      Serious, Unknown, i don't see how the problems you have with metaphysics are not a factor on politics. If one goes, the other will have too.

      Delete
    3. Talmid 10.00PM

      The original quote was not well formulated I grant you. It was a partly emotional reaction born of exasperation to some quote that had been recommended as serious and interesting previously, but which I saw as a right old word salad. However, there are interesting meta issues here relating to why it is that as a species we are so bad at metaphysics ( to use Inwaagen's characterisation of the problem ), as is evidenced by the fact that we can achieve nothing like consensus on any metaphysical issue, and once a metaphysical perspective is 'selected' by an individual ( often it seems obviouly correct to them from the very beginning ), they rarely budge. It really does seem like a cake fight sometimes, especially when the metaphysics is clearly being selected and defended in the service of theology.

      So , when very intelligent and well informed people (academic philosophers say ) are members of metaphysical tribes, and spend their lives articulating and defending some position or other against another ( the A -theory of time as against the B-theory for example ) and typically end up in the same place, it is legitimate to ask what is going on and to be at least cautious of the entire enterprise, and ( with limited time at ones disposal )to treat metaphysical pronouncements with extreme skepticism.

      Delete
    4. @Unknown

      I don't know why yer obsessed with "consensus"? You either have a good argument or you don't? You can either defend yer view rationally or you can't?
      You either hold a view that is incoherent or you don't. You can either explain rationally why the other view is incoherent or you can't?

      Hundreds of years ago it was the "consensus" of scientists the Earth stood still and the Sun orbited it. It took hundreds of years for science to prove it was the Earth that moved. Galileo was and is an over rated pounce. He made a lucky guess. Nothing more as none of his actual arguments for a moving Earth are valid and no physicist worth his salt would refer to them today. A lot of good "consensus" did in knowing the truth.

      Politics in philosophy is tedious as politics in general is tedious. I can point to some Catholics running around today who believe what Ed Feser believes on the Resurrection & the Trinity and the Truth of the Catholic Faith but love Biden (Mark Shea comes to mind). I also personally know a few Atheist who think Biden is a disaster and long for Orange Man to return.

      Feser is a conservative and he has recommend Thomistic writers to us like Herbert McCabe who was a Christian Socialist to the far left of Bernie Sanders.

      So we don't need the politics. We need philosophical argument. Nothing more.

      Treating metaphysical pronouncements a priori with extreme skepticism is itself a metaphysical view and ought to held to the same skepticism or it should be rationally defended. I say it is incoherent as it refutes itself by its own standards.

      Make the argument. As Feser says Philosophy is like science in that you will either do it well or you will do it badly but one must do it.

      BTW don't think I haven't noticed all yer response here have been philosophical in nature? Well done. That is what I want to see.

      You could be a great skeptic philosopher once you get with philosophizing and not politicizing. I look forward with great pleasure to testing myself against you.

      PS people change their minds all the time. A few Decades ago I thought Intelligent Design was spectacular. Now I believe it to be rubbish and an inferior form of theism.

      Perhaps you will develop a more sophisticated skepticism and philosophical atheism? Miracles do happen sometimes even in a hypothetical godless universe.

      Delete
    5. Son of Ya'kov 4.34AM

      I think that Unknown's puzzlement at our failure to achieve ANYTHING LIKE metaphysical consensus in any area at all (expressed in his post at 12.55AM) is perfectly understandable, and a meta question worth persuing. He does not have an obsession with consensus at all costs, but wants to understand what it is about metaphysics which makes its absence a very characteristic feeture of the field. The force and point of what he is trying to say quite escapes you. To phrase the question as Van Inwaagen apparantly does ' Why are we as a species so bad at metaphysics?'

      By the way, I am sure that Unknown is not at all concerned with what you would like to see, so cut out the condescending tone.

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    6. >cut out the condescending tone.

      That is unlikely.

      >He does not have an obsession with consensus at all costs,

      You know Unknown you may address me directly and if you ask me not to condescend I might out of courtesy comply.

      Delete
    7. Anonymous

      Son of Ya'kov 7.07AM

      Unknown made a commitment to Feser not to interact with you again directly in the interests of maintaining peace and order here. I just thought that I would appeal to you to show some self awareness and psychological maturity, and cease being condescendung and provocative , as there is clearly a danger of unpleasantness erupting again. I see from your response above that you have absolutely no intention of doing this.

      One would have hoped that your peers on this site would interject and have a quick word with you about your conduct.

      Delete
    8. Buddy that you would know what Unknown thinks tells me he is you and it doesn't break yer promise to Feser interact with me civilly and I will return the favor as long as we debate philosophy and you make philosophical arguments to defend yer view or critique mine.

      Like Feser told you this is not a trial in the Hage.

      Chill.

      PS I am sorry if I was condescending to you.
      Now let's have go philosophically.

      Cheers.

      Delete
    9. @Unknown

      Okay. But is that not a problem in any area? I mean, you can find pretty inteligent and educated fellows discussing things like "is solipsism true?" Or "is logic universally valid?" Or "Proudhon or Marx?" for years and and not making any progress. Would you mistrust all your answers to these questions too? While this say that we should be more open-minded with our metaphysical views, i don't see any reason to doubt that we can arrive at truth. Cartesian certainty is not possible, but we can have a pratical one and i don't ask for more.

      Not to mention, as Daniel said, people do change their views. I, for instance, was a pretty libertarian guy some years ago, way closer to you in social issues, but in my study of philosophy i was kinda forced to abandon this view and become something that i saw as pathetic before. A similar thing happened with Christianity, i tried to abandon it but my intellect would not let me! So the idea that our subconcious is the principal factor on our worldview seems to me hardly the whole history.

      Delete
    10. (Not negating that it does a important part, of course)

      But i can understand why it puzzles you, one of the most bizarre things about us is that both are true:

      1. We can know a lot about reality

      2. We suck at it.

      This strange fact is strange but very certain. No wonder that most mythologies, religions and ideologies have this "fall of men" element or some general pessimism on our origin. But i don't see why we should let it throw us into skepticism. It is also a claim to truth at the end of the day and a pretty bad one.

      In fact, doing the reverse uno card move i ask: don't you think that YOUR atitude can in fact be the one that is motivated by non-rational factors and not the average academic metaphysician?

      If you are the british guy, them you likely grown up on a society where metaphysics is treated as endless nonsense for quite some time, after all. So give us metaphysicians a chance!

      Delete
  19. "But like Platonic realism, it holds that universals are to be located first and foremost somewhere distinct from both the material world and finite minds – namely, in the infinite mind of God, where they function as the archetypes according to which God creates the world of concrete things."

    Not all creaturely minds are finite. Some creatures have some knowledge of infinity while other creatures do not. There are people with no knowledge of justice, whose closest idea of justice is "just be nice to everyone and give peace a chance!" or "give pleasure and avoid causing pain." These people have no knowledge of infinity. There are people who CANNOT learn how to program, no matter how hard they try, because programming requires reasoning about temporally infinite sequences of code. And it does not have to do with IQ.

    End digression. The presupposition in the blogpost that all creature minds are finite needed to be corrected, because it points to another alternative to either Scholastic realism or Aristotelian realism.

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    1. >Some creatures have some knowledge of infinity while other creatures do not.

      But wouldn't that knowledge of infinity be conceptional or intuitive? I know in theory if I was absolutely immortal I could count forever and it would never end.

      OTOH the brain has a hard drive limit. I remember Adam Savage once claimed on a TV show he did about life extension. So at about 500 years my brain would be full and my capacity to remember the last number I counted would be gone.

      I am not sure my soul minus my body could do intellectual feats by itself?

      Thoughts?

      Delete
  20. BTO 3.01PM

    Do not theologens mean by an 'infinite mind' one that is not limited in any way, ie one that is able to achieve anything that is logically possible instead of just this or that for example, and which has knowledge of the truth value ( if one exists ) of all propositions? They do not mean a mind that is quantitatively infinite in any way, or which has 'knowledge of infinity '.

    If universals only exist by virtue of being 'located' in finite minds, then they did not always exist and will one day cease to do so.

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    1. Here you go. This should update you as to the Catholic view of divine divine omniscience which is identical to the Classic Theistic view in general.

      It also goes into the distinct theories held by Thomist vs the Society of Jesus.

      https://www.newadvent.org/cathen/06612a.htm#IID1

      God knows all potentials and God know all actuals and God knows the future as He wills it to come about by Providence and God knows all thing as He knows Himself as their ultimate cause.

      >If universals only exist by virtue of being 'located' in finite minds, then they did not always exist and will one day cease to do so.

      Which sounds like a good argument against a purely Aristotelian realism in favor of Plato or the Scholastic.

      Delete
  21. Noticed the comment from “Simon” at the start of this combox. As this person is not me, and the Unknown from the exchange above with Son of Ya’Kov is my most loyal fan, (his comment at 4.51 a.m. yesterday was a dead giveaway) there is an unpleasant conclusion to be drawn: George m (already weighed down by numerous identities) has started to create identities with manifestly false viewpoints, not just to have conversations with himself, but to provoke others. In this case Dr. Feser and Son of Ya’kov have been trolled big time. People may make of this what they will, and draw other conclusions, but they now know what I know.

    It’s long been his purpose in life to run the blog. Remember when he pressured for someone else to takeover running the combox (presumably himself) a few months ago? The games always end up with the same goody two shoes whining at Dr. Feser: eliminate, exterminate. Why he can’t speak for himself is known to me and the views have “developed” as I thought they would. How predictable and silly - defending esoteric ideas now? What a waste of obsessive reading of philosophical texts (Jonathan Pageau the occultist and Kabbalist is his latest pin-up). I hope Fr. Shane can arrange to send a vat of holy water over – he needs more than rebaptising.

    I make no excuses for criticising anyone as is well-known, but I don’t need to play games. I can speak for myself.

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  22. Cervantes

    Who the hell is George M?

    You must realise that the claims you make are inherently improbable. Don't you think that you are being just a little paranoid Cervantes, and that there is a simpler explanation for the phenomena you seek to explain?

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    1. Cervantes

      And what is the significance of the fact that (allegedly ) 'Simon' is not you? So you subscribe to his views or something, and so feel that you are being trolled??

      Delete
  23. How is a multiplicity of distinct numbers, propositions, and so on within God compatible with Absolute Simplicity?

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  24. As there are an infinite number of integers,and a higher order of infinity of fractions, not to mention other mathematical entities such as irrationsl and imaginaty numbers, how can all numbers, arithmetical propositions and - more generally - mathematical ones exist within God? Doesn't that conflict with the widely held claim on here that actual infinities of things cannot actually exist.?

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    1. It depends where you base your foundation of reality. If you’re a physicalist, then your base reality is physical objects and the stuff they are made of, and an infinity of objects would seem impossible. Having matter as a fundamental reality is itself problematic in many ways, but that’s a separate discussion.

      When you’re talking about the realm of “ideas of god”, you’re going well beyond what we can conceptualise. Just take the number 5, and try to remove from it any notion you have applied to it as a character and a word etc. There is something about it’s essence that is difficult to grasp, even though it’s something we use all the time. If that’s the case with our shadowy re-representation of the real root of numbers that shape the universe (of course anti-realists would disagree with this), how can we expect to understand how numbers are conceived of as divine ideas? You take a very short formula for a Mandelbrot set, and find that within it are infinite patterns and details that you could spend a lifetime studying. My guess is that the essence of numbers themselves are something a bit like that, and so infinities would not be a problem like they are for us.

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    2. Simon Adams 12.50AM

      I cannot begin to make sense of the notion that numbers "float free' of the world, and so am attracted to anti- realist views about them, and would only demur from this for extremely compelling reasons indeed. There sure is something about the 'essence" of a free floating integer say that is difficult to grasp, and this should be a hint that this way of understanding numbers is wrong. But it seems to me that you are just obscuring the issue at hand. My contention is that because an infinite number of elements is by definition completely unbound , even God could not apprehend them all ( there not being an 'all' to apprehend ), and pointing out that 1. we cannot grasp the essence of free floating numbers 2. we cannot expect to understand how they are conceived as divine ideas, does not help at all in illuminating how God could apprehend and ground an infinity of them in principle. It just says that you believe that is what happens and will continue to do so come what may , under cover of our cognitive and epistemic limitations relative to your hypothetical God.

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    3. I’m not dismissing the empirical approach at all. It’s a valid epistemological way of understanding things. But even if you look at the things we know in the world and which we derive our limited concepts from, such as physical objects, we have good reason to believe from quantum mechanics that what we observe with all of our senses, and measure as physical properties, only exist as part of an interaction. On the other hand, there seems to be ‘something’ out there which is consistent, such that when I turn my back on it, I can be confident that something is there. So how do we explain what is actually there? All we can really say is that there is a probabilistic mathematical mapping (via the shrodinger equation) to ‘something, which represents as physical properties as part of an interaction. So matter is a kind of snapshot of something that in philosophy you could call a form. If you take quantum field theory, these forms are effectively excitations of a field.

      So when you talk of numbers “floating free, out of the world”, what do you mean by the world? What do you know of this field (assuming it is one, and not three fields), or more specifically of what drives and sustains the forms within this field, for you to imagine that concepts of maths are not deeply connected to it?

      Essentially you have a re-representation in your mind of this mathematical realm (displayed through nature), which has been informed through all kinds of great mathematicians who have reconstructed a version of the maths that drives nature. The experience of doing this maths is usually described as discovering rather than constructing. Sometimes they go off on tangents where the maths is beautiful but doesn’t seem to correspond to anything in nature. Other times the construct bizarre concepts like imaginary numbers, which DO seem to correspond to something in nature (although we don’t understand why). What should nonetheless be self evident, is that our reconstruction of maths is not the same as the reality. At best it’s like a map of Everest that climbers use. It can reliably get you around the mountain, but is not the mountain.

      Now take infinity, or even the infinities of Cantor, and you seem to be imagining sets of objects called numbers. I don’t think that is a reasonable assumption for how this ‘real maths’ is. That’s why I used the example of a Mandlebrot set. We have a way of writing the whole set as a short expression. Within that expression is an infinite amount of detail, shapes, structures etc, but in a way that short expression contains it all. I’m not suggesting a direct comparison, but a vague analogy as to why I don’t think your concerns about infinity are grounded on any reasonable assumptions.

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    4. I’ll add that although I think an empirical approach is A valid epistemological approach, it’s certainly not the only one. In fact it’s quite limited in many ways, which is why so much ‘modern’ philosophy has it’s knickers in a twist. Yes you can learn huge amounts about a great painting examining it with a microscope, but you’re making it very difficult to get a sense of what the painting is actually all about.

      Delete
  25. They already objectively exist in the abstract how can they not exist in the mind of God as well?

    We cannot have an actual physical infinity but God is not physical. There is no reason why we can't have an immaterial actual infinity otherwise we couldn't have infinite numbers.

    If yer trying to cast God in physicalist/materialist terms that won't succeed.

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    1. Well, it seems to me an odd thing to imagine that numbers do in fact exist, and my untutored inclination is to think that they are fictions, which can be related to something in the physical world, such as the size or cardinality of collections of things. If something like that could be made to work, there would not really be any numbers at all, let alone an infinity of them, but we could still count on indefinitly.

      I am not sure why you would find an actual infinity of physical elements problematic , but not an infinity of items in the mind of God, after all, the problem is meant to be conceptual. How can you do away with the problematic nature of an actually existing infinite number of things just by declaring that the medium is immaterial? An infinite number of numbers and mathematical propositions is no actual number at all, so how could even God apprehend them all simultaneously? There is not an 'all of them' to apprehend.

      So locating numbers in the mind of God ( granting for the sake of argument that He exists ) does not seem to work.

      So grounding

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    2. >Well, it seems to me an odd thing to imagine that numbers do in fact exist,

      Of course numbers exist but we still have to determine how they exist.


      Forgive me Unknown but you seem to be contradicting yerself?

      You said before:
      "Doesn't that conflict with the widely held claim on here that actual infinities of things cannot actually exist.?"

      But then you said:
      "I am not sure why you would find an actual infinity of physical elements problematic".

      So do you think an actual infinity can exist or not? Pick a side(if only for the sake of argument please).

      I will at my end assume an actual physical infinity is impossible from the classic arguments of Scholastics and Aristotle. I won't state them here for sake of brevity but you can look them up at your leisure.

      >but not an infinity of items in the mind of God, after all, the problem is meant to be conceptual.

      God is not material ergo the material limits do not apply to Him. Are you imagining God is material? Well there is no such "god" and I assure you I am a strong atheist towards belief in said God. It would be better for us to discuss the God I(&we Catholics) believe in and not one neither of us believes in. That would be a waste of time IMHO.

      Or are you trying to positively conceive of what God is as God? That is another mistake as Classical Theism presupposes negative Apropotic Theology. The divine essence is incomprehensible. But since we know God is not material that is God is not Matter or Energy than God does not have the limits placed on either.

      Material things possess form and matter and have a physical presence. Something that is not material has no such limitations.
      Or are you imagining immaterial things are just like material things but made of some "ghost" substance? Like we see in the cartoons or in old Abbot and Costello movies? (I actually blame Descartes for that silly popular concept. But I blame him for everything when I am not beating up on Hume)

      >An infinite number of numbers and mathematical propositions is no actual number at all, so how could even God apprehend them all simultaneously?

      It is not a number that represents something in a physical reality. Just like Zero doesn't represent anything but an absolute lack of a thing.

      No physical "god" could apprehend all numbers. Not even Q from Star Trek even if he has a galaxy sized brain. Because he could only know some vast uncountable (to us)finite number like one googol. But not infinity.

      > There is not an 'all of them' to apprehend.

      In the physical sense yes but we are not talking about the physical.

      >So locating numbers in the mind of God ( granting for the sake of argument that He exists ) does not seem to work.

      It doesn't work for a material "god" I agree.

      Depends what God your are are imagining exists? Are you imagining Cosmic Gandalf White Bearded Guy from Family Guy? Or the God-Collided-With-A-Super Computer from Futurama?

      I have no such "deity" my friend. Mine is more Ground of All Being less anthropomorphic

      Cheers.

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    3. @Unknown

      >So grounding...

      I think something you tried to post go cut off? Cheers.

      PS. I thi

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    4. Son of Yakov 9.50PM

      Your reply is riven with confusions and misunderstandings.

      You say that ' of course numbers exist', but that has to be established. On a fictionalist account ( which I have now read up on more fully ), they do not. Numerals are then symbolic representations of our inventions.

      I did not simply write' ' i am not sure why you would find an actual infinite number of physical elements problematic' - you falsely truncate me. That was the first part of a sentance which concluded 'but not an infinity of items in the mind of God, after all the difficuly with the existance of an actual infinity of things is meant to be conceptual' . The contradiction you claim with my previous statement simply does not exist.

      Simply declaring that God is not a physical thing does not give you license to declare anything you like about him with reckless abandon. If the notion of an actually existing infinite number of things is puzzling to you, it should do so per se. How can it suddenly disappear with a declaration that God is not physical? The issue is a conceptual one, not a matter of medium.

      When I state that ' there is not an ' all of them to apprehend' ( meaning numbers, if they exist ), you say ' in the physical sense yes, but we are not talking about the physical'. No SOY, there is not an all of them to apprehend period. That is what it means to have an infinite number of things.

      So I do not think that your reply works. I still have no idea how God can apprehend an infinite number of elements simultaneously, and you just declaring that he magically can is not illuminating. In any case, there is a major philosophical perspective in the philosophy of mathematics - fictionalism - which seeks to do away with numbers as real entities, and this seems to me to be the one most worth persuing as it does not bring with it such exotic metaphysical baggage as the mind of God or non-spatiotemporal Platonic realms.

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    5. Yakov @ 9.50PM
      "God is not material ergo the material limits do not apply to Him. Are you imagining God is material? Well there is no such "god" and I assure you I am a strong atheist towards belief in said God. It would be better for us to discuss the God I(&we Catholics) believe in and not one neither of us believes in. That would be a waste of time IMHO."

      Then how do you know IT'S out there beyond time, beyond space, thinking about delivering you a miracle? Why do you bother praying to this non-material god as if hears you and responds to your wishes... maybe? What is the difference between praying to a bottle milk and praying to your catholic god? SEE THIS REVELATION

      George H Smith [renowned libertarian and American author] notes:

      "God is not matter; neither is non-existence. God does not have limitations; neither does non-existence. God is not visible; neither is non-existence. God cannot be described; neither can non-existence".

      I think there is a lesson in reality here for all of us, wouldn't you say?

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    6. Papilinton 1.37AM

      Yes, this God of classical theism is supposedly immaterial - whatever that means in other than a negative sense - non spatiotemporal, metaphysically simple , immutable and exhibits aseity. Seems a bit problematic to me how such an entity could act in any way at all , let alone interact with human worshippers. But believers have no real conception of what it is they think they are worshipping anyway, as it is suis generis, completely alien and its qualities can only be known analogically!

      These are different but related points to those you make. The believers make it more than problematic to understand how they could know and have a relationship with their God in principle. They might just as well believe they are having a relationship with a bottle of milk.

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    7. Anon
      That believers truly believe their god is 'metaphysically simple', tells us absolutely nothing about this entity, but does speak volumes of something that only a metaphysical simpleton would deliver. Very sad really.

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    8. Good summary of the Catholic position Anonymous 3:23. It is true that it is problematic for God's creatures to relate to him based on their own understanding and power. That is why we believe he has done this on his end. The primary road to know the Christian God is through what he has told us about himself. Philosophy can only give us the vaguest outlines of what we Christians know by faith.

      I understand that you reject this point of view, but at least you have a good grasp of Christian understanding with regard to what we can know from the light of reason reguarding God and that more is needed to truly be able to relate to this being.

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    9. Papalinton "God is not matter; neither is non-existence. God does not have limitations; neither does non-existence. God is not visible; neither is non-existence. God cannot be described; neither can non-existence".

      This was probably meant to be profound, but if there is any conclusion to be drawn it is not that God and non-existence are the same thing. Such a conclusion would be much larger than the premises, as they say.

      If my parrot is not a dog, and my horse is not a dog, it doesn't mean my horse is a parrot. I don't think your analogy advances the question of why God is invisible to us.

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    10. Anonymous, Papalinton and Daniel

      The supposed divine attributes are problematic when thinking about creation too, which must be here after all for there to be humans to supposedly relate to God. It is hugely problematic to understand how a simple, immutable God can do anything at all.

      A fellow called Albius appeared on the Lacondaire thread quite recently, and he displayed great courage and honesty in articulating some of his ongoing difficulties with Roman Catholicism, even though he had been a long time believer and passed through seminary. He had become unconvinced that any revelation had actually occurred, though he maintained a basic classical theism and still considered that part of him was immaterial. With regards to the metaphysically simple and immutsble necessary being which supposedly grounds existance, he was quite rightly stumped as to how to get from there to our contingent world, as clearly, such a reality would be causally inert. He said that he was sympathetic with the idea that a further being would necessarily proceed from the first, urburdened by the divine attributes
      and so able to create the world. I suppose that would have to be the case if you wish to hold onto the God of classical theism, but I did think to myself 'who ordered that', as the introduction of the second being did seem rather gratuitous. I wish that I had posted to ask him about it.

      I do hope that Albius posts again in future, as it is interesting to hear the views and critiques of intelligent and well informed theological free thinkers and maveriks , as well as atheists and the orthodox.

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    11. Daniel beat me to the punch in recognizing of the three responses only Anon's feedback presupposes the presuppositions of Classic Theism and Scholastic Philosophy & offers anything that can be said to be a valid critique of that view.


      Unknown and Paps it seem to me are presupposing anti-realism and materialism/physcicalism and thus beg the question. Unknown still had the better response of the two. Paps was worthless. He has truly learned nothing in decades.

      Anyway let me respond to them individually.

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    12. Son of Ya'kov 6.29AM

      How are you getting on with your non- condescension practice?

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    13. @Unknown

      Part One:

      >Your reply is riven with confusions and misunderstandings.

      That is my line for example you write:
      " On a fictionalist account ( which I have now read up on more fully ), they do not. Numerals are then symbolic representations of our inventions."

      Then they exist as beings of reason and fiction. I wonder if out of the gate you are not understanding I am using "being/exist" as an analogical term not an unequivocal one? Also I don't presuppose what exists is only the physical.

      So what have here is a failure to have a common terminology.

      Of course if you are going to ask me how God can know all infinite numbers if numbers are real then I don't see what a theory of anti-realism has to do with anything? Other than beg the question?

      >I did not simply write etc etc....The contradiction you claim with my previous statement simply does not exist.

      I clearly said it "seemed" like a contradiction. I never claimed anything. Please read more carefully in the future.

      But that having been said I thank you for clearing that up but it would help if you acknowledge my points.

      Quoting myself"So do you think an actual infinity can exist or not? Pick a side(if only for the sake of argument please).

      I will at my end assume an actual physical infinity is impossible from the classic arguments of Scholastics and Aristotle. I won't state them here for sake of brevity but you can look them up at your leisure."END

      So?

      >Simply declaring that God is not a physical thing does not give you license to declare anything you like about him with reckless abandon.

      I am presupposing the God of Classic Theism. If you will not do the same then we can have no meaningful discussion. BTW I can make inferences about God based on his negative properties such as if God is not material then God is not subject to the limits of material things. How can that be wrong? I also pointed out Classic Theism presupposes negative theology and that we cannot positively assert what God is as God. The closest we can come is by analogy as Anon correctly notes.

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    14. Part II
      >If the notion of an actually existing infinite number of things is puzzling to you,

      So are you going to take a position? Are you going to accept Aristotle arguments against an actual infinity or nay? What is your argument against it?

      I am presupposing and if you are not presupposing it if only for the sake of argument then we cannot in principle have a coherent discussion.

      > How can it suddenly disappear with a declaration that God is not physical?

      If something does not have property X then by definition it cannot have the limits of having property X. How is that wrong in any coherent rational universe or are you presuppose irrationalism? In which case further discussion between us would be futile.

      >The issue is a conceptual one, not a matter of medium.

      Well that assumes you are trying to conceive it vs merely imagining it. That is Hume's mistake.

      >When I state that ' there is not an ' all of them to apprehend' ( meaning numbers, if they exist ), you say ' in the physical sense yes, but we are not talking about the physical'. No SOY, there is not an all of them to apprehend period. That is what it means to have an infinite number of things.

      Declaring an anti-realism position in terms of the essence of numbers ad hoc isn't a counter argument sir. It merely begs the question.

      >So I do not think that your reply works.

      I don't think your questions are coherent then.
      I think we have an equivocation problem. Do have a solution? I am all ears.

      >I still have no idea how God can apprehend an infinite number of elements simultaneously, and you just declaring that he magically can is not illuminating.

      If your looking for Cataphatic theology in Classic Theism that is a contradiction in terms. You might as well talk of Papal decrees that cite the Koran.

      Classic Theism is Apophatic. I already informed you God is unknowable as God in His essence. You questions are meaningless if you are not presupposing that. We are discussing my God and the God of Catholics and Classic Theists. Not the other gods.

      What I can't figure out is why you seem to deny the obvious? If something lacks property X totally then it lacks all the limits of property X. God is not material. Ergo God cannot be limited by the material. Thus there is no reason to believe He cannot know all numbers.

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    15. Part III

      Unknown do you affirm or deny there can be an actual infinity of physical objects? Pick a side(at least we established you believe numbers exist as beings of reasons as beings of fiction. So I thank you for that).

      >In any case, there is a major philosophical perspective in the philosophy of mathematics - fictionalism - which seeks to do away with numbers as real entities, and this seems to me to be the one most worth persuing as it does not bring with it such exotic metaphysical baggage as the mind of God or non-spatiotemporal Platonic realms.

      If fictionalism in mathamatics is true then obviously all forms of realism are false. But you still have to make the positive philosophical case for that view and answer defeaters to that view.

      Can you do that? That is the hill you must climb.

      You also have to formulate defeaters to the various theories of realism. Merely ad hoc saying fictionalism is true doesn't cut it.

      Now granted nobody here expects you to argue this particular metaphysical view in a combox.
      Especially if you haven't learned how to do so before.

      But if you wish to counter the realist view you will have to formulate actual defeaters to show the scholastic view is incoherent.

      Anon does a better job than you (but I think he ultimately fails) because he is presupposing the Classic View. You I believe are begging the question by presupposing the materialist/physicalist anti-realist view.

      That is where we are at this point.

      Cheers.

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    16. @Paps

      Now let us do a short work of you. Man you really didn't learn anything?

      >Then how do you know IT'S out there beyond time, beyond space,

      God's existence is first established by philosophical argument. Make one please? Or formulate a defeater for one. You refuse to learn philosophy and ask simplistic "Mommy! Mommy!" childish questions. What is the point of you?

      Still thinking of God in Theistic Personalist terms are we? God is not an isolanti "out there". Geez I do seem to recall going over this with you over at Dangerous Idea decades ago. Obviously it has slipped yer mind. Getting old son...

      >"God is not matter; neither is non-existence.

      My shirt is Red and so is the Car down the street. So can I fill up my shirt's gas tank with Super? Can I wear the car to Church?

      Sharing a negative property does not translate into having an identical essence. Geez yer sophistry is tedious.

      > God does not have limitations; neither does non-existence.

      Non-existence is a total lack of Being and God is Being Itself therefore He cannot lack existence since He is Existence Itself. So how can Existence not exist Paps? Also what exists has Act and God is Pure Act. Non-existence is not Act.

      >God is not visible; neither is non-existence.

      Same fallacy of equivocation as the Car and Shirt.

      >God cannot be described; neither can non-existence".

      You cannot describe non-existence? Since when? Of course you can! It is an absence of being. It is a lack of something vs having a landfall of something.

      Take everything and subtract it from itself. Boom! You have nothing. It's not hard.

      >I think there is a lesson in reality here for all of us, wouldn't you say?

      Yes decades of reading Loftus and you can't get past your fallacies of equivocation and sophistry. Sad....& I am not interested in your lame arguments against prayer. Deal with the philosophical arguments for Classic God please.

      Paps you have nothing intelligent to contribute.

      Why are you here?

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    17. Hi Son of Ya'kov

      Thank you for your very full replies, but you need to work on being a bit more concise and disciplined in the way you present your arguments. I think that you are confused at various points, as well as resorting to rhetorical tricks. I also agree with Anonymous in stating that you are insufferably condescending ( Do you get into frequent altercations or even fights when you go to the supermarket or pub )? In any case, I disagree with you on so many points that it would generate a ludicrously long and tedious exchange to explore them, and it would come to absolutely nothing. If you see this as an admission of defeat on my part in this cake fight, that is perfectly OK by me. Cheers!

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    18. @Anon

      Well you at least present a challenge to the actual Classic Theist position. (Thought the ending was very disappointing & lame) Well done! Let's get into it shall we?

      >Yes, this God of classical theism is supposedly immaterial - whatever that means in other than a negative sense -

      Well that is the point. Apophatic theology! It is what is happening now!

      > Seems a bit problematic to me how such an entity could act in any way at all , let alone interact with human worshippers.

      If you want a professional explanation I recommend Brian Davies AN INTRODUCTION TO PHILOSOPHY OF RELGION.

      But I shall try to channel him from memory for you. It is the least I can do since you are the only one thus far to "bring it".

      From God's end God interacts with us all at once in one single divine Act from all eternity. For example with prayer. God knows all the prays I will say and from all eternity He chooses which ones to answer and which to not and wills the universe unfold accordingly.

      From my perspective it is a person to person interaction but God is not a person like we are as God is Infinite an unknowable.


      >But believers have no real conception of what it is they think they are worshipping anyway, as it is suis generis, completely alien and its qualities can only be known analogically!

      That is the best part about Him. If God was "knowable" I wouldn't waste my time with such a boastful shite.....

      >These are different but related points to those you make. The believers make it more than problematic to understand how they could know and have a relationship with their God in principle.

      Oh you can't have a relationship with God on yer end. God has to do it on His end. Grace and all that.....I thought this was known?

      >They might just as well believe they are having a relationship with a bottle of milk.

      Here is where you fall flat and you where doing so well? Milk is conceivable God is not so they are not equivalent.

      You started out with a good criticism "How does an immutable God act? How do you have a relatinship with such a God? Then you devolved to base ridicule."

      Ah well.....

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    19. >That believers truly believe their god is 'metaphysically simple', tells us absolutely nothing about this entity,

      If God is knowable as God then how is He God? Paps you can't get past yer tedious positivism.

      >but does speak volumes of something that only a metaphysical simpleton would deliver. Very sad really.

      Paps this is like the Young Earth Creationist mocking evolution by ridicule "Apes don't give birth to humans".

      It is lolcow even for you.

      Pathetic.....

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    20. @Anon April 13, 2021 at 7:08 AM

      >How are you getting on with your non- condescension practice?

      Quite well that other Anon made an intelligent opening then devolved with his comical milk analogy. Paps is as stupid as always and Unknown has begged the question and is not making any philosophical arguments.

      How are you?

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    21. @Unknown you wrote:

      >The supposed divine attributes are problematic when thinking about creation too, which must be here after all for there to be humans to supposedly relate to God. It is hugely problematic to understand how a simple, immutable God can do anything at all.

      How does an immutable God act? Well THAT is a valid challenge. I will go back to Davies and get back to you tonight on this. He explained it much better. But now I have other stuff to do.

      Cheers.

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    22. @Unknown.

      >Thank you for your very full replies, but you need to work on being a bit more concise and disciplined in the way you present your arguments.

      Thank you and I have the same criticism of you and to be honest I am not presenting arguments. I am not here to convince you to be a Classic Theist. You are here to convince me Classic Theism is wrong. If you are not interested in that well that is Ok. I won't think less of you (not that you care what I think but really I won't think less of you.) if you do but I am not making the positive case. You must do yer own reading for a positive case.

      > I think that you are confused at various points, as well as resorting to rhetorical tricks.

      Great minds think alike. That is what I think about you.

      >I also agree with Anonymous in stating that you are insufferably condescending ( Do you get into frequent altercations or even fights when you go to the supermarket or pub )?

      I think you are Anon. After all anon professes to know what you are thinking. How can he do that? If you are going to make personal attacks and not arguments then you are to fragile to discuss anything.

      OTOH I respect an honest asshole. If you and I will agree to be that way to each other we can still get on. It's a custom for us Scots and working class English to be jerks to one another and still get on. So yer choice. I won't think less of you. I really won't.

      >In any case, I disagree with you on so many points that it would generate a ludicrously long and tedious exchange to explore them, and it would come to absolutely nothing.

      I don't hold it against you that it would require we discuss book loads of info and you need to do a bookloads of reading and if you feel it too daunting I understand.

      I confess I don't have the skill to explain Thomism like Feser to you.

      >If you see this as an admission of defeat on my part in this cake fight, that is perfectly OK by me. Cheers!

      Not at all! I don't much care for the passive aggressive "don't be condescending" nonsense (because it comes off as condescending).

      But hey if this is too much I appreciate yer honesty. (PS I still think you are one of the Anon. But you need not confirm nor deny that. )

      Anyway peace be with you. It was fun.

      Delete
  26. The problem with physicalism, materialism, determinism and a host of other reductionisms, is that their own presumed truth gets reduced to the same factors they specify.

    That crypto-theism of reason showing behind the curtain is nasty stuff, impossible to get rid of.

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    Replies
    1. True, but it needs developing. Otherwise people are left with vague notions, myths and dreams. What Aristotle groped about in, was revealed in brilliant light by revelation. Metaphysics has developed in leaps and bounds as a result. Let's keep the light switched on.

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  27. I don't understand how his "fictional" objects are any different from the abstract objects of Frege. If you can infer with them and get the right answers, they can't be fictional in the normal sense of the word, because there are no "right answers" in fiction. There is a notion of consistency. If a story says, for example, that Batman caught the Joker, then the proposition that Batman caught the Joke is true within that work (assuming the work is intended to be self-consistent), but if Batman kills the Joker within that work, you can't conclude that the Joker is dead and is not coming back. You can't make inferences, because fiction is free form.

    Math, by contrast is not free form and you can make rigid inferences. The reality of the concepts of math is used to explain how those objects are different from fiction, that they can be used to come to new conclusions that are true rather than conventional.

    Modern "Platonism" doesn't make any more claims about abstract objects than this, so if Franklin is willing to countenance these "fictional" objects, well, that's what (modern) Platonic objects are, so he should be willing to countenance (modern) Platonic objects.

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  28. What is quite sad about George as "unknown", or as "BenG". "GregS", "Tim", "Mr. Green" etc., plus any number of anonymous (predictable denials notwithstanding), is the the sheer volume of stuff he has generated in these "discussions" (mostly with himself) over several years. It might not be more serious initially than needing company or a job, but when it becomes obsessive trolling and the manic wish to see others disappear at any cost, it needs marking.

    I've noticed this consuming desire to see people they detest annihilated socially among certain unstable women. Perhaps those who know him should gently tell him this place is not his social club, and to try to reduce his scribblings from up to 50% of what is written here to 10% tops.

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    1. Cervantes 1.31AM

      I do not know you, so I am keeping an open mind here , but my first impression is that you are either a troll or unwell. However I will persist.

      Who is 'George', why do you believe that he manifests under all these tags, and why are you disturbed ( in oppose to annoyed or frustrated say ) about this?

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    2. Miguel Cerventes, if you are suggesting that I am some sort of sock puppet for this other person, you are mistaken. This is me: http://brainlegions.com http://unobtainabol.com.

      I just wanted to make a point about the topic of the blog post. The level of hostility and bickering in these comments is off-putting.

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    3. David, if you look, you'll notice that my comment above wasn't in reply to yours. I'm sorry if you got that impression. Your point was pertinent and interesting, of course.

      I agree the hostility here is unpleasant. George has a track record going back years of trolling me, then begging the blog to ban me. I know him well: I was at his baptism, and if he had taken Fr. Joseph Pfeiffer's advice, would have been his godfather. Unfortunately, he wants fans, not friends. He has dumped his antipathies here (there are scores of abusive one-liners from him a while back which are still there to see). That's the background.

      He has to accept the presence here of people who don't agree with him, or even with this blog on certain matters (it's 2021 and nobody needs to make excuses for that). I like what Son of Ya'Kov is trying to do with him, but the strain of normal dialogue will probably be too much for his interlocutor.

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  29. I think many of the Gnus and other Atheists can't get past the idea God isn't the subject of quantitative analysis (because God's existence and natural knowledge of his attributes is not a scientific question) but qualitative only since God existence is a philosophical question.

    We can make rational inferences about God. But we cannot know him directly other than to know He is by reason.

    I cannot know directly a Googolplex plus One is greater than a Googolplex other than to rationally and logically infer it by the Axioms of math. The number itself thought finite is too absurdly large to count even with a Trillion quantum computers.

    But we can infer Pure Act which we take to be God and from there know God's attributes. This is the starting point before we get into divine revelation and other things.

    We are doing philosophy here not empirical science.

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  30. @Unknown

    If yer still interested I went back to read Davies. BTW I was mistaken. The info I seem to remember came from his work THE REALITY OF GOD AND THE PROBLEM OF EVIL.

    Which I quote"Yet the thought of God intervening in the created order (or intruding into it) is an exceedingly odd one. It would not be so if we took
    God to be an agent akin to a human being (albeit an invisible agent)living alongside the world and observing it from outside. Such an agent might well be thought of as able to intervene, just as I can be thought of as able to intervene in a brawl. Yet God, so I have been arguing, is not such an agent. I take God to be the cause of the existence of everything other than himself, and it seems hard to see how God, so understood, can be thought of as literally able to intervene in or to interfere with what he brings about. For something can only intervene by entering into a situation from which it is first of all
    absent, while God, as I am conceiving of him, cannot be thought to be absent from anything he creates. If God makes the universe to be (at any time), then God is creatively present to everything at all times as making it to be and to be as it is. From this it seems to follow that God cannot intervene in the world. He is, as creative cause, already in everything at the outset. As Alvin Plantinga puts it, commenting on
    Mackie's definition of 'miracle', 'on the theistic conception the world is never "left to itself but is always (at the least) conserved in being by God'.
    Talk about God as intervening has to presuppose that there is commonly a serious absence of God from created things. Yet if God is (in my sense) indeed the Creator of all things, then he is never absent from any of them (a point to which I shall later return)."END page 75 Reality of God etc Brian Davies.

    Hope this helps.

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  31. It would help if our Gnu friends and other Atheists would go read the distinction between Classical Theism vs Theistic Personalism. We don't believe in a Theistic Personalist deity here.

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    1. How old are you Son of Ya'kov?

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    2. Old enough not to tell people my age and if I was a woman I'd lie about it.

      ;-)

      Cheers.

      Delete
  32. Go on, give us a brief auto, but be honest about it. Just curious. Who is Ya'kov anyhow - it does not sound like a Scottish name?

    Do you ware a kilt and sporan?

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