At YouTube,
mathematician and philosopher James Franklin, author of An
Aristotelian Realist Philosophy of Mathematics, offers a brief introduction to the
subject. Also check out the website he
and some others have devoted to Aristotelian realism, as well as Franklin’s personal website.
A public lecture on
mathematics and ethics that Franklin is scheduled to give on April 2 will,
in light of the COVID-19 situation, be pre-recorded and posted online.
So, how does the Aristotelian explain the existence of mathematical necessities in the world? What James Franklin is saying is that Mathematics is describing features of the real world but unlike Platonism, I don't see how Aristotelianism gives an account of that , rather than just admitting it. In Platonism, at least as it's commonly conceived, you have the World of Forms which contains mathematical ideas and we see their shadows in our physical, perceptible world. The Aristotelian just admits the existence of mathematical patterns in the world, as a lot of materialists would. Now of course the materialist has a problem in explaining why the world and stuff around us seem to have to follow the rules of symmetry, proportion etc. Does the Aristotelian avoid the problem though? So at a first glance my problems questions are the following:
ReplyDeleteA) What are the origins of the mathematical necessities in Aristotelianism if there's no World of Ideas? I understand that in the hylomorphic worldview matter and form are conjoined and inseparable, so the Forms or Ideas of Plato exist in the things themselves rather than in another abstract world, but what does that mean? Isn't that a redescription of what the materialist would accept as well? Namely, that matter has such and such properties.
B) If there are no abstract objects in the World of Forms as Plato (or Plato as commonly interpreted) thought, what about all the mathematics that have nothing to do with our physical world and don't seem to describe something there? Wasn't one of the motivations/arguments for Plato's theory that there are things that seem to be necessarily true, mind independent, that seem to be discovered rather than invented yet are not part of the physical world? How does the Aristotelian approach deal with that?
C) How do we come to learn about the mathematical necessities? I remember that professor Feser argued in a post on Mill's theory of arithmetic that we don't come to know arithmetical truths empirically. Wouldn't that point towards Plato's conception? And this does not concern only epistemology but Metaphysics as well. For as Feser explained, if we found ourselves in a world where whenever we added 2 objects to 2 others we got five, we wouldn't assume that 2 plus 2 actually equals 5 only that some strange rule applies that makes another thing appear every time we add 2 things to 2 other ones. If that's the case, then that only shows that the truth of mathematics is something thats not inherently about what happens in the physical world. Furthermore, doesn't the fact that we can coherently imagine such a world while we cannot coherently imagine that 2 + 2 could equal 5 might generate an argument for the distinct character of mathematics and the physical world. Kind of like a conceivability argument for world - maths dualism, hence Platonism. I understand though that Thomists wouldn't accept conceivability as a guide to metaphysical possibility. I think though that my other points have merit at least as reasonable questions if not arguments.
A lot of Thomists would agree with some of your points, especially B. Hence why they'd favor divine conceptualism, or at least grounding abstracta in a necessary concrete being.
DeletePlato himself proposed the world of ideas/forms. Neo-Platonists, however, proposed the ideas/forms reside in the divine intellect, the mind of God.
DeleteAristotle proposed that ideas/forms reside either in the thing itself, or in minds. Aristotle's followers, however, you could say, put Aristotle and Neo-Platonism together and proposed that ideas/forms exist first and foremost in the mind of God, the divine intellect, but also exist in the things themselves and other minds who grasp them.
Our minds grasp forms by our interaction with things with form. Things receive form, thus bringing them in to being, ultimately, from God as the divine intellect.
Therefore, even if there was no physical world and no minds like ours, or even angels, the ideas/forms would still exist in the mind of God, thus making them unchanging and necessary, and any truths about them the same.
B) If there are no abstract objects in the World of Forms as Plato (or Plato as commonly interpreted) thought, what about all the mathematics that have nothing to do with our physical world and don't seem to describe something there? Wasn't one of the motivations/arguments for Plato's theory that there are things that seem to be necessarily true, mind independent, that seem to be discovered rather than invented yet are not part of the physical world?
DeleteTwo comments: (1) How do we know that some part of mathematics "doesn't apply" to the real world? Parts of abstract algebra (Group Theory) was originally drafted as a curiosity piece with no known application, but it was (much) later applied to chemistry at the atomic level. It seems that at most we can say "we have no application right now", we are unable to prove that the math cannot possibly have an application.
(2) What does Plato do about metaphysical truths that are not "Forms"? How does he ground their existence? Say, the principle of non-contradiction? I.e. truths that take a whole proposition to express, are not conceived as one single Form? Whatever answer Plato has, probably offers some kind of parallel pathway for Aristotle.
Also, mathematical objects are not actually Forms, as they are particulars (this triangle, etc.) Plato puts them a little lower on the Line in the Republic, below Forms, but above the sensible objects.
Delete@Zeno
DeleteAristotle would probably respond to you by saying that when we observe a object of this world the intellect abstract the form of it and knows the form separate from the matter, with a similar process giving we knowledgment of his mathematical properties. After this process of abstraction of the content of the senses, we know the forms separately, they look like subsistent forms like Plato believed but only exists on objects and minds.
Maybe this will help you see how Aristotle would respond to B and C. I have no idea of how he would explain A.
(B was not very clearly answered and is also a bit strange to me so...)
DeleteOn B, he would probably respond saying that this part of mathematics is potentially in things, even if they will never really exist in a thing(like the form of a unicorn who can exist in a thing but probably won't).
15. Furthermore, that an individual contingent thing persists in existence at any moment requires an explanation; and since it is contingent, that explanation must lie in some simultaneous cause distinct from it.
ReplyDeleteCan anyone provide an example of this? I’m familiar with the contingency argument but this unique approach by Feser is leaving me a bit confused. What is an example or some kind of deeper explanation of what he’s trying to say here?
Dear Anonymous: Well, this is pretty simple, but it's the first thing that popped into my mind, so:
DeleteI am an individual, contingent, existing thing. My parents are the immediate causal explanation for my existence. They will ALWAYS remain the immediate causal explanation for my existence, even though both of them have passed away.
Strangely, even though they are both gone, they remain the simultaneous cause, distinct from me, of my own existence. Similarly, any individual contingent thing persisting in existence requires a simultaneous cause of its existence.
Ultimately, of course, this cause must be an Uncaused Cause. But the argument is true even at the proximate level.
I don't think the parents remain an immediate simultaneous cause at all. Quite the contrary.
DeleteThe parents remain as the diachronic cause which originated us. What keeps us in being by contrast is a bunch of synchronic causes (such as different chemicals operating on our organs in such a way as to keep them functioning).
What Feser is pointing out there is basically the same thing as with the Aristotelian proof and others: there must be some cause which accounts for why an object exists at any moment, and, apart from that cause, the object would fail to exist.
In a nutshell:
Kalam argument: what explains the coming into being of an object, at t0?
Leibnizian argument: what explains the fact that any object exists at all at any times rather than nothing? Alternatively, what explains the existence of all these objects at all these times?
Thomistic arguments: what explains the existence of this object at every instant/what explains the "continuous existence" of an object? If an object is contingent, it could have failed to exist when it first came into being, but it could also have failed to exist at any later time in which it exists, so that needs an explanation too.
Feser is just pointing out that Leibnizian arguments can also be given Thomistic-like defenses.
Atno,
Delete"What Feser is pointing out there is basically the same thing as with the Aristotelian proof and others: there must be some cause which accounts for why an object exists at any moment, and, apart from that cause, the object would fail to exist. "
Upon observing change there is a call for a causal process to account for that change.
Material does not change in the aspect that it exists. One can consider the Kalam in attempting to solve how all that exits came to exist from the deep past, which is in fact an unsolved riddle, for which no sound solution is presently in general circulation.
However, AT arguments are present moment arguments which simply observe what is manifest and evident to our senses right now, irrespective of how all we observe may have come to be as it is from the deep past.
Since material does not change in the aspect that it exists there simply is no call for a changer to keep material in existence.
The assertion of a first changer to account for no change is at best superfluous.
If material were to change from existing to not existing that would call for a changer. So AT has things back to front.
What would it even mean for material to "blink out" of existence? How is that at all coherent? Where would it go? What would be the cause of that change?
AT asserts that we must invoke a changer to account for no change. Somehow, AT asserts, an unseen and undetectable changer is everywhere acting upon all material in the universe in just the right way such that it is manifest and evident to our senses that material is never changing at all in the aspect that material exists.
How is that assertion of AT not an inversion of logic?
Atno: Thanks for the correction.
DeleteSP, I've had the same issue with misinterpreting Feser as well. Re-read Five Proofs when you're open to hearing it like it's the first time again, rather than (what I did) reading into it a discussion it doesn't address. I also thought there had to be this constant force acting against annihilation or something. That's not the case.
DeleteHe begins with change, but moves past it. Maybe swap "changer" for "source of actuality." For example, a painted red chair is always actually red due to its paint (for example). That paint is the source of actuality there, the continuous explanation; there is an asymmetrical dependence of the chair's redness on the paint.
No observable essence contains its being, thus we need a source of being from elsewhere. Because the essence won't begin to contain its being, it won't ever stop needing a source.
5onesis,
Delete"He begins with change"
Yes, and then he applies the principle of "Agere sequitur esse and the First Way", as he posted 27 Feb 2020. You can read my comments there if you care to.
The First Way fails as an argument for the necessity of a first mover, or first changer, because it employs false premises and invalid logic. Therefore drawing conclusions about a first sustainer on the principle of agere sequitur esse of a failed argument is invalid.
"For example, a painted red chair is always actually red due to its paint (for example)."
If you shine spectrally pure green light on that chair it will appear green, so how can the paint be the source of the chair's redness?
You raised the subject of existence. How does painting a chair account for its existence in any sense? If we paint a chair red has the chair itself become red or have we merely blocked our view of the chair with a red thing?
"No observable essence contains its being"
Agreed, we never observe an essence independent of the thing that the essence is of. Likewise, we never observe a thing independent of its essences.
Essence and existence are always found together, simultaneously co-dependent and inseparable.
Thus, to speak of a pure essence is incoherent.
To speak of a pure existence is incoherent.
"Because the essence won't begin to contain its being, it won't ever stop needing a source."
Yes, it makes no sense to assert a pure essence, just as it makes no sense to assert a pure being. It makes sense that essence and existence are simultaneously co-dependent and inseparable in structural reality.
SP hasn't read Five Proofs. He resolutely refuses to read anything on Thomism but this blog. Yet he constantly gives stupid criticisms of it. He's a troll. Don't feed him!
DeleteFrom the links in the OP
ReplyDelete"2 rabbits plus 2 rabbits equals 4 rabbits"
Does it?
What is a rabbit?
Are any 2 rabbits precisely the same such that we can coherently assert we have precisely 2 of precisely the same thing?
What we really have is 2 members of an approximately defined set plus 2 more members of an approximately defined set that we say means we have 4 members of an approximately defined set.
The subject of the OP, Franklin, asserts a false dichotomy, that mathematics either describes the real world or it does not.
Franklin neglects a third option, that some the mathematics we presently have approximately describes the real world, while the rest of the mathematics we have does not describe anything of the real world.
Today, now, humanity as a whole, or any individual, can precisely mathematically model exactly zero real objects in our universe.
At risk of posting off-topically, I wanted to let everyone know I found a new book by Feser: When Execution Isn't Enough. Presumably it's a follow-up to By Man Shall His Blood Be Shed. Can't wait to read it!
ReplyDeleteClaudio Feser?
DeleteThat's hilarious. I was expecting something like "When Execution Isn't Enough: The Case for Torture."
DeleteFeser and company use slight of hand. They say that a book has bookiness. This opens the window to their speculations. The reality is that a book doesn't have itself. It IS bookiness, which just means it's a book, something we all already knew. So you were fooled by them. Everything Christianity touches turns fake.
ReplyDeleteI also want to add that nominalism for some considers no two numbers alike, so the whole edifice of mathematics as objective falls to the ground for them. There's a logical alternative for you
ReplyDeleteTruth is not three persons. It is true that truth is literally, absolutely nowhere. This is not relativism, but you can't have a true relationship with truth because it's not an entity of any kind. Feser's argument against Mill is wrong. Studies in math map out the impossible; 2+2 equals every number except 4, at the highest abstract level. I learned this from Hegel. Thomists and Christians in general have no clue how life really works
ReplyDelete2+2 equals every number except 4, at the highest abstract level. I learned this from Hegel.
DeleteTrue wisdom is walking among us and we are too blinded by our pride to see.
"2+2 equals every number except 4, at the highest abstract level. I learned this from Hegel. Thomists and Christians in general have no clue how life really works"
DeleteLife doesn't work by 2+2 equaling everything other than 4.
Life works by approximating real objects as members of a set so that we can abstractly consider objects that are actually different as though they are in some sense the same, such that we then consider that we can add them.
2+2=4 is an abstraction, not a precise model of real objects.
Nominalism defined entities by their individuality. If I were to ask a Thomist to relate the proposition "nothing is identical so there is only one number" with the proposition " 2+2 equals everything but 4" they would be absolutely worthless at the task
Delete""nothing is identical so there is only one number""
Delete...of any particular known real object, that number being 1.
Franklin asserts he can add 2 rabbits plus 2 rabbits to equal 4 rabbits, and seems to take as an obvious given that this means mathematics is realistic.
It does not seem to occur to the good folks here, or Franklin, that no 2 rabbits are the same, and therefore it is incoherent to assert one has 2 or 4 of things that are not the same, and also assert that 2+2=4 actually models real rabbits.
Let
X=1
Y=.999
Z=.998
Can we coherently state?:
2Y + 2Z = 4X
In what sense can we coherently state we have 2 of different things?
In another post Dr. Feser stated that there "are" triangles, which frankly shocked me as being so obviously false it was surprising for me to read it coming from a PhD who teaches at a public college in California.
Mathematics as we presently have available can precisely model exactly zero known real objects in the universe.
Yet, mathematics is so seemingly about real aspects of the material universe. A rock thrown through the air follows a fundamentally parabolic path. Big rock, small rock, this angle of throw, that angle of throw, thrown so hard, thrown harder, thrown on this continent, or on a ship at sea, or on the moon, all these various throws will all follow a fundamentally parabolic trajectory, never precisely parabolic, but always converging on parabolic as a highly accurate trend line.
So, it seems that a parabolic flight path is a realistic aspect in an incompletely defined superposition of aspects of how real material interacts and progresses through time and space.
Thus, we have clues that in principle, at base, there are a finite number of aspects of how real material really progresses over time through space and that those fundamental aspects of material can be precisely modeled mathematically, in principle.
So, in principle, we can hypothesize that at base, if we are ever able to discover that base, there are aspects of reality are can be modeled precisely by mathematics, but at this time we are missing many of those superposed aspects so we presently have the capacity to precisely model zero known real objects in the universe.
In the mean time, apes such as we muddle through functioning under the delusion that our crude models are realistic.
So, our brains pick out certain features that an object has and classifies that object as a member of a set. Then another object is classified as being close enough to be considered a member of a set.
1 member assigned to set X plus another member assigned to set X equals 2 members assigned to set X.
We function by abstracting, simplifying, and treating as the same objects that are not really the same, so that we can abstractly add them.
The error of Thomists is that they seem oblivious to all this, and somehow think 2 + 2 = 4 is a true model of real known objects.
Trolls me gone both of you..idiots.
DeleteAnon,
Delete"both of you..idiots."
Interesting...
Can you please give me an example of a single real object in the universe that we can precisely mathematically model?
Can you please provide an example of a real object that is a triangle?
The topic of this thread, broadly, is the philosophy of mathematics, does that subject interest you at all?
Thus far your only apparent interest is virtue signaling via ad hominem.
Good post Stardust. I don't think youre a troll. Thomists can often be arrogant so I think you are just reacting to this, as an I. Thomist say no one can live life without worshipping something. This is a false anthropology. Considering how 2+2 can equal 5 has.been a part of the koan tradition for a long time. Thomson is about slowing thoughts as much as possible. Aquinas himself was called the dumb ox because he was a master of this. Koan therapy is about quickening the thoughts as much as possible in order to be able to relax them. You can then focus on nothing and be without an idol. And then be free
ReplyDeletestardusty has been banned by Feser himself and we have been told not to feed him. Nice respect for the blog you have...
DeleteIt's obvious that it's him posting as "Anonymous", agreeing with himself. The guy has serious issues.
DeleteNop,two people. If stardusty is a troll, why isn't he re-banned? Christianity is a trolling religion, and idolatrous. Christians think some super daddy is going to save them. In reality you have to do it youself. Feser was an atheist for a puny ten years. He's really been an idolatrous theist his whole life. Does he ever smile? Him talking about capital punishment is creepy
DeleteNo, he's the Secret Troll. He's into New Agey interpretations of Buddhism and Hinduism, fideism, has a personal and irrational hatred and fear of Natural Theology, thomism and analytic reasoning and logic, and a grudge against Christianity. A lot of people don't know about him since he always posts anonymously, but it's easy to catch him. He's the Secret Troll. Don't bother arguing with him. He is, in fact, much, much worse than Stardusty.
DeleteYou can't literally ban people on blogspot, troll. Feser would have to delete his comments manually or put on comment moderation. He's probably too busy for both right now, so he's told us not to feed SP or any like him, like you.
DeleteWhat if James Franklin adopted some intro music:
ReplyDelete"Hey it's Franklin...do do do do do do do do do do..."
Some millennials growing up with Nick Jr. (like myself) might understand this reference. Alas, it's on Youtube:
https://www.youtube.com/watch?v=8MLrpdS7lRY
"Truth is not three persons. It is true that truth is literally, absolutely nowhere. This is not relativism, but you can't have a true relationship with truth because it's not an entity of any kind. Feser's argument against Mill is wrong. Studies in math map out the impossible; 2+2 equals every number except 4"
ReplyDeleteThese five sentences make me very sad. The Internet can be a wonderful tool, but it also offers an open forum for exhibitions such as this. Somewhere out there, there is an anonymous person who believes that these words link together to make a meaningful argument. Isn't that at least a bit sad?
Usually I am opposed to banning people, but this thread provides a textbook example of hijacking by a swarming band of loonies. Why would anyone get angry with Ed Feser when posters such as these are banned?
He is one of the weirdest trolls, but since he always posts anonymously, we don't have a name for him yet. It's easy to identify him though - he's always making cryptic, mumbled critiques of Thomism, Christianity, and sometimes reason in general (he seems to have personal issues with it, like he's genuinely angry that people like Thomistic philosophy or analytic reasoning); makes contradictory and sometimes meaningless assertions, butchers logic and reason; then sprinkles some New Agey attempts at existential wisdom.
DeleteI call him the "Secret Troll". Don't feed, people. We shouldn't even be discussing him, but I felt like it was important to point out since some people are unfamiliar with Secret Troll - he is secret, after all.
Craig,
DeleteI agree that the wording of those sentences is somewhat scattered and incomplete at best. There are some interesting points buried in there, but the poster did not really develop them into clear arguments.
I attempted to do so by completing one assertion and then developing it further here
April 3, 2020 at 7:04 PM
https://edwardfeser.blogspot.com/2020/03/franklin-on-aristotelian-realism-and.html?showComment=1585965898034#c3123792572206423001
The topic of this thread includes the philosophy of mathematics as stated by Franklin. I provided arguments as to why I think Franklin has some things fundamentally wrong on that subject.
If you have some disagreements on the merits of the arguments I presented you are welcome to express them.
Dear SP: Your argument appears to be based on the nominalistic claim that, since individuals are always different, they can't be added together in any realistic way. One carrot and another carrot, for example, are different carrots, and so can't be put together (realistically) in a grouping of two carrots.
ReplyDeleteIf that is your argument, it's not really worth a lot of trouble to engage. If Carrot 2 is so much different from Carrot 1 that they cannot realistically be grouped, how do you even know they are both carrots?
Aquinas would agree that both carrots have different and individual acts of existence, but that doesn't make them so different in reality that they cannot be classified (realistically) in the same category, and subsequently added. One plus one equals two of them.
Craig,
DeleteYes, you have the first part of my argument correct, and I did in fact acknowledge the second part of your response. So we are both discussing pretty much the same things here.
In order to add two different things we must abstract each object, observe key aspects about them that we consider qualifies them to be placed in a particular set, and thus designate them both as being approximately similar enough to be thought of as members of the same set. One object that has been abstractly approximated as a member of a set, plus another object that has been abstractly approximated as a member of that set, equals two objects that have been abstractly approximated as members of the same set.
That is rather too cumbersome so typically we just say 1 carrot plus 1 carrot equals 2 carrots.
But mathematics is a form of logic that requires exactness in an equation. Yes, we have means such as sets, or plus/minus tolerances to cope mathematically with the inaccuracies of the real world, but those are just approximations, not realistic mapping.
Approximately correct is not good enough to claim mathematical realism.
Newtonian mechanics was considered for a time to be realistic. Then it was discovered to not be realistic because inaccuracies were discovered.
Unfortunately, we have no precise mathematical models of any real object in the universe, none whatsoever. Thus, clearly, the maths we presently have are not demonstrably realistic because they cannot be mapped precisely onto any known real objects.
That is not to say math cannot possibly be realistic in principle. In principle is seems as though at base material does progress through time and space and interact in a finite number of perfectly regular ways, and in principle those base regularities seem as though they should be able to be described precisely with some sort of maths.
So, in principle, we have strong clues that at base some subset of mathematics, as yet unidentified, is realistic.
No presently available maths are demonstrated to be realistic with respect to any known real object.
Craig, what are you doing? You know better than to feed him.
DeleteI think Stardusty fits in the second, milder category of trolls that Feser has mentioned:
Delete"But there are other, less extreme trolls whose sins are more minor or who show a willingness to reform. Marks of this milder kind of troll would be: monomania, rudeness, logorrhea, etc. that manifest only occasionally; irremediable ignorance or muddleheadedness that makes a commenter tiresome and not worth engaging, but that is not manifested in a rude or otherwise obnoxious way; a predilection for comments that are not quite off-topic but are nevertheless banal, ill-informed, weird, or otherwise not substantive; and so on. Most of these people I simply tolerate. There are also some who I have had to ban temporarily, but whose return to the comboxes I have tolerated when they have given signs of a willingness to restrain their more obnoxious tendencies."
I still think SP is generally not interested in sincere discussion, and just likes to write speeches confirming his own idyosincratic views; I also think that conversations with him tend to be fruitless. But he's not as bad as, say, CR, Cervantes, or the Secret Troll.
If someone wants to waste their time and argue with SP, I think they're allowed to. It's a bad idea, but he's not nearly as bad as the extreme trolls, so I think he falls into that category which Feser tolerates.
CR, Cervantes, Secret Troll, etc. really should be ignored, however.
Feser explicitly banned SP. Discussion with him is always pointless. Has anyone ever had a worthwhile conversation with him here? I doubt it. There's no engagement with him. It is like talking to a brick wall. This has been shown by long experience. He was the original first category and of troll, perhaps with Santi. He should be ignored.
DeleteSP is logorrheic and monomaniac all the time..he is never worth engaging..he is often quite rude and a proven liar... definitely.he doesn't fit the redeemable troll category..he spreads and takes over the place of you feed him.. you shouldn't.
DeleteSP, I'll give you the benefit of the doubt that you're pursuing truth and give you some push back.
Delete"In order to add two different things we must abstract each object, observe key aspects about them that we consider qualifies them to be placed in a particular set"
This position requires us to abstract shared characteristics from different ones and further, different properities of one carrot. If we can distinguish ORANGE in a carrot from SWEET, then we are able to know one property abstracted from others in the same object. But if we can do this, we can abstract what is precisely shared by two carrots and we thus have an essence. Thus we have 2 carrots truly.
We have been told to stop feeding the trolls.. seriously....stop it. SP is not new. He was banned twice at least by Feser..he has never shown the slightest hint of not being a troll..have some respect.
Delete5onesix,
Delete"If we can distinguish ORANGE in a carrot from SWEET, then we are able to know one property abstracted from others in the same object."
Approximately, yes, precisely, no.
"But if we can do this, we can abstract what is precisely shared by two carrots and we thus have an essence."
An abstraction can be defined as precise. We can define X to exactly equal Y as mathematical symbols.
But even the sensation of orange (the color) is not precise. The color orange, for people with ordinary color vision, results from the stimulation of red and green receptors in the eye. One can view a single wavelength of spectrally pure orange light, which will stimulate both sorts or receptors in a particular proportion that the brain interprets as orange. However, the same perceived color can be produced myriad ways, for example on your computer monitor by a certain relative intensity of red and green emitters in a pixel on your screen, such that the spectral distribution of such light that you perceive as the same shade of orange is actually very different materially, being composed not of spectrally pure orange light but, rather, a mix of various wavelengths from red to green.
So already, what might seem precise at first consideration turns out not to be the same material at all.
"Thus we have 2 carrots truly."
Or we have the citrus fruit, an orange, which can also be sweet and orange in color.
One could abstract a concept of the essence of carrotness, but that is just another way of saying that certain key features of objects are observed such that they are considered to be in the set called carrot.
You can call it an essence, a set, a species, a kind, or whatever sort of classification system you wish to employ, they are all abstractions that ignore individual differences between objects to abstractly consider as the same, different objects that are not in fact precisely the same.
So still, we have no demonstrably precise mathematical model of any real object, nor do we have any means to show that any two objects are the same so we can add them coherently, saying we have two of the same thing.
All we can do is abstractly approximate objects as being the same sort of thing so that we can by convention add them as members of an abstract set.
Feser can you please put on comment moderation. The trolls are getting unbearable here. Thanks.
ReplyDeleteOrdinarily I wouldn't jump into a discussion with some folks, but I think Dusty's comments in this thread do fit into the general topic, which is realism and mathematics. The other Anonymous, however, is just really disturbing, in a disturbing sort of disturbing way.
Deletei hope God smites them all with nasty urinary tract infections...
DeleteCraig,
DeleteIt doesn't matter whether Dusty is fitting in to the topic in this one instance. He is not welcome here. He is still a troll who will carry on trolling, which has to stop. The only way to do that is to ignore him, even when he is behaving. He simply needs to go away.
Now ignoring the troll bullshit, I have a question wrt the Augustinian argument and Scholastic realism, which of course is related to abstract objects and realism.
ReplyDeleteThe main idea behind "abstract objects exist as forms in real objects... or as abstractions in the mind" is an anti-platonic intuition that grounds abstracta in concreta. But why assume that "abstractions in the mind" are the only alternative here? Why couldn't the abstracta be grounded in causal powers of concrete substances? So a form (and even a mathematical concept such as "5") could be grounded in a being having the power to cause that form, or to cause 5 things. This would avoid the Augustinian idea of a divine intellect being required for grounding abstracta, and would still maintain the anti-platonic intuition.
So it seems to me Scholastic realism might move a bit too quickly to the idea that forms are grounded in thoughts, more specifically, divine thoughts. One can, however, make an inductive argument for abstracta being better understood as thoughts instead of just causal powers, because of how similar thoughts and abstracta would be (both are about things; both can be true or false; both exhibit structures that arguably are harder to capture just through causal powers).
Atno,
Delete"Now ignoring the troll bullshit, I have a question wrt the Augustinian argument and Scholastic realism, which of course is related to abstract objects and realism."
Indeed, it is the merits of the arguments, focused primarily on the subject of the OP, that are interesting, The rest is boring noise.
" Why couldn't the abstracta be grounded in causal powers of concrete substances?"
In principle, they can be. In principle mathematics can be about something real. My key point here has been that as yet we have not demonstrated that principle with precision. But it is possible, and it seems likely, that we have identified some maths that are realistic as elements in a superposition of real aspects of material, which may be what you mean by concreta.
For example, a straight line. It seems realistic that an object will travel, in principle, in a straight line in uniform linear motion in space. But no object actually travels in a straight line to demonstrate that the mathematical description of a line segment is realistic. There are always asymmetric fields distorting the path of any real object such that it does not travel in a straight line.
Still, at base, in principle, perfectly uniform linear motion seems to be a real aspect of material as an element in a superposition of real aspects of material.
So, some subset of mathematics can, in principle, be about the real aspects of concreta, if that is what you mean by being grounded in concreta.
@Atno
DeleteI'am trying to find a good way to defeat Aristotelian Realism so i can defend the Augustinian Proof and ended up thinking about something like that. The idea that the forms than are not actual exist as potentials in what is actual makes sense.
A difficult of mine that is probably not on the subject but related: what about things that can't really be caused by us or the material universe?
Think about something like a angel*: like a unicorn, the fact that they can be described with no contradiction shows that they are possible even if you think they do not exist, unlike liquid ice or a married bachelor. But if they are possible, there must be something that can cause their existence, a thing i believe only God can do.
Sure, my oponent can claim that a angel is not metaphysically possible, but i can't think of a non-question-begging way of arguing that and i believe the fact that we can't reject the concept a priori is enough to show that it is possible, so this objection seems weak.
I don't know if Aristotelian Realism can answer that, do you guys find some flaw here?
*i do believe they actually exist so obviously are possible, but you can't assume that if you are trying to show that there is a God
Talmid,
Delete"a unicorn, the fact that they can be described with no contradiction shows that they are possible"
It is important to distinguish between a logical possibility versus an existential possibility.
Just because an abstraction is logically possible in no way necessitates that it be existentially possible.
To assert that an abstraction that is logically possible must necessarily be existentially possible is to commit the fallacy of reification.
"my oponent can claim that a angel is not metaphysically possible,"
That claim by your opponent commits the error of asserting to be able to prove a universal negative, which does not follow merely from an observation of a local negative.
There is no proof that any of our present mathematics are realistic, that is, about a real aspect of material, or as been described elsewhere here, concreta. The reason being that exactly zero real objects in our universe can be precisely modeled with any existing mathematical formulations.
All presently on hand formulations are no better than highly accurate trend lines, as far as has been demonstrated.
However, the high accuracy of those trend lines over a multitude of circumstances very strongly indicates that at base there are real material processes and aspects that do proceed with perfect regularity that can in principle be described precisely with some mathematics we merely have not yet discovered.
If by "Aristotelian realism" you mean grounding abstracta in contingent concrete beings, it's easy to refute that. Abstracta are necessary, so they must be true (and must be grounded) even if no contingent being whatsoever existed, so they must be grounded in a necessary concrete being.
DeleteIf you want to establish that the necessary concrete being is a mind instead of just some being with causal powers, that is more difficult. The best I can come up with are two arguments:
1- an abductive/inductive argument on how similar thoughts and abstract propositions really are. Both are about things. Both can be true or false. Both share a similar structure, etc. So it is plausible to identify abstracta with thoughts, or to ground them in thoughts;
2- as you said, the possibility of angels. But we can use something less controversial: the possibility of intelligent beings like us. Given the arguments for the immateriality of consciousness and intellect, it is plausible these are pure perfections and therefore whatever grounds their possibility must also be a mind. Alternatively, these arguments show that immaterial minds are at least possible.
@Atno
Delete"If by "Aristotelian realism" you mean grounding abstracta in contingent concrete beings, it's easy to refute that. Abstracta are necessary, so they must be true (and must be grounded) even if no contingent being whatsoever existed, so they must be grounded in a necessary concrete being."
I know this objection to this form of realism but i still fail to understand it exactly. What i understand is that a necessary truth like "1 + 1 = 2" or "Cats have four legs" need to be grounded on something necessary because they are necessary truths.
But i have two issues with that:
1. We do say a lot of things that are true but who have singular terms that do not exist, like "He did it for our sake!", so something like William Lane Craig alethic realism seems a possible alternative view.
2. Truth is "adequation of thing and intellect", truth is on minds and not on things, as Aquinas defends. Won't them say that there is truth when there are no contingent intelects be question-begging against the atheist? For he believes there are no necessary intelect, meaning that for him there are no truths when there are no contingent minds.
I do believe that Aristotelian realism loses to the Thomistic one, but arguing for that directly is kinda hard.
1- If we adopt realism, the truthmaker principle, and the anti-platonist intuition, it's pretty obvious that at least some propositions will need to really be grounded in real entities. Things such as "unicorns could possibly exist" need to be grounded in reality somehow, and given the necessity of the possibility it must be grounded in a necessary concrete being. Whether or not some propositions can be accounted for by other means, it is clear that given what we accept at least some abstracta will have to really be grounded in concrete entities;
Delete2- It might be question-begging in the sense that every argument is question-begging, but there's nothing wrong with pointing it out. Either the Aristotelian accepts that there are no necessary truths, or that necessary truths don't have to be grounded in concrete beings. Both are absurd - the first horn is actually the more absurd one, but the second is also unacceptable for the Aristotelian, of course.
I think it's super easy to demonstrate that abstracta, or some abstracta, must be grounded in a necessary concrete being if we accept realism and anti-platonist.
I think i get it now, thanks! I was thinking about something on the truth-maker principle but only really saw how it was important here now.
DeleteThe Augustinian Proof now seems way easier to argue for.
Talmid,
Delete"What i understand is that a necessary truth like "1 + 1 = 2" or "Cats have four legs" need to be grounded on something necessary because they are necessary truths."
Some cats have 3 legs, so how can "Cats have four legs" be a necessary truth?
It would be better understood as "Cats normally have four legs"; the "normally" here refers not to statistical regularity but to a formal-cum-teleological structure. The essence of a cat is to have four legs; it's possible for a cat to have three legs, but it will be a defective one. The powers involved in the formation of a cat have a disposition towards forming four legs instead of five or three (and this disposition is what, in turn, would predict and account for the statistical regularity of cats commonly having four legs).
DeletePeople should accept this Aristotelian thesis for its adequacy and explanatory power, but if they reject it, there would be many other examples of necessary truths anyway ("unicorns are possible" etc).
Atno,
Delete"It would be better understood as "Cats normally have four legs";"
Ok, that seems like a reasonable additional detail of wording. But in that case, what observed natural trend is not a necessary truth? In that case all aspects of the universe are necessary truths since they have a disposition for forming as they do.
Yes, I agree with that, given a primordial being that is necessary, and the Principal of Sufficient Reason, every real aspect of the universe is therefore necessary.
This combox is a vindication of Sartre:
ReplyDelete“Hell is other people.“
"So is Heaven."--Payne
DeleteHowever, this is all the posting I'll be doing for a while. God bless, everybody!
Take care and God bless!
DeleteI find the comments by Stardusty Psyche to be the only ones worth reading - they encourage one to think outside of the tediously boring group-think which dominates this blog.
ReplyDeleteIf you find everyone *except* Stardusty "tediously boring" and examples of "group-think", then why are you wasting your time here? Go away. One thing the combox does not need is coward anonymouses whose only contribution is cheering for idiots.
DeleteGood for you. You're free to enjoy his posts.
DeleteI have never found anything of worth in his comments, ever. He clearly has not the slightest idea what he is talking about not does he take any time to acquaint himself with what Thomists actually believe. There maybe decent critiques of Thomism out there, but Stardusty won't be the one offering them. I suppose it takes all sorts though.
DeleteSorry for the off topic comment, Dr. Feser, but by the way, Atno, I left you a message at the classical theist forum.
DeleteWell yeah, cuz what's better than watching some guy completely dominate every discussion with book length replies, thundering errogance, and chest-beating bravado? And bad arguments to boot. Why nothing of course.
ReplyDeleteIt looks like Franklin's public lecture had been posted: https://www.satcathedral.org/2020/mathematics-and-ethics-the-two-sciences-with-demonstrable-truths/
ReplyDelete