Friday, August 11, 2017

Rucker’s Mindscape


In his book Infinity and the Mind  (which you can read online at his website), Rudy Rucker puts forward the notion of what he calls the “Mindscape.”  He writes:

If three people see the same animal, we say the animal is real; what if three people see the same idea?

I think of consciousness as a point, an “eye,” that moves about in a sort of mental space.  All thoughts are already there in this multi-dimensional space, which we might as well call the Mindscape.  Our bodies move about in the physical space called the Universe; our consciousnesses move about in the mental space called the Mindscape.

Just as we all share the same Universe, we all share the same Mindscape.  For just as you can physically occupy the same position in the Universe that anyone else does, you can, in principle, mentally occupy the same state of mind or position in the Mindscape that anyone else does.  It is, of course, difficult to show someone exactly how to see things your way, but all of mankind’s cultural heritage attests that this is not impossible.

Just as a rock is already in the Universe, whether or not someone is handling it, an idea is already in the Mindscape, whether or not someone is thinking it.  A person who does mathematical research, writes stories, or meditates is an explorer of the Mindscape in much the same way that Armstrong, Livingstone, or Cousteau are explorers of the physical features of our Universe.  The rocks on the Moon were there before the lunar module landed; and all the possible thoughts are already out there in the Mindscape.

The mind of an individual would seem to be analogous to the room or to the neighborhood in which that person lives.  One is never in touch with the whole Universe through one’s physical perceptions, and it is doubtful whether one’s mind is ever able to fill the entire Mindscape.  (pp. 35-36)

When Rucker speaks of “thoughts” all preexisting in the Mindscape, he is evidently using the term the way Gottlob Frege does in his classic essay “The Thought,” viz. to refer to what contemporary philosophers prefer to call propositions.  (Though he also seems to have concepts in mind.)  A proposition is what is expressed by a declarative sentence, but is distinct from any sentence.  To take a stock example, the English sentence “Snow is white” expresses the proposition that snow is white, but that proposition is not identical to the sentence.  For one thing, the same proposition could be expressed instead in the German sentence “Schnee ist weiss.”  For another, the proposition would remain true even if no sentences in English, German, or any other language existed.  Notice, however, that the proposition would also remain true even if no human mind ever entertained it.  Propositions (or “thoughts” in Rucker’s and Frege’s sense) transcend not only language, but also any individual human mind or collection of human minds.  They are not to be confused with particular psychological episodes occurring in such minds.

They also transcend the material world, in Rucker’s account as in Frege’s.  Mathematical propositions would remain true even if no material world had ever existed.  Some propositions about the material world would remain true even if it went out of existence tomorrow (e.g. it would still be true that Caesar was assassinated on the Ides of March).  Even if there were no material world, so that the proposition that chairs exist was false, even that proposition would in some sense be real.  (By way of analogy, think of the way that a picture or sentence which misrepresents things still exists qua representation.)

For this reason, it is probably best to understand Rucker’s term “consciousness” in a loose sense.  At least much of what we think of as falling under the category of conscious experience has an essentially bodily character – pains and other sensations, visual and auditory experiences reflecting a specific point of view in time and space, etc.  If the Mindscape is distinct from the material world, then the aspect of the mind that accesses it does not do so by way of perceptual experiences tied to bodily organs like eyes, ears, and the like.  What Rucker regards as that which “moves” through the Mindscape is thus presumably the intellect, specifically, as opposed to the senses or the imagination (understood as that faculty whereby we form mental images of a visual, auditory, tactile, or other sort). 

The Mindscape, then, is essentially the collection of all the propositions and concepts that might possibly be grasped, entertained, affirmed, denied, etc.  The Pythagorean theorem would be an example of a denizen of the Mindscape.  When you entertain the theorem and I do not, you are accessing a part of the Mindscape that I am not, at least at that moment, accessing.  When we are both entertaining it, we are accessing the same part of the Mindscape.  But the theorem was there before either of us accessed it and will remain there long after we are gone.  The same is true of every other proposition or concept.  They are all out there waiting to be accessed, as it were. 

This is a very attractive idea, not only for metaphysical reasons – to which I will return in a moment – but also for moral reasons of a sort.  We are all familiar with the notion of the mind as a redoubt that even the jailer or torturer cannot reach.  “Do what you will to my body,” the prisoner might say to himself, “my soul remains my own.”  The comfort this provides can be pretty cold, though, if this refuge is thought of as a Cartesian prison.  The idea of the Mindscape makes of the mind a gateway to a whole other world, rather than a mere private cell into which one’s tormenter cannot trespass.  One can escape rather than simply hole up – escape into the very same world of thought to which every other mind has access.  This is perhaps what Winston Smith tries to reassure himself with when, in Orwell’s 1984, he meditates on the fact that 2 + 2 = 4 regardless of what the Party says or tortures him into saying. 

A natural way to interpret the Mindscape is as a Platonic “third realm” distinct not only from the material world but from any mind whatsoever.  Indeed, this seems to be more or less how Rucker understands it, just as it is more or less how Frege understood the “thoughts” he spoke of.  But there are other ways to interpret it.

Is a materialist interpretation possible?  It might seem that Jorge Luis Borges’ famous fantasy of “The Library of Babel” would provide a model for such an interpretation.  In this infinite library, every possible combination of the characters of an alphabet (at least within a certain page length) is said to exist in one of the library’s books.  It might seem, then, that any proposition or concept that exists in the Mindscape would have an analogue somewhere in Borges’ library.  Since the library and its books are material things, it might therefore seem that we essentially have the Mindscape in a physical form.

But this is an illusion, and the reason is not just that the Library of Babel doesn’t really exist.  Even if it did exist, it would not be relevantly like the Mindscape, and neither would any other material system made up of physical representations parallel to those in the library.  For one thing, many of the combinations of letters in books to be found in the library would be entirely random gibberish, expressing no proposition or concept at all.  There is nothing in the Mindscape comparable to that. 

To be sure, Borges tells us that none of the combinations of characters in the library would in fact be “absolute nonsense,” because there is always going to be some possible language in which a given combination conveys a meaning.  That is true, but it brings us to the deeper problem that the meaning of the combinations of symbols in any language, including that of Borges’ volumes, is entirely conventional.  That is to say, the symbols have meaning only insofar as we impart meaning to them, so that there must already be some independent realm of meanings we first grasp before imparting them to the symbols.  In effect, the Library of Babel presupposes the Mindscape, so that we cannot coherently reduce the Mindscape to the Library of Babel.  (Related to this is the problem that no physical symbol or system of symbols can have the sort of determinate or unambiguous content that a thought can have, so that a thought cannot be reduced to any set of physical symbols.  I have developed this line of argument in several places, most fully here.)

How about Karl Popper’s World 3 concept as a way to model Rucker’s Mindscape?  This is much closer to the mark, but still not quite right.  Popper thinks of the occupants of World 3 as man-made, whereas the occupants of the Mindscape pre-exist our discovery of them.  World 3 is a like a building we erect, whereas the Mindscape is a terrain we explore. 

A better alternative to the Platonic realist model is an Aristotelian realist one.  On this view, there is no “third realm” over and above the material world on the one hand and the mind on the other.  Still, the universal patterns and truths we grasp when we entertain concepts and propositions are neither reducible to any collection of material things nor mere constructs of the human mind.  The universal triangularity, for example, cannot be identified with any particular triangle or collection of triangles, and it is something we discover rather than make out of whole cloth.  However, rather than existing in a Platonic realm, it exists in actual triangles themselves, mixed together, as it were, with all their individualizing features.  Qua universal, it exists when an intellect abstracts it out of individual triangles by ignoring their diverse individualizing features and focusing its attention on what is common to all of them.

On this interpretation, the occupants of the Mindscape, though they are not reducible to or identifiable with anything in the material world, might nevertheless be thought of as embedded in the material world until the intellect pulls them out, as it were. 

The body of mathematical truths (which is Rucker’s special concern) is, however, a tricky one to fit into the Aristotelian realist scheme.  The reason is that the material world is finite and mathematics is concerned with infinities.  This brings us to a third brand of realism which claims to capture the strengths of both the Platonic and Aristotelian brands – namely, Scholastic realism.  For the Scholastic realist, Aristotle is correct to say that there is no third realm additional to the realms of matter and mind.  But Plato is correct to say that the ultimate ground of the truths and concepts we grasp must lie both beyond the material world and beyond finite minds.  It is to be located in the infinite, divine mind.  This is an idea that Scholastic thinkers like Aquinas inherited from Augustine, who in turn adapted it from the Neo-Platonic tradition.  (See chapter 3 of the forthcoming Five Proofs of the Existence of God for a detailed exposition and defense of Scholastic realism.)

How does Rucker’s Mindscape relate to Scholastic realism, then?  Here it seems there are at least two possible interpretations.  One might identify the Mindscape with the divine intellect.  On this interpretation, when the human mind explores the Mindscape, it is as if we are thinking God’s thoughts after him.  Or it is as if we are “streaming” content from the divine server, the way one might stream content from Netflix or Amazon on one’s computer. 

To the extent that this sort of idea is defensible at all, however, it would require thinking of the divine intellect more in Neo-Platonic terms than in strictly Scholastic terms.  For Neo-Platonism, the divine intellect is really a second divine hypostasis rather than God full stop.  It has to be, because God – the One – is absolutely simple or non-composite, and thus does not have within him anything like the distinctness that thoughts in a human intellect have.  Hence if the Mindscape is a divine intellect, it is something like the second divine hypostasis of Neo-Platonism, and not anything in God strictly speaking.  (Cf. the Averroist conception of the human intellect.)

Now, the Scholastic realist agrees that God is absolutely simple or non-composite.  But he rejects the notion of any second divine hypostasis a la Neo-Platonism.  Hence when universals, propositions, and the like are identified by the Scholastic realist with ideas in the divine mind, he means both that they are in God himself rather than in any secondary divine reality, but also that they are not in God in the manner in which the Neo-Platonist takes them to exist in a secondary divine hypostasis (viz. as distinct entities).

Here the Thomist doctrine of the analogical nature of theological language is indispensable.  When we say that universals and the like exist as ideas in the divine mind, we are not using “ideas” in either a univocal or equivocal way, but in an analogical way.  There is something in God that is analogous to our idea of triangularity, something in him analogous to our idea of the Pythagorean theorem, etc.  But it is not strictly the same sort of thing as our ideas.  (I’ve discussed the nature of the divine intellect in a couple of earlier posts, here and here, but see Five Proofs – which should be out in a matter of weeks – for a more thorough discussion.) 

The Mindscape, then, cannot be identified with the divine intellect as the Scholastic understands it, because the latter is simple or non-composite and the former is not.  But again, how then does the idea of the Mindscape relate to Scholastic realism?

The answer, I think, is that the Mindscape should after all be interpreted in more or less the Aristotelian realist terms discussed above, but with a qualification that brings in the distinction between metaphysics and epistemology.  Metaphysically speaking, universals, propositions, and the like are ultimately grounded in the infinite divine intellect rather than the finite material world.  But our knowledge of them is not acquired by directly accessing the divine intellect.  Rather, that knowledge is acquired by abstraction from the particular things of our experience, whose natures are reflections of the ideas pre-existing in the divine intellect.  The created world mediates our knowledge of God’s mind.

The Mindscape we know arises by way of this process of abstraction, and is a simulacrum of the divine Mindscape rather than identical with it.  Like any other simulacrum, it contains features which reflect, not the thing the simulacrum represents, but rather the nature of the simulacrum itself.  A black and white line drawing of a person may be extremely realistic and thereby convey much accurate information about its subject.  But the person himself is nevertheless not black-and-white, or two-dimensional, or surrounded by black lines the way that things in the image are.  Those features reflect the limits of the medium rather than the nature of the subject.  In the same way, the concepts and propositions to which we have access in the Mindscape reflect something which really is there in the divine intellect.  But the distinctness between the denizens of the Mindscape reflects the limitations of our own minds rather than the absolutely simple divine intellect itself.

Bonus link: Rucker’s essay “Memories of Kurt Gödel.”

62 comments:

  1. This is the argument I am most looking forward to from Five Proofs. By the way, in the UK, Amazon releases your book on the 18th so just one more week!

    I glad you brought up maths specifically. Would you say the Augustinian proof or scholastic realism is the stronger, deductive form of what more modern apologetics deem the applicability of mathematics argument? It tends to be an inference to the best explanation however. The Augustinian approach would still seem to explain the language of maths in physics.

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    1. Wait, are you saying that Augustine's argument from eternal truths is only probabilistic, rather then a deduction or induction?

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    2. Hmm, I'm not getting that impression from Callum's post. It looks more like he's saying that Augustine's argument was the deductive form, and that modern versions are more probabilistic.

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    3. Wait when does the book release for US?

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  2. One very interesting thing to note is that Augustine believed that God was greater than infinity.

    And it makes sense.

    After all, if mathematical concepts are located in the divine mind, and infinity is a mathematical concept which it is logically possible to instantiate (infinite amount of chairs, infinitely big universe, infinitely hot star), then God must by definition be greater than anything infinite.


    Another very interesting thing about Rudy Rucker's book is that he talks about the various types of infinity that exist.He mentions Cantor's discovery of larger and smaller infinities, and how, say, the amount of natural numbers is infinite, but the amount of real numbers is actually bigger.

    One way to understand this is the following:

    Traditional infinity can be drawn with the symbol of aleph-0.So the amount of all natural numbers is infinite, and that infinity is aleph-0.However, even though the natural numbers are infinite in amount, the amount of real numbers and all possible geometrical points is even bigger.

    They are both aleph-1.

    However, the amount of all possible aribtrary and non-arbitrary functions is even bigger than the amount of all possible geometrical points, and is called aleph-2.And this can go on forever, which means there are infinitely many infinities, all greater than the last. Now, if this series of infinites exists in the divine mind, then this means that the divine intellect must be bigger than infinite, because it contains all possible infinites.

    So I think the Scholastic, who holds that the Divine Mind is infinite intellect, should perhaps try to explain how an infinite intellect could contain bigger infinities within it.

    It seems that God's Divine Intellect might be bigger than infinity, and thus His intellect is even greater than an infinite intellect.


    Thoughts?

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    1. That the cardinality of the set of reals is aleph-1 is Cantor's Continuum Hypothesis. He spent years trying to prove it but failed. In 1963 it was shown to be independent of the standard axioms of set theory. In the decades since then, no one has given a noncontroversial extension of the axioms which is strong enough to decide the truth or falsity of the Continuum Hypothesis. All anyone can actually prove about the size of the reals is that it is at least aleph-1. It is consistent that it is quite a bit larger than that.

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    2. And this can go on forever, which means there are infinitely many infinities, all greater than the last.

      I would make a guess, Joe, that you actually have something specific that would back up this hand-waving. For it surely is just hand-waving.

      Not that it matters much.

      Just to note in passing: The "infinity" you are talking about (of aleph-0) can be understood by the human mind, so there is something qualified about its infinitude.

      And because "infinity" is a negative concept "it is not limited", there is formally no upper limit to the quality of infinitude: while God may be greater than all OTHER infinities, this does not put him outside of "infinity" as a descriptor, because the term is a negation of limit.

      Nevertheless, there is almost certainly a kind of equivocation in trying to compare God's mind with the infinities of math. (Or even our own - which was part of my point.) The way that a mind surpasses a number or a cardinality is not wholly expressed by mathematical "greater than".

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    3. Tony: "I would make a guess, Joe, that you actually have something specific that would back up this hand-waving. For it surely is just hand-waving. "


      Well, I did write this in a bit of a rush. But my main point was to ask whether or not God's Intellect is bigger than mere infinity because it contains cardinalities far bigger than the infinity of natural numbers.


      Tony: "Just to note in passing: The "infinity" you are talking about (of aleph-0) can be understood by the human mind, so there is something qualified about its infinitude. "


      Well, it is true that the human mind can grasp the difference between the infinities and easily understand how and why there could be an infinite number of infinities.


      Tony: "And because "infinity" is a negative concept "it is not limited", "


      Actually, we could also understand finiteness to be a limitation and thus infinity as the removal of that which makes a thing limited.

      Tony: "there is formally no upper limit to the quality of infinitude: while God may be greater than all OTHER infinities, this does not put him outside of "infinity" as a descriptor, because the term is a negation of limit. "


      So what you are saying is basically that the concept of infinity as a whole actually contains all possible infinities, including large cardinal properties, in it's definition because it is without limit, and thus we could have a concept of infinity that includes all mathematical infinities and large cardinal properties as well?

      Tony: "Nevertheless, there is almost certainly a kind of equivocation in trying to compare God's mind with the infinities of math. (Or even our own - which was part of my point.) "


      Well, it's certainly true that the human intellect is in a sense greater than the number 3 because it can both visualise and intellectually grasp it. But in a sense the number 3 is also bigger because a human being only has 1 intellect for himself.

      Tony: "The way that a mind surpasses a number or a cardinality is not wholly expressed by mathematical "greater than"."


      Ah, so the way the Divine Intellect is greater than all of the mathematical concepts related to infinity is basically because the Intellect ''contains'' and realises them. The mathematical infinities exist in God's Divine Intellect, but His Intellect is greater than the infinities in kind, and not just in degree.

      However, what is interesting is that all mathematical concepts are in the end present in God's Intellect, but that infinity is also a mathematical concept.

      So the very concept of infinity, not just mathematical infinity by the way, exists in the Divine Intellect. But this implies that the Divine Intellect is greater than the very concept of infinity because it contains and ontologically grounds the very concept, just like the Divine Intellect is greater than the concept of triangularity because it contains and ontologically grounds the very concept of triangularity.

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    4. @Tony,

      I am also reminded of a comment made by commenter rank sophist in 2012, who some of you might be familiar with, that he left on Ed's "Who Wants To Be An Atheist?", which states the following:

      <<<"Maximally" means "best", which implies degree. Classical theism denies that God can be described by degrees. If you increased a created goodness by an infinite amount, you still would not reach God's goodness, because the difference is in kind and not in degree.>>>

      So it seems that the infinity of God is altogether different from the infinity of any concept and level of infinity or concrete instantiation of such types of infinity.

      In other words, God's infinity is greater than any of the infinities we know from math, whether it be infinitely infinite sets, or large cardinal properties, both because God is the Intellect which grounds and contains all of them, but also because these mathematical concepts exist in degrees when compared to God.

      (Of course, difference between say, inaccessible cardinals and indescribable ones is a difference of kind, and not just degree. There are infinitely many inaccessible cardinals, but an infinity of them will not get you to an indescribable cardinal, because the difference between these 2 large cardinal properties is one of kind, not just degree. That is why I added the qualifier "when compared to God", because all of these LCP's are in the end like degrees unto God)

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    5. So it seems that the infinity of God is altogether different from the infinity of any concept and level of infinity or concrete instantiation of such types of infinity.

      In other words, God's infinity is greater than any of the infinities we know from math, whether it be infinitely infinite sets, or large cardinal properties, both because God is the Intellect which grounds and contains all of them, but also because these mathematical concepts exist in degrees when compared to God.


      Works for me.

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  3. Good article. I read that book as an undergraduate. It was one of two books (the other being Douglas Hofstader's "Gödel, Escher, Bach") which convinced me to switch majors to mathematics. Almost all mathematicians are Platonists to a greater or lesser extent, even if they have never systematically worked it out. Tangentially, you might enjoy the book "Naming Infinity" by Graham and Kantor, which explores a surprising historical connection between a somewhat heretical Russian Orthodox spiritual movement and certain work done in descriptive set theory -- that branch of mathematics which studies what it means to use logic to describe infinite sets. At least into the 20th century, some major mathematicians were drawing inspiration from their religious beliefs.

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  4. The Mindscape, then, is essentially the collection of all the propositions and concepts that might possibly be grasped, entertained, affirmed, denied, etc.

    It’s not clear whether only true propositions belong to the Mindscape. If all propositions belong to it the we arrive to a problem similar to Babel’s library: The whole Mindscape would be chaotic with hardly any true proposition in it. On the other hand if the Mindscape only contains true propositions then it is extremely dependent on the real world, indeed like a shadowy projection of it. For example in the case of our world it will contain the position of every molecule of matter throughout its history.

    In any case I object to the claim that the Mindscape exists in a way independent from actual reality - that the Mindscape is a “whole other world”. For propositions entail meaning, and meaning is not independent from the world in which the proposition is claimed. So there are many types of Mindscape as there are many types of possible worlds. Here is a case in point:

    Mathematical propositions would remain true even if no material world had ever existed.

    The meaning of our arithmetical propositions would not obtain if our world did not contain countable things. Consider for example a world in which nothing whatsoever exists - no material things, no spirits, no space, no time, nothing whatsoever. In that world then nothing countable exists, therefore an arithmetical proposition such as 2+2=4 has no meaning in it, therefore arithmetical propositions are not true in this world.

    My argument is that when we say that the proposition “2+2=4” is necessarily true we really mean that this proposition is true in all possible worlds in which 1) it is meaningful, 2) it has the same meaning. It’s a trivial point really, but I think one we should keep in mind.

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    1. Dianelos,
      You ask us to consider a world in which nothing whatsoever exists. As several previous posts have shown, such a world is impossible.

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    2. Tim,

      Well I doubt that, at least if by “impossible” one means “logically impossible”. After all philosophers have always discussed about the possibility of there being nothing. And properly speaking nothing means nothing at all: no things, no ideas, no space, no time, no laws, no potential, nothing whatsoever. The argument from contingency and the question “why is there something instead of nothing?” assume that the empty world is possible, otherwise neither the argument nor the question make any sense.

      Moreover I hold that the empty world is provably possible. A world is logically possible if and only if the set of all true propositions that hold for it is logically consistent (i.e. devoid of logical contradictions). The set of true propositions that hold in the empty world is empty, and thus it can’t possibly include logical contradictions.

      One can object and suggest that the proposition, say, “No material things exist” is true for the empty world. But only meaningful propositions may be true, and the concept of “existence” is meaningless in a world where not even the potential of existence exists. Such propositions only make sense for us who from the outside discuss the possibility of such a world.

      To me it seems overwhelmingly obvious that the empty world is logically possible. Given theism it is of course metaphysically impossible, as is any non-theistic world. But here we are discussing mere logical possibility. In any case if you would point me to a post you think conclusively shows that the empty world is not even logically possible I’d by thankful.

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    3. Dianelos:
      Philosophers have been discussing the possibility of empty worlds because they are conceivable. But being conceivable does not mean it's logically possible; the two overlap, but not completely. Indeed, if we could have a sufficient grasp of God's nature, we would realize that it's logically impossible for Him not to exist. But even if God were only "metaphysically necessary," rather than "logically necessary," that would suffice for Tim's objection.

      On the other hand, I would think that a statement like "2+2=4" would be true even in an empty world, since even though nothing could ever instantiate "twoness" or "fourness" in such a world, we're discussing in some sense the nature of these numbers, and specifically how they relate to each other.

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    4. Philosophers have been discussing the possibility of empty worlds because they are conceivable.

      I think the right way to put it is that they have been discussing why there is anything at all. And this question only makes sense if they already thought that the empty world is possible.

      But being conceivable does not mean it's logically possible; the two overlap, but not completely.

      Well, who knows? “Conceivability” refers to a property of our own mind, and in the context of logic I think it would be best leave such subjective matters out of the discussion. I am not saying that the empty world is logically possible because I can conceive it (I am not at all sure I can), but because it is defined by the empty set of true propositions and thus is demonstrably logically consistent.

      Also, as a general principle, I hold that the one who claims impossibility has the burden of proof. Why? Because the one who claims impossibility is the one who claims we should remove an idea from the set we are considering – and such a move demands a good reason.

      Do you know of any reason why the empty world is not logically possible?

      Indeed, if we could have a sufficient grasp of God's nature, we would realize that it's logically impossible for Him not to exist.

      Given that God is the metaphysical ultimate it is wrong to think that God is subject to anything whatsoever. So it’s not like there is something called logic that makes it necessary for God to exist. Similarly, to mention another example, there isn’t something called the good that makes it necessary for God to be good. To push the point: If God so wanted God would produce a shape that is both round and square; the idea is inconceivable to us but it’s not like God is limited by our powers of conceivability. Anselm’s statement that God is the greatest conceivable being should not be understood as a definition of God, but as a definition of the right way for any intelligence to think about God, namely as no less than the greatest being it can conceive. If according to our sense of greatness God would never will the creation of a round square then we should believe that God will never create that shape; but not that logic makes it impossible for God to create it. God is absolutely sovereign.

      As for logic please observe that its domain of applicability is not universal. By its nature logic only applies to mechanical systems. So, for example, logic is not applicable to our experience of the color red. It makes no sense to ask “Is there a logical contradiction in our experience of the color red?” or “Is there is logical contradiction between our experience of the color red and algebra?”

      Finally we theists would be wary of the phrase “God exists” let alone of “God necessarily exists”. The proposition “X exists” is normally understood as “X is a member of the set of all existents”, and this does not hold for God. Rather God is what grounds all existence, or who defines the set of existents. You may have the right understanding of the phrase “God exists” but many people (including I would say many atheist philosophers) misunderstand it, and this leads to much confusion. Theism is *not* the claim that among all that exists also God does, but rather a claim about the nature of existence, namely that it is grounded in God. I have this short piece on this.

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    5. I know I am going to regret this, but...

      You ask us to consider a world in which nothing whatsoever exists. As several previous posts have shown, such a world is impossible.

      Moreover I hold that the empty world is provably possible. A world is logically possible if and only if the set of all true propositions that hold for it is logically consistent (i.e. devoid of logical contradictions). The set of true propositions that hold in the empty world is empty, and thus it can’t possibly include logical contradictions.

      One can object and suggest that the proposition, say, “No material things exist” is true for the empty world.


      Guys, please stop. This is just awful. First, Grace and Rust, when Dianelos was talking about an "empty" world, he did not mean a "world" without God (at least, I am pretty sure that's what he meant). He meant a "world" empty of OTHER stuff, like material and space and laws. It is true that "a world" without God is just impossible.

      Dianelos, your use of "empty world" is so confused it's almost hopeless. Since God is truly free, he was free to create a world or not create a world. It is logically possible that God would not have created anything. IF he had not created anything, there would be no "world" and thus also no things, no space, no time, and no world laws.

      It would not be "an empty world". That there is terrible terminology. If there was no creation, there would not be a world, so it could not be empty. Calling it "an empty world" just confuses the mind, getting a person to try to mentally assert "a world" while also asserting "nothing there" that was created - a contraditiction.

      Nevertheless, there are things that would be TRUE regardless of whether God created a world or not: truth is dependent on God more than on a world, especially universal truth. It would have been true that "God could created a world" even if God had not created a world. It would have been true that God exists (or "exists") in three persons. In some sense numbers would "be", and laws of numbers would be valid, for IF God created a universe with many things, then the laws of numbers would be instantiated, which means they held truth even insofar as He could create such a world - i.e. their truth did not need to wait until separate things existed. God would have known their truth, because their truth would be just as true being about a possible world as about a real one.

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    6. Tony,

      I know I am going to regret this, but...

      Even though I think it’s a handicap not to take into account one’s feelings when doing philosophy (after all feelings are also data points, indeed incorrigible data points of reality), I find it that as a practical matter one should not take into account one’s feelings about one’s interlocutor. And much less express them. But I will here make an exception: I fear you will come to hate your guts for reading what follows. So I say fair warning has been given.

      Dianelos was talking about an "empty" world, he did not mean a "world" without God (at least, I am pretty sure that's what he meant).

      Actually that’s not what I meant. I used “world” to refer to the whole of reality, and not to refer to creation – the world God creates and in which we exist. Sorry for the ambiguity. Perhaps it would be best if I used “reality” instead of “world”.

      So, for example, the proposition “It’s logically necessary that theism is true” means the same as “In all logically possible realities theism is true”. (I use “theism is true” as synonymous to the misleading “God exists”). My argument is:

      1. The empty reality is logically possible. (For its set of true propositions is empty, and therefore free from any logical contradictions.)
      2. Theism is not true in the empty reality. (Obviously – actually theism as any other claim is not even meaningful in the empty reality.)
      3. Therefore, theism is not logically necessary.

      I would say that in the context of discussing metaphysics the claim of mere logical possibility is a very weak claim and is therefore a safe starting position. Conversely, the claim of logical impossibility or of logical necessity is a very strong claim and the one who makes it has a heavy burden of proof.

      There is also the related concept of metaphysical possibility, namely not what could be true without logical contradiction, but what could *in fact* be true. Our own free will offers a good demonstration of the difference: So, for example, yesterday I had dinner with friends. To have suddenly emptied my plate of food over my head would be a logically possible event. After all I was entirely free to choose to do just that; had I done that no true proposition would be logically contradicted. But knowing myself I know that I would never *in fact* choose to do such an absurd thing. Even though I am free my mind is beyond that particular level of stupidity. So such an event even though logically possible was metaphysically impossible.

      Now consider that there is no logical impossibility in God deleting himself from reality: if God so chose, God being all-powerful and subject to no limitation whatsoever, could do so and thereby convert actual reality from theistic to empty (since when God goes, everything goes – as it were God would remove reality from being). But God, the greatest conceivable being, would never actually choose to do such a thing. Thus it is metaphysically impossible for theism to be false (aka for God not to exist). Conclusion: If theism is true then it is metaphysically necessary that theism is true.

      Given that doing philosophy is a practical enterprise what really matters is what is metaphysically possible, not what is merely logically possible. Still in the context of discussing whether theism is true or not, one realizes that it is logically possible for theism not to be true. But this does not stop a philosopher (perhaps a Thomist) to argue thus:

      [continues below]

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    7. [continues from above]

      1. All metaphysically possible realities are such that the human condition obtains. (By “human condition” I mean the whole of the human experience, including of course our experience of nature. By this premise we radically restrict the set of realities under consideration from all logically possible realities to the tiny subset where the human condition obtains. Furthermore this premise is clearly true: the human condition is a given fact, so it couldn’t in fact be the case that reality is such that the human condition fails to obtain.)

      2. In all logically possible realities in which the human condition obtains theism is true. (Why? Because of a separate argument according to which the structure of the human condition is such that it wouldn’t obtain unless theism is true.)

      3. Therefore in all metaphysically possible realities theism is true. (Which is the same like saying that it couldn’t in fact be the case that theism is not true.)

      Now I understand Thomists are convinced that premise (2) is true. I think that premise (2) is false because I have a counterexample, namely metaphysical naturalism properly constructed. I can describe a purely mechanical reality that would produce the whole of the human condition, and which, being purely mechanical, is not theistic. Of course it’s not like because the above argument fails its conclusion (3) must be false. In fact I think it is true. I have already mentioned the argument which proves it – it would look something like this:

      1. Actual reality is in fact theistic.
      2. It is not in fact possible for a theistic reality to be non-theistic.
      3. Therefore, it is not in fact possible for the actual reality to be non-theistic. (Which is the same as saying that in all metaphysically possible realities theism is true.)

      As we saw premise (2) is not trivial; given theism it is possible for God to delete all reality from being. One might point out that any proposition of the form “It is not in fact possible for A to be not-A” is a tautology (the law of non-contradiction); but it is not in the context of theism, for God is not limited by logic. Thus, after a point we must abandon logic (and thus propositional logic) when thinking about God. This is a general religious insight. For example in the religious tradition of the Far East one reads stuff like: “It is not ‘this’, it is not ‘not this’, it is not ‘neither this nor not this’”. At some point all differentiation stops and the mind encounters God pure and simple.

      This, incidentally, is not some limitation of logic; logic as all tools is meant for a particular domain of use. Logic can help our theistic thought a great deal, but it can’t apply to the simplest experience of God. It can’t even touch on our simple experience of a color. Brainy philosophers should take a moment to consider how logic stops at the reality of any knowledge by acquaintance.

      So can one do philosophy after abandoning logic? Depends on what one means by philosophy. One can certainly do art, and friendship, and theology – without using logic. Should one define philosophy as the right contemplation of life then I’d say that philosophy without logic is quite fine. If one restricts philosophy to analytic philosophy then by definition the answer is no, since analytic philosophy stops at the non analyzable aspects of reality. How poor would reality be – how much less than the greatest conceivable being our creator would be – if all would be analyzable! Actually, interestingly enough, analysis is self-restricting even in the domain of mechanical systems as per Goedel’s incompleteness theorem.

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    8. Well, since the conversation is still ongoing...
      Dianelos, I wrote this for the post you made above Tony, but it seems to apply to some of your latest comments.
      "I think the right way to put it is that they have been discussing why there is anything at all. And this question only makes sense if they already thought that the empty world is possible."
      The 'right way to put it' seems like a distinction without a difference. But if there is a difference, it only helps my case by highlighting that possibility and conceivability aren't the same, which is enough for my answer to succeed.
      So saying, the question *can* make sense without assuming that empty worlds are in any sense possible. My distinction between possibility and conceivability showed how. Saying "X is conceivable, and /if/ X is possible, then given A, B, and C, it should be the case," does not commit us to the antecedent "X is possible." Whether X is possible is occasionally one of the issues the question "why isn't X the case?" seeks to address.
      And all of that holds even if conceivability were subjective in the required sense. However, you're wrong about that, being that conceivability is a property of the /intellect/, which decidedly is not subjective--the intellect grasps the real natures of things, which are objective. The only subjective limit on conceivability is what we prevent ourselves from thinking. The objective limits are what we can grasp with our intellects, and whether there is content to grasp at all. This is important to observe, considering that it seems we *can* have inconsistent concepts (this is one reason why people are developing "paraconsistent logics"), at least so long as the inconsistency doesn't eliminate the defining content. For example, a "square circle" is inconceivable because each term 'eliminates' the content which defines the other term--"square circle" therefore has no content, and so is not a concept. Even if I'm wrong about "square circles" being inconceivable, they are still logically impossible, because we're asking for something which both is and is not a circle, and both is and is not a square. Thus, to refute this example (or certain others) only reinforces my point that conceivability and logical possibility do not completely overlap. This is a necessary point to make, because it shows that empty worlds might be conceivable despite being inconsistent.
      Now, you asked me for a reason for thinking that empty worlds are logically impossible. *I already gave you one.* Let me spell it out: A possible world is just a consistent "maximal" set of propositions. An empty world is one where every proposition of the type "x exists" is false. Consequently, such a world is one where "God exists" is false. But God, as I argued previously, is /logically necessary/. Hence, the statement "God does not exist" is a logical contradiction. So a world where *all* propositions of the type "x exists" are false is an inconsistent world; it contains one proposition that is a contradiction, and no contradiction is consistent. Because not even God can create a logical impossibility, as I will show in my next comment, God cannot nullify Himself, and so not even God can bring about an empty world.

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    9. Dianelos, you said: "As for logic please observe that its domain of applicability is not universal. By its nature logic only applies to mechanical systems. So, for example, logic is not applicable to our experience of the color red."
      The fact is, logic applies to more than just mechanical systems--the laws of logic are the laws of *being.* Everything that exists is subject to them for that reason. Your own examples for where it supposedly fails to apply are mere category errors on your part. I can never both experience the color red and *not* experience it at the same time, in the same sense, and so forth. And our experience of red is entirely unrelated to the truth of algebra, so that they can never be jointly inconsistent. Your arguments for a "domain-specific" theory of logic entirely misunderstands what logic is.

      You also said: "Given that God is the metaphysical ultimate it is wrong to think that God is subject to anything whatsoever. So it's not like there is something called logic that makes it necessary for God to exist. . . . If God so wanted God would produce a shape that is both round and square; . . . it's not like God is limited by our powers of conceivability. . . . God is absolutely sovereign."
      Because the laws of logic are laws of being, God cannot violate them, for whatever He brings into being, by virtue of its existing, will be subject to these laws. We must understand that this in no way constrains God, for God is Being Itself. If He were to violate the laws of logic, He would be violating His own nature! But a sovereign wouldn't go against His own nature, because violating one's nature makes one less perfect, and nothing compells a sovereign to make himself less perfect.
      As for conceivability, although our powers of conceivability do not limit God, that's not the problem. The problem is that inconsistencies are impossible because they violate the laws of being. So even if a higher being can conceive of a square-circle, they can't exist.

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    10. Moreover I hold that the empty world is provably possible. A world is logically possible if and only if the set of all true propositions that hold for it is logically consistent (i.e. devoid of logical contradictions). The set of true propositions that hold in the empty world is empty, and thus it can’t possibly include logical contradictions.

      Dianelos, your condition ("the set of all true propositions that hold for it is logically consistent") is a very weird concept, and it is my suspicion that it harbors some very seriously problematic pre-suppositions that don't bear examining too closely. Just for starters, what would you mean by "true propositions" that that is not the same thing as "that hold for it"? Is that just redundant?

      For another, why would you insist on the negative defining form, "devoid of contradictions", instead of a positive form of some sort, like "has logic"? Does it REALLY make sense to call the "empty set" something that is "logical"? Isn't "logic" what you get when 2 or more truths lead to another truth? If you don't have A and B, you don't have the logic of getting C, so ... you don't have logic going on. Isn't what you have described merely "the 'worlds' that don't harbor logical contradiction", making an artificial category that has to contain your "empty world" by mere definition?

      Next, how can you prove that 'the empty world' has no propositions true of it? Is the proposition "this world has no propositions true of it" true of it? What about "this world has no numbers" and "this world has no bodies" etc?

      As that last point suggests, the concept of "a logically possible world" as having a "set of all propositions true of it" depends very much on pre-suppositions about what counts as "a proposition about it", and gets into serious issues of set theory. Which Cantor and Frege and others tried to work out, leaving us with the fact that you have choose (i.e. postulate) a framework of set rules for meaning and about-ness that you wish to apply, it isn't that there is ONE framework of rules that just is the right framework. Which, you know, tends to be a bit question-begging in reference to an empty world that has no true propositions.

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    11. @ Grace and Rust,

      I agree that conceivability does not imply possibility. I only mentioned the fact that some of the oldest and presumably best theistic arguments (e.g. the argument from contingency) entail the possibility of the empty reality, which would make no sense if the empty reality were not even logically possible. My argument was: If the empty reality is not even logically possible then this can’t be an obvious truth since many philosophers thought it is logically possible. As proven by them asking why it isn’t in fact the case.

      Why do I think that conceivability does not imply possibility? Because I am aware that I can conceive of a complicated state of affairs without realizing that a logical contradiction is hidden in it. Actually that’s often the case. Consider any unproven mathematical hypothesis; in all cases both it being true and it being false is conceivable. Take for example the four colors hypothesis which was proven only recently. We could plainly conceive both it being true and it being false, that’s why we weren’t at all sure. So as a matter of fact we could conceive something that was in fact logically impossible. So, I say, it is provable true that conceivability does not imply possibility; we have a counterexample from mathematics.

      Now somebody who holds that conceivability does imply possibility may argue that I am not talking about what is conceivable but about what is imaginable. But I fail to see what conceivability means beyond a particularly convincing sense of imagination. If imagination in general fails, then our impression that a particular case of imagination is especially clear may well fail too.

      Finally please observe that in my argument about the empty reality being logically possible I didn’t use conceivability. Rather I used a necessary and sufficient condition about which worlds are logically possible, namely those in which the set of all true propositions is logically consistent.

      The objective limits are what we can grasp with our intellects, and whether there is content to grasp at all.

      Well, there are certainly limits to our intellect. For example for a person born blind it is impossible to grasp how it is like to experience the color red no matter how otherwise intellectually strong she may be. Also intellectual work is a communal enterprise, so the solution to very difficult problems may be grasped only little by little by intellectual work that spans millennia; the case of theodicy comes to mind. Considered as a historical phenomenon the human intellect appears to have a life of its own. And of course on theism God directly participates in that process, which leads us to the thought that the limits of our intellect may be much further than one might think. On theism the human intellect is not a given creaturely power, since part of its power comes from God’s guidance – part of God’s special providence. I believe that as all other special actions of God in creation (except for miracles) God’s guidance of the human intellect (normally called “revelation”) is a gentle power which does not violate the epistemic closure of the physical reality. Why that should be so is a matter for theodicy.

      it seems we *can* have inconsistent concepts (this is one reason why people are developing "paraconsistent logics"

      Interesting, it’s the first time I hear about this.

      a "square circle" is inconceivable

      A square circle is certainly inconceivable. It is also provably logically impossible. On theism it is also metaphysically impossible: given God’s rationality a square circle can’t in fact be. But can’t in fact be, only because God will not want to create it, and not because it is logically impossible.

      [continues below]

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    12. [continues from above]

      An empty world is one where every proposition of the type "x exists" is false.

      No. Only meaningful sentences can be propositions and thus be true or false. For example in actual reality the sentence “Such seven is joint to water” is meaningless (it does not say anything about actual reality) and thus is neither true nor false. In the empty reality “x exists” is meaningless because in that reality existence is a meaningless concept. The concept of “existence” is meaningful only in such realities where existence is at least (metaphysically) possible.

      Further consider that if the empty reality allowed for any false propositions it would also allow for true propositions, namely their negation. By definition there are no true propositions that hold for the empty reality. Perhaps such a reality is inconceivable for us, but as we agree what we can or can’t conceive is irrelevant.

      Actually let’s put this last point on the table and analyze how the human intellect’s conceivability HC relates to logical possibility LP.

      There are cases where HC and LP are both true, for example in the case of the proposition 2+2=4

      There are cases there HC and LP are both false, for example in the case of the proposition 2+2=5

      As we agreed, there are cases where HC is true and LP is false. So we can conceive of four colors not sufficing for distinguishing all countries on a complicated plane map, but, as was recently proven, that’s logically impossible to obtain.

      Are there cases where HC is false and LP is true? Are there cases where our intellect fails us in the sense of finding something inconceivable which is nonetheless logically possible? An example would be non-euclidean geometries. Or an actual infinity.

      (If the reader can suggest other examples, please do so.)

      What about the relationship between human conceivability and *metaphysical* possibility? After all the philosopher is interested in what in fact may be true in actual reality.

      Let’s first consider this question assuming theism. Since God is rational God would never have logical impossibilities be actual. Thus on theism the set of metaphysically possible realities is a subset of the logically possible realities. So, if human conceivability is irrelevant to logical possibility, it is also irrelevant to metaphysical possibility, namely to what could in fact be the case. It is easy to think examples of how conceivability relates to metaphysical (factual) possibility in the required four combinations:

      Conceivable and metaphysically possible: “If you put two beans and two beans together and count them you’ll find they are four”. (Observe that experience is part of reality – in general, phenomenal reality is part of reality indeed an epistemically certain part.)

      Inconceivable and (on theism) metaphysically impossible: “The coin is both inside and not inside the box”.

      Conceivable and metaphysically impossible: “The Earth is flat, so if you walk towards the same direction you will get farther and farther from your starting point.” On theism another example would be “Naturalism is true”.

      Inconceivable and metaphysically possible: “Two observers looking at the same sequence of events will agree which came first”.

      [continues below]

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    13. [continues from above]

      How would be the relation between conceivability and metaphysical possibility be if one doesn’t assume theism (where conveniently for us God imposes logical order on being)? Well, in this case there is nothing to make it not be the case that what is logically impossible may not in fact be true and thus metaphysically possible. And, interestingly enough, that’s exactly what modern science forces a naturalist to think, here’s an example: Quantum mechanics describes the state of a coin as a wave which is both inside and outside the box. The so-called Copenhagen interpretation can be understood as a methodology for using the equations of QM to make predictions about experiential results, but also, if one is a physical realist, as a description of actual reality. The physical realist must then accept that the Copenhagen interpretation is metaphysically possible. Not withstanding the fact that according to that interpretation until an observation obtains the coin is at the same inside and outside the box, which is a logical impossibility. Even though phenomenal reality does not entail any logical impossibility (when one looks the coin will be seen either inside or outside the box), on naturalism a metaphysically possible reality may contain logical impossibilities. It’s kind of interesting to observe that it is logically possible that a logically impossible reality when mechanically projected into phenomenal reality to become logically consistent. Remarkably, some atheists argue just that, namely that according to modern science reality is logically impossible, and then use that fact as a universal defeater of theistic arguments (which are all based on the assumption that reality is logically consistent). Listen for example to physicist Lawrence Krauss in his debate with William Lane Craig.

      So how is the theist who is a physical realist to think about the Copenhagen interpretation? The theist on separate grounds believes that reality is rational and thus does not include logical impossibilities. If the Copenhagen interpretation is understood as a description of reality and not just as a functional aid for applying QM’s equations, then this theist is forced to hold that the Copenhagen interpretation is not metaphysically possible and therefore false. I happen to think the theist should reject physical realism in the first place. From where I stand it is as if God designed physical law (i.e. the mathematical order present in physical phenomena) in such a way as to strongly suggest to us that physical realism is false. But that’s another story.

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    14. Are there cases where HC is false and LP is true? Are there cases where our intellect fails us in the sense of finding something inconceivable which is nonetheless logically possible? An example would be non-euclidean geometries.

      Yup, I was right. I regret saying anything. Sheesh. Even though non-Euclidean geometries WERE ACTUALLY conceived by Riemann and Lobachevsky and others, they are "inconceivable". Wow, the logical possibilities of that are just amazing.

      Dianelos, what makes you even remotely imagine that your "concepts" (I am using the term in the loosest possible sense) of HC and LP are "well-defined" in the set-theory sense? I can pretty well guarantee you, they aren't.

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    15. @Dianelos, after sifting through all that verbiage, you don't look like you're helping out your original case. Sorry this isn't directly under your comment, but Blogger seems to be acting up right now.

      "I only mentioned the fact that some of the oldest and presumably best theistic arguments . . . entail the possibility of the empty reality, which would make no sense if the empty reality is not even logically possible."
      The distinction between conceivability and possibility suffices to show that there is /nothing/ in the question of empty worlds that commits us to saying they must be possible. Saying "X is conceivable" justifies believing "X is possible," because of the apparently significant overlap between the two, but the belief can be false and is open to revision. Your own examples for why conceivability and possibility don't perfectly overlap proves exactly that point. I already told you this, and nothing here or farther down actually handles it.

      "My argument was: If the empty reality is not even logically possible then this can't be an obvious truth since many philosophers thought it is logically possible. As proven by them asking why it isn't in fact the case."
      First, nothing in my arguments suggests that I think my claim, that empty worlds are logically impossible, is obvious. In fact, you're giving an argument for something we already agree on, namely, that conceivability does not entail possibility, and then do it again in the next paragraph! Part of what makes this so hard to see appears to be your conflation between conceivability and imagination, but that doesn't matter right now.
      Second, that hasn't been your argument, or at least it isn't in any way clear in your previous comments. Your first post in this thread was on how mathematical truths assume the existence of concreta, and following up, you've been trying to defend that empty worlds are possible.

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    16. "[P]lease observe that in my argument about the empty reality being logically possible I didn't use conceivability. Rather I used a necessary and sufficient condition about which worlds are logically possible, namely those in which the set of all true propositions is logically consistent."
      First, I *never* accused you of appealing to conceivability. Reread my arguments, you'll never find anything remotely like it.
      Second, I already showed you why your conditions are unworkable. I'll address your rebuttals in due time.

      "Well, there are certainly limits to our intellect. . . ." etc.
      I'm sorry, but where does any of what you said fit into any of the points raised in the discussion so far? You may want to look back at what I said about the limits our "powers of conceivability" face. The original point was to handle your assertion that we shouldn't let this "subjective" faculty into our discussions, and I only put it there to cover my bases after I said my prior arguments would work even if conceivability were subjective.

      "[G]iven God's rationality a square circle can't in fact be. But [it] can't . . . be, only because God will not want to create it, and not because it is logically impossible."
      If logical impossibility doesn't matter, you shouldn't object when I suggest that empty worlds are logically impossible. After all, that could be true, while still granting that they can obtain!
      But logical impossibility *does* matter, and I already gave reasons for saying it does, which you don't even bother addressing.

      Now we move to your second post.
      "No. Only meaningful sentences can be propositions and thus be true or false. . . . In the empty reality "x exists" is meaningless because in that reality existence is a meaningless concept. The concept of "existence" is meaningful only in such realities where existence is at least (metaphysically) possible."
      First, nothing about an empty world makes existence metaphysically impossible; nothing ever will exist in such a world because from nothing comes nothing, but that does not make it metaphysically impossible.
      Second, a concept can be meaningful even if it's metaphysically impossible. It's metaphysically impossible for things to come into being without a cause, but it makes sense to talk about that happening. Your own commentary about the difference between conceivability and possibility assumes that your assertion is false; it's perfectly meaningful to discuss whether the four color theorem is false, even though we now know it's metaphysically impossible (seeing as whatever is logically impossible is ipso facto metaphysically impossible). Your denial is clearly unfounded.

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    17. "Further consider that if the empty reality allowed for any false propositions, it would also allow for true propositions, namely their negation. By definition there are no true propositions that hold for the empty reality."
      You obviously don't know what you're talking about. A possible world is a maximal set of consistent propositions, Dianelos. Do you remember the law of Excluded Middle? No matter what world you have in mind, the proposition "Superman exists" is either true or false, with no middle ground. As such, every possible world *must* have some propositions that are true "at" that world. It should be clear without anyone pointing it out to you that a "world" without any true propositions isn't even a meaningful concept; a "world" that "does not allow for any true propositions" is one you can't say /anything/ about, not even that it's "empty," or else there are propositions that are true "at" that world (namely, that "for all x, x does not exist"). Your description of an empty world is incoherent (and so impossible on all accounts). I can only wonder how you intend to salvage it.

      The rest of your material doesn't appear to have any bearing on whether empty worlds are possible, or whether such a world contains any mathematical truths (among others). It just slides away from a commentary on the gaps and gluts between conceivability and logical possibility (giving a few false examples along the way) into a discourse on your beliefs about what our universe is actually like. I'll let someone else handle them.
      But since I'm still here, I'll add that I *didn't* agree that conceivability is irrelevant to the question of empty worlds. I said it was irrelevant to what God can do, and that's only because it doesn't control His power. At best, it only tracks His power, and loosely at that. A map tracks a territory without thereby limiting the territory.

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    18. @ Grace and Rust - August 15, 2017 at 12:26 PM

      logic applies to more than just mechanical systems--the laws of logic are the laws of *being.*

      I fairly agree but would like to develop this point:

      Existence is made by God and thus strictly speaking no laws need apply to it.; God’s will makes what is. What is certain is that nothing that is in actual reality entails logical impossibility in relation to the rest of reality. On theism reality is rational from the bottom up.

      Logic only applies to mechanical nature. “If A then B” is a paradigmatic case of the description of a mechanism. Many existents have an essence which has mechanical aspects and thus are partially analyzable by logic. Our experience of vision is such – as you point out if one experience red then one isn’t experiencing green. But the experience itself and alone of the color red has no mechanical aspects and thus logic does not apply to it.

      I’d say that the closer one comes to God the less one encounters mechanical aspects of being and therefore the less logic applies. At the core of God, that of God which is the metaphysical ultimate, all distinction disappears.

      Because the laws of logic are laws of being, God cannot violate them, for whatever He brings into being, by virtue of its existing, will be subject to these laws.

      I think it is important to realize that “God cannot do X” is incoherent. What makes sense is to say that given God’s character “God wills not X”.

      Also I think that God at the core is beyond any positive propositions. Strictly speaking we should only apply positive propositions to our relationship to God, which after all is what makes practical sense. And I don’t know if there is anything that makes sense beyond practical sense; I don’t know of any such examples.

      for God is Being Itself

      You see that’s an example of a positive proposition I feel does not ultimately, to the core, apply to God. All propositions of the form “A is B” express a *given* relation. But no given relation, no given differentiation, applies to the core. Nothing is a given to Whom is the giver of all.

      If He were to violate the laws of logic, He would be violating His own nature! But a sovereign wouldn't go against His own nature, because violating one's nature makes one less perfect, and nothing compells a sovereign to make himself less perfect.

      I agree completely. And please observe that to write “If God were to violate the laws of logic then [...]” entails that God could if God so willed violate the laws of logic.

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    19. Dianelos, you're still misunderstanding logic. Let me take your points out of order:
      "And please observe that to write "If God were to violate the laws of logic then [...]” entails that God could if God so willed violate the laws of logic."
      My conditional statement in no way commits me to saying God can violate the laws of logic. Either you haven't learned anything from the skirmish over conceivability vs. possibility, or you're putting too much emphasis on the word "were." God can't violate His own nature, so God can't violate the laws of logic, which are an aspect of His nature as Being Itself.

      "Logic only applies to mechanical nature. "If A then B" is a paradigmatic case of the description of a mechanism. Many [existing things] have an essence which has mechanical aspects and thus are partially analyzable by logic."
      First, no inference rule is solely a description of mechanism, nor do they assume mechanism. This should be plain, since the connection between propositions is not necessarily one of efficient or material causation (and not even these are strictly mechanical), but can be formal or final, or perhaps bear other relationships. That the connections display law-like regularity is not evidence that they are mechanical, you're simply stipulating.
      Second, your very assertion bars you from making any inferences about anything not part of "mechanical nature;" all trustworthy inferences are logical. Your approach dictates that you can't defend your other assertions about God, and so you have no right to expect me to agree with you.
      Therefore, although you may say "the closer one comes to God . . . the less logic applies," you have no way to defend it rationally. It's a proportional statement and, by your own standards, mechanical. At best, it's your experience, which I trust less and less.
      Nor can you argue that "God . . . is beyond any positive propositions." That's probably for the better, since we both know you don't really believe that. You hold that God is omnipotent, which is clearly a positive statement, and not one strictly about our relationship to God. And omnipotence, especially your over-extended concept of it, commits us to other positive truths about God. The same things can be said about your belief that God is rational. By the same token, you can't demand that anyone believe that "Nothing is a given to Whom is the giver of all," since God must be identical to Himself (hence, we have a given relation by your standards), whatever He happens to be like.
      Lastly, you can't defend the idea that "At the core of God, . . . all distinction disappears." You have to take it as a given (which contradicts your last assertion). Doubtless for all of these assertions you have some argument or other, but you can't use them, because the subjects are outside of your strictly defined domain of logic. You would have to apply "mechanical" rules to something which isn't mechanical, which you consider a no-no.

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    20. Now let's handle two other points:
      "[T]he experience itself and alone of the color red has no mechanical aspects and thus logic does not apply to it."
      You already agreed that non-contradiction applies to our experience, *considered by itself.* You must also agree that the law of identity applies to it as well, even if you happen to reject excluded middle. That's sufficient to show that logic applies to my experience by itself, even though it obviously has no mechanical aspects. The other laws of logic, keep in mind, are *never* about a single fact by itself, but they still apply by virtue of the fact that /if/ one fact relates to at least one other fact, then we can draw inferences.

      "I think it is important to realize that "God cannot do X" is incoherent."
      Nonsense. It's perfectly intelligible to think that God can't do certain things, especially if we're willing to to count contradictions and gibberish phrases under the domain of possibilities. You're the one who's more than willing to put them into that domain, I'm not. Your previous arguments for this decision don't even pan out, seeing as they rest on questionable assertions and in most cases don't even make good sense. (Out of curiosity, do you believe that God can know that He doesn't exist? Descartes purportedly did, on account of God's omnipotence and all...) It even makes sense to think God can't do certain things because they go against His nature. But I ought to explain why He can't violate His nature, which is simple enough: If He did, then He would not perfectly instantiate His nature. In that case, He isn't identical to His nature. Which means there can be other instances of the Divine Nature. That there aren't ends up being an accident of the world, rather than something necessarily true.

      @Tony, I agree that his concepts don't seem well defined. Although when he said that non-Euclidean geometry is inconceivable, he based that assertion on a conflation between imagination and conceivability. You'll notice above that he had said "But I fail to see what conceivability means beyond a particularly convincing sense of imagination." In other words, if one can conceive of it, one can imagine it "convincingly." I suppose that he finds himself unable to "convincingly imagine" alternative geometries, and so he figures:
      (1) Nobody else can, and
      (2) So they aren't conceivable.
      I can only imagine how this particular conflation shapes the other strange errors he's been advertising on Dr. Feser's blog.

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    21. @ Tony, August 15, 2017 at 8:27 PM

      your condition ("the set of all true propositions that hold for it is logically consistent") is a very weird concept, and it is my suspicion that it harbors some very seriously problematic pre-suppositions that don't bear examining too closely.

      The many-worlds semantic is a standard tool of modal logic, which is the logic about propositions of the form “it is possible that P” and “it is necessary that N”. Plantinga, surely one of the greatest epistemologists of the 20th century, often uses it. The idea is this: Consider the set of all worlds that are possible in a particular context. Then in that context the proposition “it is possible that P” means the same as “P is true in at least one world in the respective set”. And the proposition “it is necessary that N” means the same as “N is true in all the worlds in the respective set”.

      How do we check whether P or N are true in a member of the set of logically possible worlds? We simply check that world’s so-called “book”, which is the set of all true propositions in that world. The book exhaustively defines the world as far as propositional logic goes.

      How do we define the set of the possible worlds? Depends on the context. If we are discussing *logical* possibility, then that set includes all logically possible worlds. And how do we know whether a world is logically possible? We check whether its book of true propositions is free of logical contradictions. Or, in other words, the book of a logically possible world is characterized by the fact that all propositions in it are mutually compossible.

      Other contexts are possible, for example what is logically possible on naturalism. Or what is metaphysically possible. Or what is metaphysically possible on theism. Or what is metaphysically possible on determinism. Statements of modal logic have no meaning unless one defines the context.

      what would you mean by "true propositions" that that is not the same thing as "that hold for it"? Is that just redundant?

      It is redundant, but perhaps helps one avoid confusion. In modal logic there are worlds in which “George Washington was the first president of the USA” is a false proposition. There are worlds in which that sentence is meaningless and thus not even a proposition. Which, incidentally, introduces a problem of circularity: A possible world is defined by the set of all true propositions that hold in it, and the meaning of these propositions depends on how that world is. But this is a normal problem of cognition: Formalism alone does not suffice, it is is no substitute for understanding.

      [continues below]

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    22. [continues from above]

      Isn't what you have described merely "the 'worlds' that don't harbor logical contradiction", making an artificial category that has to contain your "empty world" by mere definition?

      I don’t think so. Something is logically possible only when the set of true propositions that hold on it are free from logical contradictions, or in other words are logically compossible. And one needs the set of *all* true propositions. So for example propositions A, B, C, D may appear to be compossible but perhaps A and B imply E and C and D imply not-E. To even discuss the empty reality requires the recognition that its book is empty and thus that it logically possible.

      Is the proposition "this world has no propositions true of it" true of it? What about "this world has no numbers" and "this world has no bodies" etc?

      A minor point: To start a sentence with “this world” is redundant; all propositions in the “book” of a world are by definition about it. On the empty reality the sentence “there are no true propositions” or even “there are no propositions” is meaningless, and thus not even a proposition. Since in the empty reality there is nothing there is also nothing about something and thus no meaningful concepts.

      I find it important to discuss the logical possibility of the empty reality not only because it is required for the theistic argument from contingency, but also because it demonstrates that the proposition “theism is logically necessary” is false. I recall Plantinga has made an analysis of Anselm’s modal argument and found that what it proved is “If theism is possibly true then it is necessarily true” where “possible” stands for “metaphysically possible” or “could in fact be possible”. Since it is unreasonable to believe in something that could not in fact be possible one could rewrite this result as “If it is not unreasonable to believe in theism then theism is true”. But these impressive sounding results also hold for naturalism.

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    23. @ Tony, August 17, 2017 at 4:19 PM

      Even though non-Euclidean geometries WERE ACTUALLY conceived by Riemann and Lobachevsky and others, they are "inconceivable".

      I’d say they were constructed, not conceived. The story as I know it is that mathematicians for a long time were suspicious of Euclid’s fifth axiom, which had a different style and which was not used in a many geometrical proofs. So they thought that perhaps it is not a true axiom but is implied by the first four in some complicated way- but couldn’t find the respective proof. Thus they assumed the negation of the fifth axiom to see if they could find a contradiction with the first four (which would lead them to the proof), and discovered that they could prove many crazy theorems on this crazy set of axioms without ever finding a contradiction. They realized that they had constructed a new kind of geometry.

      Still, the fact that something can be formalized does not mean it is conceivable. The Copenhagen interpretation is absolutely formal, but it is inconceivable that a coin is both inside and outside of a box, or that a cat is both alive and dead. As for non-Euclidean geometry I cannot conceive of a triangle (three straight lines connecting three points) where that sum of the three inside angles is 270 degrees. (Can you?) Nor can I conceive of curved spacetime. A lot of inconceivable models turn out to be useful as functional formalisms. The theist, or at any rate the theist who is not a physical realist, has no problem with that: God created phenomenal reality (the reality which we experience) in such a way that specific formalisms produce correct results. That when we try to imagine what physical reality would produce the respective results we find it is inconceivable is just as good: it is God’s way of telling us that this reality does not exist.

      I don’t understand A-T metaphysics well enough to know if it entails physical realism; but as far as I understand it, it doesn’t. If so, perhaps the wise things would be for Thomists to eject physical realism as (given the deliverances of modern physics) incompatible with reason.

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    24. Dianelos, your discussion on possible worlds semantics doesn't seem to address the problems Tony raised with your scheme, at least not in a consistent way.
      For one thing, you still haven't tried to offer any framework for what makes propositions meaningful, and without that, saying that some propositions, though meaningful in the actual world, are meaningless in some world w, is itself a meaningless assertion, or at least an indefensible one. Why should the statement "George Washington exists" be meaningless in an empty world? You can't appeal to metaphysical possibility, since even in an empty world his existence is metaphysically possible; as I've remarked before, nothing about his existence violates the metaphysical principles of such a world. (If you dispute that, please construct an empty world were it does. Mere stipulation isn't a reason for anything.) It seems that even the statement "George Washington is the first president of the United States" is meaningful, once we understand what all the terms describe. Judging by those apparent truths, your assertion that "the meaning of these propositions depends on how that world is" is false. Maybe you can defend it if you provide a framework. Saying that formalism alone is insufficient isn't reason not to provide one, and I'd love to see what you develop.
      For another, you can't argue that all propositions are meaningless in an empty world, and you wouldn't be able to do so even if you provided some framework for meaningful propositions. A world in which all propositions are meaningless isn't even a concept, because it has no content (in the same way as "square circle" has no content); such a world can't be described at all, since, as you yourself note, every true proposition in a world is a truth about that world. Moreover, a world where all propositions are meaningless can't be called consistent or inconsistent, because those terms describe content. Hence, your extreme version of the empty world is not provably consistent, else it would have content, and you effectively deny that it does. Your entire enterprise is incoherent.
      It should be easy to see from the above points that your statement "there is nothing about something" in an empty world doesn't pan out. There must be some meaningful propositions, even if they're all negative, or else you aren't talking about a possible world. Likewise, some of them must be true, as (P&~P) is inconsistent, and a world where all meaninful propositions are false is one where we have this kind of inconsistency. Where P is false AND ~P is false, we get ~P&~~P, which is a contradiction (and it gets worse on multi-valued logics). This is all true even if it's logically possible for God not to exist.

      "I find it important to discuss the logical possibility of the empty reality not only because it is required for the theistic argument from contingency, but also because it demonstrates that the proposition "theism is logically necessary" is false."
      First, whether empty worlds are logically possible is important to the cosmological arguments, but that they are logically possible is not. You never answered that distinction, stop pretending this is settled.
      Second, although the logical possibility of an empty world would refute the claim "Theism is logically necessary," you haven't given any good rebuttals to the argument I made that theism actually is logically necessary. You've given failed reasons for rejecting the premises, and ultimately asserted that logic doesn't really matter to God, so He could make Himself cease to exist anyway. That latter point, even if it miraculously succeeded, wouldn't show that His non-existence is logically possible.

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    25. Dianelos:
      Let's move to your third post...
      I already told you that you seem to be conflating conceivability and imagination, but I never bothered saying anything more. That mistake may let you assert that we can't conceive of non-Euclidean geometries, but it also means we're unable to conceive of law, causation, and logic, among a host of other things, since strictly speaking we can't imagine those, either, let alone "convincingly." Indeed, any images we make to symbolize them with are not images of those things at all, but are to some extent arbitrary, with no actual resemblance between the object and the image. Yet we can obviously understand those things. This is why we can have concepts of them, and thus why we can conceive of them. In a similar way, we can understand non-Euclidean geometries and have concepts of them. That's the difference between being able to conceive of something, versus being able to imagine it.

      I'll add that your idea that God created a world with a physical phenomenology, but nothing actually physical there, seems inconsistent with your idea that angels have bodies, and undercuts your own arguments for that conclusion. Just as there can be phenomenology about a physical world without that world producing it, so can one have a phenomenology of being embodied without actually having a body in any sense of the word.

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    26. @ Grace and Rust, August 18, 2017 at 8:36 AM

      God can't violate His own nature

      Perhaps our difference is with the semantics of “can”. You use “cannot” in the way I use “will not”.

      That the connections display law-like regularity is not evidence that they are mechanical, you're simply stipulating.

      By my definition what characterizes a mechanism is that it displays law-like regularity. It seems to me that under “mechanism” you only understand material causes. And not, say, law-like final causes or even efficient causes. Such a definition strikes me as arbitrary.

      your very assertion bars you from making any inferences about anything not part of "mechanical nature;" all trustworthy inferences are logical.

      Well, yes and no. I cannot make *logical* inferences about anything that is not of a mechanical nature. But from this it doesn’t follow that I cannot make any inference whatsoever about anything that is not of a mechanical nature. For example on theism the good is grounded in God’s character. Thus I can make inferences about the good based on my direct perception of God’s character - which is not of course of a mechanical nature. Cognition goes way beyond logical formalisms. Way beyond. And God is way way beyond logic. I hope you won’t miss the mystery and beauty that is God.

      although you may say "the closer one comes to God . . . the less logic applies," you have no way to defend it rationally. It's a proportional statement and, by your own standards, mechanical.

      True, it is a statement about a mechanical or law-like property of my relationship with God. On the other hand it is commonly agreed, is it not, that ultimately in God all distinctions disappear. And since logic is about the relationship among distinct things it follows that all applicability of logic also disappears. For all distinctions and logical structure require a ground that is metaphysically more basic still, so to say that there are distinctions or logical structure in God’s being the metaphysical ultimate is to say a logical impossibility. Logic, I insist, is a tool of great but limited use. Interestingly enough, one use it has is to produce its own limits – as the argument above shows.

      Nor can you argue that "God . . . is beyond any positive propositions."

      I wrote “God at the core is beyond any positive propositions”. Any positive proposition requires differentiation in its subject matter. By “God at the core” I mean that in God’s nature that is the metaphysical ultimate, and in which no differentiation exists and thus about which no positive statements can be said. But God is much more than just the metaphysical ultimate.

      You hold that God is omnipotent, which is clearly a positive statement, and not one strictly about our relationship to God.

      Omnipotence refers to God’s doing what God wants. To do what one wants does not refer to the undifferentiated core of God, since to want A instead of not-A is already a differentiation. But one can refer to God without meaning the undifferentiated core (or “Godhead” as some theologians used to put it). Again, God is simple but not just simple. Obviously. Something that is just simple is far from being the greatest conceivable being.

      So what belongs to God? Strictly speaking all belongs to God. God is immanent in creation and its multitude of things. The fact that each pebble is upheld in creation by the will of God means that there is a divine aspect even in a pebble. Given this picture perhaps we can say that when we speak of “God” we mean that which necessarily belongs to the greatest conceivable being – or if you will belongs to it without having any non-divine aspects. Such as omnipotence. But not the pebble.

      [continues below]

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    27. [continues from above]

      And omnipotence, especially your over-extended concept of it [snip]

      My understanding of omnipotence and omniscience is that God, the greatest conceivable being, simply does what He wills and knows what He wills – without any complications and indeed metaphysical paradoxes about what is logically possible to do and about what is logically possible to know. Thus I find that the classical understanding is the one over-extended; I find that people have the tendency to assume that perfect power entail infinities, rather than just the absence of limits.

      you can't defend the idea that "At the core of God, . . . all distinction disappears." You have to take it as a given (which contradicts your last assertion)

      Right, I think I see what you mean. Well, at the core, at that which is metaphysically ultimate, nothing is given because there is nothing more basic to give it or to make it so. Thus even by the lights of logic we see that in the metaphysically ultimate no differentiation exists. These are general principles of metaphysics and hold on naturalism also. Now on theism at the core God’s will becomes identical to God’s nature, and thus it is just conceivable to us how on theism the metaphysical ultimate supports itself. But it is hard to conceive how on naturalism the metaphysically ultimate supports itself. But then again, as I think we agree, conceivability does not imply possibility and neither inconceivability implies impossibility.

      he based that assertion on a conflation between imagination and conceivability.

      As for “conceivability” meaning “clear imagination” that’s the way many philosophers use the concept. For example Putnam writes: “We can perfectly well imagine having experiences that would convince us ... that water isn't H2O. In that sense, it is conceivable that water isn't H2O. It is conceivable but isn't logically possible! Conceivability is not proof of logical possibility.” You seem to disagree with Putnan’s and my sense, but I notice you do not mention what “conceivability” means according to you.

      In any case and as a matter of observational fact about our cognitive processes we do put some worth on what we can conceive. So for example when we have to choose between alternatives X and Y and can conceive X being possible and can’t conceive Y being possible then, all other things being equal, we choose X and not Y. Not to give any weight on what seems conceivable to us would be unreasonable. So even though conceivability does not imply possibility, it is a good thing to take it into account. The proposition “If I can conceive X being possible and know of no reason why X might not be possible then it is reasonable to believe that X is possible” makes eminent sense.

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    28. Dianelos, the more I read you, the less sense you make, and I know I'm not the only one with that opinion. I'll be frank that you're filled to the brim with misconceptions about what logic is, and what other concepts even mean. We'll go over some of these. And for the record, no, by "cannot," I mean what all normal people mean. I don't mean anything like your "will not," unless you mean "He won't because He can't," and we both know you don't. Your definition of omnipotence doesn't reconcile us.
      Now, the fact is, even having defined "mechanical" to mean "law-like regularity" (which is an ahistorical definition, unlike the one I assumed beforehand; in other words, yours is the arbitrary one, not mine), your points about why logic doesn't apply to "non-mechanical nature" are obviously wrong, and don't even make sense, as will be seen. Moreover, you either don't believe those particular assertions, or you're confused. If you were neither of those things, you wouldn't be trying to defend any of your claims about God or logic, because doing so requires acknowledging that you're wrong that logic doesn't apply to non-mechanical nature or God; but you repeatedly apply it to those things! That obviously isn't showing that logic doesn't apply to those things. You also show that you don't believe God can break the laws of logic, or else you would happily say just leave the points I've made alone, and retort "Well, since God can break the laws of logic, my assertions stand, even if my arguments don't," and leave it at that. My entire scheme becomes irrelevant to your project, unless God actually can't break the laws of logic.

      Misconceptions
      1. Having defined mechanism in your ideosyncratic way, it is still obvious to everyone who understands logic that it applies to things that don't exhibit law-like regularity. For one thing, the laws of identity, non-contradiction, and excluded middle still apply to everything, even God. Even your "core of God" concept is necessarily identical to Itself, and either exists (in some sense) or doesn't exist (in that same sense), and cannot be both. It doesn't make any sense to assert otherwise, and it never will. Indeed, to deny these assertions is to say that theism and atheism are equivalent, and you don't believe that. For another, the rules of inference still apply for the reason I gave previously, namely that if one fact is connected to another fact, then we can make inferences. Third, logic works just fine for understanding and making inferences about randomness and human cognition, even though neither of those things is law-like, and especially not randomness. Clearly, logic doesn't depend on law-like regularity in order to derive inferences.
      2. Logic is not about the relationship among distinct things. Why in the world do you believe that? The theological tenets of scholastic thought, at least where they are statements solely about what God is like, were not derived by some relationship between distinct things. Logic is about the most basic aspects of being. Because propositions are ultimately about being, logic deals with how they relate, and allows us to get at the truth because the way propositions validly relate to each other reflects what being is like.
      3. Logic does not require a more metaphysically basic ground than being, and is in fact a set of assertions first and foremost about what being is like. (I made this clear earlier, Dianelos, this shouldn't be so hard!) Moreover, there can be nothing more fundamental than being, for anything we suppose is more basic would in some sense exist. Being is being, being is not non-being. To deny these assertions is to destroy the very foundation of truth, for truth is about being, and if what is and what is not happen not to be distinct, then truth and falsehood are not distinct, either.

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    29. 4. Your attempt to distinguish between logical inferences and other kinds isn't supported by your illustration. Either your knowledge of God's character directly gives you knowledge of the good, in which case you are not making any kind of inference whatever (because you have immediate acquaintance with the truth at hand); or your knowledge of God's character somehow mediates your knowledge of the good, and so you must infer what the good is like. In either case the laws of logic still apply for reasons I've given several times, which you haven't even tried to answer. The first case is irrelevant to your point about "non-logical" inferences, and the second doesn't warrant the claim that you aren't making logical inferences.
      5. You also misunderstand my stance about cognition. I agree that cognition outstrips mere formalisms (I'd hold an incoherent position otherwise!), and nothing I have ever said assumes or implies otherwise. All the same, that does not mean that logic doesn't apply to cognition! To reiterate, that point should be obvious from our ability to study it logically. I'm starting to think that your problem is a mistaken belief that logic is nothing but a collection of formalisms and clunky processes.

      The nature of God
      1. You're very difficult, Dianelos. You want to hold that God is the metaphysical ultimate, and then distinguish between the "core of God" and other aspects. I confess I don't know what you mean, because you seem to hold that these "other aspects" are really distinct from the core, rather than simply conceptually distinct. Yet clearly that can't be quite right, since this would mean God is composed of parts, and thus cannot be the metaphysical ultimate, even though it is a "part" of Him. Whatever is composed depends on those parts for its existence.
      2. It is not commonly agreed that ultimately all distinctions disappear in God, not in the way you mean when you say that. As it strikes me, your mistake is misunderstanding Divine Simplicity. The idea, in a nutshell, is that God is identical to His Essence, which in turn is analogous to all the attributes we correctly predicate on Him. This doesn't commit us to your proportional statement that distinctions disappear as we get closer to God, and so you can't infer that logic applies less as we get closer to God. Hence, not only are you being inconsistent by applying that proportion, and defending it, you're also wrong to hold to that proportion in the first place.
      3. In the same vein as item (2), we can still make positive statements about God. The assertion "God is eternal" is an example, which must be true as the metaphysical ultimate. In fact, the assertion that there is no differentiation in the "core of God" doesn't do the heavylifting for your assertion; a denial of the Scholastic doctrine of analogy does. You ought to familiarize yourself with it, if only because it will help you understand the rest of Thomist thought.
      4. Your assertion that everything that God sustains in being has a Divine Aspect is mistaken. Because everything possesses such an Aspect, everything is to some extent divine. The "core of God" ends up being the most Divine thing around, but you still have pantheism here. It's just like how my entire body is human, but my mind is what most perfectly reflects my humanity.
      5. Your definition of omnipotence is over-extended, not the classical definition. It is your model which leads to infinities, because now God can most certainly construct them, whether or not He could on the classical treatment. So saying, the classical treatment did say that God's power has no limits, without saying that it entails "infinities," so your criticism is entirely wrong to begin with!

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    30. Your Conflation, Again
      1. Conceivability does not mean imaginability, Dianelos, and if you had understood that snippet of Putman, you would know better than to cite him as evidence of your view. Chances are that you've misunderstood the other "many philosophers" you have in mind as well. Saying "We can imagine X, therefore we can conceive of X" does not commit us to saying that the two are the same thing. What it does show is that imaginability is a subset of conceivability, and I never denied that.
      2. I've repeatedly told you what I think conceivability means. You're either a liar for saying otherwise, or you haven't been paying attention. I'm tempted to take the latter explanation, given our long exchange on whether fertilized ova are people. Indeed, if you were paying attention, you'd also know that your closing sentences assume one of my previous statements, namely that conceivability is evidence (but not proof) that something is possible. We wouldn't value our ability to conceive of something if conceivability and possibility overlapped to a reasonable extent.

      I hope that covers everything. This is getting too long!

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  5. I was surprised that no mention was made about how the "Library of Babel" can't track the mindscape because every meaningful combination of letters would only be a token of the propositions; you would find "snow is white" in every possible language--which of these is the real proposition that snow is white? None of them. But then, maybe that point is implicit in the statement that no purely material state is determinate?

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  6. Great post. I want there to be a mindscape, I think that's a really beautiful idea. As a minor point of contention, the distinction between Platonism and Aristotelianism doesn't really hold up anymore, and so neither does the idea that a third realm is "Platonic."

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  7. OP "Just as a rock is already in the Universe, whether or not someone is handling it, an idea is already in the Mindscape, whether or not someone is thinking it. "
    --Pure speculation against evidence.

    There is no such thing as a mind independent of a brain that has ever been identified. The notion that ideas are somehow floating about out there is pure speculation against all evidence for minds, which is that a mind is always associated with a brain.

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  8. OP "the same proposition could be expressed instead in the German sentence “Schnee ist weiss.” For another, the proposition would remain true even if no sentences in English, German, or any other language existed. Notice, however, that the proposition would also remain true even if no human mind ever entertained it."
    --No, the notion that snow is white requires an intelligence to consider it. White is a color perception, requiring a perceiver.

    The physical reality is that solid water reflects certain wavelengths of electromagnetic radiation and absorbs others, if illuminated at all. If illuminated with red light snow will appear red.

    Different spectral reflection functions will appear white to a human being, even though they are measurably different.

    Absent a perceiving brain to process the conditions of lighting and reflection characteristics snow simply reflects whatever radiation it reflects absent any sort of proposition supposedly floating about or somehow existent absent a brain.

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    1. didn't know you were some kind of Berkeleyian

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    2. "...the proposition [solid water reflects certain wavelengths of electromagnetic radiation and absorbs others, if illuminated at all] would remain true even if no sentences in English, German, or any other language existed. Notice, however, that the proposition would also remain true even if no human mind ever entertained it."

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    3. Don't feed the trolls.

      SP, Go away.

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    4. AnonymousAugust 14, 2017 at 10:50 AM

      "...the proposition "

      [solid water reflects certain wavelengths of electromagnetic radiation and absorbs others, if illuminated at all]"


      " would remain true even if no sentences in English, German, or any other language existed. Notice, however, that the proposition would also remain true even if no human mind ever entertained it."

      Physical reality remains true irrespective of the existence of any human mind.

      The mistake so many theists and dualists make is confusing an outside physical reality with an abstraction.

      Out of this confusion they imagine their abstractions to somehow be existent outside of their thoughts. An abstraction may or may not be analogous to some outside realized object.

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  9. I smell gayness.

    Not the cool Milo gayness but more like Rosy O'Donald.

    That is all I will say for now.

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  10. Ed,

    If you want to take down the previous post (or other useless Posts....just saying) it's cool bro. In my defense. I was bored.

    Cheers.

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  11. Hey, Five Proofs has cover art now. Also, Amazon says it's #1 in Atheism. I think they might be a little confused?

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  12. What about Teilhard de Chardin's Noosphere and this conversation?

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  13. "Metaphysically speaking, universals, propositions, and the like are ultimately grounded in the infinite divine intellect rather than the finite material world. But our knowledge of them is not acquired by directly accessing the divine intellect. "

    But, of course, the "material world" is *also* grounded in the divine intellect... so not only is there not a third realm, there is not even a second realm.

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    1. The material world is grounded in the Divine Intellect, but in a different way than the "third realm." Namely, the material world is concrete and contingent, while the "third realm" is abstract and in some sense necessary. It is the distinction between being concrete versus abstract that makes the material world a realm, while the "mindscape" isn't. This, I think, would be true even if idealism is true.

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  14. People talking about "an empty world": you have befuddled yourselves with words.

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    1. No, that isn't a befuddlement, for the term "empty world," at least if treated in the context of possible world semantics, refers to a "maximal" set of consistent propositions. An "empty world" is a "maximal" consistent set such that every proposition of the type "x exists" is false. That's a perfectly clear concept, even if, as I contend, it's impossible.

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    2. World consists of things, not propositions.

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    3. That's a perfectly clear concept, even if, as I contend, it's impossible.

      Does it "have" propositions like "logic exists"? Or "If this world DID have a thing that existed, this would not be an empty world"?

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    4. Hi, Tony. I have to admit that, yes, such a world would have to have propositions such as "logic exists." However, since that seems problematic, I'm willing to patch the original if it helps make things clearer. Perhaps I should have said "An "empty world" is a "maximal" consistent set such that every proposition of the type "concrete object x exists" is false"?

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