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.”

40 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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  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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