Thursday, July 4, 2013

Avicenna’s argument from contingency, Part II


In a previous post we looked at an outline of Avicenna’s argument from contingency for a Necessary Existent.  Suppose the argument does indeed establish that much.  Is there any good reason to identify the Necessary Existent with God?  Does Avicenna spring for any divine attributes?  You betcha.  Jon McGinnis’s book Avicenna, cited in the previous post, provides a useful overview of the relevant arguments.  I will summarize some of them briefly.

The Necessary Existent, Avicenna holds, must be unique.  For suppose there were two or more Necessary Existents.  Then each would have to have some aspect by which it differ s from the other -- something that this Necessary Existent has that that one does not.  In that case they would have to have parts.  But a thing that has parts is not necessary in itself, since it exists through its parts and would thus be necessary only through them.  Since the Necessary Existent is necessary in itself, it does not have parts, and thus lacks anything by which one Necessary Existent could even in principle differ from another.  So there cannot be more than one.

Obviously, it follows also that the Necessary Existent, being without parts, is simple or non-composite.  The Necessary Existent must also be immaterial, and thus incorporeal.  For matter exists only insofar as it has form, and what is composed of form and matter is not simple but composite.  Here Avicenna’s Aristotelianism is evident.

It is evident also in an argument he gives for the goodness of the Necessary Existent.  Goodness, for the Aristotelian, is to be defined in terms of the end toward which a thing points as to a final cause.  Now part of Avicenna’s more general metaphysics is the thesis that every existing thing “desires” or aims toward approximating necessary existence as far as it can (not necessarily consciously, of course -- a thing’s final cause need not be something of which it is consciously aware).  But then what it desires or aims at is approximating the Necessary Existent, which qua object of this desiring or aiming is (given the Aristotelian analysis of the good) the highest good.

The Necessary Existent must also be perfect insofar as for Avicenna, perfection is a matter of what completes a thing with respect to its existence.  An acorn is more perfect the closer it is to being an oak, the Venus de Milo would be more perfect if it had its arms, and so forth.  But the Necessary Existent, being absolutely necessary in itself, is lacking in nothing with respect to its existence.

It is also part of Avicenna’s background metaphysics that what makes a thing intelligible -- that is, what makes it the proper object of an intellect, a concept -- is separation from matter.  (This is a common theme in ancient and medieval philosophy.  See my ACPQ paper “Kripke, Ross, and the Immaterial Aspects of Thought” for a detailed defense of the immateriality of strictly intellectual activity, as opposed to mere sensation or imagination.)  Moreover, the further a thing is from matter, the more intelligible it is.  Avicenna also thinks of an intellect as just that which has something essentially intelligible.  Now the Necessary Existent has its existence essentially, and being an immaterial kind of existence its existence is something essentially intelligible.  Hence the Necessary Existent, Avicenna concludes, is an intellect.

Much more could be said, both about these attributes -- again, this is just a brief sketch -- and about other aspects of Avicenna’s conception of God’s nature and relationship to the world.  Saying much more would require getting into Avicenna’s general metaphysics in more depth.  But this much gives a sense of how he would expand on his argument from contingency.

What should we think about that argument itself, as summarized in the previous post?  Naturally I am sympathetic, similar as the argument is in some respects to Aquinas’s Third Way (which Avicenna’s argument arguably had an influence on, and which I defend at length at pp. 90-99 of Aquinas).  There are differences, though.  For one thing, the notion that there cannot be an infinite regress of (essentially ordered) causes does play a role in the Third Way, but not in Avicenna’s argument.  For another, though both arguments concern contingency and necessity, the notions of contingency and necessity involved are importantly different.  Aquinas begins with the difference between things which are contingent in the sense of being generated and corrupted, argues for something that is necessary in the sense of being permanent or neither generated nor corrupted, and from there argues in turn to the existence of that which is necessary in the stronger sense of deriving its permanence from nothing else (where on analysis, as I argue in Aquinas and in my ACPQ article “Existential Inertia and the Five Ways,” only what is in no way composite can be permanent or necessary in this strong sense).  Angels and human souls are “necessary” in the weaker sense, which is why Aquinas needs a further stage in the argument to get to that which is “necessary” in a stronger sense that applies only to God.

This is not what is going on in Avicenna’s argument, even though like Aquinas (and as we saw in the previous post) he does have a distinction between two kinds of necessity, viz. that which has its necessity in itself and that which has its necessity through another.  For generation and corruption play no role in Avicenna’s reasoning.  As we saw, he takes his notions of “necessity” and “possibility” to be basic, evidently in a way that he wouldn’t think needs elucidation in terms of our experience of things coming into being or passing away.  In this regard his argument might seem closer to Leibniz’s rationalist brand of cosmological argument than to Aquinas’s Third Way.

But I wouldn’t put Avicenna in the rationalist, as opposed to Aristotelian, camp.  He appeals (in what I labeled step (4) of his argument) to a variation on the principle of causality -- which, unlike Leibniz’s Principle of Sufficient Reason, is about things themselves, not about our demand for an explanation of things.  (I have discussed the difference between these principles and the more general metaphysical and epistemological assumptions they reflect here and here.)  His notions of possibility and necessity are related to the distinction between that which has an essence distinct from its existence and that which does not -- an Avicennan idea that clearly had an influence on Aquinas, and forms the starting point of the “existential proof” for God’s existence in Aquinas’s De ente et essentia (which I also discuss in Aquinas). 

So, I would say that those aspects of the argument that rest on these ideas that Avicenna shares with Aquinas are correct, since I think those ideas are independently defensible.  And the aspects that are different from anything Aquinas says also seem plausible to me, so that while I do not have a settled view on Avicenna’s basic argument, I am inclined to think it is sound.  (I would be more cautious about some of what he says about the divine attributes -- those arguments would have to be treated on a case by case basis.  And unsurprisingly, I don’t agree with Avicenna’s views about the eternity of the world, which I have not discussed here.)

Let me turn briefly to some objections raised in the combox after my previous post (which you might want to re-read if you haven’t already, in order to follow the remarks below -- it’s brief).  One reader asked:

A mathematical platonist would say that the infinite sequence of whole numbers exists necessarily, but isn't it true that this series exists only through the existence of its members?

That is consistent with Avicenna’s argument, though, since he distinguishes between what is necessary in itself and what is necessary only through another.  He could say that the series is necessary, but only through another.  In any event, Aristotelians wouldn’t accept Platonism in the first place, for reasons independent of the topic at hand.  (Not that mathematical truths are not necessary, but since they exist -- for Thomists, anyway -- as ideas in the divine intellect, their necessity is derivative.) 

Another reader wrote:

If there's a flaw in the argument, here's it: the totality of all possible things is not a thing, so the premise that all things are either possible or necessary does not apply to it. And without this, the rest of the argument fails.

But why isn’t it a “thing”?  Obviously it’s a thing in at least the very loose sense that a pile of random junk is a thing.  True, it’s not a “thing” in the stronger sense of being a substance.  But why would Avicenna need it to be a “thing” in that stronger sense?  Why wouldn’t the looser sense suffice?

A third objection went as follows:

Having difficulty with premise 4. I can think of two readings:

4a Every existent possible being has a cause.

and

4b Every possibly existent being has a cause.

4a looks equivalent to the familiarly disputed claim that everything that exists contingently has a cause, since something exists contingently iff it is possible (in Avicenna's unusual sense) and exists.

4b looks too strong: after all, possible beings that lack existence lack causes too.

End quote.  I’m inclined to read (4) along the lines of the reader’s suggested (4a).  But I’m also inclined to read “possible” as entailing “that which has an essence distinct from its act of existence,” where the essence in question is merely in potency until actualized by an act of existence.  So, ultimately (4) depends on the idea that any actualized potency is actualized by something already actual (my preferred formulation of the principle of causality, which I’ve defended in Aquinas and elsewhere).

A fourth objection was:

7 seems to be the most controversial. Whether or not one thinks that the totality of the parts of the universe is contingent depends on whether or not one thinks the universe is contingent. Although I disagree with the man who holds the material universe to be necessary, if he does so he certainly has no problem agreeing that all of the universe's parts follow necessarily from the universe's existence as well. Of course this position is absurd, because it would mean that we exist necessarily (as do our thoughts and actions). But absurdity alone won't convince the anti-realist committed to the idea that the world just truly is absurd.

I think this misses Avicenna’s point.  The “totality” in (7) refers not to “the universe” but rather to “the totality of possible things” referred to in the previous step.  Avicenna isn’t making any assumptions about what the universe of our experience is really like.  His argument is more abstract than that.  He’s just arguing from the fact that something or other exists together with the notions of possibility and necessity.

A fifth objection:

I’d object to #4 “whatever is possible has a cause”. I see no logical impossibility in X existing, not existing necessarily (i.e. not forming part of all possible worlds in the relevant sense of “possible worlds”), and not being caused by anything - but just simply being in some worlds but not in others...  [The reader’s objection continues in this vein.]

I don’t accept this way of framing the problem, though.  Like other Aristotelians, I don’t much like contemporary “possible worlds” talk, and certainly not in an argument for a claim about what is possible or necessary (as opposed to a claim about possible worlds which follows from what we independently have argued to be possible or necessary).  I don’t think Avicenna’s notion of possibility and necessity either requires making use of possible worlds, or can be challenged (in a non-question-begging way) by making use of that way of thinking about modality.  And if the above is just a variation on Humean objections to the principle of causality, I’ve dealt with that issue elsewhere (e.g. in Aquinas).

A sixth objection went as follows:

The step from 9 to 10 is invalid. Up to 9 "the totality of possible things" means the class of whatever is contingent, considered as a unit. In later steps, however, the cause of the totality of possible things has to mean not the class, but the members of the class, for the argument to hold. Specifically, in 13 the cause of the totality of possible things can be a member of the class without causing itself. Say I found a business partnership; the class of partners in the firm exists because of me, yet no member of the class exists because of me. And I do not become self-existent just because I am one of the partners, and thus a member of the class that I brought into existence.

Put differently, the step from 9 to 10 is a quantifier shift fallacy, going from "for everything in the totality, there is some cause" to "there is something that is the cause of everything in the totality."

End quote.  I don’t know why the reader thinks that (9) amounts to “For everything in the totality, there is some cause.”  Avicenna neither explicitly nor implicitly says that in (9).  What he means is that the totality considered as such (including each member but not just each member individually) requires a cause.  In other words, what he is saying in (9) is what the reader thinks he is saying in (10).  And what Avicenna actually says in (10) is not “There is something that is the cause of everything in the totality" -- again, he’s already said that in (9) -- but rather that that cause is itself either part of the totality or outside it.  So there is no quantifier shift fallacy.

Nor do I see how the reader’s analogy is supposed to work.  Avicenna is talking about what causes the totality and each part of it to exist at all, not merely to exist qua part of the totality.  But to found a business partnership is not to cause any of the participating persons to exist, but merely to cause them to come to have a certain institutional relationship to one another.  It just isn’t parallel to what Avicenna is talking about.  What would be parallel is a case where you bring both the individual members and their partnership into existence all at once (something which, of course, none of us can in fact do).  But then it is even harder to see how such an example is a problem for Avicenna, since it is hardly plausible to say that a member of the partnership could have brought each member (including himself) and the partnership into existence all together.

Finally, a reader wrote:

I would appreciate help in understanding the concept of "possibility" and "necessity" being employed here.

As I read the argument, the intuition at work here is contingent-on (X). Something is said to be "possible" if it is contingent-on-something-else. Something is said to be "necessary" if it is contingent-on-itself. [etc.]

This is a misunderstanding.  “Possible” as Avicenna uses it doesn’t mean “contingent on something else.”  It means something like “being the sort of thing which, given its essence, need not have existed.”  It follows from this in Avicenna’s view that it needs a cause outside itself, but that is a separate point rather than part of the definition.  And “necessary” doesn’t either mean or entail “contingent on itself.”  “Necessary in itself” essentially means something along the lines of what Aquinas would call something whose essence just is existence.   (Whether Avicenna would put it exactly that way is uncertain, since as McGinnis notes, he wavers a bit about whether to say that the Necessary Existent can be said to have an essence, precisely because there is nothing distinct from its existence.  But of course, Aquinas would not say that God’s essence and existence are distinct parts -- just the opposite.  So for present purposes they are saying essentially the same thing.) 

Anyway, precisely because there is no gap in what is “necessary in itself” between what it is and that it is, there is no sense to be made of it being “contingent” on anything, not even itself.  To say it is “contingent on itself” makes it sound like it had to add existence to its essence, and the whole point is that it doesn’t have any essence distinct from its existence, since it just is existence.  It doesn’t have something to which existence could be added in the first place (either by itself or by anything else).

What is “necessary through another,” meanwhile, can be said to be contingent, but not contingent on itself.  It rather depends for its necessity on another.  So again, the reader just misunderstands what Avicenna has in mind by “necessity,” in either of Avicenna’s senses of the term. 

70 comments:

Mikey said...

I'm a bit confused about the "more immaterial something is the more intelligent it is" premise.. How does this relate to things such as mathematics and forms? Aren't they types of unintelligent immaterial things?

Edward Feser said...

Hello Mikey,

For Aristotelians, a form only exists either in the concrete substance whose form it is, or in an intellect which has abstracted it. There's no such thing as a form, number, etc. that exists neither in a mind nor in a concrete substance. Hence there are no strictly Platonic entities. Indeed, even in Neoplatonism, so-called Platonic forms really exist in a divine Intellect. (The difference between this view and the one held by thinkers like Augustine and Aquinas is that Neoplatonists do not identity this Intellect with the highest reality -- the One -- whereas Augustine and Aquinas would.)

So, forms and mathematical objects shouldn't be thought of as immaterial objects in the first place. It is the intellects that grasp them (whether human, angelic, or divine) that are immaterial.

rank sophist said...

Glad to see that those objections can be answered. Avicenna deserves more contemporary interest. Also,

as McGinnis notes, he wavers a bit about whether to say that the Necessary Existent can be said to have an essence

In this he is not really acting differently than Aquinas did. Following the Church Fathers, Aquinas denied that "essence" (or even "existence") could be predicated absolutely of God. He does this in a very vague, roundabout way, but he does it nonetheless. I don't know if Avicenna supported a doctrine of analogy, but he's certainly not far from the Thomistic and Platonistic tradition of denying absolute statements of the One.

Mikey,

How does this relate to things such as mathematics and forms? Aren't they types of unintelligent immaterial things?

Mathematics and forms are considered by Aristotelians to have no mind- or substance-independent existence. Math is something that inheres within substances, which we discover via abstraction. It isn't a universal Idea that exists in a "third realm".

In any case, the point is that matter is considered by Aristotelians to be wholly unintelligible. A form can only be comprehended when separated from matter. Thus it's a simple jump to Avicenna's idea of greater separation from matter entailing greater intelligibility.

rank sophist said...

Oops, looks like Prof. Feser beat me to it.

Jawad said...

Dr Feser

The Necessary Existent, Avicenna holds, must be unique. For suppose there were two or more Necessary Existents. Then each would have to have some aspect by which it differ s from the other -- something that this Necessary Existent has that that one does not. In that case they would have to have parts.

Could there not in principle be a number of wholly different necessary existents? There being wholly different entails that they do not resemble other existents, and so there is no reason to think them composite.

dd said...

Dr. Feser, great post.

Rank,

"I don't know if Avicenna supported a doctrine of analogy..."

He did. In his school, it's known as tashkik al-wujud (analogy of existence).

"...but he's certainly not far from the Thomistic and Platonistic tradition of denying absolute statements of the One."

This needs to be qualified for Avicenna. What do you mean by 'absolute statements'?

Jason Cebalo said...

Prof. Feser,

You say that, for Neo-Platonists, forms exist in an intelect but not in the intelect of The One. I'm slightly unclear, are they in the intelect of the Word or of the World Soul?

Christian said...

I'm glad to see this post. Avicenna's brand of Aristotelianism seems pretty interesting. I'll have to read McGinnis’s book sometime. Thanks Dr. Feser.

rank sophist said...

dd,

Thanks for telling me about Avicenna's version of analogy. I find that really interesting. Anyway,

This needs to be qualified for Avicenna. What do you mean by 'absolute statements'?

Well, traditionally, the One was thought to be beyond even being and non-being, in the sense that none of our concepts apply to it in an absolute way. The fact that Avicenna endorses analogy makes it easier to explain. At least in Christian thought, analogy means that everything we say about God falls short and yet, in some respect, remains true. You can't say that God has existence or an essence (or simply is his existence) in absolute terms, but it's still kind of true--an analogy.

dguller said...

It makes sense that Avicenna would endorse a Neoplatonic participatory scheme of causality, which would be the underlying ontological ground for how analogy between creation and creator is possible.

Anonymous said...

Jason,

For the Platonist the One that is Beyond Being is supraformal. The Forms are a reflection, prolongation, and manifestation (all these terms are approximate and not exhaustive) of the One.

The Forms are the things that make up Intellect, so to speak. They are what Intelligence is about.

The Forms are necessary, says the Platonist, to explain the Corporeal or Sensible, especially its multiplicity and cause. But they are themselves an Intellectual multiplicity and are explained, first, by the One and the Dyad (well, technically, the lesser ideas are explained by more general ideas, which are explained by Qualitative Numbers, which are explained by the One and the Dyad) and then by the One that is Beyond Being.

For the Platonist because the corporeal requires the existence of levels of being above it - the Psychic or Subtle (and mathematical) and then Formal Realms -for it to exist, and because we can grasp these levels of being separately, and in Platonism there is a nexus between Knowing and Being, as the corporeal does exist, so must the higher levels of Being. The corporeal is a sort of coagulation of the Formal. The One cannot bring the corporeal realm into being and somehow not manifest the higher realms of being as well (of course, it is not the case, by an means, that the corporeal is what the One wanted to manifest and the rest is just support or baggage - in fact, the corporeal is a lesser realm of being compared to the Formal or Intellectual).

On Numbers and Mathematics, there are two distinct perspectives into which they enter Platonic-Pythagorean metaphysics. On the one hand they are a bridge between the sensible and the lowest level of Forms, being connected to the subtle and psychic levels of being. This is the level of mathematical entities. They share the imperishable and intellectual nature of the Forms and yet the indefinite multiplicity of the sensible.

-Jeremy Taylor

Anonymous said...

Sorry, forgot to add that there is also the existence of Qualitative Numbers, to the Platonist-Pythagorean. These are inoperable Numbers that are the highest levels of Forms and represent essential aspects of Being; ie., one represents unity and so forth.

Michael Brazier said...

Sixth objector here. I may have mistaken just where the problem with Avicenna's argument is, but I do think it involves a quantifier shift fallacy. To be as clear as I can: consider two members of the totality of possible things, say my left sock and the Washington Monument. Each of these, being possible, has a cause; but is it true that both have the same cause? If we restrict our examination to immediate causes, it clearly isn't. If two members of the totality of possible things don't have a common cause, the totality as a whole does not, and the argument fails.

To save the argument we have to look beyond the immediate causes of possible things to their ultimate causes, following causal series per se until they reach a terminus. But once you've shown that doing this is well-defined because all causal series per se do in fact reach a terminus, you no longer need to consider the totality of possible things to prove that something exists necessarily. The distinctive part of Avicenna's argument does not go through without the distinctive part of Aquinas' argument.

monk68 said...

Michael,

You wrote:

"If we restrict our examination to immediate causes, it clearly isn't. If two members of the totality of possible things don't have a common cause, the totality as a whole does not, and the argument fails.

To save the argument we have to look beyond the immediate causes of possible things to their ultimate causes, following causal series per se until they reach a terminus."

One response that might be made is that all possible things *do* have a common cause with respect to their very existence; that is, their first act of being. Moreover, the first act of being (participation in existence per se) is the most immediate, fundamental and immanent of acts. In the order of essence, it is true that possible things often do not share common causes with respect to their coming to be, or ceasing to be: that is, their generation or degeneration as *this* thing or *that* thing often flow from a multiplicity of secondary causes.

But with respect to their participation in existence per se (the underlying requirement for their having any essence at all whereby they are *this* or *that*); all possible things share a common cause, namely Existence itself. That, at least, is the direction I would take in approaching your objection. It seems to me that Dr. Feser is looking in that direction as well when he writes the following with respect to your objection:

"Avicenna is talking about what causes the totality and each part of it *to exist at all* . . ." [asterisk enclosed text italicized in original quote].

Pax

Michael Brazier said...

"But with respect to their participation in existence per se (the underlying requirement for their having any essence at all whereby they are *this* or *that*); all possible things share a common cause, namely Existence itself."

This is true, but it is one of the things Avicenna's argument was trying to prove, so introducing it as a premise would be circular reasoning.

Scott said...

@Michael Brazier:

I don't think there's a quantifier-shift fallacy. Avicenna's step 9 says that the totality of possible things, considered as a unit, itself has a cause. This is said to follow from step 8 (the totality of possible things, considered as a unit, is itself possible), not from any consideration of the individual members of the totality and their own causes.

I think your disagreement might actually start further back, with step 6. You seem by implication to be objecting to the treatment of the totality of possible things as a unit that itself is either necessary or possible; maybe it's neither, perhaps because it's somehow improper to treat it as a unit.

dd said...

Rank,

"Well, traditionally, the One was thought to be beyond even being and non-being, in the sense that none of our concepts apply to it in an absolute way. "

Avicenna would simply reject this.

Anonymous said...

I don't understand why two necessarily existing objects must differ from each other in some respect. It's easy to imagine two objects that are identical with each other. It's easy to imagine a clone of yourself who is identical to you down to the last atom and has all your psychological experiences. Why can't there be two simple, non material necessarily existing objects?

Anonymous said...

Anon, then they would differ in spatial location. You and your clone can't both be in the exact same location.

Anonymous said...

why can't necessarily existing objects be in different spatial locations?

Anonymous said...

If necessarily existing objects are in different spatial locations how does it follow that one must be composed of parts? That seems like a complete non sequitur.

Daniel Smith said...

Dr. Feser The Necessary Existent, Avicenna holds, must be unique. For suppose there were two or more Necessary Existents. Then each would have to have some aspect by which it differ s from the other -- something that this Necessary Existent has that that one does not. In that case they would have to have parts.

Anonymous: If necessarily existing objects are in different spatial locations how does it follow that one must be composed of parts? That seems like a complete non sequitur.

I had the same thought.

Or, take numbers for instance: in the equation 2+2=4, what's the difference between the first 2 and the second 2?

Edward Feser said...

You guys seem to be thinking of physical parts. But "parts" as used in discussions of divine simplicity includes more than that. If you have two objects at different points in space, then for one thing, each will be material and thus composed of form and matter. Form and matter are parts in the relevant sense. Each will be actually at one place and potentially at another. Potency and act (where act is limited by potency, unlike in the case of pure actuality) are parts in the relevant sense. Etc.

Daniel, the first 2 and the second 2 are not different. They're both the same thing, the number 2. When you're counting concrete objects -- two apples and two further apples -- then of course they are different, but they're not numbers.

Johannes said...

IMV, Ibn Sina's argument for the Necessary Existent to be unique is unsuccessful, simply because there is no reason in principle why "each would have to have some aspect by which it differs from the other(s)".

I will share below my own recent thinking on the subject. Instead of the term "Necessary Existent", I will use "Subsistent Being", shortened as SB. Let's start by agreeing on the essential attributes of the SB: uncreated (ens a se), absolutely infinite, and eternal and immutable.

Let's assume there are two or more SBs, each of which creates ex nihilo one or more contingent universes. Thus there are two levels of universes:

- one or more contingent universes, such as ours, each created ex nihilo by one SB, and

- one subsistent universe, comprised of all the (uncreated, absolutely infinite, and eternal and immutable) SBs, truly a world of equals.

It is important to realize that any problems, if at all, arising from the existence of more than one SB do NOT affect the creatures within each contingent universe, because each contingent universe depends exclusively on, and interacts exclusively with, its own creating SB. Not only cannot the other SBs interact with that contingent universe, they cannot even know of its existence if the creating SB does not tell them about it. Thus, the hypothetical existence of multiple SBs would not pose a challenge to monotheism in each contingent universe. Rather, it would mess up the subsistent universe itself, as I will show next.

The first problem created by the existence of more than one SB is the nature of their mutual interaction. Either SBs can affect each other or they cannot. In the first case SBs would not be immutable, so it must be ruled out. Therefore we end up with a subsistent universe of SBs effectively unable to interact with each other, each of them being absolutely omnipotent in the contingent universe(s) he has created and absolutely impotent in the world of equals to which he properly belongs. This is already getting ridiculous, but there is more.

The second problem, which is on top of the first, is that, if there are more than two SBs, they cannot even recognize each other, as they are all identical. With only two SBs there would be no problem, because for each of them the situation would be quite clear: "me" and "the other guy". The point is that there is no reason whatsoever why, if there are more than one SB, there are only two of them. Morevoer, whatever the actual number of SBs happened to be, it would be totally arbitrary. Thus we have the ridiculous situation that, by making sense of our contingent universe, we have inferred the existence of a SB, which itself is part of a subsistent universe which does not make sense, both ontologically (whatever N is) and also operationally (if N > 2). Which should lead us to think that there is a basic logical flaw in the very assumption of multiple SBs, which is precisely the third problem.

The third problem, which is the basic logical flaw in the assumption of SB multiplicity, is just that, if there are two or more equal SBs, neither of them is truly ABSOLUTELY infinite, and therefore neither of them is truly SB.

Johannes said...

BTW, my previous comment does not intend to improve or correct the treatment of the subject of (non-)multiplicity by St Thomas Aquinas, for the simple reason that I have not read it. I just did some thinking on the subject "ex nihilo" and thought it might be useful to share it with an intellectually discriminating (not discriminatory!) audience.


Scott said...

@Johannes:

"IMV, Ibn Sina's argument for the Necessary Existent to be unique is unsuccessful, simply because there is no reason in principle why 'each would have to have some aspect by which it differs from the other(s)'."

Ed has addressed this point; where, if at all, do you disagree with what he has to say about it?

Johannes said...

To Scott: if you refer to Prof. Feser's last comment "You guys seem...", I just had not read it when composing mine.

Reading it now, it does not seem to show the truth of Avicenna's proposition as stated in the main article ("each would have to have some aspect by which it differs from the other"). Because spiritual beings, both created and uncreated, are not "at different points in space". They are not in space, period.

Anyway, my first comment can be viewed as an alternative way of demostrating SB uniqueness when we do not assume Avicenna's argument. Thus, if, for someone, Avicenna's argument as explained by Prof. Feser is clearly true, good for them. If, on the other hand, someone still does not "see it", I offered an alternative.


Anonymous said...

Look at it this way: if these two necessarily existing beings are completely identical then how are they not the same being? How can one even talk of two of them?

Scott said...

@Johannes:

"Because spiritual beings, both created and uncreated, are not 'at different points in space'. They are not in space, period."

Then how are they distinguished? As the anonymous poster above me is implying, if they're not at different spatial locations and they can't be told apart otherwise, then the principle of the Identity of Indiscernibles applies and there aren't "two" of them at all.

Robert said...

How Is spatial location relevant to immaterial entities?

dguller said...

Robert:

Immaterial entities do not exist in space-time. To exist in space-time is to be a material entity, because existing in space-time necessarily involves change, i.e. from place to place and from time to time, and matter is the principle of change for Aristotle.

Robert said...

Agreed duller.

So, how does one discount the possibility of multiple non-material entities existing independently though the same in all respects except for that of their independent existence.

FZ said...

This is lightly off topic, but what about the AT understanding of angels? If angels do not have a material cause, then can they exist "within" space time like material beings? If not, then how is possible for there to be more than one angel?

FZ said...

"So, how does one discount the possibility of multiple non-material entities existing independently though the same in all respects except for that of their independent existence."

How do you know that they are independently existing rather than the same being? That's what Scott is asking. Electron 1 and electron 2 can be told apart and proven to be independent beings based on their different spatio-temporal location (1 is there, 2 is here, etc). But you cannot use that to "tell apart" two non-material beings. In that case, how do you prove that there are indeed multiple beings rather than just one?

Scott said...

@Robert:

"So, how does one discount the possibility of multiple non-material entities existing independently though the same in all respects except for that of their independent existence."

By recognizing that if they're genuinely the same in all respects, they can't be distinguished and are therefore not "multiple" at all. "Two" things that are fully identical in every way are really one thing.

That's why I'm asking Johannes how the spiritual beings in his hypothetical example are to be distinguished. There must be some way to tell them apart if there are more than one of them. Once we know how that's done, we may be able to explain how that implies they must be composed of "parts" in the broad sense at issue here.

Robert said...

Scott, if they exist independently, then regardless of the fact that they share all other attributes in common, they are still distinct. This regardless of the ability of another to distinguish between them.

dguller said...

Robert:

Scott, if they exist independently, then regardless of the fact that they share all other attributes in common, they are still distinct. This regardless of the ability of another to distinguish between them.

Existence itself is not sufficient as a differentiating principle, because that existence would have to be bound to a particular essence into a particular entity, which either exists in space-time (if the entity is material) or not in space-time (if the entity is immaterial). Two immaterial entities would only be distinguished on the basis of their different essences. The act of existence, or esse, would be the same in both cases, and differ only in that it actualized a different essence in each case.

Brandon said...

if they exist independently, then regardless of the fact that they share all other attributes in common, they are still distinct.

But the point in question is precisely how you get the antecedent in the first place: what would be distinguishing them in such a way that they exist independently? (Scott's question is not about "the ability of another to distinguish between them" but is about how you are ruling out the identity of indiscernibles here.)

Scott said...

@Robert:

"Scott, if they exist independently, then regardless of the fact that they share all other attributes in common, they are still distinct."

Adding to dguller's reply: This assertion begs the question. That multiple non-material entities can "exist independently" without differing in any way is exactly the point you need to establish—and as dguller has already pointed out, sheer existence doesn't suffice as a differentiating principle.

Robert said...

However this is trivially false as below.

One equlateral triangle side 4
Another equilateral triangle side 4

2D and occupying the same x y coordinates.

Are you saying that there are not now, in fact, 2 triangles simply because they are indistinguishable?

I would say that there could not only be 2, but there could be an infinite number of such with no logical contradiction. Perhaps the unavoidable consequence of non-material existence itself.

dguller said...

Robert:

One equlateral triangle side 4

Another equilateral triangle side 4



2D and occupying the same x y coordinates.



Are you saying that there are not now, in fact, 2 triangles simply because they are indistinguishable?




You would first have to understand that, according to Thomism, triangles do not exist as such, but rather exist either as material triangles in spatio-temporal reality, or as ideas of triangles in an immaterial intellect. So, your triangle is either a material triangle in the empirical world, or is an abstract concept in the mind. If the former, then if the two sides occupied the exact same spatio-temporal region, then they would, in fact, be the exact same material triangle (if the rest of the sides similarly occupied the same spatio-temporal regions). If the latter, then it would be the same abstract and formal idea of that particular triangle, but it could be thought by different minds.

dguller said...

Robert:

Here's a better way of putting it.

Say you have the form of an equilateral triangle with a side measured 4 units. The form could either occur in matter as a material triangle, or in an immaterial intellect as a concept. It is the same form, but instantiated in different modes of being, one material and another immaterial. The former would be F-in-matter, and the latter would be F-in-intellect. F is the same in both, but F does not exist in itself, but only as F-in-matter or F-in-intellect.

Scott said...

@Robert:

"One equlateral triangle side 4
Another equilateral triangle side 4

2D and occupying the same x y coordinates.

Are you saying that there are not now, in fact, 2 triangles simply because they are indistinguishable?"

If by "triangles" you mean triangles objectively existing in Euclidean 2-space independently of our thinking of them, then yes, of course those "two" triangles are one and the same triangle.

If it seems otherwise to you, that may be because you're thinking of each triangle as "created" by your act of defining it or thinking of it. In that case there would be two distinguishable mental acts of which each triangle was the object. Even in that case, though, I'd be inclined to say the two acts had the same object.

Be careful throwing around phrases like "trivially false."

Brandon said...

FZ

This is lightly off topic, but what about the AT understanding of angels? If angels do not have a material cause, then can they exist "within" space time like material beings? If not, then how is possible for there to be more than one angel?

Aquinas's view is that angels cannot exist within spacetime like material beings (they are not circumscribed by place), but they can be located with respect to it by their application of power (they can be definitely acting here rather than there). Angels are distinguished by specific differences: every angel has some fundamental distinguishing feature making it a different kind of angel (ST 1.50):

That which agrees specifically and differs numerically, agrees in form and is distinguished materially. If therefore angels are not composed from matter and form, as is said above, it follows that it is impossible for there to be two angels of one species, just as it would also be impossible to say that there are many separate whitenesses, or many humanities, since whiteness are not many save according as they are in many substances. Even if the angels had matter, neither could there then be many angels of one species, for it would then be necessary that the principle distinguishing one from another be material, not according to quantitative division, since they are incorporeal, but according to diverse potencies. Which material diversity causes a diversity not only of species, but of genus.

Scott said...

I see that as I was posting, dguller also replied with a more strictly A-T answer.

I agree with his response, but as I was trying to suggest in my previous post, I don't think the answer actually depends on whether we take an Aristotelian or a Platonist view of the ontological status of mathematical objects.

Robert said...

Scott, this is an analogy. The triangles exist independently of our thinking about them. Again, trivially false seems to be apt in this context. You seem to want to fence off certain things as part of your argument. However, I am not sure why I should be content not looking over said fences. Immaterial entities open the door to many consequences.

Scott said...

@Robert:

"Scott, this is an analogy. The triangles exist independently of our thinking about them."

And in that case, as I've said, yes, I would say that "they" are one and the same triangle.

I'm mystified by your talk of fences; look over all the fences you please. You asked me a question and I've answered it quite directly—twice now, not counting the answer I'd already given even before you asked it.

Robert said...

The fence is your assertion that 2 triangles were in fact one triangle when I specifically posited 2 triangles as part of the analogy.

Anonymous said...

"I specifically posited"

There's your problem, thats an assertion. I can specifically posit bigfoot all I want, but that doesn't prove that bigfoot exists. Scott isn't asserting, he is arguing based on the identity of indiscernibles.

Brandon said...

The fence is your assertion that 2 triangles were in fact one triangle when I specifically posited 2 triangles as part of the analogy.

But positing is not adequate without stating what it is that distinguishes the two beyond the positing, which is your act, and not something to do with the triangles themselves. That was Scott's point: you haven't given any reason to think the triangles objectively different, you've just distinguished two acts of mind.

Scott said...

@Robert:

"The fence is your assertion that 2 triangles were in fact one triangle when I specifically posited 2 triangles as part of the analogy."

Anonymous and Brandon have already replied sufficiently, but I'll amplify a bit by repeating that your "positing" is actually a begging of the very question at issue. That question is whether you really can "posit" two identical triangles, or whether you're really just "positing" the same triangle twice.

Scott said...

In any event I see no "fence" in my " assertion that 2 triangles were in fact one triangle when [you] specifically posited 2 triangles."

You asked me directly: "Are you saying that there are not now, in fact, 2 triangles simply because they are indistinguishable?" I am in fact saying, that, so the answer was, and is, yes. Where's the "fence"?

By the way, you've called your proposed counterexample an "analogy" twice now. What's it an analogy for?

Anonymous said...

So ed, are you going to convert to Islam?

Another Anon said...

"So ed, are you going to convert to Islam?"

Lol, I don't think that this argument directly entails Islam; rather it entails monotheism in general.

Dianelos Georgoudis said...

Ed,

I find that the possible worlds paradigm helps one think more carefully about modality – it’s simply a thinking aid. But you say you dislike this modern way of talk. You define “possibility” based on Aristotelian metaphysics and write that X is possible if it is the “sort of thing which, given its essence, need not have existed”. Fine, but apart from Aristotelian metaphysics, the fact remains that “X need not have existed” means the same as “there is a possible world in which X does not exist”.

My deeper point is this: It looks like you define modality by what’s *metaphysically* possible (i.e. define possibility by what is the case in the actual world but need not be, and by what is not the case but could have been). If you define modality in this way then on all rational metaphysical theories there is one necessary being, which grounds everything, which is simple, etc. There is nothing special to Aristotelian metaphysics that leads to this result. (By “rational” I mean those metaphysical theories which one can rationally conceive, and in particular those who do not entail infinite regressions, nor some kind of pasticcio situation with a mixture of metaphysically entirely independent entities.)

The proof would very roughly go like this:

1. Everything that exists is grounded on something which is metaphysically not less basic.
2. Therefore, given the absence of infinite regressions and of pasticcio situations, there exists exactly one ultimate metaphysical ground of all existents.
3. This ultimate metaphysical ground is simple, because if it weren’t then its non-simplicity would be grounded on something which is metaphysically more basic.
4. Therefore, the ultimate metaphysical ground is identical in all metaphysically possible worlds.
5. Therefore, the ultimate metaphysical ground exists necessarily, i.e. it could not be the case that it is absent or different from what it is.

One difference between the above sketch and Avicenna’s proof is that it uses metaphysical grounding and not creative causing. Philosophers like to let their most important concepts be somewhat vague, but I think the concept of grounding is a little clearer than the concept of causing, and in particular completely excludes the concept of time – which by itself is a “thing”. Another difference of course is that my sketch simply rules out infinite regressions whereas Avicenna does some fancy footwork there to avoid doing that. But infinite regressions of grounding are impossible to rationally conceive, so I find the extra work is not required.

Rethinking Avicenna’s proof, I think the second objection above has some real teeth best seen when restated thus: “Granted that every possible thing has a cause, why can’t a set of possible things have two causes rather than one?” My own sketch actually allows such a state of affairs. But by ruling out pasticcio metaphysics as unintelligible it limits the number of ultimate metaphysical grounds to one.

A final point. The necessary and simple metaphysical ground of all should not be identified with God, but should perhaps be identified with the “Godhead” some speak of. One reason is that the necessary and simple metaphysical ground of all does not comport with St. Anselm’s definition. Another reason is that it does not comport with the God of religious experience. The latter reason is a showstopper. Consider an easier concept, say that of tables. Philosophers may ruminate about tables as much as they wish, as long as they stay within the limits of our given experience of tables. If philosophers think they have discovered some truth about tables which is not compatible with our actual experience of tables, then, obviously, they have gone wrong somewhere, or else they misuse language and use “table” to refer to something which is not a table.

Brandon said...

Fine, but apart from Aristotelian metaphysics, the fact remains that “X need not have existed” means the same as “there is a possible world in which X does not exist”.

Actually, this is an operator shift fallacy, since it takes a predicate modality to be equivalent to a propositional modal operator. It's an open question what the exact conditions are for which they can be treated as if they were equivalent, or the best inference rules relating them; but it's not difficult to have logical systems in which the difference is recognized. In Englebretsen's modalized term-functor logic, for instance, "X need not exist" would be a very different claim than "There is a possible world in which X does not exist" (if "There is a possible world" just is a locution meaning Diamond modality, with no further baggage, it would be a much stronger claim; if one takes possible world semantics to explain Diamond modality, on the other hand, then the relation depends on the strength of the assumptions required to establish this).

Austin said...

Hi Professor Feser,

I was going to ask if you could do a post on Aquinas' view of providence and predestination. At first glance of Summa Theologiae, it seems as if he holds an essentially Augustianian view, as did Calvin. My understanding was that the Catholic church did not hold to predestination or providential reprobration. It would be helpful if you could expound on Aquinas' views, the church's views, and your own.

Thanks!

Scott said...

@Dianelos:

"Fine, but apart from Aristotelian metaphysics, the fact remains that 'X need not have existed' means the same as 'there is a possible world in which X does not exist'."

I don't think they mean the same thing even apart from Aristotelian metaphysics. It's arguable that the second follows from the first (though even in that case I'd still have to know the first before I could infer the second). But the inference doesn't appear to work in the other direction; the fact that X doesn't exist in some other possible world doesn't seem to me to entail that X need not have existed in this one.

And whether that's so or not, the fact that we can even raise the question means that the two statements have different imports. If we can distinguish their meanings sufficiently to ask whether one follows from the other, then they must not "mean" quite the same thing.

And it's surely obvious on the face of it that we can thus distinguish them: they're not even statements about the same "world"!

Glenn said...

1. Everything that exists is grounded on something which is metaphysically not less basic.
2. Therefore, given the absence of infinite regressions and of pasticcio situations, there exists exactly one ultimate metaphysical ground of all existents.


But "not less basic" is not equivalent to "more basic", so the statement "No thing which exists is grounded on something which is metaphysically more basic" is not inconsistent with 1. above.

Scott said...

@Dianelos:

"Rethinking Avicenna’s proof, I think the second objection above has some real teeth best seen when restated thus: 'Granted that every possible thing has a cause, why can’t a set of possible things have two causes rather than one?'"

Because in that case neither of the causes alone would be the cause; the cause would be the two of them together.

At any rate I don't see anything in the earlier part of the argument that depends on the uniqueness of the cause; as far as I can tell, step 4 might just as well read "Whatever is possible has at least one cause." Avicenna does after all go on to argue for the uniqueness of the Necessary Existent.

Anonymous said...

'Since the Necessary Existent is necessary in itself, it does not have parts, and thus lacks anything by which one Necessary Existent could even in principle differ from another.'

Apologies if this seems like a dumb question (I think even calling me a layman would be generous), but how do you square this with the doctrine of the Trinity?

I've never studied philosophy or theology but am really finding this blog, or at least what I can understand of it interesting. If anyone could recommend any books/resources as a good starting point I'd really appreciate it.

Daniel Smith said...

Ed: Daniel, the first 2 and the second 2 are not different. They're both the same thing, the number 2. When you're counting concrete objects -- two apples and two further apples -- then of course they are different, but they're not numbers.

I'm probably just being obtuse but... If the two's are the same thing, how can you add them? Or how can you speak of them as "both" being this or that? Don't they have to be separate but identical?

Jan said...

Dr Feser,

I believe the modal version of the cosmological argument is in some ways an improvement over Avicenna's:

P1. A Chevrolet Corvette Stingray 5.7L L46 essentially requires a cause for its existence.
P2. It is metaphysically possible that the only contingent being that ever existed was an eternally existing Chevrolet Corvette Stingray 5.7L L46.
---
T1. In the situation described above the cause of the Chevy must be necessary (because the only contingent being there ever was is the Chevy itself, and it can't be the cause of its own existence).
T2. Possibly, there is a necessary being that has the power of causing Chevies into existence (from T1)
T3. There is a necessary being that has the power of causing Chevies into existence (from T2 and S5 axiom of modal logic).

The advantage over Avicennian argument is that it does not suppose that a collection of things is a thing in the relevant sense. Thus, it forestalls the Humean objection that to explain a collection is just to explain its every member.

The disadvantages are the dependance on S5 and the supposition that requiring a cause is a part of the essence of a thing. The latter might be disputed by some, but Thomists are I believe already committed to this view.

(I've first seen a similar argument made by Alexander Pruss.)

grodrigues said...

@Daniel Smith:

"I'm probably just being obtuse but... If the two's are the same thing, how can you add them? Or how can you speak of them as "both" being this or that? Don't they have to be separate but identical?"

Are you not confusing the name used to denote the object (e.g. "2") with the object itself? You can have several names, but they all name, denote, refer the same object (if you know a programming language like C think in terms of pointers), whatever the exact nature of the referent of "2" is.

It is in fact the exact opposite of what you seem to be implying: if the two "2" in "2 + 2" do not name the same thing, then what the heck are they names for? And what is the problem of adding something to itself? I can for example, easily speak of the ordered triple consisting of me, myself and I (to borrow from De La Soul).

Daniel Smith said...

grodrigues: And what is the problem of adding something to itself? I can for example, easily speak of the ordered triple consisting of me, myself and I (to borrow from De La Soul).

When you "add" your three selves together are there then three beings? Or is there always and forever just the one?

Dianelos Georgoudis said...

@ Brandon,

I don’t understand most of what you write, but let me try this argument:

Modal logic is regularly used to formalize arguments about alethic modalities, the type of argument that concerns us here. I assume you accept the validity of modal logic as an epistemological tool. In turn modal logic can developed on the possible worlds paradigm. Thus if modal logic is valid so is the use of possible worlds semantics, in the sense that any formal proof in modal logic can be translated into English using the respective possible worlds semantics. (Actually, the possible worlds semantics has more expressive power, since it can distinguish between, say, logical and metaphysical possibilities.)

So I don’t think a philosopher can get away with the argument “I like modal reasoning but I don’t like possible worlds semantics”.

Finally a clarification. For me the possible worlds paradigm is just a conceptual model, a thinking aid, and has no ontological relevance whatsoever. Only the actual world exists. Reality consists of the actual world and nothing else.

Dianelos Georgoudis said...

@ Scott

the inference doesn't appear to work in the other direction

Right, but please observe that Ed was discussing the meaning of “being possible” in the context of actual existents.

Because in that case neither of the causes alone would be the cause; the cause would be the two of them together.

Even though I agree that two different things can be considered as one thing (namely one which consists of the previous two), I don’t think that two different causes can be considered as one cause. For example I don’t think it makes sense to say “there is one cause for the fact that the grass is wet and the window is broken, namely that it has rained and that children have thrown a ball into the living room.”

On further thought I wish to point out that premise #4 “Whatever is possible has a cause” is ambiguous. Does it mean “Whatever is possible has exactly one cause” or “Whatever is possible has one or more causes”? It seems only the latter alternative makes sense and thus is perhaps true. But then there’s trouble with the argument’s steps #9 “So the totality of possible things has a cause (i.e. one or several)” and #10 “This cause is either internal to the totality or external to it”. For if the totality of possible things has several causes then some of them can be internal and some external to it. By equivocating on the meaning of “a” the arguments sneaks in the premise that the totality of possible things has only one ultimate cause. Which of course we theists hold to be true, but which is not proven by the argument.

I mean, even you want to assert that a set of different causes is one cause (in the same way that a set of different things is one thing), the argument’s logic starting with #10 breaks down.

Now compare my sketch. One can define the grounding relation between things quite flexibly, allowing for one thing or set of things to have multiple grounds, but if one restricts matters according to what is rationally conceivable (no infinite regressions, no pasticcios) then one finds that the grounding relations of the totality of things represents a directed graph in which there is provably one node at which all grounding chains end.

At this juncture the naturalist will probably point out that what is “rationally conceivable” is contradicted by the realist model of, say, general relativity. Curved spacetime is not rationally conceivable but is nevertheless accepted as true (at least by physical realists, which I take it include Thomists).

Brandon said...

Danielos,

It is simply an error to take "modal logic" to be a single thing. When you say modal logic, you actually mean "standard propositional modal logic". But there are many other modal logics; there are quantified modal logics, for instance, and there are modalized term logics and propositional dynamic logics and the like, and none of these can be simply ignored as if they didn't exist. The notion that there is one single modal logic for alethic modalities is thirty years out of date, at least. And in some of these modal logics, like modalized term logic, there is a very sharp division between propositional modalities and predicate modalities, one that is not merely formally consistent but also motivated on philosophical grounds. But possible world semantics is structured for use with standard propositional modal logic, and even has the very structure of propositional modality built into it; it is also known to be difficult to apply to any kind of system of hybrid modalities, because it was made with only monomodal systems in view. Its application outside of its original focus on standard propositional modal logics has to be justified, not assumed.

Further, there is the fact that the very use of the term 'possible worlds' regularly introduces baggage into discussions that doesn't belong there. We see this precisely with your comment about ontological implications, since despite claiming this, you immediately go on to assume that the level of discussion is a world. But why are you even assuming this? Formally, the "possible worlds" in possible world semantics can be anything: possible situations at moments of time, possible paths or branches on a graph, possible actions, anything. And because of this, the only restriction on alethic modalities is that the modality be sufficiently similar to traditional necessity, possibility, etc., to count as alethic. There are lots of applications of alethic modalities that are not concerned with worlds at all. So if it has no ontological implications, why are you assuming that the relevant ontological counterpart to a possible world in possible world semantics is a world in the ontological sense? There is no formal justification for this; you are dragging it in as an ontological assumption, influenced by this talk of 'possible worlds' into just naturally slotting worlds into the ontological counterpart slot. And this is directly relevant here, since it is utterly implausible that predicate modalities, if distinct from propositional modalities as they are in some modal logics, would have worlds as their ontological counterparts. Terminology is not everything, but it is dangerous to assume that the particular words you use to talk about modality have no influence on the assumptions you make about it. It's entirely reasonable to suggest that possible world semantics is too clunky an apparatus, or too misleading in its terminology, to be the best way to approach a modal question. Whether it is or not will have to be determined according to the case.

Homer Simpson said...

Hello Dr Feser,

I have come across an objection to his uniqueness argument:

"While I agree that the search for never ending particles may be never ending, the proof provided here is invalid. It only works when the parts in reference are intrinsic, as opposed to extrinsic. That is, the two fundamental particles are similar intrinsically, but they are not different intrinsically as well. They are different because of their different spatial positions, and spatial position isn't an intrinsic property of the particle, rather it is an extrinsic property. For example, I can say that since the name of God is "Allah", and the pagans used to call their idols "Allah", then there is a similarity between Allah and the pagan idols (they have the same name). Hence Allah must be composed of parts as well by this argument, since He shares something with the idol (the name "Allah") but doesn't share the other parts. But obviously that is a false claim, since a name of a thing is an extrinsic property of that thing, and not an intrinsic property. So just because a person can name something "Allah" does not mean it has a similarity with Allah. In the case of the fundamental particles, the two different particles are similar (actually, identical), so, yes, there are parts that one shares with the other. But there isn't really a part that it doesn't share with the other, since the difference between the two is their spatial position, and spatial position is not a "part" of those fundamental particles. Just like the name "Allah" is not part of Allah, the location of the particle is not part of that particle. It is an extrinsic property of those particles, hence the argument that "it shares something with the other and doesn't share the other parts" is not really valid in this case. "

http://www.shiachat.com/forum/index.php?/topic/234973297-is-finitude-a-property-of-a-contingent/?p=2011706

Is that not a strong objection?

mashsha'i said...

Homer Simpson,

that objection fails. first, spatial location is a property of bodies. but the Necessary Existent is not a body. hence, it cannot differentiate any two putative necessary beings. second, even if it could, what is the relation of the particular spatial location of one necessary being to that beings' essence? either it is caused by the essence of that necessary being or not. if so, then given that the other necessary being has the same essence (for the assumption is that it also is a necessary being), the two would be identical. if not though, then their particular spatial locations are caused by something other than their essences. but if that is so, then they are caused. but this is a contradiction. therefore, etc.