If Nothing Exists, is it True that Nothing Exists? Well Yes, but Then . . .

Here is a puzzle for London Ed and anyone else who finds it interesting. It is very simple, an aporetic dyad.

To warm up, note that if snow is white, then it is true that snow is white. This seems quite unexceptionable, a nice, solid, datanic starting point. It generalizes, of course: for any proposition p, if p, then it is true that p. Now the connection between antecedent and consequent is so tight that we are loathe to say that it just happens to hold. It holds of necessity. So here is the first limb of our aporetic dyad:

a) Necessarily, for any p, if p, then it is true that p.

Equivalently: there is no possible world in which both p and it is not true that p. For example, there is no possible world in which both 7 + 5 = 12 and it is not true that 7 + 5 = 12.

Intuitively, though, there might have been nothing at all. Is it not possible that nothing exists? Things exist, of course. But might it not be that everything that exists exists contingently? If so, then there might never have existed anything. Our second limb, then, is this:

b) Possibly, nothing exists.

Equivalently: There is at least one possible world in which nothing exists.

Both limbs of the dyad are plausible, but they can't both be true. To see this, substitute 'nothing exists' for 'p' in (a) and drop the universal quantifier and the modal operator. This yields:

c) If nothing exists, then it is true that nothing exists.

But (c) can't be true in every world given (b). For if (c) is true, then something does exist, namely, the truth (true proposition) that nothing exists. But (c) is true in every world given (a).

Therefore (a) and (b) cannot both be true: the dyad is logically inconsistent.

So something has to give, assuming we are not willing to accept that the dyad is an aporia in the strict sense, a conceptual impasse that stops the discursive intellect dead in its tracks. A-poria: no way. Do we reject (a) or do we reject (b)? If a solution is possible, then I am inclined to reject (b).

But then I must affirm its negation:

d) Necessarily, something (or other) exists.

(Note that if it is necessary that something exist, it does not follow that some one thing necessarily exists. If there is no possible world in which nothing exists, it does not follow that there is some one thing that exists in every world.)

Yikes! Have I just proven by a priori reasoning the necessary existence of something or other outside the mind? Of course, I have not proven the necessary existence of God; I may have proven only the necessary existence of those abstract objects called propositions.

(Father Parmenides, with open arms, welcomes home his prodigal son?)

Posted

January 7, 2019

Aporetics, Existence, Nothingness, Truth

Bill Vallicella

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7 responses to “If Nothing Exists, is it True that Nothing Exists? Well Yes, but Then . . .”

Casey

January 7, 2019

This article, which you outlined on May 18, 2013, argues that the existence of necessary truths entails God’s existence (since truths are best construed as propositions, and propositions are best construed as thoughts of a mind, with necessary propositions being both infinite and eternal, the sort of mental content only thinkable by a divine mind).
https://www.proginosko.com/docs/The_Lord_of_Non-Contradiction.pdf
It is interesting how pithily Aquinas rejects the argument for God from truth at ST I 2.1ad3, saying, “The existence of truth in general is self-evident but the existence of a Primal Truth is not self-evident to us.” Regrettably, he does not deal with any sophisticated version of the argument there, though his main thrust seems to be not that God can’t be proved from truth but that truth does not make God’s existence self-evident. He seems to assume that the argument from truth (truth exists, therefore God exists) being sound would imply God’s existence is self-evident. A thing being self-evident will apparently be known immediately by all as a psychologically undeniable truth, akin to a first principle. He characterizes truth, mundane truth short of God, this way because no one can carry off denying the existence of truth, since to deny it is to affirm it; he means no one can accomplish this feat psychologically, not just that it would breach of logical normativity for one to do so. But by contrast, for Aquinas one can deny the existence of God (God’s existence is not self-evident). It seems to me that, pace Aquinas and only tangentially related to your argument above, it is psychologically possible to deny the existence of truth; some philosophers have done so (this proves that point), even if incorrectly (assuming truth turns out to be necessary).
There is a suite of concepts (mind, truth, goodness) stubbornly littering our lived experience, and to me so many philosophical questions hinge on whether we are apprehending something real through these or whether there is a misleading quirk of our minds whereby we construct and reify this entire realm, apropos of your post “Could it be like this?” from January 5. Whatever is ultimately true, it is fascinating that reality is so ordered as to allow for these sharp disagreements about reality.

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The Bad Ostrich

January 7, 2019

I think you know what my view on this will be.

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Archie Dawson

January 7, 2019

Hi Bill,
How one thinks about “truth” bears on this problem. I tend to think of ‘truth’ as ‘accuracy of representation’ (I think I heard Dallas Willard put it that way and it stuck with me). ‘truth’ = ‘being as known’ is another way to put it. On these conceptions, truth seems to presuppose mind.
I don’t have any formal philosophical training but, for what it’s worth to you, here are my thoughts on this:
Thinking this way, when I read (a), I paraphrased it as “Necessarily, for any p, if p, then a mind that thinks p is right.”
But then (c) becomes “If nothing exists, then it is true that a mind that thinks nothing exists is right”. That’s clearly wrong for the simple fact that if nothing exists then there would be no mind so truth (which, on my understanding, presupposes mind) wouldn’t exist either.
The mind easily forgets itself when thinking so the concept of ‘nothing’ seems tricky. I’m not sure we can legitimately deduce a positive consequent from it. “If nothing exists then…” you can stop right there. That would be a conceptual impasse of sorts since, if the mind is going to entertain the idea that nothing (at all) exists then that would include itself and it would need to stop acting for as long as it wanted to pretend that nothing exists. Not very useful.
So I suspect that, if we’re using a system of logic that’s any good, putting anything after “If nothing exists…” would force you to eventually affirm something like (d).

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BV

January 7, 2019

Ostrich,
Yes, you agree with me! See here and the very good comment thread: https://maverickphilosopher.typepad.com/maverick_philosopher/2010/04/a-counterexample-to-p-it-is-true-that-p.html

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BV

January 7, 2019

Archie,
How do you get from the well-nigh self-evident
a)Necessarily, for any p, if p, then it is true that p.
to
*) Necessarily, for any p, if p, then a mind that thinks p is right?
(*) is not a paraphrase of (a). (*) is false: substitute ‘5 is an even number’ for ‘p.’ If 5 is an even number, it does not follow that a mind that thinks that 5 is an even number is right.
Now try the substitution with (a). If 5 is an even number, then it is true that 5 is an even number. That follows.
If p is true, then ‘it is true that p’ is true. If p is false, then ‘it is true that p’ is also false.
Stating that a proposition is true doe not make it true!
Same with assertion. If I assert that p, I assert that p is true; but that is consistent with p’s being false. I can’t make a proposition true by asserting it.

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BV

January 7, 2019

Casey,
Very interesting comment, and thanks for reminding me of that passage in Aquinas. I don’t have time to go into all the questions your comment raises, but I’ll mention one thing.
>>It seems to me that, pace Aquinas and only tangentially related to your argument above, it is psychologically possible to deny the existence of truth<< A related issue bugs me. I believe I can show that the existence of truth (truths) is a transcendental presupposition of all our cognitive operations. But there seems to be a gap between showing this and showing that truth is ontologically grounded and not merely an exigency of our intellects. Bang on the link I gave to the Ostrich above for a dertailed discussion.

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Archie Dawson

January 7, 2019

Bill,
I got to (*) by expanding what I take ‘true’ to mean. But with the fuzziness around what ‘true’ means exactly, I can understand how (a) would be self-evident to almost everyone while (*) may not be.
I don’t see how the consequent of (*) is inconsistent with its antecedent being false though…
Using your clarifying substitution, in your response to me, are you saying both of these:
– Necessarily (in every possible world), if 5 is an even number, then it is true that 5 is an even number”
– There are some possible worlds where 5 is an even number but a mind there that thinks 5 is an even number is wrong to do so
(I expanded that 2nd statement a bit to import more of what I meant by “for any p, if p, then a mind that thinks p is right”)
I don’t see why it doesn’t follow that, if 5 is an even number, then a mind that thinks 5 is an even number is right. The following flow looks right to me:
(a) If 5 is an even number, then it is true that 5 is an even number
(b) If it is true that 5 is an even number, then a mind that thinks 5 is an even number is right
Therefore,
(c) If 5 is an even number, then a mind that thinks 5 is an even number is right.
I’m aware that stating a proposition is true does not make it true. While the antecedent is *actually* false in each case, if the antecedent *were true* then it looks like the consequents would all be true as well.
What am I missing? I assume that you have a problem with this flow and that it’s mainly with (b). Is it simply that you disagree that saying ‘p is true’ is equivalent to saying that ‘a mind that thinks p is right to do so’? Or is it something else? Is this flow formally invalid somehow?
I appreciate your time. Thanks! I’ll also check out the thread you referred Ostrich to. That may help clarify things for me as well.

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