*(A cosmological argument that operates from the interesting assumption that the universe is a necessary being.) *

C = what is conceivable to some mind. This means *inter alia* what can play the role of a true premise or conclusion in a coherent and true system. This is why complex numbers, four-dimensional space, and immaterial souls or angels are not *picturable* but are still C.

U = The totality of physical things. The universe or multiverse, whichever theory pans out. We operate under the hypothesis that it *exists necessarily*.

*Assumption*: there is not an infinite history of minds going back as long as there has been a U. As far as anyone can tell, this is wildly true and such minds only go back for a vanishingly small fraction of its existence.

1.) The possible is C. (*axiom*)

2.) C exists relative to a mind. (*by definition*)

3.) U is possible. (*look around*)

4.) U exists relative to mind. (*1, 2, 3*)

5.) If U exists relative to a mind that is not necessary then the universe is not necessary.

6.) U exists relative to a mind that exists necessarily. (*consequent of 5 is contrary to hypothesis*)

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## Allen Hazen said,

May 10, 2016 at 7:09 pm

Re:

C = what is conceivable to some mind.

Distinguo. There is a scope ambiguity here, between the existential quantifier (“some”) and the possibility operator (“-able”). If we make the quantifier broad scope (so: there is a mind such that the thing is conceivable by that mind), then it lacks plausibility: any mathematical truth is conceivable, but it would be very bold to say that some actually existing mathematician is smart enough to understand all of them.

If we make the possibility broad scope, then the argument fails: U is possible, so conceivable, but there is no necessity that it was conceivable by a mind present at the beginning of things.

## James Chastek said,

May 10, 2016 at 10:08 pm

it would be very bold to say that some actually existing mathematician is smart enough to understand all of them.The argument does not assume that a mind has to be the sort of thing that can contain only a finite number of facts. If you are basing this on experience (i.e. all minds in our experience contain only finite amounts of facts) why not just deny the conclusion and say we have no experience of a mind without contingency?

Can’t we take the conclusion of the argument as evidence that, if we start off indifferent to whether minds are limited to finite facts, we can prove that there is at least one that isn’t?

(I have a deeper problem with considering “some” as an existential quantifier anyway. My controversial and crazy position is that I don’t see “some” as existential but as a negation of universality, but even setting aside this craziness, in this

particularexplanation “some” doesn’t mean much more than an indefinite article. In fact, I originally wrote “some mind or other”, in an attempt to tell the reader I wasn’t restricting myself to one sort of mind.)## Allen Hazen said,

May 13, 2016 at 1:08 am

“Existential quantifier” I understand in purely formal terms: the dual of the universal quantifier. So — given classical negation — the negation of a universal just IS, in my preferred terminology, an existential. I was a Quinean in my youth, and have preserved since then a sense that — in the most general metaphysical contexts — “existence” is just what the existential quantifier signifies: deny a universal and in some sense you are committed to the, um, existence of a counterexample. So I’m not sure I disagree with you on this point: in calling it the ‘existential’ quantifier I’m not claiming that it commits one to anything more than a minimal and generic sort of existence. (A Meinongian former colleague was deeply offended by my use of “existential.”)

Scope again when I said no actually existing mathematician has to be able to understand all of them: ability of one mind to comprehend all the infinitely many mathematical truths wasn’t at issue. What I intended (choosing my word order to suggest intended scope) was

It would be very bold to say that, for every mathematical truth, some actually existing mathematician is capable of comprehending it.

Experience may lead me to actually DENY what it would be bold to say, but I don’t think I need to appeal to it here. What I was arguing was that I find the “possibility implies conceivability” premiss plausible ONLY if understood as “conceivable by some possible mind.” I think your argument depends on taking it as “conceivable by some actually existent mind.”

## Brandon Watson said,

May 13, 2016 at 2:03 am

It would be very bold to say that, for every mathematical truth, some actually existing mathematician is capable of comprehending it.Surely not any bolder than saying that God exists — indeed, the claim could very well be one way of saying that God exists. If we look then at the analogue of the statement in the argument, it seems that the first part your objection about its plausibility amounts to saying that it would be very bold to say that you could assert the conclusion of the argument, which may be so, but I don’t see that it clarifies anything.

But I’m not sure I understand, in any case, why you think the argument requires that ‘some’ not be ‘some possible’.

(1) What is possible is C (= conceivable to some possible mind).

(2) C exists relative to some possible mind.

(3) U is possible.

(4) Therefore U exists relative to some possible mind.

So far, there doesn’t seem to be much of a problem. And then the power premise, which introduces necessary existence:

(5) If U exists relative to some possible mind that does not exist necessarily then the universe does not exist necessarily.

But given the hypothesis that U exists necessarily,

(6) U exists relative to some possible mind that exists necessarily.

You seem to be treating (1) as doing all the work of the argument, but it’s (5) that actually makes the leap to a new level; (1) is just setting up the stage, and as long as (5) builds on precisely the stage it sets up, the argument will still reach the conclusion. The real question is why one should believe (5), whether we are dealing with ‘some possible mind’ or ‘some actually existent mind’.

## Brandon Watson said,

May 13, 2016 at 2:25 am

Hmm; re-reading that, I’m not sure my first paragraph is very clear at all, nor even that the point is particularly important enough to clear. But it does suggest a Leibnizesque cousin of the Berkeleyesque argument above:

Hypothesis: Mathematical truths are necessary.

(1) What is possible is C.

(2) C exists relative to some possible mind.

(3) Mathematical truths are possible.

(4) Therefore mathematical truths exist relative to some possible mind.

(5) If mathematical truths exist relative to some possible mind that is not necessary, mathematical truths are not necessary.

(6) Therefore mathematical truths exist relative to some possible mind that is necessary.

## James Chastek said,

May 13, 2016 at 8:37 am

St. Thomas and Augustine hit the same conclusion by slightly different premises.

## James Chastek said,

May 13, 2016 at 8:46 am

In the early drafts of this argument I spent the most time on the analogues to the 5 premise, because the argument won’t work if you could have an actual universe relate to a merely possible mind (you just ended up proving a tendency to reason in the universe, or some such.) Since cosmological arguments write themselves for a contingent universe, I figured if you got one on the assumption of the universe being necessary that the cosmological argument becomes necessary.

I took it as axiomatic that one can’t have a necessary being with a necessary relation to what was merely contingent, but that’s a claim with a lot of moving parts and I haven’t considered all of them.

## Brandon Watson said,

May 13, 2016 at 10:00 am

Leibniz’s actual closest argument to the Leibnizesque argument above is an argument for the existence of God from eternal truths, and I wouldn’t be surprised if he were influenced by Aquinas and/or Augustine in developing the argument.

## James Chastek said,

May 13, 2016 at 8:54 am

But the doubt that one has about there being a matamatician for every possible mathematical truth is perfectly consistent with the existence of a knower who exhaustively knows this totality. You could even make the assumed absence of these mathematicians a feature of a cosmological argument! (I think I might even be doing this)

## Allen Hazen said,

May 17, 2016 at 12:54 am

Sorry, not feeling well (shingles!), not up to considered reply.

But quickly, to Brandon.

You’re right, I didn’t think much about 5. But my concern with the relative scope of the existential (™) quantifier and the possibility operator is related. Assuming that the possible Conceiver is necessarily existent gives (S5) the scope shift: If it is possible that (A exists and can understand theorem & necessarily A exists), then (by the last clause) A actually exists, so there actually exists something that possibly understands… I think the assumption that the possible understander actually exists is a weaker assumption than that the possible understander necessarily exists, so any doubts I had about the scope shift lead a fortiori to doubts about 5.

Sorry, that’s not very clear.