I’m starting to appreciate the confessional nature of arguments. Arguments are avenues for thinkers simply to confess to their dialectical partners what strikes them as convincing, true, or clear. They aren’t attacks, weapons, or anything of that sort. They’re simply confessions ― revelations of personal sight. “I simply confess to you that these premises seem true to me” is a motto I (and, I think others) should get accustomed to using.
With that said, here’s my confession for today: I simply confess that the following argument strikes me as deeply plausible. More than that, actually ― it strikes me as clearly sound. But don’t let my sight be a bludgeon. Don’t let my sight shackle you into chains with which you cannot disagree or escape. I simply invite you to consider the argument by your own light of reason.
Here’s the simple argument ― one that I’ve discussed before on my blog, but one that I need to put forward in standalone, clear form.
- If classical theism is true, then for any x, if x is not God, x is created by God.
- If classical theism is true, then God is free to create or not create.
- If (i) God is free to create or not create, and (ii) for any x, if x is not God, x is created by God, then for any x, if x is not God, x is contingent (i.e. can be absent from reality).
- So, if classical theism is true, then for any x, if x is not God, x is contingent. [1-3]
- There is some x such that x is not God and x is not contingent.
- So, classical theism is false. [4, 5]
Premises (1) and (2) are core commitments of classical theism (Grant 2019, ch. 1). To deny them is to deny classical theism. Premise (3) is clearly true. If there being something apart from God presupposes that God creates it, and God is free to create anything or not create anything, then anything apart from God is possibly non-existent (i.e. contingent). The only premise left is premise (5). Why believe (5)?
All we need for the truth of (5) is (i) realism about things like numbers, mathematical objects, propositions, relations, universals, etc., and (ii) the claim that if numbers, mathematical objects, propositions, etc. exist, then they necessarily exist.
Denying realism is costly. I’ll simply assume realism. There are propositions. The number 2 exists. Universals exist.
And claim (ii) is eminently plausible as well. The number 2, if it exists, wouldn’t simply exist on Mondays (say) but not on Tuesdays; it wouldn’t just happen to exist. It would necessarily exist. Same with propositions. Consider the proposition that one and one make two. [Insert your favorite necessary truth here, e.g. ‘God exists’, ‘God doesn’t exist’, ‘modus ponens is valid’, ‘LNC is true’, ‘if there are philosophers, then there are philosophers’, etc.] This proposition is necessarily true. But something cannot be necessarily true unless it necessarily exists. For suppose it could fail to exist. Then, since non-existent things cannot be anything, it follows that it could fail to be true. But it’s necessarily true; it couldn’t fail to be true. Hence, it necessarily exists.
So, claim (ii) is on good footing.
All that’s left to show is that these things (universals, propositions, mathematical objects, etc.) are not God. This is clearly true. God cannot be identical to the number 2 and the number 7, since the number 2 is even while the number 7 is not even. God cannot be both even and not even. The exact same reasoning applies to the other kinds of entities we’ve been considering. For instance, God is clearly not identical to the proposition that ‘one and one make two’ and identical to the proposition that ‘the interior angles of a Euclidean triangle sum to two right angles’. For the latter is about the angles of a triangle while the former isn’t. God cannot be both about angles and not about angles.
So, by my lights at least, premise (5) is clearly true. And from this, classical theism is clearly false. By my lights, at least ― ’tis the nature of confessions.
Author: Joe Schmid
Grant, W. Matthews. 2019. Free Will and God’s Universal Causality: The Dual Sources Account. London: Bloomsbury Academic.
Referring more generally to formal systems, which comprise axioms, elements such as numbers and operators, God knows from eternity all self-consistent formal systems, but that does not give those formal systems any kind of real existence. The rules and elements of complex numbers or of Euclidean geometry do not really exist in a world of pure forms, but only in intellects. Asumming that formal systems really exist (where? floating in a world of pure forms?) amounts to asumming hard Platonism, which is incompatible with classical theism. No wonder you “proved” classical theism false.
“God knows from eternity all self-consistent formal systems, but that does not give those formal systems any kind of real existence.”
God can only know something if it exists to be known. If something doesn’t exist — if it is precisely nothing, utter non-being — then it cannot *be* anything, let alone *be* the object of God’s knowledge or awareness. All I mean by ‘exist’ is that they have some reality/being/existence or another. The ‘manner’, ‘way’, or ‘mode’ of their existence is irrelevant to my argument. Hence, *even if* they only exist in intellects, my argument only requires that they exist.
“The rules and elements of complex numbers or of Euclidean geometry do not really exist in a world of pure forms, but only in intellects.”
My argument doesn’t require or presuppose that they exist in a world of pure forms. My argument is perfectly compatible with them existing in intellects. You have simply misunderstood my argument.
For according to classical theism, anything with positive ontological status that is not identical with God is *created*, freely, by God. This is explicit within the CT tradition and is documented extensively in chapter one of Grant (2019). Hence, so long as the abstracta (i) have some positive ontological status, and (ii) are not identical with God, it follows that they are created by God, contingent, and extrinsic to God (i.e. not located in his intellect).
So, I am not assuming Platonism or *anything* of this sort. Let theistic conceptualism be true. Then, so long as God is not identical to the existing abstracta (even if the manner of their existence is an intellective one), it follows that there is something within/intrinsic to God that is not God. And that is flatly denied by divine simplicity. [Since whatever is not God is created by God, it follows that something that is not God couldn’t be *within* or intrinsic to God, since then a part of creation would be within God. Moreover, it would entail there is potency in God, since anything God creates is contingent and hence has potency for non-being.]
Hence, the argument (by my lights) survives your misunderstandings unscathed.
“No wonder you “proved” classical theism false.”
Dude, change your tone. I was explicit and meticulously conscientious in my post that I wasn’t claiming to demonstrate or prove anything. I was explicit that this is a *confession* of my personal sight, not something that compels others or demonstrates the truth of something. Sheesh. I almost didn’t approve your comment because it is in such stark contrast to the tone and charity I wish to cultivate on my blog and my personal life.
BTW, I hold that the correct framework in Philosophy of Mathematics is not Aristotelianism but plenitudinous theistic Platonism, where the meaning of each word is:
– plenitudinous: all self-consistent formal systems are on an equal standing.
– theistic: formal systems do not exist in a real world of their own, only virtually in God.
– Platonism (as oposed to Aristotelianism) = the existence (real or virtual) of a formal system is independent of its correspondence with a feature of the physical world.
I posted a summary of that position in a previous version of a Classical Theism forum:
Regarding this comment, prior to my analysis I would have to ask for a clarification of what you mean when you say that formal systems (what I will be calling abstracta) exist ‘virtually’ in God.
From my understanding — which is derived from Feser (2014) — something’s existing virtually is a sub-category of its existing potentially. E.g., consider Feser (2014, p. 197): “the hydrogen and oxygen are in the water only virtually rather than actually. This is evident from the way water behaves… Something similar can be said of the other chemical elements, and of quarks and other particles present in inorganic and organic substances.”
But there is no potency in God, and hence surely nothing exists virtually (i.e. in potency) within God, no?
If there is at least one possible world wherein God and God alone exists, then I see the classical theist as having an excuse to reject premise five. But enlighten me, since Platonism and the like aren’t my strong suit: is there really a problem if one were to affirm that numbers and the like do not exist in at least one possible world? I don’t know if it’s due to my illiteracy on the subject but I really don’t see a problem there.
Thanks for your comment my dude! Essentially, I don’t think that is a plausible dialectical avenue. Consider propositions. Some propositions are necessarily true. But in that case, they cannot be contingently existent; for that would entail that there are some worlds in which the proposition is true, corresponds with reality, etc. but in which the proposition doesn’t even exist. And that’s surely absurd; nothing can be both true and correspondent with reality while also not existing. If something is true, it has to *exist* in order to be true. Or so many philosophers, including myself, think!
For what it’s worth, I don’t believe that numbers as *nouns* have a real independent existence. I do, however, believe that they have a reality insofar as they are considered as *adjectives*, e.g, in describing real quantitative and spatio temporal relationships. This is the sense in which numbers can be successfully applied in science and everyday life.
What would be your response to Aquinas’ argument that the objects of mathematics do have an efficient cause? In Summa Theologiae question 44 article 1, he wrote that mathematical objects do have efficient causes, as efficient causes are due to having real existence.
He also wrote that necessary things have efficient causes, as the thing would not exist without an efficient cause. An efficient cause is required due not just because the effect may or may not exist, but because it would not exist without the cause.