Wishful thinking

Start with this observation:

1. Commonly used forms of fallacious reasoning are typically distortions of good forms of reasoning.

For instance, affirming the consequent is a distortion of the probabilistic fact that if we are sure that if p then q, then learning q is some evidence for p (unless q already had probability 1 or p had probability 0 or 1). The ad hominem fallacy of appeal to irrelevant features in an arguer is a distortion of a reasonable questioning of a person’s reliability on the basis of relevant features. Begging the question is, I suspect, a distortion of an appeal to the obviousness of the conclusion: “Murder is wrong. Look: it’s clear that it is!”

Now:

2. Wishful thinking is a commonly used form of fallacious reasoning.

3. So, wishful thinking is probably a distortion of a good form of reasoning.

I suppose one could think that wishful thinking is one of the exceptions to rule (1). But to be honest, I am far from sure there are any exceptions to rule (1), despite my cautious use of “typically”. And we should avoid positing exceptions to generally correct rules unless we have to.

So, if wishful thinking is a distortion of a good form of reasoning, what is that good form of reasoning?

My best answer is that wishful thinking is a distortion of correct probabilistic reasoning on the basis of the true claim that:

4. Typically, things go right.

The distortion consists in the fact that in the fallacy of wishful thinking one is reasoning poorly, likely because one is doing one or more of the following:

1. confusing things going as one wishes them to go with things going right,

2. ignoring defeaters to the particular case, or

3. overestimating the typicality mentioned in (4).

Suppose I am right about (4) being true. Then the truth of (4) calls out for an explanation. I know of four potential explanations of (4):

1. Theism: God creates a good world.

2. Optimalism: everything is for the best.

3. Aristotelianism: rightness is a matter of lining up with the telos, and causal powers normally succeed at getting at what they are aiming at.

4. Statisticalism: norms are defined by what is typically the case.

I think (iv) is untenable, so that leaves (i)-(iii).

Now, optimalism gives strong evidence for theism. First, theism would provide an excellent explanation for optimalism (Leibniz). Second, if optimalism is true, then there is a God, because that’s for the best (Rescher).

Aristotelianism also provides evidence for theism, because it is difficult to explain naturalistically where teleology comes from.

So, thinking through the fallacy of wishful thinking provides some evidence for theism.

Optimalism about necessity

There are many set-theoretic claims that are undecidable from the basic axioms of set theory. Plausibly, the truths of set theory hold of necessity. But it seems to be arbitrary which undecidable set-theoretic claims are true. And if we say that the claims are contingent, then it will be arbitrary which claims are contingent. We don’t want there to be any of the “arbitrary” in the realm of necessity. Or so I say. But can we find a working theory of necessity that eliminates the arbitrary?

Here are two that have a hope. The first is a variant on Leslie-Rescher optimalism. While Leslie and Rescher think that the best (narrowly logically) scenario must obtain, and hence endorse an optimalism about truth, we could instead affirm an optimalism about necessity:

1. Among the collections of propositions, that collection of propositions that would make for the best collection of all the necessary truths is in fact the collection of all the necessary truths.

And just as it arguably follows from Leslie-Rescher optimalism that there is a God, since it is best that there be one, it arguably follows from this optimalism about necessity that there necessarily is a God, since it is best that there necessarily be a God. (By the way, when I once talked with Rescher about free will, he speculatively offered me something that might be close to optimalism about necessity.)

Would that solve the problem? Maybe: maybe the best possible—both practically and aesthetically—set theory is the one that holds of necessary truth.

I am not proposing this theory as a theory of what necessity is, but only of what is in fact necessary. Though, I suppose, one could take the theory to be a theory of what necessity is, too.

Alternately, we could have an optimalist theory about necessity that is theistic from the beginning:

2. A maximally great being is the ground of all necessity.

And among the great-making properties of a maximally great being there are properties like “grounding a beautiful set theory”.

I suspect that (1) and (2) are equivalent.

Leibniz and the necessity of optimality

Leibniz famously holds that:

1. God creates the best logically possible world.

In order to resist logical fatalism, Leibniz denies that (1) is a logically necessary truth.

But this causes a problem for him that I am not sure he recognizes. Either (1) does or does not logically follow from God's perfection. If it does follow, then (1) will be logically necessary, since Leibniz thinks it is logically necessary that there be a perfect God because of the ontological argument.

But if (1) does not logically follow from God's perfection, then how do we know that (1) is in fact true? Leibniz is not so blind to the evils of the world as to think we can conclude (1) from an optimistic appraisal of the world around us. His theodical work insists on our not knowing much about what the infinite universe is like, and our thus being unable to form a justified judgment that the universe is non-best. If we could see that the universe is best, he wouldn't have to go to that trouble.

Leibniz does have a backup plan. In one piece, he notes that even if (1) were true, it wouldn't logically follow that it is logically necessary that this world is best. For Leibniz, a proposition is logically necessary provided it has a finite proof, whereas contingently true propositions have only an infinite proof. Thus, Leibniz insists—and very plausibly so—that even if our world is best, that fact cannot be finitely proved. So Leibniz could simply affirm that (1) is necessary, but that fatalism does not follow. He doesn't want to do that, though.

To make it harder for Leibniz to resist the logical necessity of (1), consider the following little argument:

2. Logically necessarily, a being that fails to create the best possible world is imperfect (in power, knowledge or morality).
3. Logically necessarily, there is a perfect being, and God is that perfect being. (By the ontological argument.)
4. So, logically necessarily, God creates the best possible world.

Leibniz defends the idea that a perfect being couldn't create less than the best, so he seems committed to (2). And he is definitely committed to (3).

I think, though, there is a neat way out for Leibniz. I do not know if he ever takes this way out—it would be interesting to search the texts carefully to see. The neat way out is to deny (2). Instead, recall Leibniz's controversial but insistent claim that if a perfect being were faced with a choice between two equally good worlds, that perfect being would not create anything. More generally, it is plausible that Leibniz would say:

5. Logically necessarily, if x is a perfect being and there is no best possible world, x creates nothing.

Moreover, on Leibnizian grounds, the following is very plausible:

6. Logically necessarily, if there is a perfect being and a best possible world, the perfect being creates the best possible world.

Putting (5) and (6) together, we get a way to both deny the necessity of (1) and a way to know that (1) is true. First, there is no finite proof that there is a best world. Any proof would require comparisons between infinitely many worlds and would, plausibly, be an infinite proof. So it is not logically necessary that there is a best world or that God creates the best on Leibniz's finite-proof understanding of necessity. Second, because we can know with certainty that God created something (argument: necessarily, anything other than God is created by God; I exist and am not God because I lack many perfections; hence, something is created by God), by (5) we conclude that there is a best possible world, and by (6) that God created it.

I do not know if this line of thought is in Leibniz's texts, but I think every step in the story is one that he should endorse given his other views.