Almost twenty years before I met Fitch, he had published what he described as an empirical, a posteriori, proof of the existence of God:
“On God and Immortality”. Philos. and Phenom. Research 8 (1948), 688-693.
In that proof God had turned out to be a theory.
At first blush the argument looks, besides having a conclusion entirely irrelevant to religion, not just simplistic, but dated, and most likely trivial. However, I became quite intrigued with the argument when I started asking myself what unstated assumptions Fitch was bringing to bear. Most especially, what must the language be like in which such an argument could be formulated?
I began to realize that it was a shot fired in the war Curry and Fitch were waging with a conventional wisdom derivative from Tarski and Carnap.
The crucial claim in this paper, argued to be well confirmed, indeed as well-confirmed as any empirical theory could be, is that every class of facts in the universe has an explanation.
Reading his preliminaries we are at once taken aback by how explanation and confirmation are defined. Explanation is equated with implication by a consistent theory, and confirmation with positive instances. But this was a time when the agenda for those notions was set by Hempel, and they were acccepted in the literature just as Fitch presents them.
His one departure from the orthodoxy of the time was this: a fact disconfirms a theory X iff it confirms some theory inconsistent with X. Thus confirmation and disconfirmation may come at the same time! Many facts confirmed both the Ptolemaic and Copernican theory, and thus disconfirmed both of them as well.
The crucial claim looked trivial. It is critique rather than applause for Freudian theory when people say it explains everything. Also, I’m used to reading “theory” in the way, introduced by Tarski in his ‘calculus of systems’, as “set of sentences closed under deduction, i.e. containing all its own consequences”. Then if Z is any set of true sentences the deductive closure of Z is a theory, which implies — and so, by the above definition, explains — all of Z. Trivial! But Fitch has a stronger, more demanding concept of theory, requiring a character familiar in philosophy of science:
“A theory is a proposition (that is, an hypothesis) which involves no mention of any particular thing, event, or moment of time, though propositions mentioning particular things, events, and moments of time may be deducible from it.”
So read the crucial claim is not trivial, but looks obviously false, as long as explanation equated to implication. For a theory of this sort will not imply the sort of singular facts that scientific theories take as data or boundary conditions. To be charitable, let’s just say that Fitch needs a considerably more sophisticated concept of explanation, to run his argument. A theory of that sort might unify a whole realm of particular facts in a way that could count as explanatory, for example. But the details in Fitch’s deductive steps in the overall argument do not hinge on this, anyway, so, charitably, let’s continue.
Now Fitch formulates a theory that will bear the brunt of his reasoning, the theory S:
“Let us designate by S the proposition that every fact or class of facts has at least one explanation. The proposition S is a theory because it does not mention any particular thing or any particular event or any particular moment of time. The proposition S is also clearly consistent; hence it is an explanation of any fact that it implies, and any such fact is a con- firmation of it.”
S is an empirical theory, and is very well confirmed, he argues. For it is confirmed every time any theory is confirmed, any time when any class of facts is explained. And even if some theory is disconfirmed, which is a disconfirmation of S as well, by definition some other theory was confirmed, and that is an additional confirmation of S. Hence S is as well confirmed as any theory is, was, or ever will be! This conclusion is going to have remarkable consequences.
But stop, for a moment: what is the language like in which this argument is conducted?
S is a theory about theories, for it says that fore every class of facts there is a theory that explains that. To introduce this is not just to assume that theories can be formulated in the language in use, but that they can be talked about in that language. And indeed, S itself purports to be one of those explaining theories, about the class of facts which involve relations between facts and theories, so it is also about itself. This is where we see the contra-Tarski theme of many of his writings: our language is one in which much of the semantics of that very language can be formulated.
Theories are sets of sentences in this language, but here it is presumed possible to talk about theories in general in this language, about implication in the language, about relation to facts, about truth and falsity. So to a significant extent, it is possible in this language to talk about that language itself, about a great deal of what we would classify as belonging to its semantics.
Thus Fitch is relying on something he argued for , notably in “Universal metalanguages for philosophy” and “Self-reference in philosophy”. (I’ll have to devote another post to this!) It is part of the controversy in which Curry and Fitch were on one side, and the only side now generally accepted or even known at all, was Tarski’s.
Well, let’s quickly finish up with the startling consequences of theory S, including the existence of God:
“A corollary of S is that the class of all facts has an explanation.”
Is it possible to talk about the class of all facts, in his language in use, given that he equates facts with propositions, and propositions with what his sentences express? Paradoxes threaten, but they are just the paradoxes that he takes himself to have solved or dissolved or otherwise avoided, in his conception of language.
Let us call an explanation of the class of all facts an ultimate explanation . That there is such an explanation, Fitch argues, “means that the universe as a whole is a system”.
He derives at once that an ultimate theory, by definition consistent, must be true, for if it implied the contradictory of any fact it would still have to imply the fact itself (since it implies all facts), and so would be inconsistent. Furthermore, it is unique:
“there can be only one true explanation of all the facts in the universe, for if there were two different explanations, the fact that one of the explanations was true would be a fact to be accounted for by the other explanation, and so the two explanations would imply each other and hence be equivalent.”
And this ultimate explanation, that we must all agree to call God. For it is the “guarantee that no event in the universe is altogether without connection and relevance to the over-all scheme of things” — what else, then, could it be, other than God?
Of course he sees the obvious objection. Whatever the conception of God might be, it is not a conception of a mere theory! But, Fitch says, this is not a mere theory! For it is true and it is the ultimate explanation of everything.
To his commentator Charles Baylis at the APA, who did not see anything worthy of worship in even such a theory, Fitch retorts:
“I grant that my conception of God as the ultimate system in the universe differs considerably from the anthropomorphic conception of deity held by many people in both primitive and modern times. God seems to me indeed worthy of worship, but my account of the nature of worship cannot easily be summarized here.” (same journal and issue, page 698)
I kept an eye out for the secret smile that I suspected behind much of what Fitch used to say, in his characteristically gentle, courteous voice. But sometimes it is hard to see.
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