A memory of Frederick Fitch (1) Heaven

When I came to Yale in 1966 I was the most junior of our little logic group there and Frederick Brenton Fitch was the most senior. Fitch was only one of the very unusual people I found at Yale, but he was ‘the’ logician, and I learned some very strange things from him. So I am going to start with personal memories of Fitch, and then take that as departure point for bits of logic that have fascinated me ever since.

Fitch was a gentleman, and a gentle man, with a deceptively understated sense of humor. He would tell us very calmly things that you’d think any logician would scream at. Our little group — Rich Thomason, Bob Stalnaker, Charles (Danny) Daniels, Bob Fogelin, Fred Fitch, and me — would meet for lunch, practically every day because Yale provided that free for us. On one of the first days Fitch mentioned quietly that he was sure he would go to heaven. After all, he said, he had done something for God: he had proved his existence.

It seemed that each year he would end his seminar by proving God’s existence. On that first occasion, though, he confessed that he was still not satisfied with his proof, because by his reasoning, God turned out to be a relation. But before I left Yale, and I asked him about it, he was satisfied: in his improved proof, God turned out to be a proposition. Not just any proposition, but the one true proposition that implies all true propositions — which, he said, was surely so special that it deserved to be worshipped.

Today Fitch is especially known for the Knowability Paradox. It’s called a paradox, but he offered as just a straightforward proof, that if all truths are knowable then all truths are known. Articles about this have never stopped appearing, even now, more than thirty years after his death. Self-reference was another of his topics, and we all vied to explore its paradoxes. Danny came to lunch very excited one day, brandishing a piece of paper, saying “I’ve just proved that God is not omniscient!” On the paper he had written

This proposition is not known to be true by anyone.

If it is false, then obviously it is not known to be true by anyone, so what it says is the case, so it is not false. Fine, it is not false — therefore it is true. Being true, what it says is the case, so it is not known to be true by anyone. Here is a true proposition that is not known even by God! Corollary: God is not omniscient!

Danny, Danny, we said, God was listening, so now he knows! Well, that led to more paradoxical conclusions ….

Talking with Fitch about his proof of the existence of God as a proposition, however silly that seemed (and Fitch’s gentle smiling rendition was perhaps a bit like that secret smile that was becoming quite prevalent in those mid-sixties) was perhaps the most memorable of all the signposts to alternative ways of thinking about language and logic. At first blush it may not look like much of a muchness, to think about interpreting language in terms of propositions rather than truth-values, universals, worlds, what have you … But when you start, there is a lot there …

So I’ll write the next post about some of that