Formal Philosophy for Dummies

For dummies like me, that is.

Inspired by the populist orientation of the new "Masses of Formal Philosophy" project, I'll be serially posting my answers to the survey questions over the next five days.

1. Why were you initially drawn to formal methods?

I always loved math as a kid. Part of the draw was that it was definitive: unlike literature and social studies classes we could propose a definitive answer. It's not at all that I thought there weren't definitive answers in those other fields, it's just that we couldn't often give them.

So mathematics was my first introduction to the notion of formal reasoning, reasoning that was precise and canonical. Both the answers and the reasons could be stated crisply and clearly (in the range of math we did). Most importantly, the answers could be verified or refuted. Perhaps my interest was and is the result of an overly retentive or competitive personality (wouldn't be the first time that answer was proposed), but I thoroughly enjoyed the closure of coming to the solution of an equation.

On the other hand, there was plenty of mystery there as well. Even to a seventh-grader in a school in one of the most rural sections of the Midwest--the school was literally (in the literal sense of "literal") on grounds which were a block carved out of a corn field, and farm kids were bussed in from miles around from all four directions--as I say, even to one in my limited circumstances it was clear that the world of mathematics promised plenty of intrigue.

When I accidentally discovered non-Euclidian Geometry trying to solve a puzzle in seventh grade I was told to stay in from recess until I would stop being a smartass. (I don't recall the exact words, but the teacher thought I was toying with her and then it got heated.)

When I started poking around I found that--rather than being moribund--mathematics was full of mysteries, paradoxes, unsolved problems, and unexplored territory I was at first shocked--"how can there be disagreement or ambiguity even here"--but then fascinated.

Both aspects of formal methods fascinate me today in my study of philosophical logic and probability theory (motivated by the same problems as but coming to different conclusions than my teacher Henry Kyburg for whom the notion of a *canonical* proof is very important). I am fascinated by the obvious success of probability theory in an almost total absence of a solid semantic theory.

The mathematical theory of probability is straightforward but the interpretation and application of the formalism is a rich and diverse matter. And I am fascinated with the issue of how to adjudicate debates between alternative systems of logic, the so-called deviant logics and classical logic. I love fuzzy logic, but wonder if it isn't just a form of bayesianism by another name and I love supervaluationism and love the idea of setting fuzzy logic in a supervaluationist framework.

In some sense there is just One Logic underlying them all, I'm not a pure conventionalist. But on the other hand there are some domains of discourse which have different rules. Intuitionism might be appropriate for mathematics, but not for empirical discourse. How many more distinctions like this might there be? How to strike the balance between the absolute and the pragmatic still fascinates me the way it did when I was a kid.