Further to my last post about categoricity in relation to the Fraenkel-Carnap problem, I found a couple of interesting papers on the history which provide technical background.
My very concise "explication" of categoricity (and related concepts) can be seen spelt out more fully and very clearly by Awody and Reck in:
Completeness and Categoricity, Part I: 19th Century Axiomatics to 20th Century Metalogic with the history continued in Completeness and Categoricity, Part II: 20th Century Metalogic to 21st Century Semantics.
I have not read much yet, and I'm sure that it soon gets tough going, but it starts off gently, and comes in early with two points which I like.
The first is to point out the importance of Fraenkel and Carnap to the development of these topics. The second is to say that higher order logics are good and that the tendency in parts of mathematical logic to focus exclusively on first order logic is not so good, either from the point of view of historical or contemporary understanding.
RBJ
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Good. I am a Victorian in orbit at heart, so ANYTHING with an air of nineteenth-century philophy (or logic) about it appeals me! I'm writing this today when if you enrol to a course in logic, the fact that you have, say, the 6th printing of the 2th edition of the instructor's favourite manual will NOT get you a passing grade, since he will enforce you to buy or somehow acquire the 3rd printing of, of course, the fourth edition!
ReplyDelete---- Give me a break! I LOVE history of logic! It puts so much scholasticism of the worst type in a better perspective!