Re: Gödel’s Lost Letter • The Graph Of Math

GLL:

Kurt Gödel is said to have been a latecomer to appreciating the power of Model Theory.  He was of course the greatest architect of Proof Theory, which stands in contrast to Model Theory.  Model Theory concerns itself with what could be true, while Proof Theory deals with what can be proved.  The latter sounds more definite, but they are supplementary:  a statement is capable of being true somewhere precisely when its negation cannot be proved.  The question is, where is that somewhere?  And when?

What — if anything — is the common sense that connects the different senses of the word model, as it has been used over the years in logic, mathematics, and the special sciences?  It’s a problem I’ve been running into for several decades now and I think I can trace the roots of it going back as far as Aristotle’s treatment of analogy.

Resources

• Functional Logic • Inquiry and Analogy
• Survey of Abduction, Deduction, Induction, Analogy, Inquiry

cc: Academia.edu • Cybernetics • Laws of Form • Ma^thstodon
cc: Research Gate • Structural Modeling • Systems Science • Syscoi