(February 4, 2022 at 1:14 am)vulcanlogician Wrote: Is math identical with logic?
If not, what distinguishes the two?
There are a number of differences.
For example, the study of logic.al fallacies (ad hom, etc) would not be considered a part of mathematics. It is often considered to be a part of logic, however.
On the other hand, *formal* logic can be considered a topic in mathematics: it is the study of a formal system. So, Russell and Whitehead were doing both logic and math when they wrote Principia Mathemtica.
Typically, the distinction between logic and math is placed in such a way that logic gets the propositional and quantifier calculus and the study of equality and math begins when sets are considered.
Even so, there is a lot of overlap between logic and the foundations of math. Godel is usually regarded as a logician, for example, even though he studied set theory and model theory. By the time of Cohen and Shelah, though, set theory and model theory were seen as definitively inside of math.
On the flip side, topics like abstract algebra, topology, differential geometry, etc, are never considered to be part of logic, even when they enter into the arguments for set theory or model theory.