(February 4, 2022 at 9:29 am)polymath257 Wrote:(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.
Yeah Godel is who I had in mind when I asked. Because he tried (and failed) to unite the two. I might be oversimplifying here... not too familiar with Godel's work...
But I now realize I mis-worded my question. Maybe I should have asked: "Treated strictly, should logic be considered part of math?" Logical fallacies needn't be included because that's more so about the foibles of our human brains. And things like geometry needn't be considered logic.
Aside from thinking of Godel, I was thinking that some discrete mathematics reminds me of logic, while symbolic logic reminds me of math.
