How important is a solid understanding of Logic

[Nyxie]

How important is a solid (or better) understanding of Logic, especially Symbolic and Mathematical, for an aspiring mathematician? For a physicist? Other scientists?

Are there variations in how important it is for Analysis, Topology and Algebra?

A mathematically inclined physicist told me that Logic could "cut through" any mathematical argument.

An undergrad, I have little formal training in Logic and was wondering if I should take a Logic class, though it's not required for my degree (physics).

 

[micromass]

For a mathematician, I consider logic to be essential. Logic tells us what proofs are and which arguments are solid. Furthermore, it would be quite difficult to do things like set theory and topology without a decent understanding of logic and things like truth tables.

For a physicist, I think logic is a bit less important. Physicists are less obsessed with proofs and have no need to understand mathematics as deep as mathematicians do (unless you're aiming to be a mathematical physicist). So, if I were a physics major, then I would take more useful classes than logic.

Unless you're really interested in logic and the structure of logical arguments, of course. Then you should take it by all means...

 

[Stephen Tashi]

How important is a solid (or better) understanding of Logic, especially Symbolic and Mathematical, for an aspiring mathematician? For a physicist? Other scientists?

A solid understanding of logic is important for mental stability of anyone who tries to think and reason about the world, even if the thinking is being done about politics or religion. The main gift of understanding logic is not that it leads to any definite conclusions about the world. Instead, it makes clear how much carefully reasoned theories of the world must depend on assumptions and subjective judgements.

A particular technical aspect of formal logic that is useful in mathematics is the logic of quantifiers. There are some rare human beings who can navigate through proofs involving "for each epsilon" and "there exists a delta" without any formal training in quantifiers. Most people are greatly in need of help.