As an engineer I got into logic through the philosophy department. It was very eye opening for me.

Engineers are not models of logical thinking that they assume they are. Illogic is everywhere and it takes constant vigilance to avoid always going with your gut feelings.

In the very least, I think every engineer should take a "philosophy of science" class. We tend to focus quite intensely on how to do things. Borrow a little bit of "where do proofs and the scientific method sit in the grand pantheon of human knowledge" from philosophy is a bit grounding. Anyway it is probably a gen-ed that is at least somewhat useful.

It depends. Some people have really weak philosophical foundations and really need to hear about it if there is something out there that grounds them a bit better.

We can't say if any particular approach to life is the best, but we can say that if you change your mind about which approach is best at age 70 you've spent a lot of years setting up for the wrong outcome. It is never to late in theory. But as a practical matter 70 is a bit late to sit down, take a step back, ask why and try to act on it. Better for people to line themselves up with good foundations from their 20s or maybe 30s. It is good to explore the options early, and think a bit about what the word 'option' even means philosophically.

I agree. Philosophy gives you a level of abstract reasoning of the form: "if we agree (with Kant) that we should only take those actions which could be universal law, does it follow that the death penalty is morally justifiable?" There is some degree of reasoning from premises here, but all of the objects you deal with are things that you come into with a bunch of intuition that you never really leave behind.

On the other hand, something like:

> Given a one-dimensional invariant subspace, prove that any nonzero vector in that space is an eigenvector and all such eigenvectors have the same eigenvalue.

really forces you to grapple with an entirely different level of abstraction