I guess there are a lot of STEM people that have never taken a course in first/second order predicate calculus, which is usually lumped in under philosophy. The field of computer science builds on and is rather indebted to philosophers such as Wittgenstein and Godel; their finds provide the theoretical background for all modern theoretical CS.
While what they teach at the university today for a philosophy degree may let you focus on things that look imprecise, I find your statement is rather ironic. The difference between someone, especially coming out of school, who is well versed as a logician (hint they may have a math degree, but it's still philosophy) versus some one who has been exposed only to computer science, often parallels what I have seen interviewing people with a physics background versus an engineering background: almost all of the time the engineer might be able to give you enough to solve many of the problems, and have a little background, but the physicist will typically have a far stronger "toolkit" to analyze the problem, especially when the problem is novel. So goes it with a CS grad versus a math grad, typically around here, though YMMV.
Not an accident. Maths is philosophy in the same sense that physics is philosophy (in fact it was called "natural philosophy"): both are subsets of the general thing.
Philosophy is the "science of everything", and as such, all fields of (western, academic) knowledge are considered parts of it. Math in particular is formally equivalent to logic, which is the universal language on which philosophy is written.
While what they teach at the university today for a philosophy degree may let you focus on things that look imprecise, I find your statement is rather ironic. The difference between someone, especially coming out of school, who is well versed as a logician (hint they may have a math degree, but it's still philosophy) versus some one who has been exposed only to computer science, often parallels what I have seen interviewing people with a physics background versus an engineering background: almost all of the time the engineer might be able to give you enough to solve many of the problems, and have a little background, but the physicist will typically have a far stronger "toolkit" to analyze the problem, especially when the problem is novel. So goes it with a CS grad versus a math grad, typically around here, though YMMV.