Because philosophy is too imprecise. When you dig down to the most fundamental concepts of CS you end up in what is usually considered the territory of philosophers, only with a better mental toolkit to explore it.
There is an interesting paper by Scott Aaronson about the intersection of those two disciplines and how the more CS-y approach can help solve philosophical problems:
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.
Have you taken a philosophy department logic course? I learned way more useful logical thinking in philosophy classes. My CS classes didn't even come close. Sure I learned to make a mindless machine calculate the proper result, but that's far less important than reading the writing of another person an being able to understand their ideas.
I think it is interesting to note here that there are a number of people who are well regarded as computer programmers who have degrees in philosophy. I wish I could remember who they were at the moment.
Then you have never taken a philosophy course in a western analytic department. The "Logic" that's used in computer science is a very small part of all possible logics. The discipline of logic is studied and expanded almost exclusively by philosophers. Computer Science Logic is to Philosophy what Physics is to Mathematics.
That's interesting. Is it because these other forms of logic can not be implemented on a computer in a straight forward way, or because computer scientists are just ignorant of these other possible logics?
Well one feeds into the other. Computer scientists just have no real use for them. They can't be straightforwardly modelled on a computer nor are they straightforward models of computers.
That isnt to say there are no uses of them in CS or that CS ignores them all. But many systems were invented to deal with explicitly philosophical problems (eg. modal logic for metaphysical necessity, para-consistency for paradoxes, etc.).
In some very specialized areas non-standard logics do get used (theorem proving uses intuitionist logic, AI/Machine Learning might use fuzzy, etc.) but its still a limited subset over all.
No doubt, in heavily mathematical CS departments there might be courses on logic in a more complete sense.
CS researchers do develop logical systems of a kind: in particular they have developed ways of writing logic systems programatically (and usually end up having to ditch a few things and thus invent a new system).
However if you bought any major books on logic (as a subject) or looked into any contemporary research in logic (as a subject, not "doing logic on an ARM, etc.") you'd find the authors were philosophers. Occasionally mathematicians, and esp. mathematicians who then became philosophers.
There are a lot of logic systems out there, and we tend to use ones that have happened worked out, and momentum builds. Of course, sometimes things are missed because our chosen tools are inept for some problem. Those are usually only solved with paradigm shifts.
You can also study there via a math department and have a more obviously rigorous path.
Edit: to be clear, I didn't mean to imply the philosophy dept isnt rigorous, but instead, merely, that nearly the same classes would be offered in each dept and math, unlike philosophy, suffers from the perception of being too formal if anything.
I think it's a common misconception that philosophy is an imprecise discipline. I think what makes people think that is the fact that often philosophy deals with topics that have not yet been (or may never be) formalized.
There is philosophy and there is philosophy. What a lot of laypeople have experience with is mostly the type of philosophy that is just meandering with thoughts and overanalyzing the meaning of words to the point of breakage. I think this is the part that makes many people treat the word "philosophy" as synonymous with "nonsense".
I agree that philosophy often deals with topics that have not yet been properly formalized - after all, this is the discipline that's on the frontlines of important problems, asking questions that later get answered with more formal approach.
There is an interesting paper by Scott Aaronson about the intersection of those two disciplines and how the more CS-y approach can help solve philosophical problems:
http://www.scottaaronson.com/papers/philos.pdf.