Uh, logic is a branch of mathematics. From wikipedia:
Logic is the study of the principles of valid demonstration and inference. Logic is a branch of philosophy, a part of the classical trivium, as well as a branch of mathematics.
Only by tradition, and in my experience the philosophy department only teaches the class that serves to introduce formal logic to all undergrads. Philosophers deal with words. They like to discuss the various ways a verbal problem might be reduced to logic, and they might be interested in what can be said (in terms they already use) about a system of logic, but that's the limit of their interest. If you take a graduate-level math class in logic (or metamathematics or foundations or whatever your local math department calls it) or even if you just take an upper-division set theory class, you'll learn more about mathematical logic than anyone in the philosophy department wants to know.
Most or all undergrad pure logic classes, as far as I've ever seen. There aren't usually a whole lot of pure logic classes, so it's entirely possible that your school(s) might only have had one.
Philosophers deal with words.
Philosophers deal with logic in arguments. I took a couple logic classes during my undergrad and they were entirely symbolic logic. I also took a couple philosophy classes, and they used symbolic logic extensively to describe the flow of logic in arguments. Skimming through MIT OpenCourseWare indicates it's similar there: http://is.gd/qaE0
If you take a graduate-level math class in logic ... even if you just take an upper-division set theory class, you'll learn more about mathematical logic
So you are saying that heavily mathematical logic is more heavily mathematical? Interesting. Do you also learn about tautologies in these classes?
I'm guessing that you are actually implying that mathematical logic is more useful to programmers. As I stated elsewhere, during my undergrad I took classes that touched on both philosophical and mathematical logic concepts and I definitely find myself using both. In my experience: symbolic/philosophical concepts in high level development, symbolic/mathematical concepts in low level development.
The distinction I'm making is between logic that is purely symbolic, where conclusions follow mechanically from assumptions and rules, and logic that is applied to verbal argument. You can describe verbal argument using symbolic logic, but applying symbolic logic to words easily results in ludicrous conclusions unless you apply other filters.
I'm not saying that mathematical logic is more heavily mathematical, I'm saying that philosophers are only interested in mathematical logic concepts they can extract from their mathematical context and apply in words. Aside from that, they are not interested in mathematical logic at all. Whether they are interested in mathematically defined concepts such as "complete," "consistent," and so forth depends entirely on whether the concepts have suggestive names that seem to imbue mathematical results with meanings beyond mathematics.
I'm arguing that the application of logic to arguments and ideas that was part of philosophy has greater impact on high level application design and architecture than math. Taking a real world concept, need or set of actions and translating them into a structure that can be constructed with a programming language uses logic in fundamentally the same way philosophy does, although in an academic setting this area is computer science. Math is most useful at an implementation level, generally coming into play when dealing with components, algorithms and other more narrow implementation details.
The point is that logic used in computer science/information science is a hybrid that is informed by other forms of logic (including linguistics), not just math.
I'm saying that philosophers are only interested in
I don't know what philosophers are only interested in because I don't know what a "philosopher" is.
I think I misunderstood you; I thought you meant mathematical logic (the kind that can be generated mechanically from axioms and rules) and not the kind of logic that requires judgment and applies to words and concepts. If you meant the second kind, then I retract what I said. But you did say, "formal logic, with symbols," and that kind of logic is a pretty weak tool to apply to arguments and ideas.
As for what a philosopher is, we're all philosophers, but not all of us get paid for it.
That raises an interesting question, doesn't it? I wonder how many mathematicians turn out to be good programmers vs how many philosophers turn out to be good programmers?
From experience, I have concluded that whether mathematicians become good programmers depends on whether they have an engineering aesthetic. Mathematical elegance and engineering elegance are not exactly the same thing. A mathematically trivial solution can be a huge practical mess. Mathematicians with no engineering aesthetic can't see the difference and tend to produce big blobs of unmaintainable code. Mathematicians with an engineering aesthetic are some of the best programmers I've worked with.
I've only worked with one philosopher. He's very creative and produces reams of working code, but new requirements always mean new reams of code. Everyone suspects there must be a lot of redundancy in his code, but then, nobody has needed to look, because it all works....
Logic is the study of the principles of valid demonstration and inference. Logic is a branch of philosophy, a part of the classical trivium, as well as a branch of mathematics.