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.
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.