First, is it true that academic philosophers reside in ivory towers? And that their ivory tower is filled with books and greek sculptures? Second, There seems to be an interesting feature of many logicians or philosophers of language, that they have a background in the field of mathematics or being related to the field of mathematics in some other way. Is this in your opinion a coincidence? Does the field of mathematics grant those capable of handling it some clarity of mind or perspective in observing the world? This could be interpreted as a question to what sort of intelligence, if any, is more favorable to logicians and philosophers of language(presupposing that the distinctions made in the theory of multiple intelligences hold). It was an interesting and, in my opinion, true prediction of Alfred N. Whitehead when he said that science in its evolution becomes more and more mathematized.

As for the first question, I do (as it happens) work on a college campus in which my office is in an ivory covered building with a tower, and there are some Greek sculpture here and there on my floor, though the most common things (except for other professors, students, books, furniture) in our department are dozens and dozens of owls (symbol or wisdom), owl statues or as dolls, etc. But speaking to the ivory tower as a metaphor, I think philosophers today and certainly at many points historically, very much engage the world and culture at large. Socrates did philosophy at the market place, and now there are many philosophers who seek to engage others through popular culture, their courses that involve very practical moral concerns (e.g. bio-medical ethics, environmental ethics, courses on just war theory and so on), and in publications that have a wide, educated readership (e.g. New York Review of Books, Times Literary Supplement, and so on).

On the second point, I think it is rare to find a philosopher who is strong in logic but weak in math or vice versa. Both do employ some level of abstraction and formality that make the two areas good, if not overlapping neighbors. As for philosophers of language, some have strong backgrounds in logic and math, but I do not think this is as obvious. Philosophers of language are sometimes impressed by the vagueness of our terms and modes of references; to be sure, they want to be as clear as possible about the nature and scope of vagueness (a popular topic at the moment), but philosophers of language as well as those in logic sometimes make a point of recognizing when clarity (you refer to "clarity of mind or perspective in observing the world") is elusive. There is even an area of logic called "Fuzzy Logic" that addresses what some call "fuzzy sets." In classical logic, there is a tendency to adopt the law of excluded middle (everything is either A or not-A), but in more modern times some of us have come to see that an object might be a member of some set to some degree, and this is not an all or nothing matter. For an interesting book that argues that vagueness is a matter of our ignorance, see T. Williamson's Vagueness (Routledge 1994).

I appreciate your appreciation for Whitehead's observation, which I share. I might only add that the increased mathematization may sometimes be a reflection of more precise ways of mapping out a world that could turn out to be indeterminate, at least at the sub-atomic level, and resistant to certain predictions. In a word (well, actually in several words), we may need more math in order to think probabilistically rather than to think in ways in which we could predict with iron clad certainty the ways of the world. (I am not suggesting you disagree, just adding a thought which I hope might stimulate further thinking.)

Maybe to connect the various topics your questions raise: I suggest that it is because philosophers today tend not to be in (metaphorically) ivory towers, but connected with current science, events, issues, that the task(s) of philosophy are so exciting. We want to understand logic, math, language, science, as it is actually practiced as well to explore the implications of such practices and future developments. Also, philosophy often seeks to be integrative or to explore integration: how might different modes of inquiry (math, logic, natural and social sciences, the humanities) interrelate?

Good wishes in your own inquiries!

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