My Mom told me that "there's always somebody better than you!". I was thinking if that was true or not because there are not an infinite number of people in the world, so at some point you will reach somebody who is the best, right? For example, if person A was the best person at art in the world, there wouldn't be anybody else who can possibly be better at art than them.

Perhaps you are very gifted and your mother was humorously commending humility. Maybe you won an award and she did not want you to think you were the best and could therefore retire. In any case, on the matter at hand: if your mother told every (to use your example) artist that there was always somebody better than that artist, then there would indeed have to be infinitely many artists --just as there cannot be a greatest possible number, there could not be a greatest possible artist. Going further, if we have reason to believe there are finitely many artists (which we do), it would be hard to argue that there must be a single best artist. There might be many equally talented artists. Also "if person A was the best person at art in the world" there might be many artists who can POSSIBLY be better at art than them, but they never try to be. PS: I suggest that you may be good at something and nobody could be better: being you.

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...