The Mathematical Approach

Below are the very first paragraphs of Robert Sokolowski's Introduction to Phenomenology.  What follows is, I believe, a critical distinction, and should probably explain why I personally take a non-academic approach to philosophy. Academic philosophy is inveterately "scholarly"; it seems to take the approach of a legal proceeding 90% of the time (actually, all the humanities seem to proceed this way, and certainly the so-called "human sciences").

"[A professor of mathematics and philosophy, Gian-Carlo] Rota had often drawn attention to a difference between mathematicians and philosophers. Mathematicians, he said, tend to absorb the writings of their predecessors directly into their own work. They do not comment on the writings of earlier mathematicians, even if they have been very much influenced by them. They simply make use of the material that they find in the authors they read. When advances are made in mathematics, later thinkers condense the findings and move on. Few mathematicians study works from past centuries; compared with contemporary mathematics, such older writings seem to them almost like the work of children.

"In philosophy, by contrast, classical works often become enshrined as objects of exegesis rather than resources to be exploited. Philosophers, Rota observed, tend not to ask, 'Where do we go from here?' Instead, they inform us about the doctrines of major thinkers. They are prone to comment on earlier works rather than paraphrase them. Rota acknowledged the value of commentaries but thought that philosophers ought to do more. Besides offering exposition, they should abridge earlier writings and directly address issues, speaking in their own voice and incorporating into their own work what their predecessors have done. They should extract as well as annotate."

A is A, and Truth is Truth; thus just as all mathematical truths are public, available to all, so should all philosophical truths be. The big difference, of course, and the place where philosophers get stuck, is that truth is "located" in propositions, and propositions are composed of words. And all the disputes among philosophers derive from disagreements over the meanings of words. Math doesn't have this problem because numbers are invariable; every number is identical to itself. Academic philosophy is, as I said, inveterately "scholarly" because the academician has tons of ground to cover about the philosopher(s) they're following before they can make their own case; they have to establish that, say, Aristotle in fact "meant" X rather than Y, before they can go on and proceed to "move forward." Though I am by no means fond of Logical Positivism, I can sympathize a great deal with the idea that in order for philosophy to proceed, the question of "various meanings" has to be excluded, that one needs the clarity in logical terms that one has in numerical terms. Ultimately, since words/terms are based on concepts which are in turn based on fact/reality, they do have a manifold of meanings, because reality is, as C. S. Lewis once put it, knobbly and complicated. Husserl's a priori of every object having a subject-relative pole for each subject (i.e., each person) makes matters even more complex because the activity of consciousness is even more complex than the object one is conscious-of. I think a metaphysical realism is the only way to achieve the kind of "progress" that Rota spoke of. The question of what something "means" will go on infinitely if it doesn't eventually reach an absolute ground of being-in-itself; our meanings, in other words, have to be based on beings, and thus we must strive to reach a meaning which is objective. If there can be no agreement as to meaning, no "progress" can ever be made; and if agreements of meaning are not founded on real objects, they are, as it were, meaningless. This, I take it, is the objection of Postmodernism, viz. that since we can't access things-in-themselves, we can never achieve objective truth and thus no progress of any kind will be possible. This is more or less the contrary to the Logical Positivist. The latter excludes meaning from the outset, and the Postmodernist says the meanings are infinite. What they both have in common is that they each think objective meanings are impossible. But each position is untenable because each of them rely on statements of their case which are formulated in terms that have meanings which they take to be communicable, and to achieve communication requires both parties appealing to standards which they both agree upon.  If meanings are arbitrary or factitious, they should never have been able to tell one another why or how they disapprove of one another.  Logical and metaphysical realism -- i.e., truth is found in propositions consisting of terms founded on concepts which are teleologically oriented to objective entities -- is the aurea mediocritas of the deficiency of Positivism and the excess of Relativism, and the only way to proceed philosophically.