The Mathematician’s Approach

Philosophy in contemporary academia is inveterately ‘scholarly’, much of the time seeming to take the approach of a legal proceeding rather than a speculative inquiry into the nature of things. In fact, much in the humanities these days appears to proceed in this fashion—which seems rather contrary to their original spirit—and certainly all of the so-called ‘human sciences’ (e.g., psychology, sociology, etc.). Just below are the very first paragraphs of Robert Sokolowski’s Introduction to Phenomenology.  An important distinction is introduced here, one which suggests some of the rationale for why one may wish to take a more non-academic approach to philosophy.

“[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 very many disputes among philosophers derive from disagreements over the meanings of words, which denote terms  (in the logical sense). Mathematics does not have this problem because numbers are invariable; every number is identical to itself. Academic philosophy today largely takes the ‘scholarly’ approach because the academician has a substantial amount of ground to cover about the philosopher(s) they’re following before they can make their own case; they have to establish that, say, Plato “‘really meant’ x, rather than y,” before they can take on any forward momentum.

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 and terms are based on concepts which are in turn based on fact and reality, they do have a manifold of meanings — for reality is, as C. S. Lewis once put it, “knobbly and complicated.” Husserl’s  a priori  principle that every object has a ‘subject-relative pole’ (i.e., a personal consciousness) makes matters even more “knobbly” because the activity of consciousness is arguably even more complex than the object one is conscious-of.

An ontological realism is the only way to achieve the kind of philosophical progress of which Rota spoke, that which would be analogous to progress as it occurs in mathematics. The question of what something ‘means’ will go on indefinitely if it does not eventually reach an absolute ground of being-in-itself: our meanings, in other words, must be founded upon beings — we must strive to reach meanings which are 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, indeed, meaningless. This, presumably, is the objection of Postmodernist Relativism, 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 Logical Positivism. The Positivist excludes meaning from the outset, while the Relativist says the meanings are infinite. What they both have in common is that they each think objective meanings are impossible. Both of these positions are untenable, however, for the very reason that each of them relies on statements of their case which are formulated in terms that have meanings which they presuppose to be communicable, and to achieve communication at all requires that both parties appeal to standards upon which they both implicitly agree. In other words, if meanings are arbitrary or factitious, the Positivist and the Relativist should never have been able to tell one another why or how they disagreed with one another!

Realismlogical and ontological — i.e., truth is located in propositions consisting of terms founded upon concepts which are teleologically oriented to, and abstracted from, objective entities — is the aurea mediocritas  between the deficiency of Positivism and the excess of Relativism, and the only way to proceed philosophically if one opts for the mathematician’s approach described by Rota.

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