Constructions as the Subject Matter of Mathematics

Abstract

The vision informing 20th Century philosophy has been aptly described as one of a desert landscape. Philosophers behave as if in expectation of an ontological tax collector to whom they will owe the less the fewer entities they declare. The metaphysical purge is perpetrated under a banner emblazoned with Occam’s Razor. But Occam never counselled ontological genocide at all cost. He only cautioned against multiplying entities beyond necessity His Razor is thus in full harmony with the complementary principle, known as Menger’s Comb, which cautions against trying to do with less what requires more. The two methodological precepts are just two sides of the same coin.