New Directions in the Philosophy of Mathematics [antikvár]

PrefaceThe origin of this book was a seminar in the philosophy of mathematics held at Smith College during the summer of 1979. An informal group of mathematicians, philosophers and logicians met regularly to discuss common concerns about the nature of mathematics. Our meetings were alternately frustrating and stimulating. We were frustrated by the inability of traditional philolsophical formulations to articulate the actual experience of mathematicians. We did not want yet another restatement of the merits and vicissitudes of the various foundational programs platonism, logicism, formalism and intuitionism. However, we were also frustrated by the difficulty of articulating a viable alternative to founda-tionalism, a new approach that would speak to mathematicians and philosophers about their common concerns. Our meetings were most exciting when we managed to gUmpse an alternative. Occasionally some reading would suggest a new perspective on mathematics or pose fresh problems with philosophical merit and mathematical relevance. Then the philosophy of mathematics would seem to come alive again.Toward the end of the seminar, my colleague, Stan Stahl, mathematical logician turned computer scientist, suggested the idea of an anthology of readings suited to the modern reader. From the first, we conceived of the anthology as a bridge hnking those disciplines concerned with the general character of mathematics. So we insisted that it include representatives from mathematics, philosophy, logic and related fields. In addition, we preferred accessible articles written in English or generally familiar notations. It seemed prudent to direct the essays to a sophisticated amateur since most of us are only amateurs in at least one of the fields relevant to the philosophy of mathematics!Originally the anthology was to be divided into three major sections. The first was a group of essays that challenged the dogmas underlying founda-tionalist views of mathematics. The second focused on mathematics as actually practiced, thereby reexamining the data from which the philosophyIX