Recent Parallels Between the Philosophy of Science and Mathematics
Following World War I European philosophy of science formed an alliance with mathematics culminating in an attitude of certainty and autonomy that rejected all non empirical claims to truth and purported to make all science presupposition less. The rise and fall of logical positivism has been one of the major themes of of twentieth century thought and illustrates the danger of placing too much emphasis on science and mathematics as an ideal for all knowledge. The restriction of rational inquiry to the modes of scientific verification and the processes of mathematical logic was far too confining for the containment of truth. Even after the rejection of logical positivism as a general epistemology on the ground that not all empirical knowledge was like scientific knowledge, it continued to survive as a philosophy of science and became the dominant influence on American science after World War II. Thus science became isolated from other realms of thought. This dichotomy has only recently been bridged by a more historically oriented approach. This paper discusses how the philosophies of science and mathematics have experienced a number of parallels in the development of these trends.