Remarks on the philosophy of mathematics ( 1969 ) Paul

When we compare mathematics with logic in regard to the role assigned to these two domains of knowledge within philosophical thinking, we find a disagreement among philosophers. For some logic is singled out; for them, logic in the broader sense is the λóγoς, that what is rational, and logic in the narrower sense is the inventory of elementary insights which should lie beneath all considerations, i.e., the inventory of those truths that hold independently of any particular factual content. Thus, logic in the narrower sense (“pure logic”) has a primary epistemological status. A different starting point takes the method of mathematics as exemplary for all scientific thinking. While for the first point of view the logical is re[1] garded as the obvious and unproblematic, for the second point of view the mathematical is epistemologically unproblematic. Accordingly, understanding is ultimately mathematical understanding. The idea that all rational