Remarks on the philosophy of mathematics ( 1969 )

When we compare mathematics with logic in regard to the role these two domains of knowledge [Erkenntnisgebieten] are assigned to within philosophical thinking, we find a disagreement among the philosophers. For some logic is primary [das Ausgezeichnete]; for them, logic in the wide sense is the λóγoς, that what is rational, and logic the narrower sense is the inventory [Bestand] of elementary insights which should lie beneath all considerations [Überlegungen], i.e., the inventory of those truths that hold independently of any particular matters of fact [Sachhaltigkeit]. Thus, logic in the narrower sense (“pure logic”) has a primary epistemological status. A different starting point [Ausgangspunkt] takes the method of mathematics as exemplary [als Vorbild] for all scientific thinking. While that which is logical [das Logische] is regarded as self-evident and unproblematic [unproblematisch] from the first point of view, from the second point of view that which is