The contemporary situation of
philosophical logic.
(Psychologism and the question of truth)

Logical Investigations grew out of efforts to provide philosophical clarity to pure mathematics. Husserl, who originally was a mathematician, was led to some principled considerations about the basic concepts and laws of mathematics, and as he said, he soon realized that logic in our day fell short of being an actual science and thus that the fundamental resources of logical reflection lagged behind the basic concepts of the sciences—especially in this case, of mathematics. He was faced with the question of the specific kind of conceptuality and ways of proof, and the significance of knowledge and truth in mathematical cognition. Finally, he came to reflect on the universal essence of mathematics, which had become all the more complicated insofar as Cantor’s development of a pure theory of groups had shown that authentic mathematics was constituted not by the quantitative but by the formal and its law-giving character. So his reflections as a whole came to be focused on the question of the meaning of truth, and especially on the meaning of formal truth. In the beginning, around the 1890s, Husserl tried to carry out these philosophical reflections by means of the traditional philosophy of his day, that is, predominantly by way of so-called psychological reflections. Using a psychological analysis of mathematical thinking, he tried to get behind the specific structure of mathematical objectivity.

But he soon saw the principled difficulty contained in this analysis: Granted that mathematics does not attempt to understand empirical facts, is it even possible to establish [32] something fundamental about this science by using psychological ideas, that is, explanations ordered to the empirical sciences? By arguing out these basic questions, he finally came to realize that psychology has absolutely no qualification to be the science that can aid us in discussing questions like the structure of mathematics and of mathematical objects. Husserl’s impartial pursuit


Martin Heidegger (GA 21) Logic : the question of truth

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