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By Richard Tieszen
Providing a set of fifteen essays that take care of concerns on the intersection of phenomenology, common sense, and the philosophy of arithmetic, this booklet is split into 3 elements. half I encompasses a normal essay on Husserl's belief of technology and common sense, an essay of arithmetic and transcendental phenomenology, and an essay on phenomenology and smooth natural geometry. half II is targeted on Kurt Godel's curiosity in phenomenology. It explores Godel's principles and in addition a few paintings of Quine, Penelope Maddy and Roger Penrose. half III offers with undemanding, optimistic components of arithmetic. those are parts of arithmetic which are toward their origins in basic cognitive actions and in daily event. This a part of the publication includes essays on intuitionism, Hermann Weyl, the inspiration of optimistic facts, Poincaré and Frege.
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Extra resources for Phenomenology, Logic, and the Philosophy of Mathematics
Example text
The view that logic was concerned with mental processes and entities, as these would be studied in empirical psychology, was especially prevalent at the time. Frege railed against this psychologism about logic, and by 1900 Husserl also subjected it to extensive criticism. Logic is a formal, deductive, and a priori discipline, and as such it is distinct from all of the empirical sciences. Husserl’s critique of psychologism in particular broadens to include any effort to found logic on an empirical science.
Whereas mathematics and logic set the standard for what is clear, distinct, and precise, the empirical sciences deal with indistinct or vague typifications of or generalizations from sense experience. The empirical sciences depend on the inexact essences associated with sensory objects. Even though the empirical sciences may be vague in this way and trade on various contingencies, they will presuppose various kinds of essences and essential truths. It is this latter ‘material’ a priori domain that will form in each case the subject matter of a regional ontology (which then has lying behind it the purely formal level).
In the theory of manifolds, however, the term axiom does not signify judgments or propositions but forms of propositions, where these forms are to be combined without contradiction. In the same vein, Husserl speaks of emptying the meaning of mathematical natural science through ‘technization’. Through calculating techniques we can become involved in the mere art of achieving results the genuine sense and truth of which can be attained only by concrete intuitive thinking actually directed at the subject matter itself (Husserl Crisis, § 9g).