By Pierre Wagner (auth.)
The e-book includes a chain of chapters on Carnap's excellent of explication in its place to the naturalistic conceptions of technology, atmosphere it in its old context, discussing particular circumstances of explications, and enriching the on-going debate on conceptual engineering and naturalism in analytic philosophy.
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Additional resources for Carnap’s Ideal of Explication and Naturalism
An explication of Becker’s philosophical thought will help us to mediate between the positions of Carnap and Heidegger. 5 Becker’s main philosophical work, Mathematische Existenz (Mathematical Existence), was published together with Heidegger’s Sein und Zeit (Being and Time) in 1927, in volume 8 of the Jahrbuch für Philosophie und phänomenologische Forschung (Yearbook for Philosophy and Phenomenological Research). While Heidegger was concerned with the phenomenology of the humanities, Becker was meant to phenomenologically investigate the field of mathematics and the sciences.
The reasons for this neglect, according to Thyssen, are ‘a lack of interest’ on the one hand, but also, on the other hand, ‘that realism has been forced onto the defensive by positions in some way linking the world to the subject’ (Thyssen 1959, p. 42). Such (in a broad sense) idealistic positions include neo-Kantianism and Husserl’s phenomenology, but also Heidegger’s existential ontology, which is ‘epistemologically dependent upon the latter’. Thyssen even goes as far as labeling Husserl’s epistemology ‘the most subtle form of neo-Kantianism’, probably because of its transcendental turn.
Since Carnap’s own ideals of explication relied, by his own lights, on clear answers to them, we would do well to focus on how they were resolved by Turing. In general, to prove an impossibility result in mathematics one must give an analysis of what precisely it is that cannot be done: to show that something is not true of a notion, the general notion itself must be clear. 13 Turing used his notion of a machine to prove that there is no such ‘definite method’ (or ‘process’). A negative resolution of the Enscheidungsproblem first appeared in Church (1936), but Turing had worked out his ideas independently and his proof was quite different.