After a very brief outline of what I take to be the essential characteristics of mathematical, as contrasted with empirical thinking, the paper briefly discusses Kant’s concept of a priori and develops a theory of mathematical thought experiments (MTEs) that is at once reflexive-transcendental and operational, in the sense that it brings together the reflexive-transcendental point of view of the Kantian tradition and the empirical or formal point of view of naturalised epistemologies. The attempt to extend thought experimentation from the natural sciences to mathematics succeeds for applied mathematics, but works only in a limited sense in the case of pure mathematics. Even though visualisation plays a certain role in the TEs of pure mathematics, MTEs are more similar, in their epistemologically fundamental aspects, to formal proofs than to TEs in the natural sciences.
On Mathematical Thought Experiments
BUZZONI, Marco
2011-01-01
Abstract
After a very brief outline of what I take to be the essential characteristics of mathematical, as contrasted with empirical thinking, the paper briefly discusses Kant’s concept of a priori and develops a theory of mathematical thought experiments (MTEs) that is at once reflexive-transcendental and operational, in the sense that it brings together the reflexive-transcendental point of view of the Kantian tradition and the empirical or formal point of view of naturalised epistemologies. The attempt to extend thought experimentation from the natural sciences to mathematics succeeds for applied mathematics, but works only in a limited sense in the case of pure mathematics. Even though visualisation plays a certain role in the TEs of pure mathematics, MTEs are more similar, in their epistemologically fundamental aspects, to formal proofs than to TEs in the natural sciences.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
