Abstract

In §69.b of BT Heidegger attempts an existential genetic analysis of science, i.e. a phenomenology of the conceptual process of the constitution of the logical view of science (science seen as theory) starting from the Dasein. It attempts to do so by examining the special intentional-existential modification of (human) being-in-the-world, which is called the "mathematical projection of nature"; that is, by examining that special modification of our being, which places us in the state of experience that presents the world to us as taught by, e.g., Galileo and Newton. The idea he puts forward is that modern mathematical physics and the corresponding experience of the real is the result of the mathematical projection of nature. Modern science, Heidegger says, stands out because it is mathematical. But we cannot get the answer to what this mathematicality consists in from mathematics, because mathematics is only a special manifestation of mathematicality. Here is what Heidegger means by "mathematicality" and, accordingly by "mathematical projection of nature." If one were to let two bodies of different weights fall simultaneously from the top of the tower of Pisa, Heidegger notes, both Galileo and an Aristotelian would see that the two bodies would reach the ground with as little time difference as possible, and not at exactly the same moment. Galileo, however, does something decisive: he claims that under conditions that would be impossible to ensure (if we removed absolutely all resistance to the motion of the bodies), the two bodies would reach the ground absolutely simultaneously. This is not something that he or the Aristotelian sees happening empirically. How, then, does Galileo insist so firmly on his position? How exactly does it happen that he has before him such a view of things? Heidegger's answer is that Galileo is mathematically projecting nature. In his Dialogues Galileo says "I conceive with my mind" (mente concipio) a body thrown to move on an infinitely extending horizontal plane, having eliminated from its path every possible obstacle. Finally, I argue that from the detailed interpretation of Heidegger's points of the mathematical and of the notion of mathematical projection of nature, we can arrive at the conclusions I had arrived at in my doctoral dissertation (2000) as regards the meaning and function of thought experiments in physics as seen from a Husserlian phenomenological point of view as intentional acts. In a nutshell, in thought experiments physics constitutes the special metaphysics (to use the Kantian term) of the primordial ontological region it investigates as well as attempts to make natural sense of the mathematical formalism in cases it proves necessary.