Considering the instability of nonlinear dynamics, the deductive inference rule Modus ponens itself is not enough to guarantee the validity of reasoning sequences in the real physical world, and similar results cannot necessarily be obtained from similar causes. Some kind of stability hypothesis should be added in order to draw meaningful conclusions. Hence, the uncertainty of deductive inference appears to be like that of inductive inference, and the asymmetry between deduction and induction becomes unrecognizable such as to undermine the basis (...) for the fundamental cleavage between analytic truth and synthetic truth, as W. V. O. Quine pointed out. Induction is not inferior to deduction from a pragmatic point of view. (shrink)

On the basis of what I call physico-formalist philosophy of mathematics, I will develop an amended account of the Kantian–Reichenbachian conception of constitutive a priori. It will be shown that the features attributed to a real object are not possessed by the object as a “thing-in-itself”; they require a physical theory by means of which these features are constituted. It will be seen that the existence of such a physical theory implies that a physical object can possess a property only (...) if other contingently existing physical objects exist; therefore, the intrinsic–extrinsic distinction is flawed. (shrink)

The paper comments on a rather uncommon approach to mathematics called physicalist formalism. According to this view, the formal systems mathematicians concern with are nothing more and nothing less than genuine physical systems. I give a brief review on the main theses, then I provide some arguments, concerning mostly with the practice of mathematics and the uniqueness of formal systems, aiming to show the implausibility of this radical view.