El logicismo russelliano: su significado filosófico

Abstract

After a brief presentation of Russell' s logicism, I attempt a global explanation of its philosophical significance. I reject the existence of two different kinds of logicism (Putnam) with the argument that Russell was trying to justify the existing mathematics and, at the same time, to escape from a mere formal calculus. For the same reason, the logicist definitions cannot be regarded as new axioms to be added to Peano's postulates (Reichenbach): according to Russell it is necessary to show that there is a constant meaning satisfying those postulates. The lack of a clear definition of logic in Russell (and Frege) is a consequence of his whole philosophy, therefore we must not look for it in the concept of necessity (Griffin), nor must we interpret this lack as a gap in the system (Grattan-Guinness). Russell's starting point was Moore's notion of truth as something indefinable and intuitive according to which we immediately recognize the true propositions. The problem of logicism is rather the deep tension between the ontological preeminence of relations (structures) and their terms (fields).
[F.R.C.]