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Example text
Finally, there is another, more direct line of influence from Le´sniewski to Tarski, which is likely relevant to the Finitist-Nominalist project: intuitionistic finitism. In a 1930 paper, Tarski says that his “personal attitude” concerning the “foundations of mathematics” is “intuitionistic formalism,” a view found “in the writings of S. Le´sniewski” (Tarski 1983, 62). What is this view? If we follow the reference Tarski provides, we find Le´sniewski discussing his proposed sentential logic: Having no predilection for various ‘mathematical games’ that consist in writing out according to one or another conventional rule various more or less picturesque formulae which need not be meaningful or even.
For Neurath, it seems that the problem is not merely that the superficially mathematical/analytic axiom of infinity is extra-logical/synthetic, or even that it is false, but rather that the very concept of infinity is, in some sense, unacceptable for an anti-metaphysical empiricist. Perhaps there are theological residues also. . in certain applications of the concept of infinity in mathematics. The attempts to make mathematics finite, especially in applications to concrete events, are certainly part of tidying up [the language of science].
That is, a speaker understands a particular sentence if and only if she knows that sentence’s meaning. ) Verständlichkeit is thus intimately connected to discussions of meaning and meaningfulness, notions which have occupied center stage in analytic philosophy throughout much of its history. There is another, derivative sense of ‘understanding’ that Carnap offers, both at this time and later in his career; to examine it, a brief detour is needed. This second sense does not appear in Carnap’s discussions of semantics in general, but rather in his treatment of the semantics of fundamental scientific theories.