Wittgenstein and Atomism

The Logicism of the Tractatus and of Russell is, furthermore, Atomistic--it holds not merely that Logic is the objectively necessary, universally valid, essence of Language, but that it is a system based on irreducible, self-evidently true, propositions. In contrast, Wholistic Logicism, e. g. Leibniz's, holds that the whole of the system precedes its parts. Hence, the Tractatus and Russell can be challenged from two main directions--Pragmaticism disputes the objective necessity of Logic, while, e. g. Whitehead rejects its Atomism, while remaining a Logicist himself. Both types of repudiation are to be found in the Investigations. On the one hand, Wittgenstein's 'language-game' device is a Pragmatist rejection of the universal validity of Logic. But on the other, he presents numerous examples of what might be called a 'sub-atomic' analysis of the purported Atoms of that theory, which results in the exposure of those propositions, and of propositions in general, as being not as simple as the theory presumes them to be. So, one seeming incoherence of the Investigations is the relation between Wittgenstein's two lines of attack, i. e. the Sub-Atomic analysis can undermine Atomistic Logicism, but in the name of Wholistic Logicism, leaving it at odds with his Pragmatism.