Wittgenstein's Criticism of Russell's Distinction Between Pure and Applied Logic

Abstract

Sections 5.552-5.5521 and 5.557 of Wittgenstein's Tractatus contain some enigmatic
remarks about the distinction between logic (presumably pure logic) and its
application. I will argue here that these passages, like so much else in the
Tractatus, are directed against Bertrand Russell's philosophy of logic. In
particular, they constitute an important criticism, previously overlooked in the
literature, that goes to the heart of Russell's philosophy of logic: Russell's
logical Platonism cannot explain how the applications of logical propositions are
necessarily true. If sound - and I will argue that it is - then this is a very
serious objection to Russell's account of logic. For any philosophy of logic holding
that logical propositions are necessarily true and can be applied must also be able
to account for the necessary truth of the applications of these propositions.