Proponents
include Bertrand Russell, Alfred Ayer, Willard Quine.

Russell thought that logic should be defined in terms of the universality or generality of its truths or as arising in some way from the form of the sentences which express logical truths.
However he had some difficulty in seeing how this could be carried through.
His concerns are described in a brief passage from the Introduction to the second edition of The Principles of Mathematics.


Topic Neutrality
It is traditional to take the view that logic is topic neutral.
To the extent that necessary truths, being true in all possible worlds, can say nothing which is particular to any one of those possible worlds, a necessary truth can be considered to have no subject matter in the real world.
However, some propositions widely accepted as necessary are most naturally supposed as having a subject matter.
For example, the truths of arithmetic may be considered necessary propositions whose subject matter is the collection of abstract entities known as the natural numbers.




Even if the logicist thesis that mathematics is logic is put aside, the claim of topic neutrality seems to me difficult to justify.
Classical propositional logic is the theory of boolean operators, they are its subject matter.
There are many nonclassical variants of propositional logic most of which have some purpose and rationale.
For these alternatives to have any validity we must surely accept that they differ in subject matter.
Neither intuitionistic nor manyvalued logics are about boolean operators, even though they may use exactly the same symbols as classical logic.


