On a Logician’s Mantelpiece: Frege

Three Logicians: Aristotle, Saccheri, Frege

Frege on Identity

Frege’s most celebrated paper “On Sense and Reference” begins with a puzzle. The sentences “a=a” and “a=b” superficially strike the reader as being different kinds of claims. Among other things, “a=a” seems to be trivially true, even self-evident. On the other hand, “a=b” is an informative sentence. It is of a kind important to many episodes in the history of science. Deeper reflection, however...

Frege on Identity Statements

ion is no patch, for the notion of numerical equivalence onto which it is to converge must presuppose a notion of number such that distinct numbers, given by distinct numerical symbols, can be the same number. This is to be the accomplishment of abstraction, by which, Frege says, “things are supposed to become identical by being equated.” But how can abstraction, a “capability of the human mind...

Peirce and Frege on Logic

Though Peirce and Frege played crucial roles in the development of modern logic, there has been so far little scholarly work comparing their positions on the nature of logic. I offer here a comparative study of their views on logic and I show that, although they developed their views independently from each other and with very different projects in mind, their positions are extremely similar (e...

On Discourses Addressed by Infidel Logicians

We attempt to address here some alleged criticisms against the philosophical import of the so-called Brazilian approach to paraconsistency, especially by providing some demanded epistemic elucidations to the whole enterprise of the logics of formal inconsistency. In the way of elucidating, we substantiate the view that difficulties in reasoning under contradictions in both the Buddhist and the ...