Peirce used the word "formal" in a couple of senses, the first of which
is closer to its general meaning of "concerned with form", and here he
can mean either the forms of objects or the forms of syntax, whereas
the tradition following Russell tends to focus on syntax exclusively.
In that sense of "formal", Peirce's concept of logic as formal semiotic
would incorporate both the syntactic or proof-theoretic forms of Russell
and the semantic or model-theoretic forms of Tarski.

But Peirce also used the word "formal" in another, more specialized sense,
in which it became the practical equivalent of "normative". In that sense,
his definition of logic as formal semiotic places logic within the sphere
of the normative sciences, where it normally belongs.

Jon

CC: Arisbe, Inquiry, Conceptual Graphs, Peirce List

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