Charles Sanders Peirce on Logic as Semiotic

"Logic, in its general sense, is, as I believe I have shown, only another name for 'semiotic' (Greek 'semeiotike'), the quasi-necessary, or formal, doctrine of signs. By describing the doctrine as "quasi-necessary", or formal, I mean that we observe the characters of such signs as we know, and from such an observation, by a process which I will not object to naming Abstraction, we are led to statements, eminently fallible, and therefore in one sense by no means necessary, as to what 'must be' the characters of all signs used by a "scientific" intelligence, that is to say, by an intelligence capable of learning by experience. As to that process of abstraction, it is itself a sort of observation.

"The faculty which I call abstractive observation is one which ordinary people perfectly recognize, but for which the theories of philosophers sometimes hardly leave room. It is a familiar experience to every human being to wish for something quite beyond his present means, and to follow that wish by the question, "Should I wish for that thing just the same, if I had ample means to gratify it?" To answer that question, he searches his heart, and in doing so makes what I term an abstractive observation. He makes in his imagination a sort of skeleton diagram, or outline sketch, of himself, considers what modifications the hypothetical state of things would
require to be made in that picture, and then examines it, that is, 'observes' what he has imagined, to see whether
the same ardent desire is there to be discerned. By such a process, which is at bottom very much like mathematical reasoning, we can reach conclusions as to what 'would be' true of signs in all cases, so long as the intelligence using them was scientific."

- Charles Sanders Peirce, 'Collected Papers', CP 2.227. Eds. Note. "From an unidentified fragment, c. 1897".

Cap tip Jon