Jon, That's an important topic to explore:
JA
we can take up the issue of propositions in more detail as it arises in the relevant context.
For a good analysis of the issues, I recommend the following book: Stjernfelt, Frederik (2014) Natural Propositions: The Actuality of Peirce’s Doctrine of Dicisigns, Boston: Docent Press. I wrote a 5-page article on propositions from a Peircean perspective: http://www.jfsowa.com/logic/proposit.pdf That article is based on Peirce's notion of equivalence (CP 5.569):
A sign is only a sign in actu by virtue of its receiving an interpretation, that is, by virtue of its determining another sign of the same object. This is as true of mental judgments as it is of external signs. To say that a proposition is true is to say that every interpretation of it is true. Two propositions are equivalent when either might have been an interpretant of the other. This equivalence, like others, is by an act of abstraction (in the sense in which forming an abstract noun is abstraction) conceived as identity. And we speak of believing in a proposition, having in mind an entire collection of equivalent propositions with their partial interpretants. Thus, two persons are said to have the same proposition in mind. The interpretant of a proposition is itself a proposition. Any necessary inference from a proposition is an interpretant of it. When we speak of truth and falsity, we refer to the possibility of the proposition being refuted; and this refutation (roughly speaking) takes place in but one way. Namely, an interpretant of the proposition would, if believed, produce the expectation of a certain description of percept on a certain occasion. The occasion arrives: the percept forced upon us is different. This constitutes the falsity of every proposition of which the disappointing prediction was the interpretant. Thus, a false proposition is a proposition of which some interpretant represents that, on an occasion which it indicates, a percept will have a certain character, while the immediate perceptual judgment on that occasion is that the percept has not that character. A true proposition is a proposition belief in which would never lead to such disappointment so long as the proposition is not understood otherwise than it was intended.
In the article, I formalize Peirce's notion of equivalence in terms of *meaning-preserving translations* (MPTs), which specify a class of equivalent sentences in some language or languages. It's easy to define MPTs for formal logics, but much harder for natural languages. John
----------------------------- PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . To UNSUBSCRIBE, send a message not to PEIRCE-L but to l...@list.iupui.edu with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
