Storing this here for later discussion ... On 6/28/2017 11:53 AM, John F Sowa wrote: > 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 >
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