That is an important question: (02)
> But its not at all obvious what a proposition *is*. For sure, it can't
> be simply a sentence or even an equivalence class of sentences. It
> can't be anything that is defined purely in terms of syntax, because
> propositions, unlike sentences, are typically *about* something.
> Consider for example, the proposition that I, Pat Hayes, am an
> American citizen. You can write a sentence
> (American PHayes)
> but what ensures that the name "PHayes" refers to me? (03)
And as usual, Peirce anticipated that question and answered it.
He coined the term 'indexical' and said that every proposition must
contain at least one indexical (pointer, such as a gesture, physical
link, or convention) that ties its symbols to the intended referent. (04)
He said that proper names, such as 'PHayes', are symbols whose
conventional meaning is to serve as indexicals of their referents.
The method of following that pointer to its intended referent
depends on the conventions of the culture and available technology.
He didn't anticipate the WWW. (05)
As an example, he said that a portrait hanging on the wall is
an icon, and it does not state a proposition. But a name in the
corner of a portrait, by convention, asserts the proposition
that the named person was the artist. A name on the frame beneath
the portrait, by convention, asserts the proposition that the
portrait is an icon of the named individual. (06)
I'd also like to comment on your note to Mark: (07)
> As we invented the "that" operator and its semantics
> (see http://www.ihmc.us/users/phayes/IKL/SPEC/SPEC.html )
> from whole cloth in order to create IKL, and AFAIK it has not
> been used in any other formalism in the entire history
> of formal logic (08)
I agree that the IKL semantics is indeed an important innovation.
But metalanguage has been used informally long before writing.
For their extensions to Aristotle, the medieval Scholastics coined
the terms 'first intention' for language about things in the world
and 'second intention' for language about language. (09)
Both Peirce and Brentano were familiar with those terms.
Brentano had a strong influence on the Polish school of logic,
where Tarski wrote his famous papers on model theory and
But Peirce did not develop the logic of metalanguage beyond
the notation I cited. In order to avoid paradox, Tarski
developed stratified levels of metalanguage. (011)
What's unique about the IKL semantics is the ability to avoid
paradox without requiring stratified metalevels. (012)
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