On Jun 16, 2014, at 1:05 AM, John F Sowa <sowa@xxxxxxxxxxx> wrote: (01)
> That is an important question:
>> 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?
> 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.
> 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.
> 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. (02)
Right. Another term that has been used is 'rigid designator'. (We used this
idea, implicitly, in the RDF 1.1 model theory, by the way, in defining the
meanings of typed literals. The semantics assumes that the Web conventions in
use somehow attach a fixed meaning to IRIs used to denote detatypes: in
Peirce's terminology, that datatype names are indexical. This small concession
to a realistic semiotics was extremely controversial :-) (03)
> I'd also like to comment on your note to Mark:
>> 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
> I agree that the IKL semantics is indeed an important innovation.
> But metalanguage has been used informally long before writing. (04)
But my point is that the IKL 'that' operator is not metalanguage in the usual
sense of that term. Metalanguage usually refers to language *about language",
ie about sentences. But the (that ...) construction denotes a proposition, not
a sentence. And in order to achive that, we had to give a model-theoretic
account of what propositions actually are, which AFAIK had not previously been
done. I do not know if this construction can be smoothly adapted to other
formalisms: in any case, one should not claim or assume that it can without
doing the actual work of checking that the resulting system is internally
coherent, as this stuff skirts very close to paradox. (05)
> 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.
> 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.
> What's unique about the IKL semantics is the ability to avoid
> paradox without requiring stratified metalevels. (06)
Well, we hope :-) This is still an open research issue, in fact. (07)
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