Chris, (01)
Before commenting on today's notes, I'd like to return to Dunn's point
that his approach could be extended to Quantified Modal Logic (QML)
by a substitutional interpretation of quantifiers. I reread his paper,
and he did not rule out other methods. Any method of extending Kripke
semantics to QML could just as easily be adapted to Dunn's semantics. (02)
For the first comment, note that I used the word 'specify', not 'is': (03)
JFS
>> In fact, Hintikka had used the term 'model set' to specify what
>> Kripke called a possible world. (04)
CM
> Not really. Hintikka's model sets are sets of sentences.
> In a model *system* -- basically, a set of model sets -- the model sets
> *correspond* to the "worlds" of a corresponding Kripke model, but they
> are not the same; the worlds of a Kripke model are featureless points. (05)
Yes. I said that in my papers laws.htm and worlds.pdf. (06)
CM
> I'm getting pretty tired of you making Kripke out to be some sort of
> villain and possible world semantics as vaguely (or explicitly) sinister. (07)
My complaint is not about what Kripke did or said, but about professors
who teach modal semantics with featureless points and ignore the fact
that people who implement possible worlds use sets of sentences. (08)
CM
> To anyone who is capable of reading Kripke's work on the model theory
> of modal logic it is *perfectly* clear that his "possible worlds" are
> nothing more than indices on, essentially, models for classical
> propositional or (as the case may be) first-order logic. (09)
I said that in my papers, and I taught that to students before I came
across Dunn's paper. But I was teaching students who were primarily
interested in applications to AI, comp. sci., and linguistics. In
those fields, they represent possible worlds by the *sentences* that
are true in those worlds. That's D's method, not K's. (010)
It's fine to teach them K's method for historical reasons. But it's
even more important to show them that D's method is what they actually
use in their applications. (011)
CM
> Kripke refers first and foremost to *model structures* and *models*
> and only briefly appeals to the metaphor of possible worlds to provide
> a simple intuitive gloss on the formal structures. But it is absolutely
> clear that there is no philosophical baggage to the model theory... (012)
I am against *useless* baggage. But the sentences in the applications
of modal logic are not useless baggage. (013)
> formally speaking, once again, the set of "possible worlds" in a model
> structure is (as far as the models tell us) a set of featureless points... (014)
I grew up as a mathematician. I studied algebraic topology and
categories of abstract mappings. You don't have to preach to me
about mappings to and from featureless points. (015)
> *Nobody* who understands this material is confused about this. (016)
I learned Kripke's method first, and I actually liked it. But I have
spent a lot of time teaching students who are not mathematicians.
When I started teaching them Dunn's method, they learned it much
faster and acquired a more intuitive understanding. (017)
JFS
>> 1. Logical possibility. A proposition p is possible iff it is not
>> provably false. Impossible means inconsistent or provably false. (018)
CM
> This won't do. Provably false in what theory? Consider the continuum
> hypothesis (CH) ... (019)
I was trying to give a very brief summary of Peirce's many pages of
writings about multiple modalities. C. I. Lewis and Arthur Prior
both drew a great deal of inspiration from CSP's writings in their
pioneering work on modal logics. (020)
CSP was familiar with Cantor's work, but he had obviously not read
publications that had not been written. I just wanted to say that
his writings still have a lot to offer for the 21st century. (021)
John (022)
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