Re: [engelang] Xorban: Properties - engelang messages

On Sat, Oct 27, 2012 at 2:50 PM, John E Clifford <kali9putra@hidden.email> wrote:

From: Mike S. <maikxlx@gmail.com>

Yes, it is good to point out that a proposition amounts to a set of worlds. I found the word I was looking for: A formula with no free variables is a "statement", and instead of "situation" the extension of that is just a truth value as you point out. That's all an improvement.

No, a statement is a sentence asserted in a situation (or, in this case, context).

There's no perfect answer. It seems desirable to do what we have already been doing, i.e. use the linguistic definition of "sentence", as well as use "sentence" as the start symbol of the formal grammar.

Propositions are different from sets of worlds, belonging to a different theory (well, in fact, both theories use the word, but the meanings are so different that it seems a bad idea to use the same for both and this usage has the longer history). And states of affairs are different from truth values. There are two types of extensions and intensions at each line.

Sorry, I didn't realize until now that you were giving me two theories at once.

I think that the Fregean "state of affairs" is behind the scenes so to speak of the Montagovian truth value, and the Fregean "proposition" is behind the scenes of the Montagovian set of worlds, but it's not fully clear to me how. Can you comment a bit more on how the two intensional logics line up?

I would say that the monadic predicate (i.e. function from entity to truth values) is the extension of the "monadic formula" and isomorphic to the set. I don't fully understand what you mean by "monadic propositional function". I am glad we agree on "property" at least.

OK. I'll buy "monadic formula" saving "predicate" for the atomic case, but "predicate" for the non-linguistic item is going to be confusing, since we use it so often as an English translation of selbri and the like.

In linguistics, "predicate" is already ambiguous, so there's no sense in worrying about confusion. I would just assign "predicate" its logical definition.

Again, a property is not the same as a function from worlds to sets. We can, of course, make the Montagovian extension of a monadic formula a set, and that would fit better with the intension, but, as you say, the two are practically interchangeable. The Fregean property on the other hand is not the same as either.

I think that we agree that there's no harm in using "set" and "predicate" interchangeably. An explanation of the Fregean concept of property would be appreciated.