On Sat, Oct 27, 2012 at 11:29 AM, John E Clifford
<kali9putra@hidden.email> wrote:
From: Mike S. <
maikxlx@gmail.com>
grammatical entity / extension / intension
--------------------------------------------
formula with no free variables / situation / proposition
sentence/ state (of affairs) ("situation" is used for mini-universes in the metalanguage) - truth value / proposition - set of worlds (in each case, the first is for the Fregean notion, the second for the Kripkean (Montagovian) one) (C-sets throughout)
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). 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.
formula with 1 free variable / set of entities / property
monadic predicate/ monadic propositional function/ property - function from worlds to sets (in the extensional case, the Fregean notion differs from the Montagovian in just what it is: in Frege a propositional function is a state with a hole in it, not just a function. Sorry, it is hard to get clearer than that and it doesn't seem to make much of a difference at this level of detail anyhow.
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. 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.
formula with 2 free variables / set of ordered pairs / binary relation
n-adic predicate/ n-adic propositional function/ relation - function
from worlds to sets of ordered n-tuples.
n-adic formula / n-adic predicate = set of n-tuples / n-ary relation = function from worlds to sets of n-tuples
Again the problem with "predicate", and the sepearator is one of contrast, not identity
I think Barwise has a prior claim on "situation" or at least a more useful one.
That word is a little fuzzy, but useful when describing things intuitively. We can explain a truth value as intuitively meaning simply that a _particular_ situation in (usually) _this_ world is true.
Errm, how does this explain a truth value. Also, we are outside intuition into terms of art here, so we have to choose our words with care.
"Sentence" is a well established term for a syntactic entity and I see no reason to change it. Questions, commands, hypotheses and the like are all sentences, regardless of their illocutionary force.
You can take that position and I want to take it too, but others see things differently. I would use "statement" to refer to formulas with everything bound (which includes sentences with no explicit illocutionary operator). I would define "sentence" as simply the start symbol of the grammar and let others make up their own minds on whether questions and commands are statements.
I would be surpised if anyone thought a question were a statement -- but I admit that in the world of linguistics cum philosophy cum logic almost any sort of craziness can happen, despite (or often, I suspect, because) of the confusion that ensues. Your advice is essentially mine as well, though your surrounding remarks suggest you don't heed it.
In no way would it be proper to call the extension of a sentence a sentence, since the latter
is not a linguistic item.
I would not suggest otherwise for Xorban.