On Fri, Oct 26, 2012 at 10:29 PM, John E Clifford
<kali9putra@hidden.email> wrote:
Knowledge and belief have the same abstractors because they are the same things, propositions (or whatever you will, so long as it works out right).
I agree: "du'u" marks a proposition. The argument place of djn-x2 downsteps that proposition to a "situation" in the same world as the knower, and krc-x2 ranges over worlds that contain the situation believed in by the believer.
It would nice to be able to agree on some terminology for the following correspondences, but I would consider any suggestion in order to reach consensus:
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)
formula with 1 free variable / set of entities / property
monadic predicate/ monadic prop0sitional 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.
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.
formula with 3 free variables / set of ordered triplets / ternary relation
etc.
All we did today was discuss how to "package up" (CLL's words, section 11.4) a formula with N free variables using fV + (N) kV.
There's nothing unusual about this terminology, except that "situation" is somewhat novel (and I am not sure how it meshes with the work of Davidson, who popularized the term). Usually, both a formula with no free variables and/or its corresponding extension would be called a "sentence", but in Xorban we have given that term a particular meaning involving illocutionary force, so I suggest "situation" to fill the gap.
I think Barwise has a prior claim on "situation" or at least a more useful one. "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. In no way would it be proper to call the extension of a sentence a sentence, since the latter
is not a linguistic item.
No slip through; you just ignored what is going one. And perhaps saying it all out would make the point clearer. The claim "I know that p" entails p (not "that p", which isn't a statement), but "I believe that p" does not.
Yes. Rather like "I found a unicorn" entails that some unicorn exists, while "I sought a unicorn" does not.
We could derive a long word glossed as "having a relatively-high temperature" even while providing "glr", glossed as "hot" as a shortcut. These would be synonyms, but the long form would serve to make the meaning of the short form transparent.
We can do abbreviations, but it would be a good idea to get the basics straight before going for economy. Otherwise you may economize yourself into contradictions or at least not quite getting what you want. Have you though about how to deal with scalar properties?
I increasingly consider that part of lexical design. Frankly I think we should be checking out Morneau's monograph. No sense in reinventing the wheel.
--
co ma'a mke
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