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Re: [ontolog-forum] Ontology, Information Models and the 'Real World': C

To: "John F. Sowa" <sowa@xxxxxxxxxxx>
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Thu, 31 May 2007 11:57:41 -0700
Message-id: <p0623090ec284c51600be@[]>
>One reason for introducing a technical term, such as proposition,
>is to make distinctions that are confused in more common words
>such as 'meaning'.  However, technical terms are always defined
>in some theory, and people who hold different theories are likely
>to have different and incompatible definitions.    (01)

True, true. But we did not choose "proposition" 
carelessly, but with a reasonably 
well-thought-out philosophical position on what 
propositions actually are; one on which Chris 
Menzel is more of an authority than I, but which 
I know is based on a body of technical 
philosophical logic done over the past few 
decades.    (02)

>Quine has been cited as an authority, and he is for many purposes.
>But Q. has stated some strong views, which are not accepted by a
>large number of logicians and philosophers.  In particular,....    (03)

Reading through your list, I realize how deeply I 
have been influenced by Quine. I learned logic by 
reading Quine, and have always found his views 
and thinking to be the most convincing and 
clearly stated of almost any writer. I too find 
modal logics essentially meaningless, I don't 
believe in possibilia (how many possible men are 
standing in an empty doorway?), and I think that 
natural language - *real* natural language, not 
the prissified academic stuff that philosophers 
write and read to one another - is beyond the 
pale of any attempt to formalize its actual 
meanings. About half the stuff we say to one 
another isn't even intended to convey meaning: 
its more like a kind of verbal grooming. But in 
any case, I also think, purely now as a matter of 
engineering, that to confuse natural language 
with ontological formalisms is a serious 
methodological blunder.    (04)

>   1. Q. rejected any version of modal logic.  His opposition amounted
>      to more than merely ignoring it while working on other issues.
>      Instead, he denied the value, usefulness, or even the possibility
>      of having a coherent system of modal logic.
>   2. Point #1 is compatible with Q's denial of any clear or coherent
>      distinction between intension and extension.  That distinction
>      is central to any version of modal logic, which allows a sentence
>      s (with no unresolved indexicals) to have different truth values
>      in different worlds, contexts, or universes of discourse.
>   3. Since Q's primary work has been in formal logic, he never
>      developed a complete semantics for natural languages (and he
>      has been skeptical of the possibility of developing a complete
>      semantics).  Yet he made many comments about various sentences
>      in NLs and their translations to logic.
>   4. In those comments, Q. avoided directly addressing the question
>      of indexicals by coining the term 'eternal sentence' for a sentence
>      whose referents are all fixed (either bound to explicit quantifiers
>      or to explicitly named individuals).  In effect, he defined that
>      term to mean 'absence of indexicals' without using the terms
>      'indexical', 'context', 'possible world', etc.
>These views gave Quine's writings an admirable clarity, but at the
>expense of ignoring or even deprecating all talk about subjects he
>was not prepared to discuss clearly -- which includes the most serious
>issues about natural languages.    (05)

Perhaps. But why should that bother us in this forum?    (06)

>For these reasons, I believe that taking the word 'proposition' as
>synonymous with Q's term 'eternal sentence' would force us to adopt
>aspects of Q's philosophy that are incompatible with applications
>for which IKL (and other logics) might be used.  Among them is the
>semantics of NLs, for which many people would like to use IKL.    (07)

Hmm. News to me. It wasn't designed with that purpose in mind, for sure.    (08)

I really don't think we need to be this fussy 
about terminology. IKL is a formal logic, and 
without the proposition names it really is just 
common logic, which is FOL written in an 
unusually slack syntax. That part is surely 
fairly clear and (at this level of discussion) 
uncontroversial. Now, the extension that gets one 
to IKL is simply the idea that any sentence *of 
this formalism* expresses a proposition, which is 
true exactly when the sentence is. So any 
discussion of propositions in English is really 
beside the point for IKL: it does not set out to 
capture all propositions expressible in English 
(a tensed, modal, indexical, elliptical language 
which evolved to convey speech acts in a social 
context), but rather all propositions expressible 
in FOL (an untensed, non-modal, non-indexical, 
explicit classical logic which knows nothing of 
contexts.)    (09)

>Since IKL uses the word 'proposition' as a technical term, it is
>important to use that word in a way that minimizes confusion among
>IKL adopters.    (010)

Well, let us refer to "IKL propositions" then. 
That should make it clear that we are talking 
only about propositions which can be expressed in 
IKL.    (011)

>  I think I agree with Pat about the IKL formalism,
>and I think that I know what he meant by the following statements:
>   1. A proposition has a fixed truth value.
>   2. But a proposition might have different truth values in different
>      contexts.    (012)

I've already admitted that this way of talking is 
confusing. I suggest we avoid it. A proposition 
does not have different truth values, period. 
What it can have, however, as well as a (single) 
truth value, is a truth-value-in-a-context, also 
known as a C-truthvalue, where C is a context 
parameter. Truth, and truth-in-a-context, or 
C-truth, need bear no relation to one another 
whatsoever, and are related only by a relation 
called IST: the C-truthvalue of P is the 
truthvalue of (IST C P)    (013)

>However, this conjunction is likely to cause confusion (or at least
>lengthy discussions such as this thread).
>My recommendation is to replace the above statements with something
>along the following lines:
>   1. The IKL model theory defines an evaluation function Phi, which
>      for any proposition p, determines a truth value Phi(p).
>   2. Inside a nested context, however, the proposition p could have
>      a truth value that is different from the value Phi(p) that would
>      be determined outside any nested context.    (014)

Well, no. That is strictly false and I think 
definitely misleading. The truth-value of P is 
what it is, no matter what context it is 
'inside'. And strictly speaking, there is no 
notion in IKL of a proposition being 'inside' a 
context, or of contexts being 'nested'. All of 
this structure can be *described* in a suitable 
IKL ontology, using IST, but IKL as a logic has 
no contexts and no context nesting. It is just 
plain vanilla FOL with proposition names added 
(which, BTW, one can accurately describe as 
lambda-expressions with an empty argument list: 
that is, one can read the IKL syntax    (015)

(that <sentence>)    (016)

as meaning    (017)

(lambda () <sentence>)    (018)

Pat    (019)

>This avoids the word 'fixed' without introducing the word 'changing'
>or any term such as 'proposition-in-a-context'.
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