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

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Tue, 29 May 2007 10:15:41 -0400
Message-id: <465C358D.9030008@xxxxxxxxxxx>
Wacek and Ingvar,    (01)

It happens that English has no tenseless verb forms.
In predicate calculus, you could write:    (02)

    ~(Ex)(rose(x) & blue(x)).    (03)

This statement has no reference to any time or place.
In English, it is possible to make a statement without
reference to place, but not to time.    (04)

vQ> The sentence "no roses are blue" was true some time ago,
 > and is false now;  but does it correspond to the same
 > proposition in both cases?    (05)

I would like to express the proposition stated by the
above formula in predicate calculus.  That statement
is independent of any time, place, or context.  The
proposition it states has no unbound variables that
could be bound, explicitly or implicitly, to any context.    (06)

Yet that proposition can have different truth values
in different contexts despite the fact that its meaning
does not change.    (07)

IJ> I would say that there is only one *sentence meaning*
 > "no roses are blue", but two *used sentence meanings* and
 > two propositions, one which is true and one which is false.
 > Propositions cannot change truth-values.    (08)

I would identify 'sentence meaning' with 'proposition'.
Then you could apply the word 'used' to either one, if you
like.  I wouldn't say that propositions or sentence meanings
change -- they just represent configurations of individuals,
properties, and relations, real or hypothetical.  But they
can be used for different purposes.    (09)

vQ> Note that I do not argue for this or other theory of
 > propositions;  I am just curious, and it seems to be
 > an issue that should not be just neglected (e.g., for
 > the purpose of precise documentation of IKL, a very
 > practical task).    (010)

Since IKL (like predicate calculus and conceptual graphs) has
no default tenses, it has no implicit context dependencies.    (011)

vQ> As above;  if a proposition is fixed to a fact, it cannot
 > be refixed to another fact -- or would this be what you suggest?
 > If the fact is (was) that Osama slept at t1, the proposition
 > that Osama slept at t1 was true, remains true, and will always
 > be true.    (012)

That raises some important questions:    (013)

  1. What is a fact?    (014)

  2. What are the references in a proposition bound to?
     To individuals in a particular fact?  To individuals
     independent of any specific fact?  Or to configurations
     of individuals, which may be considered independently
     of any specific binding?    (015)

I would claim that facts (at least facts about the world,
not facts such as 2+2=4) are bound to specific chunks of
space-time.    (016)

But I would say that propositions are abstractions about
configurations, which could characterize different facts in
different contexts.  If a proposition names an individual,
such as Osama or Bob, it is not necessarily bound to a
particular fact in which that individual participates.    (017)

For example, you might ask "How often did Bob wake up last night?"
To answer that question, I would consider the proposition that
Bob wakes up and try to determine how many times the corresponding
configuration was a correct characterization.  (Perhaps Bob fell
asleep in front of his web cam, which was on for the whole night.)
I could answer that by checking each event in the record for which
the configuration of Bob waking up occurred.    (018)

An interpretation of that kind is required to support hypothetical
statements, which may refer to actual individuals.  For example:    (019)

    If Gerald Ford had been elected president in 1976,
    Ronald Reagan would not have been elected president in 1980.    (020)

That counterfactual statement refers to actual individuals and
possible outcomes of actual events.  Both of the propositions
in the antecedent and the consequent could be translated to
different languages while retaining the same meaning, but there
are no facts to which either of the propositions could be bound.    (021)

This interpretation is consistent with the claim that a proposition
represents an abstract configuration, which might include references
to actual individuals independent of any specific facts in which
those individuals participate.    (022)

John    (023)

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