From: amnell@klaava.Helsinki.FI (Marko Amnell)
Newsgroups: sci.philosophy.meta
Subject: Re: Excluded Middle (Long)
Date: 8 Nov 92 13:45:39 GMT
Organization: University of Helsinki

In <TORKEL.92Nov8110735@bast.sics.se> torkel@sics.se (Torkel Franzen) writes:

>But first you need to explain "all true propositions".
>The idea that there is a totality of true propositions is by no means
>self-explanatory. What, in your scheme of things, is the relation
>between propositions and sentence in languages? How is the totality of
>propositions delimited?  Is "the totality of true propositions"
>assumed to be a notion better defined than "the totality of true sentences
>in all possible languages"?

I think that when one makes a true statement (this is a psychological act)
what one does it to assert that a certain sentence in a language in which
one is fluent is true.  Now, depending on the circumstances of the act
of assertion, the sentence assumes a certain meaning for speakers of the
language.  This meaning is by no means always (or even never) totally
clear.  Ambiguities remain (about indexicals eg.).

Also, one must remember that I am here talking about descriptive use of 
language, as distinguished from other acts of speech with other types
of "illocutionary force" or however one wants to classify speech acts.
I am also limiting myself to spoken language.  This is arbitrary, and
the relation between spoken assertions and assertions in written texts
is not trivial.

Now, if the statement is judged to be correctly asserted in totality of
the state of affairs which it describes (this judgement is made by those
who are fluent in the language, and is really an idealization of the whole
linguistic community in the sense that if one refers to "gold" then all
the expert knowledge about gold could affect the judgement) then we would
say that it was a true statement.  Note the enormous tacit complexity
of such a simple descriptive speech act (and even now there are over-
simplifications).

If we wish to introduce the notion of propositions as distinct from both
sentences and statements, then what it added is this:  The true statement
about the contingent state of affairs in its human context picks out one
of an infinity of timeless abstract objects called propositions.  These
objects are timeless in the sense that they are not indexed by time.
All true statements will correspond to some proposition.  In the case of
mathematical propositions, many instances of "2+2=4" uttered by various
people at various times in various circumstances, will correspond to
the one timeless arithmatical truth that 2+2 indeed equals 4.

Other propositions will be picked out in a similar way.  Things are
simple if we assume a deterministic ontology--a reified universe of
4-space.  The universe exists as one abstract object, and we are
certain chunks of this objects--what we experience as time is our
extension on the t-axis.  If we allow for free will things get more
complicated.  We have to introduce some kind of possible-worlds
structure and say that a person can pick out where his timelines
will stretch in this profusion of possible universes.

In any case, we have here a way of matching up true assertions by
people with abstract objects called propositions.  The nature of
propositions is not clear.  One can think of them as objects whose
nature is wholly exhausted by considerations of structure.  A part
of this structure is truth value.  Each proposition is either
true or false.  What these truth values are is also not clear.
One can think of them as abstract objects that are the values of
propositions--considered as functions (as in the _Tractatus_).

This whole scheme up to now is a model.  We set up a metaphysical
model of the world and hope that it has some explanatory value.
If it is a good model we gain some understanding of our place in
the scheme of things.  To what extent one _believes_ that the
real world is like this metaphysical model is also unclear.  There
are other possible models.  What I have been describing is a 
simplification of the various "metaphysical realist" positions of
analytic philosophers like Plantinga or Lewis.  There are other
schemes in the analytic tradition and further schemes from
other contemporary schools and history (think of Heidegger, or
Leibniz's monadology, or Spinoza's Ethics).  All of these
metaphysical theories are to me different models of the world.
And one of the primary tasks of philosophy is to survey these
possibilities and compare their merits.  By understanding as many
different models as possible, we can begin we formulate desiderata
for what we would like from a metaphysical theory.

The metaphysical realist model satisfies some of the desiderata that
seem appealing.  It posits an objective reality (as distinguished
from relativist or constructivist pictures).  It has the idea of
an ultimate standard of truth (as distinguished from pragmatist or
"inner realist" pictures).  Why we see these two desiderata to be
appealing is a value judgement.  We value objectivity and certainty.
So here I agree with Putnam that the ultimate justification of one's
metaphysics is ethical.  This is in agreement with my conviction of
the supreme importance of ethics in philosophy.  Here I mean my own
`philosophy of life'.  I have certain ethical values, and these
values lead me to desire a certain kind of explanation of experience.
It is pointless to ask where these values come from.  Explanations
must end somewhere.

Now, in this metaphysical realist theory, the key object is the
totality of all propositions.  There are also the truth values and
the physical universe as an abstract object with a certain mathematical
structure--it is a 4-space with some TOE imposing a structure on
it (also fundamental constants, initial conditions, and so on).
This is pure Platonism--and so all other objects, physical objects,
people, and so on are merely abstract objects fleshed out by the
way we experience ourselves and other 4-space slices.  This is only
a picture--if it aids us in understanding it is good.  This is also
a caricature of the metaphysical realist picture.  A fuller picture
along these lines can be found in John Post's _The Faces of Existence:
An Essay in Nonreductive Metaphysics_.  The main simplification here is
the replacement of a suitable supervenience relation by a relation
of reduction.  A better picture would not say that there are only
abstract objects (including 4-space slices).  It would say that all
other entities--people, physical objects, emotions, metaphors, gods,
and so on--supervene on the objective level of existence here
described as the totality of propositions, truth values and 4-space
with a certain mathematical structure.

A collection of all true propositions is a sub-collection of the 
totality of all propositions.  Tarski's paradox appears to say that
in a classical logic with two truth values, the elements of this
sub-collection cannot be picked out.  There are also arguments
that the collection of all propositions cannot exist and would
be contradictory.  These are not orthodox arguments (Grim presents
several in _The Incomplete Universe).

If one has this kind of metaphysical model as an ideal, then one
would like to find some way of chaning logic so that one could
pick out the sub-collection of all true propositions.  I have this
as an ideal, but to be frank, I only _play_ with it as a model,
I have virtually no faith that the real world is like this.  If
I am asked to describe my own world view, I can say this:  For a
long time I was a nihilist and even today my hold on my own ethics
is tenous at best.  I like to quote Valery to myself "God created
the world from the void, but the void shows through".  I am
interested in finding a nice picture of the world, but emotionally
I am still most at home with the void.  Even my moral values
supervene on this `existential' emptiness.  All the meaning we find
in life is of our own making.  There is only nothingness beyond
the social.  But nothing can be asserted of the void--objectivity,
the world, these are all ideas we have brought.

-- 
Marko Amnell
amnell@klaava.helsinki.fi
Graduate Student in Philosophy