From: holmes@garnet.idbsu.edu (Randall Holmes)
Newsgroups: sci.philosophy.meta
Subject: Re: Excluded Middle (Long)
Date: 9 Nov 92 15:59:22 GMT
Organization: Boise State University

In article <1992Nov8.120900.5613@klaava.Helsinki.FI> amnell@klaava.Helsinki.FI (Marko Amnell) writes:
>Some further notes (I cancelled an earlier version of this):
>
>Randall Holmes has made four points which seem of particular interest:
>
>- If one sets up a logic with more than two truth values, and hence
>manages to avoid Tarski's paradox, then a further paradox can be set
>up by considering the function that sends sentences to their truth
>values.  In particular, a paradox is formed by the sentence "the truth
>value of this sentence is not `true'".  So, this sentence is true iff
>it is anything but `true'.  Is it just like Tarski's, then?  Can you 
>elaborate a bit  about this paradox?  I will try to see if Hintikka's
>IF system avoids it or not.

I can't elaborate yet; I thought it up as I was writing.  I think that
many systems of multi-valued logic would avoid this paradox -- but
this would reflect an inability to introspect on their system of truth
values just as unsatisfactory as the problem with two-valued logic.

>
>- Truth vs. reality.  Certainly one can say that the truth about the
>world--if it exists--is not the world itself.  But, the interesting
>theoretical object is the collection of truths, not the Lebenswelt of
>experience.  How would one characterize the world?  In terms of the
>contingent chracteristics of human experience?  If so, would other
>beings, with different sense organs, not inhabit different worlds?
>This is why Peirce's definition of reality focuses on the Reals, not
>on how they appear to us--or to other beings--in sensation.

Here I should note an omission pointed out by M. Zeleny -- Truth
refers to what can be said about the world -- _correctly_.  The
characterization of the world is rather thin and flavorless, I am
afraid -- it is simply whatever exists.  It certainly has nothing to
do with _experience_ (specifically) -- our experience of the world is
more in the category of Truth than the category of Reality.


>
>- Truth and the iterative hierarchy of sets.  The iterative hierarchy
>is endless in the sense that in eg. ZF one builds the universe of set
>in a well-founded way and never reaches V.  The universe of eg. NF, does
>exist, but is not charaterized by a nice picture like in ZF.  How is
>the iterative hierarchy like Truth?  We don't have a picture of truths
>being built in a systematic way.  What we do have is an idea, Truth,
>that corresponds to the "ideal end of inquiry".  But there is no full
>characterization of this totality.  Hence to me Truth looks more like
>the universe of NF than the iterative hierarchy (if we wish to follow
>this conceit).  I dunno how useful it is.

The iterative hierarchy is the analogue to the "ideal end of inquiry",
not the universe of NF.

>
>- Finally, objects, sentences, facts and states of affairs.  Quine's
>ontology is not the only possible ontology.  It is legitimate to 
>have facts in one's ontology (eg. Reinhardt Grossmann's ontology).

Actually, I do admit "facts", but I regard them as sentences or
equivalence classes of sentences, so I doubt that you would regard
them as facts.  To me, truth is obviously an attribute of sentences.

>The identification of states of affairs with chunks or hunks of
>4-space is, again, not the only possibility, although it is natural.

I regard it as an expedient; I don't place any philosophical weight on
it.


>States of affairs could be characterized by way of our senses.  A
>state of affairs might be eg. a collection of sense data by one
>subject at a particular moment in his subjective sense of time.  Note
>that it is possible to build a very sophisticated notion of time
>from this subjective basis.  Saul Basri builds full General Relativity
>in such a way in _A Deductive Theory of Space and Time_.  He defines
>the "class of all living human beings who have adequately functioning
>sense organs, can communicate with each other, and do so honestly and
>without bias".  He defines the "objective universe" based on this
>collection of observers.  He then builds GR in a rigorous way.

Hmmm...

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


-- 
The opinions expressed		|     --Sincerely,
above are not the "official"	|     M. Randall Holmes
opinions of any person		|     Math. Dept., Boise State Univ.
or institution.			|     holmes@opal.idbsu.edu