From: amnell@klaava.Helsinki.FI (Marko Amnell)
Newsgroups: sci.philosophy.meta
Subject: Re: Excluded Middle (Long)
Date: 8 Nov 92 12:09:00 GMT
Organization: University of Helsinki

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.

- 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.

- 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.

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

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



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