From: torkel@sics.se (Torkel Franzen)
Subject: Re: Excluded Middle (Long)
Organization: Swedish Institute of Computer Science, Kista
	<TORKEL.92Nov9140517@isis.sics.se>
	<1992Nov9.201300.16428@klaava.Helsinki.FI>
	<TORKEL.92Nov9215154@bast.sics.se>
	<1992Nov10.103533.12104@klaava.Helsinki.FI>
	<TORKEL.92Nov10130705@isis.sics.se>
	<1992Nov10.163455.4335@klaava.Helsinki.FI>
Date: Tue, 10 Nov 1992 18:32:00 GMT

In article <1992Nov10.163455.4335@klaava.Helsinki.FI> amnell@klaava.Helsinki.
FI (Marko Amnell) writes:

   >Here is a sketch of an argument for the existence of a set of all true 
   >propositions expressible in English:

  So let us consider your requirements. First,

   >We define a sentence to be any string of
   >words ending in a full stop that is syntactically correct

  The problems of syntax may reasonably be set aside here as inessential.
Your next requirement, however, is that a sentence expressing a true
proposition must "assert something about the world":

  >Which sentences qualify would be determined by some
  >group of rational persons who were familiar with the subject matter of the
  >sentences, say, the readers of this newsgroup.  So, given enough time, we
  >could pick out from S all those sentences of which it would make sense to
  >ask whether they were true or false.

  Already at this point your definition collapses. It is a laughable notion
that the readers of this newsgroup - which readers? at which point in
time? - could collectively agree on a definite set of descriptive
sentences among those occurring in Russell's writings. In brief: not
only are the terms used in your definition - "rational persons
familiar with the subject matter" - exceedingly vague and
indeterminate, but the idea that there is some set of sentences which
any such group of persons would single out as "descriptive" has no
basis in fact.

  Next you stipulate that the sentences in S are those descriptive
sentences that we - presumably these rational and informed people -
could in principle "verify":

   >SDi (i=1,2,...,m) and check whether it is true or not.  The method of
   >verification would vary from sentence to sentence and there is no
   >simple rule for how in general it would be done.  But, a group of
   >rational persons could in principle check at least most of the SDi.

  This is quite absurd. Are you saying that these hypothetical persons could
verify the truth of e.g. all true mathematical sentences or sentences of
physical theory occurring in Russell's writings? Again, are you saying that
there is a method of "verifying" the truth of any "true" sentences concerning
human existence occurring in Russell's writings?

  To introduce some reality into this discussion, here are a few sentences
occurring in Russell's writings:

    This question is one of great importance, since it introduces us to
    the whole problem of how knowledge can transcend personal experience.

    If we confine ourselves to spoken words in one language, a word is
    a class of closely similar noises produced by breath combined with
    movements of the throat and tongue and lips.

    What cannot be verified or falsified is meaningless.

    The simplest imaginable facts are those which consist in the possession
    of a quality by some particular thing.

    To understand the Renaissance, it is necessary first to review briefly
    the political condition of Italy.

    Schopenhauer's gospel of resignation is not very consistent and not
    very sincere.

    Before philosophy began, the Greeks had a theory or feeling about the
    universe, which may be called religious or ethical.

    The Son of Man shall send forth His angels, and they shall gather out
    of His kingdom all things that offend, and them which do iniquity,
    and shall cast them into a furnace of fire; there shall be wailing
    and gnashing of teeth.

    To be a nice person it is necessary to be protected from crude contact
    with reality, and those who do the protecting cannot be expected to
    share the niceness that they preserve.


  I submit that many people will reject as simple-minded in the extreme
any proposed task of dividing these sentences into those that do and
those that do not "assert something about the world", as well as the task
of deciding which of these sentences are "true". Each of the sentences may
be questioned in many ways, elucidated or analyzed in many ways, argued
for or against in many ways, accepted or rejected on different grounds
and interpretations. If we accept one of these sentences as true or
reject it as false, what we mean by this can be understood only in the
context of our interpretations and explanations.

  I submit further that even if a bunch of people accept your two tasks
as meaningful, there is no reason whatever to believe that they will arrive
at any consensus, or that their decisions will agree with those of a
different group, or that they will arrive at the same decisions the next time
you ask them.