From: merritt@macro.bu.edu (Sean Merritt)
Newsgroups: alt.philosophy.objectivism
Subject: Re: Modern Logic -- question (was Obj. Philosophy)
Date: 7 Jan 93 15:00:08 GMT
Organization: Boston University Physics Department
In-reply-to: torkel@sics.se's message of 6 Jan 93 22:15:16 GMT


#In article <TORKEL.93Jan6231516@bast.sics.se> torkel@sics.se (Torkel Franzen) writes:



   In article <MERRITT.93Jan6154833@macro.bu.edu> merritt@macro.bu.edu
    (Sean Merritt) writes:

	[quoting me:]
      ># As we have seen amply demonstrated in this group, the terms "axiom",
      >#"theorem", "logic" have a very different meaning in Objectivism than
      >#they do in logic.
      >There has been no such thing demonstrated.

#     Sure it has. Consider "logic", where we got an authoritative explanation
#   of the Objectivist meaning of the term:
#
#       Logic is the art or skill of non-contradictory identification.
#       Logic has a single law, the Law of Identity, and its various
#       corollaries.

In the use of Logic no matter how skillfull there will be times when
Logic fails to yeild a superior course of action. If you accpet the 
Law of Identity as an absolute then you are surrendering your ability
to differentiate reality. The reality of the matter is this:
That although highly improbable, there exist a case where `A is not A'
and it is possible(not probable) that an individual will encounter
this possibility at least once in his life.

#     Let us take a couple of central theorems of modern logic: the completeness
#   theorem for first order logic, the incompleteness theorem for second order
#   logic. There is nothing in the above that even begins to give an idea of
#   the meaning or importance of these theorems.

Agreed, so what? They are improtant when you take action based on
a result of logical reasoning. The tough decisions in life are not
of first order logic in nature. They are `fuzzy' to the extreme.

#
#     Consider "axiom". As we have found out, an "axiom" to an Objectivist
#   is a formula such as "A is A", which is variously presented as a
#   "demand", a "concept", a "law", and given all sorts of
#   interpretations. This kind of gross sloppiness is alien to logic as
#   the subject is understood today. An axiom, as the term is understood
#   in logic, is a statement designated as such in a well-defined theory
#   with a well-defined language.

Do you deny the "a priori" nature of axioms as they are used in
Objectivism? If you do then for objectivism there is no special
usage of axioms, they clearly do not exist at all!(under that intrepretation)

#     Consider "theorem". In Objectivism, assuming theorems to be what is
#   yielded by Objectivist "logical deductions", a theorem is anything
#   held by Rand to follow from "A is A" and similar "axioms". In logic, a
#   theorem of a theory is a statement in the language of that theory
#   which is obtainable by applying formally specified rules of inference
#   to formally specified axioms. Of course no formal axioms or rules of
#   inference have ever been specified in Objectivism. And indeed, nobody
#   expects theorems in this sense from philosophy. The Randians, however,
#   for reasons of their own (partly sheer veneration for their founder),
#   feel compelled to speak of their various assertions as having been
#   arrived at by "logical reasoning" from "axioms".

You seem to be trying to prove that since axioms and theorems have
no real meaning to Randians, that the foundations of Objectivism
have crumbled away. Sir you are not an Objectivst? Correct?
For you there are no axioms of logic with the objectivist frame
work. Your attempt to say that they have special meaning in this context
is quite frankly, a dodge. For if an axiom is not considered "a priori"
it is not an axiom at all. Your use or your interpretation of the
Randian's use if the word is entirely incorrect and utterly meaningless.
AS such Objectivisim cannot provide a "basis for knowledge"(Epistomology).
In your mind you have already reduced Objetivisim to an absurdity.
Why then are you still here?


-sjm
--
Sean J. Merritt		         | "Every revolt is a cry of innocence    
Dept of Physics Boston University|  and an appeal to the essence of being."
merritt@macro.bu.edu             | Albert Camus, The Rebel
Newsgroups: alt.philosophy.objectivism