[Inquiry] Re: Questions Involving Pure Symbols -- Discussion

[Jon Awbrey]

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QUIPS.  Discussion Note 19

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Jim,

In connection with the attempted interpretation of words
like "and", "or", "of", etc. as syncategorematic symbols,
there is the imputed distinction between logical symbols
and extra-logical symbols that we have also talked about.

Here is a perennial passage:

| Underlying our whole construction is the division of all terms of the
| language discussed into logical and extra-logical.  This division is
| certainly not quite arbitrary.  If, for example, we were to include
| among the extra-logical signs the implication sign, or the universal
| quantifier, then our definition of the concept of consequence would
| lead to results which obviously contradict ordinary usage.  On the
| other hand, no objective grounds are known to me which permit us to
| draw a sharp boundary between the two groups of terms.  It seems to be
| possible to include among logical terms some which are usually regarded
| by logicians as extra-logical without running into consequences which
| stand in sharp contrast to ordinary usage.  In the extreme case we
| could regard all terms of the language as logical.  The concept of
| 'formal' consequence would then coincide with that of 'material'
| consequence.  The sentence X would in this case follow from the
| class K of sentences if either X were true or at least one
| sentence of the class K were false.
|
| Tarski, "On the Concept of Logical Consequence", LSM, pp. 418-419
|
| Alfred Tarski,
|"On the Concept of Logical Consequence", address given at the
| International Congress of Scientific Philosophy, Paris, 1935.
|'Logic, Semantics, Metamathematics:  Papers from 1923 to 1938', pp. 409-420,
| Translated by J.H. Woodger, 1st ed., Oxford University Press, Oxford, UK, 1956.
| 2nd ed., Edited and Introduced by J. Corcoran, Hackett, Indianapolis, IN, 1983.

Previously cited in:

RIO.  Representation Invariant Ontologies
RIO.  http://stderr.org/pipermail/inquiry/2003-April/000405.html

Jon Awbrey

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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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