ONT Pierce's three kinds of representations
Jon,
this is quote is interesting, to speak of Pierce's views,
but it doesn't even begin to address interesting logical phenomenon
like variables. unless a variable like P is intended to be a symbol.
But the way I read this, it is the VALUE of P that is intended to be
the symbol instead of the variable itself.
if an entire book is a proposition, as I read Pierce below,
then presumably each copy of the book is a variable whose value
is the proposition.
But modern predicate logic would have problems with saying X, Y, and Z
are all 'constants' whose value is the same propositional value.
since they really aren't variables in that case.
Propositional logic probably would have problems with it too, as I
understand any given proposition is only one variable. It goes against
the rules as I understand them to have P=some proposition, and Q=the same
proposition. because P and Q are expected to be independent, and this
situation makes them two names for the same proposition.
Or am I just confused about this?
David
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> | For this purpose, I must call your attention to
> | the differences there are in the manner in which
> | different representations stand for their objects.
> |
> | In the first place there are likenesses or copies -- such as
> | 'statues', 'pictures', 'emblems', 'hieroglyphics', and the like.
> | Such representations stand for their objects only so far as they
> | have an actual resemblance to them -- that is agree with them in
> | some characters. The peculiarity of such representations is that
> | they do not determine their objects -- they stand for anything
> | more or less; for they stand for whatever they resemble and
> | they resemble everything more or less.
> |
> | The second kind of representations are such as are set up
> | by a convention of men or a decree of God. Such are 'tallies',
> | 'proper names', &c. The peculiarity of these 'conventional signs'
> | is that they represent no character of their objects. Likenesses
> | denote nothing in particular; 'conventional signs' connote nothing
> | in particular.
> |
> | The third and last kind of representations are 'symbols' or general
> | representations. They connote attributes and so connote them as to
> | determine what they denote. To this class belong all 'words' and
> | all 'conceptions'. Most combinations of words are also symbols.
> | A proposition, an argument, even a whole book may be, and
> | should be, a single symbol.
> |
> | CSP, CE 1, pages 467-468.
> |
> | Charles Sanders Peirce,
> |"The Logic of Science, or, Induction and Hypothesis",
> | Lowell Institute Lectures of 1866, pages 357-504 in:
> |
> |'Writings of Charles S. Peirce: A Chronological Edition',
> |'Volume 1, 1857-1866', Peirce Edition Project,
> | Indiana University Press, Bloomington, IN, 1982.
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