[Arisbe] Re: Logic As Semiotic

[Jon Awbrey]

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| To prove then, first, that all symbols are symbolizable.
| Every syllogism consists of three propositions with two terms
| each, a subject and a predicate, and three terms in all each term
| being used twice.  It is obvious that one term must occur both as
| subject and predicate.  Now a predicate is a symbol of its subject.
| Hence in all reasoning 'à priori' a symbol must be symbolized.
| But as reasoning 'à priori' is possible about a statement
| without reference to its predicate, all symbols must be
| symbolizable.
|
| 2nd To prove that all forms are symbolizable.
| Since this proposition relates to pure form it is
| sufficient to show that its consequences are true.
| Now the consequence will be that if a symbol of any
| object be given, but if this symbol does not adequately
| represent any form then another symbol more formal may
| always be substituted for it, or in other words as soon
| as we know what form it ought to symbolize the symbol may
| be so changed as to symbolize that form.  But this process
| is a description of inference 'à posteriori'.  Thus in the
| example relating to light;  the symbol of "giving such and
| such phenomena" which is altogether inadequate to express a
| form is replaced by "ether-waves" which is much more formal.
| The consequence then of the universal symbolization of forms
| is the inference 'à posteriori', and there is no truth or
| falsehood in the principle except what appears in the
| consequence.  Hence, the consequence being valid,
| the principle may be accepted.
|
| 3rd To prove that all things may be symbolized.
| If we have a proposition, the subject of which is not
| properly a symbol of the thing it signifies;  then in case
| everything may be symbolized, it is possible to replace this
| subject by another which is true of it and which does symbolize
| the subject.  But this process is inductive inference.  Thus having
| observed of a great variety of animals that they all eat herbs, if I
| substitute for this subject which is not a true symbol, the symbol
| "cloven-footed animals" which is true of these animals, I make an
| induction.  Accordingly I must acknowledge that this principle
| leads to induction;  and as it is a principle of objects,
| what is true of its subalterns is true of it;  and since
| induction is always possible and valid, this principle
| is true.
|
| CSP, CE 1, pages 185-186.
|
| Charles Sanders Peirce, "Harvard Lectures 'On the Logic of Science'", (1865),
|'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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