ONT Re: New List & Classification of Signs

[Jon Awbrey <jawbrey@oakland.edu>]

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I will go back and pick up a bit more of what Peirce
wrote "On the Algebra of Logic" (1885, CP 3.359-403).

| I have taken pains to make my distinction of icons, indices,
| and tokens [more frequently called "symbols"] clear, in order to
| enunicate this proposition:  in a perfect system of logical notation
| signs of these several kinds must all be employed.  Without tokens there
| would be no generality in the statements, for they are the only general
| signs;  and generality is essential to reasoning.  Take, for example, the
| circles by which Euler represents the relations of terms.  They well fulfill
| the function of icons, but their want of generality and their incompetence
| to expresss propositions must have been felt by everybody who has used them.
| Mr. Venn has, therefore, been led to add shading to them;  and this shading
| is a conventional sign of the nature of a token.  In algebra, the letters,
| both quantitative and functional, are of this nature.  But tokens alone do
| not state what is the subject of discourse;  and this can, in fact, not be
| described in general terms;  it can only be indicated.  The actual world
| cannot be distinguished from a world of imagination by any description.
| Hence the need of pronoun and indices, and the more complicated the subject
| the greater the need of them.  The introduction of indices into the algebra
| of logic is the greatest merit of Mr. Mitchell's system.  He writes 'F'_1
| to mean that the proposition 'F' is true of every object in the universe,
| and 'F'_u to mean that the same is true of some object.  This distinction
| can only be made in some such way as this.  Indices are also required to
| show in what manner other signs are connected together.  With these two
| kinds of signs alone any proposition can be expressed;  but it cannot be
| reasoned upon, for reasoning consists in the observation that where certain
| relations subsist certain others are found, and it accordingly requires the
| exhibition of the relations reasoned within an icon.  It has long been a puzzle
| how it could be that, on the one hand, mathematics is purely deductive in its
| nature, and draws its conclusions apodictically, while on the other hand, it
| presents as rich and apparently unending a series of surprising discoveries
| as any observational science.  Various have been the attempts to solve the
| paradox by breaking down one or the other of these assertions, but without
| success.  The truth, however, appears to be that all deductive reasoning,
| even simple syllogism, involves an element of observation;  namely, deduction
| consists in constructing an icon or diagram the relations of whose parts shall
| present a complete analogy with those of the parts of the object of reasoning,
| of experimenting upon this image in the imagination, and of observing the result
| so as to discover unnoticed and hidden relations among the parts.  (CP 3.363).

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