ONT Re: Tone, Token, Type

[Jon Awbrey <jawbrey@oakland.edu>]

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

| There are cases where we are quite in the dark, alike concerning the creating
| purpose and concerning the genesis of things[,] but where we find a system of
| classes connected with a system of abstract ideas -- most frequently numbers --
| and that in such a manner as to give us reason to guess that those ideas in
| some way, usually obscure, determine the possibilities of things.  For example,
| chemical compounds, generally -- or at least the more decidedly characterized
| of them, including, it would seem, the so-called elements -- seem to belong
| to types, so that, to take a single example, chlorates KClO3, manganates
| KMnO3, bromates KBrO3, rutheniates KRuO3, iodates KIO3, behave chemically
| in strikingly analogous ways.  That this sort of argument for the existence
| of natural classes -- I mean the argument drawn from types, that is, from
| a connection between the things and a system of formal ideas -- may be much
| stronger and more direct than one might expect to find it, is shown by the
| circumstance that ideas themselves -- and are they not the easiest of all
| things to classify naturally, with assured truth? -- can be classified
| on no other grounds than this, except in a few exceptional cases.  Even
| in these few cases, this method would seem to be the safest.  For example,
| in pure mathematics, almost all the classification reposes on the relations
| of the forms classified to numbers or other multitudes.  Thus, in topical
| geometry, figures are classified according to the whole numbers attached
| to their 'choresis', 'cyclosis', 'periphraxis', 'apeiresis', etc.  As for
| the exceptions, such as the classes of hessians, jacobians, invariants,
| vectors, etc., they all depend upon types, too, although upon types of
| a different kind.  It is plain that it must be so;  and all the natural
| classes of logic will be found to have the same character.
|
| Charles Sanders Peirce, 'Collected Papers', CP 1.223.

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o