ONT Re: Limited Mark Universes
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It will be necessary to do a little bit of background reading.
For ease of study, I'll break up long paragraphs as I see fit.
| Still it may be well to consider the matter a little further.
| Imagine, then, a particular case under Boole's calculus, in
| which the letters are no longer terms of first intention,
| but terms of second intention, and that of a special kind.
| Genus, species, difference, property, and accident, are
| the well-known terms of second intention. These relate
| particularly to the 'comprehension' of first intentions;
| that is, they refer to different sorts of predication.
| Genus and species, however, have at least a secondary
| reference to the 'extension' of first intentions.
|
| Now let the letters, in the particular application of
| Boole's calculus now supposed, be terms of second intention
| which relate exclusively to the extension of first intentions.
| Let the differences of the characters of things and events be
| disregarded, and let the letters signify only the differences
| of classes as wider or narrower. In other words, the only
| logical comprehension which the letters considered as terms
| will have is the greater or less divisibility of the classes.
|
| Thus, 'n' in another case of Boole's calculus might,
| for example, denote "New England States"; but in the
| case now supposed, all the characters which make these
| States what they are being neglected, it would signify
| only what essentially belongs to a class which has the
| same relations to higher and lower classes which the
| class of New England States has, -- that is,
| a collection of 'six'.
|
| C.S. Peirce, CP 3.43
|
| Charles Sanders Peirce, "Upon the Logic of Mathematics",
|'Proceedings of the American Academy of Arts and Sciences',
| Volume 7, pp. 402-412, September 1867.
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