[Inquiry] Re: Peirce's Logic Of Information

[Jon Awbrey]

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PLOI.  Note 5

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Let's begin working through that last passage, bit by bit:

| We come next to consider inductions.  In inferences of this kind
| we proceed as if upon the principle that as is a sample of a class
| so is the whole class.  The word 'class' in this connection means
| nothing more than what is denoted by one term, -- or in other words
| the sphere of a term.  Whatever characters belong to the whole sphere
| of a term constitute the content of that term.  Hence the principle of
| induction is that whatever can be predicated of a specimen of the sphere
| of a term is part of the content of that term.  And what is a specimen?
| It is something taken from a class or the sphere of a term, at random --
| that is, not upon any further principle, not selected from a part of
| that sphere;  in other words it is something taken from the sphere
| of a term and not taken as belonging to a narrower sphere.  Hence
| the principle of induction is that whatever can be predicated of
| something taken as belonging to the sphere of a term is part of
| the content of that term.  But this principle is not axiomatic
| by any means.  Why then do we adopt it?
|
| C.S. Peirce, 'Chronological Edition', CE 1, 462-463

Here is a programme for keeping track of the players, that is,
the various alternative and associated terms that might occur
in the following discussion of Peirce's theory of information:

` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` Predicates` Qualities ` Comprehension Connotation Content Depth ` ` `
` Properties` o.......o ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` Characters` `\` ` `/` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` \ ` / ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` `\`/` ` ` Concept ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` Object, Class ` O<----o Symbol` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` `/`\` ` ` Term` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` / ` \ ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` Elements` ` `/` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` Instances ` o.......o ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` Specimens ` Exemplars ` Extension ` ` Denotation` Sphere` Breadth ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `

I am deploying an ample plurality of rhetorical alternatives
partly in order to emphasize the fact that the focus here is
not on defining entities like qualities and exemplars but on
the shape of the incidence relation between their rough ilks.
Some of the terms resting in the same strata of the paradigm
are close synonyms, in other cases, they are measures of the
associated dimensions.  I have placed "class" in accord with
contemporary usage in set theory, as my sense of the reading
tells me that Peirce is using "class" in a unitary sense, in
contrast with his use of "sphere" in more distributive sense.

Jon Awbrey

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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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