[Inquiry] Re: Relatives of Second Intention -- Discussion

[Jon Awbrey]

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ROSI.  Discussion Note 5

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That seems like enough source material for the moment
to begin to get a glimmer of how Peirce resurrected
the venerable notions of second intentions for his
own ends in the logic of relatives.  Let us then
look back at the opening charge of this mission
to see if we can better understand its import:

| By 'logical' reflexion, I mean the observation of thoughts
| in their expressions.  Aquinas remarked that this sort of
| reflexion is requisite to furnish us with those ideas
| which, from lack of contrast, ordinary external
| experience fails to bring into prominence.
| He called such ideas 'second intentions'.
|
| It is by means of 'relatives of second intention'
| that the general method of logical representation
| is to find completion.
|
| C.S. Peirce, 'Collected Papers', CP 3.490,
|"The Logic of Relatives", 'The Monist',
| vol. 7, pp. 161-217, 1897.

We can get a sense of what Peirce intended by "logical reflexion"
if we observe what he actually did, according to his accounts of
the matter, in noticing and naming the various terms of second
intention to which he took the time to call general attention.

Apparently, "observation of thoughts in their expressions", with
regard to the panoply of 2-adic relative terms, is not limited
to their expressions in rhematic forms such as "child of __",
"cousin of __", "husband of __", "spouse of __", and so on,
but includes, for Peirce, observation of their expressions
in extensional forms such as those that form up over the
the relevant basis of elementary 2-adic relatives like
A:A, A:B, A:C, ..., B:A, B:B, B:C, ..., and so on.

Moreover, the output of these reflections is a classification
of relative terms according to abstract commonalities of form,
for instance, the "diagonal form" A:A + B:B + C:C + ... of an
identity relation.  Given a fruitful classification, one then
inquires into the laws that affect these forms in combination.

Jon Awbrey

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