ONT Re: Logic Of Relatives
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
LOR. Discussion Note 19
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
BM = Bernard Morand
JA = Jon Awbrey
Bernard,
I now have three partially answered messages on the table,
so I will just grab this fragment off the top of the deck.
BM: Peirce gives the following definition (CP 8.343):
BM, quoting CSP:
| It is likewise requisite to distinguish
| the 'Immediate Interpretant', i.e. the
| Interpretant represented or signified in
| the Sign, from the 'Dynamic Interpretant',
| or effect actually produced on the mind
| by the Sign; and both of these from
| the 'Normal Interpretant', or effect
| that would be produced on the mind by
| the Sign after sufficient development
| of thought.
|
| C.S. Peirce, 'Collected Papers', CP 8.343.
JA: Well, you've really tossed me in the middle of the briar patch now!
I must continue with my reading from the 1870 LOR, ...
BM: Yes indeed! I am irritated by having not the necessary
turn of mind to fully grasp it. But it seems to be a
prerequisite in order to understand the very meaning
of the above table. It could be the same for:
BM, quoting CSP:
| I define a 'Sign' as anything which on the one hand
| is so determined by an Object and on the other hand
| so determines an idea in a person's mind, that this
| latter determination, which I term the 'Interpretant'
| of the sign, is thereby mediately determined by that
| Object.
BM: The so-called "latter determination" would make the 'Interpretant'
a tri-relative term into a teridentity involving Sign and Object.
Isn't it?
BM: I thought previously that the Peirce's phrasing was just applying the
principle of transitivity. From O determines S and S determines I,
it follows: O determines I. But this is not the same as teridentity.
Do you think so or otherwise?
My answers are "No" and "Otherwise".
Continuing to discourse about definite universes thereof,
the 3-identity term over the universe 1 = {A, B, C, D, ...} --
I only said it was definite, I didn't say it wasn't vague! --
designates, roughly speaking, the 3-adic relation that may
be hinted at by way of the following series:
1,, = A:A:A +, B:B:B +, C:C:C +, D:D:D +, ...
I did a study on Peirce's notion of "determination".
As I understand it so far, we need to keep in mind
that it is more fundamental than causation, can be
a form of "partial determination", and is roughly
formal, mathematical, or "information-theoretic",
not of necessity invoking any temporal order.
For example, when we say "The points A and B determine the line AB",
this invokes the concept of a 3-adic relation of determination that
does not identify A, B, AB, is not transitive, as transitivity has
to do with the composition of 2-adic relations and would amount to
the consideration of a degenerate 3-adic relation in this context.
Now, it is possible to have a sign relation q whose sum enlists
an elementary sign relation O:S:I where O = S = I. For example,
it makes perfect sense to me to say that the whole universe may
be a sign of itself to itself, so the conception is admissable.
But this amounts to a very special case, by no means general.
More generally, we are contemplating sums like the following:
q = O1:S1:I1 +, O2:S2:I3 +, O3:S3:I3 +, ...
Jon Awbrey
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o