ONT Re: Logic Of Relatives
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LOR. Discussion Note 12
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BM = Bernard Morand
BM: The pairing "intensional, synthetic" against the other "extensional, analytic"
is not one that I would have thought so. I would have paired synthetic with
extensional because synthesis consists in adding new facts to an already made
conception. On the other side analysis looks to be the determination of
features while neglecting facts. But may be there is something like
a symmetry effect leading to the same view from two different points.
Oh, it's not too important, as I don't put a lot of faith in such divisions,
and the problem for me is always how to integrate the facets of the object,
or the faculties of the mind -- but there I go being synthetic again!
I was only thinking of a conventional contrast that used to be drawn
between different styles of thinking in mathematics, typically one
points to Descartes, and the extensionality of analytic geometry,
versus Desargues, and the intensionality of synthetic geometry.
It may appear that one has side-stepped the issue of empiricism
that way, but then all that stuff about the synthetic a priori
raises its head, and we have Peirce's insight that mathematics
is observational and even experimental, and so I must trail off
into uncoordinated elliptical thoughts ...
The rest I have to work at a while, and maybe go back to the Welby letters.
Jon Awbrey
> OK. I will try to make clear the matter, at least as far as I understand it for now.
> We can summarize in a table the 10 divisions with their number in a first column, their title in
> current (peircean) language in the second and some kind of logical notation in the third. The
> sources come mainly from the letters to Lady Welby. While the titles come from CP 8.344, the third
> column comes from my own interpretation.
>
> So we get:
>
> I - According to the Mode of Apprehension of the Sign itself ; S
> II - According to the Mode of Presentation of the Immediate Object ; Oi
> III - According to the Mode of Being of the Dynamical Object - Od
> IV - According to the Relation of the Sign to its Dynamical Object ; S-Od
> V - According to the Mode of Presentation of the Immediate Interpretant ; Ii
> VI - According to the Mode of Being of the Dynamical Interpretant ; Id
> VII - According to the relation of the Sign to the Dynamical Interpretant ; S-Id
> VIII - According to the Nature of the Normal Interpretant ; If
> IX - According to the the relation of the Sign to the Normal Interpretant ; S-If
> X - According to the Triadic Relation of the Sign to its Dynamical Object
> and to its Normal Interpretant ; S-Od-If
>
> Several discussions could take place there, as to the reasons for the number of divisions, the
> reasons of the titles themselves. Another one is my translation from "normal interpretant" into
> "final interpretant" (which one is called elsewhere "Eventual Interpretant" or "Destinate
> Interpretant" by CSP.). I let all this aside to focus on the following remark : 6 divisions
> correspond to individual correlates ( S, Oi, Od, Ii, Id, If), 3 divisions correspond to dyads
> (S-Od, S-Id, S-If) and the tenth to a triad (S-Od-If). This remark would itself deserve a lot of
> explanations but one more time I let this aside.
>
> Then we have the following very clear statement from Peirce:
>
> | It follows from the Definition of a Sign
> | that since the Dynamoid Object determines
> | the Immediate Object,
> | which determines the Sign,
> | which determines the Destinate Interpretant
> | which determines the Effective Interpretant
> | which determines the Explicit Interpretant
> |
> | the six trichotomies, instead of determining 729 classes of signs, as they would if they were
> | independent, only yield 28 classes; and if, as I strongly opine (not to say almost prove)
> | there are four other trichotomies of signs of the same order of importance, instead of making
> | 59049 classes, these will only come to 66” (Letter to Lady Welby, 14/12/1908, LW, p. 84)
>
> The separation made by CSP between 6 divisions and four others seems to rely upon the suggested
> difference between individual correlates and relations. We get the idea that the 10 divisions are
> ordered on the whole and will end into 66 classes (by means of three ordered modal values on each
> division: maybe, canbe, wouldbe) Finally we have too the ordering for the divisions relative to
> the correlates that I write in my notation:
>
> Od -> Oi -> S -> If -> Id -> Ii. This order of "determinations" has bothered many people but if we
> think of it as operative in semiosis, it seems to be correct (at least to my eyes).
> Thus the question is: where, how, and why the "four other trichotomies" fit in this schema to
> obtain a linear ordering on the whole 10 divisions? May be the question can be rephrased as : how
> intensional relationships fit into an extensional one ? Possibly the question could be asked the
> other way. R. Marty responds that in a certain sense the four trichotomies give nothing more than
> the previous six ones but I strongly doubt of this.
>
> I put the problem in graphical form in an attached file because my message editor will probably
> make some mistakes. I make a distinction between arrow types drawing because I am not sure that
> the sequence of correlates determinations is of the same nature than correlates determination
> inside relations.
>
> It looks as if the problem amounts to some kind of projection of relations on the horizontal axis
> made of correlates.
>
> If we consider some kind of equivalence (and this seems necessary to obtain a linear ordering), by
> means of Agent -> Patient reductions on relations, then erasing transitive determinations leads to> :
>
> Od -> Oi -> S -> S-Od -> If -> S-If -> S-Od-If -> Id -> S-Id -> Ii
>
> While it is interesting to compare the subsequence
> S-Od -> If -> S-If ->S-Od-If with the pragmatic maxim,
> I have no clear idea of the (in-) validity of such a result.
> But I am convinced that the clarity has to come from the Logic Of Relatives.
>
> I will be very grateful if you can make something with all that stuff.
> Regards
>
> Bernard
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