Icon Index Symbol • 10

Questions Concerning Certain Faculties Claimed For Signs

Re: Peirce List Discussion • Helmut Raulien

HR:
I am not so sure, if thirdness is about any triadic relation.

It may be more a matter of exegetic strategy than anything else but it’s convenient to attribute thirdness to all triadic relations, differentiating their genus in specific and individual cases according to how generic or genuine their triadicity may be.

HR:
The categories in Peirce’s “new list” of them are quality, relation, representation.

Peirce’s paper “On a New List of Categories” is from 1867, before he had worked out his Logic of Relatives to its full strength, and he is still thinking of relation as limited to dyadic relations, as many in some quarters of logic still do today.  In his 1870 Logic of Relatives he refers to the “three grand classes” of logical terms as absolute terms, simple relative terms, and conjugative terms.

Now logical terms are of three grand classes.

The first embraces those whose logical form involves only the conception of quality, and which therefore represent a thing simply as “a ──”.  These discriminate objects in the most rudimentary way, which does not involve any consciousness of discrimination.  They regard an object as it is in itself as such (quale);  for example, as horse, tree, or man.  These are absolute terms.

The second class embraces terms whose logical form involves the conception of relation, and which require the addition of another term to complete the denotation.  These discriminate objects with a distinct consciousness of discrimination.  They regard an object as over against another, that is as relative;  as father of, lover of, or servant of.  These are simple relative terms.

The third class embraces terms whose logical form involves the conception of bringing things into relation, and which require the addition of more than one term to complete the denotation.  They discriminate not only with consciousness of discrimination, but with consciousness of its origin.  They regard an object as medium or third between two others, that is as conjugative;  as giver of ── to ──, or buyer of ── for ── from ──.  These may be termed conjugative terms.

The conjugative term involves the conception of third, the relative that of second or other, the absolute term simply considers an object.  No fourth class of terms exists involving the conception of fourth, because when that of third is introduced, since it involves the conception of bringing objects into relation, all higher numbers are given at once, inasmuch as the conception of bringing objects into relation is independent of the number of members of the relationship.  Whether this reason for the fact that there is no fourth class of terms fundamentally different from the third is satisfactory or not, the fact itself is made perfectly evident by the study of the logic of relatives.  (CP 3.63).

HR:
Maybe representation is a very special kind of triadic relation.

If representation refers to the class of sign relations then those are marked out from the general class of triadic relations by a definition that specifies the roles that signs, their interpretant signs, and their objects play within the bounds of a sign relation.  Not too incidentally, Peirce gives one of his more consequential definitions of a sign relation in the process of defining logic:

Logic will here be defined as formal semiotic.  A definition of a sign will be given which no more refers to human thought than does the definition of a line as the place which a particle occupies, part by part, during a lapse of time.  Namely, a sign is something, A, which brings something, B, its interpretant sign determined or created by it, into the same sort of correspondence with something, C, its object, as that in which itself stands to C.  It is from this definition, together with a definition of “formal”, that I deduce mathematically the principles of logic.  I also make a historical review of all the definitions and conceptions of logic, and show, not merely that my definition is no novelty, but that my non-psychological conception of logic has virtually been quite generally held, though not generally recognized.  (NEM 4, 20–21).

References

  • Peirce, C.S. (1870), “Description of a Notation for the Logic of Relatives, Resulting from an Amplification of the Conceptions of Boole’s Calculus of Logic”, Memoirs of the American Academy of Arts and Sciences 9, 317–378, 26 January 1870.  Reprinted, Collected Papers 3.45–149, Chronological Edition 2, 359–429.  Online (1) (2) (3).
  • Peirce, C.S. (1902), “Parts of Carnegie Application” (L 75), published in Carolyn Eisele (ed., 1976), The New Elements of Mathematics by Charles S. Peirce, vol. 4, 13–73.  Online.
  • Peirce, C.S., Collected Papers of Charles Sanders Peirce, vols. 1–6, Charles Hartshorne and Paul Weiss (eds.), vols. 7–8, Arthur W. Burks (ed.), Harvard University Press, Cambridge, MA, 1931–1935, 1958.
  • Peirce, C.S., Writings of Charles S. Peirce : A Chronological Edition, Peirce Edition Project (eds.), Indiana University Press, Bloomington and Indianapolis, IN, 1981–.

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