Tommi:
On Apr 27, 2015, at 9:57 AM, Tommi Vehkavaara wrote: Tommi: First, is the quote correct: "...without respect to a second..." which sounds very odd if the Secondness is talked about? Secondly, at least I have always seen Bateson's idea of information as a difference that makes difference as one clear example of triadic relation or "Thirdness" if you like. The first difference already contains a first that differs from some second someway and the difference that is made is the third (a meaning if you like). Yours, -Tommi Tommi, you are spot on. Of course it is very odd!!! Why is it odd? Because many CSP philosophers confuse the roots of "Firstness, Secondness and Thirdness" with the concept of order. (Rhetorically, this sentence is necessary for the triad to exist!) In other words, to grasp the meaning of this sentence, one must draw a mental diagram of this triad that is not an ordered relation. A challenge, to be sure. The mental icon can not be a triangle, a three-sided figure, or a random distribution of three "spots". The figure must also allow for a later association with cause-effect concepts in all symbol systems! Further, of course, is the common association of this triad with time. In these three sentences, a term for time or change does not appear. Further, of course, is the common association of this triad with cause and effect. The cause and effect interpretation also is contrary to this CSP quote. The critical distinction of this quote from other quotes is that it is a the deeper abstraction. It is an open question: Is this the deepest possible rhetorical abstraction? An abstraction that is formless? One way to look at these three sentence is that it purely metaphysical. No concrete subject, no concrete object. Merely the conjecture that anything can be coupled to anything by a relation. Of course, the existence of such a relation may be either True or False. Of particular interest to mathematical logic is the relationship between Peirce's three sentences and modern category theory (Not Aristotelian or Kantian categories.) Mathematical category theory demands closure on a diagram in the form of both objects and relations; further, the diagram must be directed. Thus, these three sentences are NOT sufficient to define the S. MacLane's structures for natural relations. Indeed, CSP's three sentences is insufficient to define even one of the three relations of MacLane's category theory BECAUSE they lack the concept of a directed relation. Within S. MacLane's category theory, the concept of "order" among the three terms is incorporated by the concept of "directed" graph. Diagrammatically, the initial term must be part of a cycle which returns to the beginning. CSP separates his topological graphs on the basis of 'chorisis' as connected graphs and 'cyclosis' as number of independent rings. see: Folder 482, Ketner, Trans. 23 (4) 539 (1987). Thus, CSP's definition of Secondness in this letter to Lady Welby has deep implications for the structures of his patterns of inferences and the forms of connectedness of parts of wholes. Cheers Jerry Post script. BTW, these sentences defining the triad of Firstness, Secondness and Thirdness can be viewed as the simplest possible form of chemical logic in which firstness is one chemical element, secondness is a different chemical element and thirdness is a potential relation between the two. Example: Sodium Chloride, ordinary table salt. Historically, CSP focused on the then prevalent concept of "Radicals" and Handedness of molecules, which necessitated this extreme level of abstraction and circuitous rhetoric. see: 3.421 for an application.
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