List, Tommi, Frederik, Gary F. Thank you for correcting my error. My apologies. I have corrected the title as well.
How does it effect the meaning of my post? Very, very, little as these three sentences/definitions are so tightly coupled to one another by parallel structures. Obviously, the issue of "oddness" must be deleted. But that was just a lead-in to the meat of the response. Surprisingly, the difference between "without" and "with" make s almost no difference in the meaning of what I wrote. Gary F. - There is no confusion in the meaning of what I wrote. Its open to rebuttal by anyone who cares to assert otherwise. In contrast with other CSP assertions on "Firstness, Secondness" and Thirdness", The Lady Welby letter is unique. What is unique is the grammatical structure of the three sentences, which is what deserves special attention. > 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. > It remains a question of existence of logical terms (nominative cases). No predication of attributes of the terms. Logically and mathematically the three terms are two nouns (of any sort, ie, variables, numbers, or whatever) and an undefined relation between them. Grammatically, the relation could a copula, a predicate, a conjunction, etc., equal sign, a chemist arrow, etc I always found it interesting that even Stoic logic would fit under this big tent, just denote the relation by a symbol for punctuation. > > > 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. > That is, all three sentences merely relate to existence. In particular, the third sentence is equally applicable to either a single pair of terms, such as two points of a set. If anyone wishes to interpret 'Thirdness' in any other way, they are free to do so. But it will not be by Peircian modality. At least, that is my reading of these critical (and controversial) sentences. > 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. > > Cheers Jerry On Apr 27, 2015, at 12:44 PM, Jerry LR Chandler wrote: > 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 > > > ----------------------------- > PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] > . To UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] > with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at > http://www.cspeirce.com/peirce-l/peirce-l.htm . > > > >
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