Jerry, I think you are making this seem more mysterious than it is. My understanding is that degeneracy means that there is a restriction from the general case (generate) to a less than general case. This is how Robert Rosen, e.g., uses the notion, and I don't see any good reason to think that Peirce is using it any differently. Basically, something is degenerate if it obscures generic differences in the way it can be produced. If we treat the degenerate as general, then we will be likely to make bad inferential extensions to general cases by overlooking crucial differences in the general cases.
In the passage from Peirce that you quote below, by way of Clark, I think the distinction is that the degenerate seconds consider them in terms of their form alone, which degenerates our understanding of them to firsts associated with them, making our understanding of something that is internal. The alternative is to regard them in terms of their true causes, which are external or extrinsic, and may be multiple for the same (indistinguishable internally) cases. A couple of examples are 1) spectral lines that can be produced by more than one transition that nonetheless indicate the same energy levels, and 2) isomers of compounds when they are regarded just in terms of stoichiometric relations, ignoring their chirality. John Collier Professor Emeritus, UKZN http://web.ncf.ca/collier From: Jerry LR Chandler [mailto:jerry_lr_chand...@me.com] Sent: Thursday, 17 December 2015 01:52 To: Peirce-L Cc: Clark Goble; Jeffrey Brian Downard Subject: Re: [PEIRCE-L] signs, correlates, and triadic relations Clark, Jeffrey, List: Allow me to expand on the nature of my ignorance of the meaning of degeneracy. Clearly, CSP's usage of this term with respect to mathematical objects, that is conic sections, is crisp and meaningful within the Pythagorean-Cartesian perspective of relations. Jeff's reference is crisp and, of course, well known within the scientific community. In this case, the generacy, which must be antecedent to the degeneracy, is also clear. The two lines cross or they do not cross. If they cross, then a new object is generated, a cone and it mirror image. And this diagram plays a critical role in the physics of the Minkowski's "space-time" debacle. My feeling is that this notion of "degeneracy" is difficult, if not intractable, when applied to ordinary linguistic terms which do not imply a "crossing" or parallelism. Another example is, of course, chemical atoms or molecules. I feel a different notion for generating functions is necessary both chemistry and biology.. However, from: On Dec 16, 2015, at 4:01 PM, Clark Goble wrote: But the relations of reason and these self-relations are alike in this, that they arise from the mind setting one part of a notion into relation to another. All degenerate seconds may be conveniently termed internal, in contrast to external seconds, which are constituted by external fact, and are true actions of one thing upon another. (CP 1.365 (1890)) one get's a better notion of the concept I was missing. Here, CSP brings the concepts of internal and external, also known as intrinsic and extrinsic properties in physical-chemical textbooks. As I understand this quote, CSP is contrasting the relations of reason (logic?) with the relation that everything has with itself, namely, it identity. In other words, the "intrinsic properties" in physical - chemical terms. A curious conjecture emerges from CSP's views. Thus, one could conjecture that the relations of reason and external properties are percepts of thermodynamics. Further, that the self-relations of identity are the antecepts of quantum mechanics. Amusing to think about. Any other conjectures of interest? A bit of light has been cast on whatever CSP may have intended. Cheers Jerry
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