Sung, I repeat, firsts are not structures and structures are not firsts. Firsts don’t permit the sort of relational properties required of structures, though there is a first corresponding to any structure, properly called an icon, but structures are never icons. Structures can exist as seconds, and be real as thirds. This is the way the notion of structure is used in logic and in network theory (nodes and connections among them, which is logically identical to a structure).
This sort of abuse of terminology undermines what you are saying, and in fact makes it false. This is a shame. On the issue of cardinality and ordinality, you have them backwards. The numbers are given in terms of the closure of equinumerosity, the closure being at least a second order property, which is just cardinality. Once this is established by some method , we can define ordinality in terms of it. This is how it has been done since at least Peano, and the contemporary set theoretic definition of the counting numbers in terms of the empty set and constructions (either Zermelo-Fraenkel or von Neumann) on it follow the same pattern by ensuring equinumerosity first through defining a second order property, and then proving the ordinality. I addressed this before, but obviously you don’t care about getting it right. John Collier Professor Emeritus, UKZN http://web.ncf.ca/collier From: sji.confor...@gmail.com [mailto:sji.confor...@gmail.com] On Behalf Of Sungchul Ji Sent: Wednesday, 02 December 2015 4:16 AM To: PEIRCE-L Subject: Re: [PEIRCE-L] signs, correlates, and triadic relations Hi Clark, ". . . Firstness is the world of raw experience, ideas or possibility, secondness the world (120115-1) of reactions, brute force & actuality and thirdness the world of signs, connections and power (not necessarily mental unless one is careful what one means by that)." (1) I agree with you on the definition of these categories of Peirce. We seem to disagree on how to assign these categories to the three worlds of Burgin and the three roses of Scotus. (2) In principle, there are 6 (and only 6) ways of assigning the three objects (whether words or roses) to the Peircean categories as shown in Table 1. Although I adopted Possibility 1 in Figure 1 of my PEIRCE-L post of 11/302015, I cannot rule out some of the other possibilities listed in Table 1. Table 1. Non-deterministic relation between triadic model of the worlds and Peircean categories. Possibilities Firstness Secondness Thirdness Context or Field of Studies 1 S* P M ? 2 S M P ? 3 P S M ? 4 P M S ? 5 M S P ? 6 M P S ? *S = World of structures P = Physical world M = Mental world (3) The non-determinism indicated in Table 1 is frustrating if we assume, whether correctly or not, that there should be only one unambiguous assignment possible if our theories are right. Such an assumption may be valid and future studies may indeed reveal an unambiguous categorial assignment. Alternatively, the non-determinism of Table 1 may be real and reflects a deep structure of reality as discussed below. (4) The non-determinism of Table 1 reminded me of a similar non-determinism in gauge field theories in physics. Simply put ". . . a gauge theory is a type of field theory<https://en.wikipedia.org/wiki/Field_theory_(physics)> in which the Lagrangian<https://en.wikipedia.org/wiki/Lagrangian_(field_theory)> is (120115-2) invariant<https://en.wikipedia.org/wiki/Invariant_(physics)> under a continuous group<https://en.wikipedia.org/wiki/Continuous_group> of local transformations" (https://en.wikipedia.org/wiki/Gauge_theory). Replacing "Lagrangian" with "Peircean categories" and identify the 6 possibilities of Table 1 with "local transformations" in (1201156-2) logically leads to "A gauge theory may be said to apply to semiotics qualitatively, if the Peircean ITR (120115-3) (Irreducible Triadic Relation) remains invariant upon transforming the nature of the objects occupying the three positions in the commutative triangle, Figure 1" f g Firstness ----------------> Secondness -----------> Thirdness (Real Rose) (Rose) (Mental Rose) [World of Structures] [Physical World] [Mental World] | ^ | | |_______________________________________| h Figure 1. The Peircean ITR as the conserved property of semiotics (or sign physics (?)) f = actualization; g = pattern formation; h = information flow. (5) The validity of Statement (120115-3) seems partly supported by the approximate symmetry that can be detected between particle physics and semiotics as analyzed in Table 1. Table 1. “Generalized’ Gauge Field theory (?) Discipline Particle Physics Semiotics (Sign Physics ?) Objects studied nucleons (protons, neutrons) Ideas (1ns, 2ns, & 3ns)* Properties angular momentum Ordinality** Conserved property Isotopic spin, I Cardinality or ITR*** Gauage Field Force Strong force 'Mind force' (?) *1ns = Firstness; 2ns = Secondness; 3ns = Thirdness. **1ns is prerequisite for 2ns which is prerequisite for 3nd. ***ITR = Irreducible Triadic Relation, stating that the elements cannot be reduced to two or one. Again, if the content of Table 1 turns out to be true in principle, one 'astounding' result seems to fall out of the symmetry of Table 1 -- the existence of what may be called the 'Mind Force' in analogy to the "Strong Force" in atomic nuclei (see the last row). (7) The 'Mind Force' postulated in Table 1 operates not only in the Mental World but also in the Physical World and the World of Structures where the Principle of ITR operates. (8) It may be an exciting challenge to find out how the "mind force" postulated in Table 1 is related to Peirce's "Mind" that operates throughout the Universe: "Thought is no necessarily connected with a brain. It appears in the work of bees, of crystals and (120115-4) throughout the purely physical world; and one can no more deny that it is really there, than that the colors, the shapes, etc. of objects are really there." (CP 4.551) I am not comfortable with (120115-4). I would agree with Peirce if he confines his "Mind" to those processes and structures in the Universe that embody ITR. With all the best. Sung On Mon, Nov 30, 2015 at 1:10 PM, Clark Goble <cl...@lextek.com<mailto:cl...@lextek.com>> wrote: On Nov 30, 2015, at 10:50 AM, Sungchul Ji <s...@rci.rutgers.edu<mailto:s...@rci.rutgers.edu>> wrote: f g Real Rose ----------------> Rose -----------> Mental Rose (Firstness) (Secondness) (Thirdness) [World of Structures] [Physical World] [Mental World] | ^ | | |____________________________________| h Peirce’s ontology doesn’t quite follow that. Firstness is the world of raw experience, ideas or possibility, secondness the world of reactions, brute force & actuality and thirdness the world of signs, connections and power (not necessarily mental unless one is careful what one means by that). So depending upon what one means by structure you’d have that in the third universe. Again though one has to be careful with terminology and Peirce’s shifts around a bit over time. ----------------------------- PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu<mailto:peirce-L@list.iupui.edu> . To UNSUBSCRIBE, send a message not to PEIRCE-L but to l...@list.iupui.edu<mailto:l...@list.iupui.edu> with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . -- Sungchul Ji, Ph.D. Associate Professor of Pharmacology and Toxicology Department of Pharmacology and Toxicology Ernest Mario School of Pharmacy Rutgers University Piscataway, N.J. 08855 732-445-4701 www.conformon.net<http://www.conformon.net>
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