Gary R., List: GR: I will have to reflect further as to whether to rename what I now call the 'vector of representation' the 'vector of continuity' as there still seem to be some good reasons to keep the original name.
My suggestion is grounded in my exposition of Peirce's late topical conception (https://philpapers.org/archive/SCHPTC-2.pdf), which in my view resolves the alleged "matters of inconsistency in Peirce on continuity" that Atila mentioned (citing Hartshorne) in his post to which I replied when I started this thread. In my view, this vector (3ns → 1ns → 2ns) matches up with not only the constitution of being in cosmology, but also the nature of semiosis in general (prescinding individual signs with their objects and interpretants) and perception in particular (prescinding predicates and hypostasizing some of them into subjects). Hence, "vector of continuity" would reflect its applicability across mathematics, phaneroscopy, the normative sciences (especially semeiotic), and metaphysics. CSP: Metaphysics consists in the result of the absolute acceptance of logical principles not merely as regulatively valid, but as truths of being. (CP 1.487, c. 1896). Peirce's next sentences are relevant to the thread topic, as well. "Accordingly, it is to be assumed that the universe has an explanation, the function of which, like that of every logical explanation, is to unify its observed variety. It follows that the root of all being is One; and so far as different subjects have a common character they partake of an identical being" (ibid.). My hypothesis that the constitution of being is an inexhaustible continuum of indefinite possibilities, some of which are actualized, entails that the one root of all being is 3ns, not 1ns (nor 2ns). Likewise, my hypothesis that the entire universe is a vast *semiosic *continuum entails that the one root of all being is the being of a *sign*--not isolated nor dyadic, but connected and triadic; not existing, but governing instances of signs and events of semiosis. CSP: It will be very difficult for many minds--and for the very best and clearest minds, more difficult than for others--to comprehend the logical correctness of a view which does not put the assumption of time before either metaphysics or logic instead of after those kinds of necessity, as here arranged. (CP 1.490) In context, the point that Peirce is making here, which he evidently expects to be difficult for many to grasp as correct, is that time is neither metaphysically nor logically *necessary*. In the previous paragraph, he gives "as the typical example of a metaphysical law, the law that whatever exists, although its existence is a matter of brute fact, irrespective of any qualities, must definitely possess or be without each monadic quality"; and he then adds that it is "the mere existential mirror of a law of logic" for "the junctions, between the possessions by a subject of contrary attributes, to be related to one another like premisses and conclusions, as before and after" (CP 1.489). As he states a few paragraphs later, "temporal succession is a mirror of, or framework for, logical sequence" (CP 1.496). Here we have a different categorial vector, that of *determination*--the accomplished past (2ns) determines the nascent present (1ns) to determine the contingent future (3ns), just as the object (2ns) determines the sign (1ns) to determine the interpretant (3ns). Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt On Sat, Oct 11, 2025 at 5:00 PM Gary Richmond <[email protected]> wrote: > Jon, Jeff, List, > > As I wrote yesterday, your exposition, Jon, seems highly consonant with > the development of Peirce’s thinking about the ordering of the categories > in his cosmology including the introduction of that late, nuanced emphasis > on an ur-continuity (the blackboard). Your arguing for an underlying > continuum (3ns) containing indefinite possibilities (1nses) some of which > become actual (2nses) certainly is in agreement with Peirce’s synechism, > continuity being the ultimate character of reality. It necessarily places > 3ns in a more explicitly foundational role than Peirce did in his earlier > cosmological narratives. The cosmological progression 1ns -> 2ns -> 3ns > corresponds to Peirce’s early evolutionary model while his later > integration of this with a deeper, timeless continuum would appear to > reconcile tychism with synechism. > > I found your observation that 3ns can appear first, second, or third > depending on the level of analysis, expressing Peirce’s own non-linear use > of the categories across logical, metaphysical, and cosmological contexts, > of great interest. Again, your analysis conforms closely to Peirce’s > category theory across these contexts as it accurately represents the > co-implication of 1ns, 2ns, and 3ns in all phenomena, their ontological > interdependence, and the synechistic priority of 3ns. So, treating 3ns as > 1st in the constitution of being doesn't contradict Peirce's earlier view, > but emphasizes the primacy of continuity as the condition for all > manifestation. > > JAS: "What I have long found interesting about these three cosmological > vectors--you call them representation, order, and process, but I would now > advocate renaming the first one continuity--is that in each case, 2ns comes > after 1ns, such that the only variation is the position of 3ns; it is first > in the underlying constitution of being, second in the overall evolution of > states, and third in the recurring sequence of events." > > I will have to reflect further as to whether to rename what I now call the > 'vector of representation' the 'vector of continuity' as there still seem > to be some good reasons to keep the original name. As you may recall, I > earlier termed what I now term the 'vector of process', the 'vector of > evolution' since 'process' was the broader term, 'evolution' being but one > -- albeit a most significant -- type of process. Is it possible that the > vector 3ns -> 1ns -> 2ns (currently the 'vector of representation') > represents continuity but is not limited to that one representation as > significant as it is? Still, this deserves further thought. > > JAS (responding to Jeff): Omit the word "random," and your supposition > basically matches Peirce's own hypothesis about the initial state--"a vague > potentiality ... of everything in general, but of nothing in particular" > (CP 6.196, 1898). *A field of potentiality is a general continuum of > indefinite possibilities*, not any individual possibility; 3ns that > involves 1ns, not 1ns by itself. This is the key distinction that I > highlighted at the beginning of my post yesterday (emphasis and underlining > added). > > Making this essential distinction appears to me to answer Jeff's two > questions: "Does such a supposition [that 'a random field of potentiality > could be described in the terms of probability theory. . .] involve > thirdness? If so, what sort?" > > Some related Peirce quotations (and one possible 'hallucination') for > mental stimulation. > > “Metaphysics consists in the result of the absolute acceptance of logical > principles not merely as regulatively valid, but as truths of being” > (1.487). > > > "It will be very difficult for many minds -- and for the very best and > clearest minds, more difficult than for others -- to comprehend the logical > correctness of a view which does not put the assumption of time before > either metaphysics or logic instead of after those kinds of necessity, as > here arranged (emphasis added). CP 1.490 > > > Google's 'automatic AI whether you want it or not' came up with this: > “Metaphysics is but the application of logic to the real world, and the > logic of the real world cannot be different from the logic of possible > worlds.” This would be too perfect, but I couldn't locate it anywhere on > the internet so that it's likely a hallucination (my own!) > > Best, > > Gary R >
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