Jon, List, I apologize for the length of this post and even after paring down some of the Peirce quotations.
JAS: "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." If the vector 3ns ->1ns ->2ns "matches up with. . .the nature of semiosis," what is that vector's relation to that of the vector of determination (2ns ->1ns ->3ns) in consideration of semiosis, that the Object 2ns determines the Sign 1ns for the Interpretent 3ns then? The material just before the snippet I quoted (beginning "It will be very difficult for many minds") is quite interesting especially as the subtitle of the manuscript, "The Mathematics of Logic" from which the quotation was taken, is "An attempt at developing my categories from within" so that most all that is analyzed, even Time, is done so to show some categorial character or relation. So, as you wrote: JAS: 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). I wonder, how does this match up with Times as a continuum as Peirce's discussion of Time elsewhere in the manuscript takes it up as such? 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) I must admit that when I first quoted that snippet I was thinking especially in terms of the *vector of *(Hegelian)* orde*r being the inverse of the *vector of involution*. In a number places in the manuscript Peirce discusses categorial *involution* (following the *vector of involution*, 3ns --> 2ns -> 1ns) as the inverse of Hegel's 'evolution' (alternatively,* dialectical method* following the *vector of order*, 1ns -> 2ns -> 3ns). (By the way, in places in "The Mathematics of Logic" Peirce refers to categorial involution as "analysis," and so at first I was tempted to call it the *vector of analysis*. But very soon I decided that by 'analysis' what Peirce meant wasn't analysis more generally speaking but, specifically,the analysis of *categorial involution*; and so I settled on the *vector or involution*.) It is also important to note that what Peirce refers to as "the method of dilemma" i.e. *dialectical method*, Hegelian 'evolution' (1ns -> 2ns ->3ns) is not at all Peirce's understanding of evolution in his -- the modern -- usual sense (such as when we refer to biological evolution) which follows the *vector of process* (1ns -> 3ns >- 2ns). But continuing, immediately following the quoted snipped above, Peirce writes: But that is an objection, not to this particular item of the development, but to the general plan of it. To admit the force of the objection and carry it out to its consequences would simply result in r*eversing the whole order of development, making it begin with polyads, analyzing these into triads, and then finding dyads in triads, and monads in dyads **[which, of course, is exactly involution]**. There is not only nothing erroneous in such an arrangement, but the conceptions cannot be thoroughly grasped until it has been carried out*. But this is only one of two sides of the shield, *both of which must be examined, and which have to be synthesized* in the really philosophical view. The reason of this is, that although *the view which takes the triad first is necessary to the understanding of any given point*, yet it cannot, from the very nature of the case, be carried out in an entirely thoroughgoing manner. How, for instance, would you begin? *By taking the triad first. You thus do, in spite of yourself, introduce the monadic idea of "first" at the very outset.* T*o get at the idea of a monad, and especially to make it an accurate and clear conception, it is necessary to begin with the idea of a triad and find the monad-idea involved in it.* But this is only a scaffolding necessary during the process of constructing the conception. When the conception has been constructed, the scaffolding may be removed, and the monad-idea will be there in all its abstract perfection. *According to the path here pursued from monad to triad, from monadic triads to triadic triads, etc., we do not progress by logical involution -- we do not say the monad involves a dyad - - but we pursue a path of evolution **[Hegelian dialectic; for Peirce evolution as we generally think of it follows the vector of process: 1ns -*>* 3ns -*>*2ns]* [. . .] So far Hegel is quite right. But he formulates the general procedure in too narrow a way, making it use no higher method than dilemma *[i.e., dialectic]*, instead of giving it an observational essence. [. . .] The great danger of the evolutionary *[i.e, Hegelian]* procedure lies in forcing steps that are not inevitable, in consequence of not having a sufficiently distinct apprehension of the features of the conception in hand to see what it is that must immediately succeed it. *The idea of time must be employed in arriving at the conception of logical consecution; but the idea once obtained, the time-element may be omitted, thus leaving the logical sequence free from time. That done, time appears as an existential analogue of the logical flow*. CP 1.490-491 Here Time would appear to follow the vector of order (1ns -> 2ns -> 3ns). Returning to a consideration of involution, in an earlier comment in the manuscript Peirce writes: The general law of quality [. . .] has *three clauses*, relating respectively to single qualities, to pairs of qualities, and to triads of qualities. The first clause is that every quality is perfect and in itself such as it is. The second more complex law is that two qualities have one or other of two sorts of relations to one another; namely, they may be, first, independent of one another, somewhat resembling and somewhat differing from one another, or secondly, one of them may be merely a further determination of the other, *this latter being essentially the first of the pair in the order of evolution, or synthesis **[vector of order]**, while it is the second of the pair in the order of involution or analysis **[vector of involution]*. CP 1.484 And a bit later bit later. . . The triadic clause of the law of logic recognizes three elements in truth, the idea, or predicate, the fact or subject, the thought which originally put them together and recognizes they are together; from whence many things result, especially a* threefold inferential process which either first follows the order of involution from living thought or ruling law, and existential case under the condition of the law to the predication of the idea of the law in that case **[involution]*; or second, proceeds from the living law and the inherence of the idea of that law in an existential case, to the subsumption of that case and to the condition of the law; or third, proceeds from the subsumption of an existential case under the condition of a living law, and the inherence of the idea of that law in that case to the living law itself. Thus the law of logic governs the relations of different predicates of one subject. CP 1.485 Also: But the event may, on the other hand, consist in the coming into existence of something that did not exist, or the reverse. There is still a contradiction here; but instead of consisting in the material, or purely monadic, repugnance of two qualities, it is *an incompatibility between two forms of triadic relation*, as we shall better understand later [. . . ]CP 1.493 The dyadic requirement of the law of time is that if a subject existentially receives contrary attributes, of the two contrary states an existentially determinate *one is first in the existential order of * *[Hegelian]** evolution and second in the existential order of involution, while the other is second in the existential order of evolution and first in the existential order of involution*; and of any two events whatever, a determinate one is related to the other in this same way (although the two events are not joined, as the two states are joined in the event), unless they are independent of one another. . . CP 1.495 So, within "The Mathematics of Logic" Peirce describes several vectors without naming them as such (they are 'orders of')' and since the Hegelian order (the *vector of order*) being the inverse of categorial involution (the vector of involution), it was suggested to me that there might be relations between the six vectors, something which proved to be the case. Indeed, I've hypothesized cycles of the six vectors, on which I need to do more research and well as regards other relations among the vectors. Indeed, it was "The Mathematics of Logic, An attempt at developing my categories from within" which first got me thinking about the possibility of there being movement through the categories, that is, categorial vectors, and further research led me to find all six in many, various places throughout Peirce's oeuvre. Best, Gary R On Mon, Oct 13, 2025 at 1:31 PM Jon Alan Schmidt <[email protected]> wrote: > 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 >> > _ _ _ _ _ _ _ _ _ _ > ► 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] > . > ► <a href="mailto:[email protected]";>UNSUBSCRIBE FROM > PEIRCE-L</a> . But, if your subscribed email account is not your default > email account, then go to > https://list.iu.edu/sympa/signoff/peirce-l . > ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and > co-managed by him and Ben Udell.
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