List: Combining what I wrote below about sequence with my earlier observation that both semeiosis and time conform to Gary R.'s vector of *determination *(2ns→1ns→3ns, object→sign→interpretant, past→present→future) prompts some additional suggestions. Peirce's speculative grammar posits an individual dynamical object determining an individual sign token to determine an individual dynamical interpretant. What I have been learning and pondering over the past year-plus is that along with instants in time and positions in space for describing *physical *motion, these discrete correlates are creations of thought for describing the real *inferential *process of semeiosis, which is likewise continuous.
CSP: Just as it is strictly correct to say that nobody is ever in an exact Position (except instantaneously, and an Instant is a fiction, or *ens rationis*), but Positions are either vaguely described states of motion of small range, or else (what is the better view), are *entia rationis* (i.e. fictions recognized to be fictions, and thus no longer fictions) invented for the purposes of closer descriptions of states of motion; so likewise, Thought (I am not talking Psychology, but Logic, or the essence of Semeiotics) cannot, from the nature of it, be at rest, or be anything but inferential process; and propositions are either roughly described states of Thought-motion, or are artificial creations intended to render the description of Thought-motion possible; and Names are creations of a second order serving to render the representation of propositions possible. (R 295:117-118[102-103]; 1906) We prescind *temporal *sequence from continuous time itself by arbitrarily marking discrete instants that stand in the relations of before and after; we prescind *spatial *sequence from continuous motion over time by inventing discrete positions that stand in the relations of distance and direction; and we prescind *logical *sequence from continuous thought/semeiosis over time by artificially creating discrete propositions that stand in the relations corresponding to leading principles. CSP: 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 ... It is true that we know the conclusion later than we know the premisses; but we do not so much think of our knowledge as following as we do that one fact is logically sequent on the other. The instinct may, therefore, be presumed to be an obscure perception that temporal succession is a mirror of, or framework for, logical sequence. (CP 1.491&496; c. 1896) CSP: Practically, when a man endeavors to state what the process of his thought has been, after the process has come to an end, he first asks himself to what conclusion he has come. That result he formulates in an assertion, which, we will assume, has some sort of likeness,--I am inclined to think only a very conventionalized one,--with the attitude of his thought at the cessation of the motion. That having been ascertained, he next asks himself how he is justified in being so confident of it; and he proceeds to cast about for a sentence expressed in words which shall strike him as resembling some previous attitude of his thought, and which at the same time shall be logically related to the sentence representing his conclusion, in such a way that if the premiss-proposition be true, the conclusion-proposition necessarily or naturally would be true. That argument is a representation of the *last part* of his thought, so far as its logic goes, that is, that the conclusion would be true supposing the premiss is so. But the self-observer has absolutely no warrant whatever for assuming that that premiss represented an attitude in which thought remained stock-still, even for an instant ... Adopting that idea, the logical argument only represents the last part of thought, for the reason that it supposes a premiss which represents some attitude of thought which can only have resulted from thinking. (CP 2.27; 1902) Adapting a specific terminological distinction from "A Neglected Argument for the Reality of God" (CP 6.456, EP 2:435; 1908), the *real *inferential process (argument) is always continuous through time, while the corresponding premisses and conclusion (argumentation) are discrete representations of *hypothetical *instantaneous states that we formulate only in retrospect. That is why a series of sheets of assertion with existential graphs scribed on them can serve as "a moving-picture of Thought" (CP 4.11; 1906), just as with "a series of instantaneous photographs ... no matter how closely they follow one another, there is no more motion visible in any one of them than if they were taken at intervals of centuries" (NEM 3:59; c. 1895). Moreover, phenomenological perception and logical reasoning are necessarily connected. CSP: The real thinking-process presumably begins at the very percepts. But a percept cannot be represented in words, and consequently, the first part of the thinking cannot be represented by any logical form of argument. Our logical account of the matter has to start from a *perceptual fact*, or proposition resulting from thought about a percept,--thinking in its own movement presumably of the same nature as that which we represent by arguments and inferences, but not so representable in consequence of a defect in that method of representation. (CP 2.27) As "the first premisses of all our reasonings," which "cannot be called into question" (CP 5.116, EP 2:191; 1903), perceptual judgments are involuntary retroductive propositions signifying perceptual facts--*perceived *states of things. Now, consider the *logical *functions of time and space. CSP: According to the metaphysical law of sufficient reason, alike in all respects two things cannot be. Space evades that law by providing places in which two things or any number, which are precisely alike, except that they are located in different places, themselves precisely alike in themselves, may exist. Thus, space does for different subjects of one predicate precisely what time does for different predicates of the same subject. (CP 1.501; c. 1896) Of course, subjects and predicates are the discrete parts (names/terms) of discrete propositions. Where do we get those? CSP: Experience is first forced upon us in the form of a flow of images. Thereupon thought makes certain assertions. It professes to pick the image into pieces and to detect in it certain characters. This is not literally true. The image has no parts, least of all predicates. Thus predication involves precisive abstraction. Precisive abstraction creates predicates. Subjectal abstraction creates subjects. Both predicates and subjects are creations of thought. (NEM 3:917; 1904 Nov 21) We prescind time and space from the continuous flow of perception and thought/semeiosis by creating discrete predicates and subjects (names/terms), composing discrete propositions that attribute the former to the latter, and recognizing that different subjects can have the same predicates at different positions, while the same subject can have different predicates at different instants. These all correspond to different states of things that such propositions can signify, and there are three modes of being involved in a *real* state of things; i.e., a *fact*. CSP: The being of the quality lies wholly in itself, the being of the thing lies in opposition to other things, the being of the reason lies in its bringing qualities and things together. (CP 1.515; c. 1896) Employing Peirce's adaptation of Aristotelian terms (cf. NEM 4:292-300; 1904), the being of a quality corresponds to *form*, the being of a thing corresponds to *matter*, and the being of a fact that brings them together corresponds to *entelechy*. Qualities are *possible *and things *exist*, while facts are *realized*. CSP: The mode of being of the composition of thought, which is always of the nature of the attribution of a predicate to a subject, is the living intelligence which is the creator of all intelligible reality, as well as of the knowledge of such reality. It is the *entelechy*, or perfection of being. (CP 6.341; 1907) Regards, Jon S. On Mon, Mar 9, 2020 at 8:19 PM Jon Alan Schmidt <jonalanschm...@gmail.com> wrote: > Jeff, List: > > JD: As Peirce points out in the 8th Cambridge Conferences Lecture in > RLT, the self-returning character of a space or time manifold is a > topological character of unbounded manifolds generally. We don't need to > add in postulates concerning straightness and a line called the absolute > needed for a projective geometry for the point about the self-returning > character of hyperbolic manifolds to hold. > > > I have not dug into RLT on this topic yet, since I only have a hard copy > rather than a searchable PDF. Which specific pages do you have in mind? > > JD: Hyperbolic manifolds come in different shapes. Some have an odd > number of twists (i.e., cross-caps) in them. Others have an even number or > no twists at all. Some manifolds, for instance, have the intrinsic > character of a torus with no twists. If a torus has two or more holes, then > it is hyperbolic in character. If it has one hole it is parabolic. If it > has no holes, then it is elliptical. Roughly, a similar point holds for the > number of cross caps found in a manifold. > > > I have already admitted that projective geometry is a conceptual stretch > for me, and topology is even more so. Is there a relatively simple primer > anywhere online for hyperbolic/parabolic/elliptical toruses in topology, > like the one that I found and linked for hyperbolic/parabolic/elliptical > circles in projective geometry? > > JD: Peirce makes this point when he suggests that the first question we > should ask about our experience of time is its Euler characteristic or > Listing number. On my reading of Peirce, it is important that we start by > asking these kinds of questions about the topological character of our > experience of time before turning to questions of how time is > ordered--projectively or metrically. > > > "Topological character" is mathematical, while "our experience of time" is > phenomenological. How would you suggest that we translate back and forth > between the two sciences? > > JD: That is, we need to ask these phenomenological questions about our > experience of time before turning to metaphysical questions about its real > nature. By asking these phenomenological questions about the character of > our experience, we put ourselves in a better position to analyze the > surprising observations that are calling out for metaphysical hypotheses. > > > I agree, and so does Peirce. > > CSP: The only important thing here is our metaphysical phenomenon, or > familiar notion, that the past is a matter for knowledge but not for > endeavor, that the future is an object that we may hope to influence, but > which cannot affect us except through our anticipations, and that the > present is a moment immeasurably small through which, as their limit, past > and future can alone act upon one another. Whether this be an illusion or > not, it is the phenomenon of which the metaphysician has to give an > account. (CP 8.113; c. 1900) > > > Our *phenomenological *experience of time prompts our *mathematical > *hypotheses > about time. We then employ *logical/semeiotic* principles in order to > ascertain the *metaphysical *reality of time. > > JD: For example, we ask: why does our experience of space seem have three > dimension while time has only one, and why is time ordered in a manner that > space is not? In turn, we hope to put ourselves in a better position to > measure the data that are being used to test those explanations. > > > The Peirce quote above explains how our phenomenological experience > requires something like the "arrow of time" to account for the undeniable > difference between our memory of the past and our anticipation of the > future. Elsewhere he suggests that this is precisely what *requires *time > to be one-dimensional, which is obviously not the case with space. > > CSP: For example, every-day experience is that events occur in time, and > that time has but one dimension. So much appears necessary. For we should > be utterly bewildered by the suggestion that two events were each anterior > to the other or that, happening at different times, one was not anterior to > the other. But a two-dimensional anteriority is easily shown to involve a > self-contradiction. So, then, that time is one-dimensional is, for the > present, necessary; and we know not how to appeal to special experience to > disprove it. But that space is three dimensional involves no such > necessity. We can perfectly well suppose that atoms or their corpuscles > move freely in four or more dimensions. (CP 1.273; 1902) > > > Along similar lines, a manuscript that was presumably an early draft of > some ideas for RLT, "Abstracts of 8 Lectures" (R 942), begins with this > interesting passage. > > CSP: We thus see that the bare Nothing of Possibility logically leads to > continuity. > For the first step a unidimensional continuum is formed. > Logically, this step is of the nature of induction. Now induction arranges > possible experience after the type of logical law. But the logical law *par > excellence* is that of logical sequence. Hence, the first dimension of > the continuum of quality is a sequence. A sequence is a unidimensional form > in which there is a difference between the relation of A to B and of B to > A. Mathematically considered, in one dimension it is a progress from a > point A to a point B, where A and B are different or A and B may coincide, > or they may both vanish [see attached "Sequences.jpg"]. Of these three > forms of sequence, the first is distinctly that of logic since the ultimate > antecedent and the ultimate consequent are different in logic. You cannot > proceed from antecedent to consequent till you reach again your original > antecedent (as in the 3rd kind of sequence, the elliptical), nor do you *tend > *to such a return (as in the second, or parabolic sequence), but the two > are distinct. > It follows that the first dimension of the continuum of possible quality* > had to be of the nature of a hyperbolic sequence. That is to say, there is > one general mode of relation, which we may name *coming after*, defined > by these conditions: > 1st, of any two qualities which are not entirely alike in their > relations of *coming after*, one *comes after* the other; > 2nd, whatever *comes after* another comes after whatever that other comes > after; or otherwise stated if N comes after M then whatever, say P, comes > after N also comes after M; > 3rd, nothing comes after itself ... > Now the logical sequence itself is essentially unidimensional, because it > is a purely internal law, and unity and interiority are inseparable. (NEM > 4:127-128; 1898) > *Peirce mistakenly wrote "quantity" in the manuscript > > > Peirce is discussing the continuum of possible quality here, rather than > time, but it is not much of a stretch to recognize the parallel between > *logical > *sequence--which he confirms to be a *hyperbolic *sequence, rather than > an elliptical or parabolic sequence--and *temporal *sequence. Both > involve "one general mode of relation, which we may name *coming after*"; > and as he elaborates in a subsequent paragraph, both proceed from an ideal > beginning toward a *different *ideal end. > > CSP: Let me say, by the way, that there is in the logical law this > difference between the absolutely first antecedent and the absolutely last > consequent, both of which are unattainable limits. The last consequent is > the very reality itself. That is our very conception of reality, the > essence of the word, namely, what we should believe if investigation was > carried to its furthest limit where no change of belief further was > possible. That is of the nature of an infinite, a true singularity of the > logical continuum differing *toto caelo* [by the entire extent of the > heavens] from every intermediate step however near to it. I mean that it > thus differs, not merely in its logical relations as leading to no > consequent other than itself, but also and more particularly, as being a > radically different kind of consciousness, a consciousness which is the > very reality itself and no mere image seen *per speculum in aenigmate* > [through a glass darkly]. But the absolutely first antecedent is simply the > blank ignorance, the *zero *of knowledge, although in its logical > relations it is singular in leading to nothing, as a needle precisely > balanced on its point will never fall, yet as a state of mind it differs > indefinitely little from other states near it. Hence, though a limit as to > the advance of logical development, it is not so as a mode of > consciousness. (NEM 4:134) > > > Just as temporal sequence has an initial state that is absolutely > indeterminate and a final state that is absolutely determinate, logical > sequence starts with "blank ignorance" and ends with "the very reality > itself," what Peirce sometimes called the ultimate opinion. A decade > later, he further connected both kinds of sequence to the concept of > *negation*. > > CSP: Indeed, so far is the concept of *Sequence *from being a composite > of two Negations, that, on the contrary, the concept of the *Negation *of > any state of things, X, is, precisely, a composite of which one element is > the concept of Sequence. Namely, it is the concept of a sequence from X of > the essence of falsity ... The question will here pop up, Why does not this > show that the concept of Sequence is a composite of three concepts; that of > some antecedent state, that of some consequent state, and between them, > that of a state of Heraclitan Flux? ... > Your question answers itself ... your supposition assumes that there is > what we conceive of as Time ... For we never think at all without > reasoning; and if we try to do so, the attempt merely results in our > reasoning about reasoning. Now reasoning takes place in Time; and so far as > we can understand it, in a Time that embodies our common-sense notion of > Time. But this common-sense notion of time implies that every state of > things that does not endure through a lapse of time is absolutely definite, > that is, that two states, one the negation of the other, cannot exist at > the same instant; which, by the way, necessarily follows, if negation be > but a particular sort of sequence; though it would be to no purpose to stop > to prove this here. > Accepting the common-sense notion, then, I say that it conflicts with that > to suppose that there is ever any discontinuity in change. That is to say, > between any two instantaneous states there must be a lapse of time during > which the change is continuous, not merely in that false continuity which > the calculus recognizes but in a much stricter sense. (R 300:52-55[51-54]; > 1908) > > > Sequence is a *simpler *concept than negation, which is why Peirce > defined a *cut *in existential graphs as a *scroll *with its inner close > containing the *pseudograph *and reduced to infinitesimal size (cf. CP > 4.454-456; 1903 and CP 4.454n; c. 1906). Moreover, logical sequence is a > *simpler > *concept than temporal sequence, such that we can prescind the former > from the latter, but not the latter from the former. The upshot is that > the negation of a prolonged state of things requires "a lapse of time > during which the change is [strictly] continuous"; i.e., a general > determination of time at which an indefinitely gradual state of change is > realized. > > Regards, > > Jon Alan Schmidt - Olathe, Kansas, USA > Professional Engineer, Amateur Philosopher, Lutheran Layman > www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt > > On Mon, Mar 9, 2020 at 1:54 PM Jeffrey Brian Downard < > jeffrey.down...@nau.edu> wrote: > >> Hi Jon S, List >> >> It looks like we are barking up the same trees. >> >> As Peirce points out in the 8th Cambridge Conferences Lecture in RLT, the >> self-returning character of a space or time manifold is a topological >> character of unbounded manifolds generally. We don't need to add >> in postulates concerning straightness and a line called the absolute needed >> for a projective geometry for the point about the self-returning >> character of hyperbolic manifolds to hold. >> >> Hyperbolic manifolds come in different shapes. Some have an odd number >> of twists (i.e., cross-caps) in them. Others have an even number or no >> twists at all. Some manifolds, for instance, have the intrinsic >> character of a torus with no twists. If a torus has two or more holes, >> then it is hyperbolic in character. If it has one hole it is parabolic. If >> it has no holes, then it is elliptical. Roughly, a similar point holds for >> the number of cross caps found in a manifold. >> >> Peirce makes this point when he suggests that the first question we >> should ask about our experience of time is its Euler characteristic or >> Listing number. On my reading of Peirce, it is important that we start by >> asking these kinds of questions about the topological character of our >> experience of time before turning to questions of how time is >> ordered--projectively or metrically. >> >> That is, we need to ask these phenomenological questions about our >> experience of time before turning to metaphysical questions about its real >> nature. By asking these phenomenological questions about the character of >> our experience, we put ourselves in a better position to analyze the >> surprising observations that are calling out for metaphysical hypotheses. >> For example, we ask: why does our experience of space seem have three >> dimension while time has only one, and why is time ordered in a manner that >> space is not? In turn, we hope to put ourselves in a better position to >> measure the data that are being used to test those explanations. >> >> --Jeff >> Jeffrey Downard >> Associate Professor >> Department of Philosophy >> Northern Arizona University >> (o) 928 523-8354 >> >>>
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