Jeff, List: JD: Focusing on the points made in 3 and 4, how might we understand the contrast being made between *our *side of things, and the part of time that is on the *further *side of eternity? A helpful approach, I think, is to start with a mathematical diagram. What kind of diagram might we use to clarify the hyperbolic evolution from the infinite past to the infinite future? Using this diagram, what is the contrast between our side of things and the further side of eternity?
Answering your questions is not an entirely straightforward matter, because Peirce made some seemingly inconsistent remarks about which *kind *of mathematical diagram best represents *real *time as a whole. CSP: At present, the course of events is approximately determined by law. In the past that approximation was less perfect; in the future it will be more perfect. The tendency to obey laws has always been and always will be growing. We look back toward a point in the infinitely distant past when there was no law but mere indeterminacy; we look forward to a point in the infinitely distant future when there will be no indeterminacy or chance but a complete reign of law. But at any assignable date in the past, however early, there was already some tendency toward uniformity; and at any assignable date in the future there will be some slight aberrancy from law. Moreover, all things have a tendency to take habits. (CP 1.409, EP 1:277; 1887-8) CSP: Time as so defined is a "hyperbolic" continuum; that is to say, the infinitely past and the infinitely future are distinct and do not coincide. This, I believe, accords with our natural idea of time. (W 8:134; 1892) CSP: Observation leads us to suppose that changing things tend toward a state in the immeasurably distant future different from the state of things in the immeasurably distant past ... It is an important, though extrinsic, property of time that no such reckoning brings us round to the same time again. (NEM 2:249-250; 1895) These passages are all basically consistent with the *hyperbolic *diagram that he described in the 1891 letter to Ladd-Franklin that you quoted. CSP: The triadic clause is that time has no limit, and every portion of time is bounded by two instants which are of it, and between any two instants either way round, instants may be interposed such that taking any possible multitude of objects there is at least one interposed event for every unit of that multitude. This statement needs some explanation of its meaning. First what does it mean to say that time has no limit? This may be understood in a topical or a metrical sense. In a metrical sense it means there is no absolutely first and last of time. That is, while we must adopt a standard of first and last, there is nothing in its own nature the prototype of first and last. For were there any such prototype, that would consist of a pair of objects absolutely first and last. This, however, is more than is intended here. Whether that be true or not is a question concerning rather the events in time than time itself. What is here meant is that time has no instant from which there are more or less than two ways in which time is stretched out, whether they always be in their nature the foregoing and the coming after, or not. If that be so, since every portion of time is bounded by two instants, there must be a connection of time ring-wise. Events may be limited to a portion of this ring; but the time itself must extend round or else there will be a portion of time, say future time and also past time, not bounded by two instants. The justification of this view is that it extends the properties we see belong to time to the whole of time without arbitrary exceptions not warranted by experience. (CP 1.498; c. 1896) CSP: But now, a continuum which is without singularities must, in the first place, return into itself. Here is a remarkable consequence. Take, for example, Time. It makes no difference what singularities you may see reason to impose upon this continuum. You may, for example, say that all evolution began at this instant, which you may call the infinite past, and comes to a close at that other instant, which you may call the infinite future. But all this is quite extrinsic to time itself. Let it be, if you please, that evolutionary time, our section of time, is contained between those limits. Nevertheless, it cannot be denied that time itself, unless it be discontinuous, as we have every reason to suppose it is not, stretches on beyond those limits, infinite though they be, returns into itself, and begins again. Your metaphysics must be shaped to accord with that. (CP 6.210; 1898) By contrast, these longer passages both appear to be saying that time is *elliptical*--in order to be truly continuous, it cannot have any limits and must instead be connected "ring-wise," such that it "returns into itself." Nevertheless, it might be the case that *events *are "limited to a portion of this ring," which is "evolutionary time, our section of time"; and if so, then the limits of that portion are still somehow in the *infinite *past and future. CSP: It may be assumed that there are two instants called the *limits of all time*, the one being Α, the *commencement *of all time and the other being Ω, the *completion *of all time. Whether there really are such instants or not we have no obvious means of knowing; nor is it easy to see what "really" in that question means. But it seems to me that if time is to be conceived as forming a collective whole, there either must be such limits or it must return into itself. This is an interesting question. At any rate, it is a help and no inconvenience for the present purpose to assume such limits. (NEM 3:1075; c. 1905) Here Peirce simply acknowledges that time as "a collective whole" either has two limits or "must return into itself," calling this "an interesting question" and choosing to assume that it *does *have initial and final instants for the sake of what follows. That subsequent exposition is where he identifies four different classes of states of things--momentary, prolonged, gradual, and relational--and describes diagrams for the first three, although he does not draw them. I have taken a stab at it myself and anticipate sharing the results in a future post. For now, though, the question is whether and how we can reconcile these seemingly incompatible descriptions. In *ordinary* geometry, an ellipse and a hyperbola are two *different *conic sections. An ellipse is a *single *closed curve, and the simplest equation for one is x2 + y2 = 1, producing a circle. A hyperbola consists of two *separate *curves that approach certain lines called *asymptotes* without ever actually reaching them; the simplest equations are xy = 1, whose asymptotes are the x-axis and y-axis, and x2 - y2 = 1, whose asymptotes are the lines defined by x + y = 0 and x - y = 0. Peirce characterizes his cosmology as "hyperbolic" because it likewise posits *ideal *limits that the universe never *actually *reaches--an absolutely indeterminate state of things in the infinite past, and an absolutely determinate state of things in the infinite future. What are we then to make of his statements about time "returning into itself," which suggest instead an *elliptical* cosmology? I will address that in another post, rather than making this one any longer than it already is. From previous exchanges, I suspect that you (Jeff) already know where this is headed; but for me and others who are not very familiar with *projective *geometry, it comes across as counterintuitive and even paradoxical, at least initially. Regards, Jon S. On Fri, Mar 6, 2020 at 11:32 AM Jon Alan Schmidt <jonalanschm...@gmail.com> wrote: > Jeff, List: > > JD: At the beginning of the post, you note that Peirce engaged in > "mathematical, phenomenological, semeiotic, and metaphysical" inquiries > concerning time. Do you have any suggestions about how we might tease out > the different threads? Each seems to involve somewhat different methods. > > > I agree that each involves different methods, and I have made several > attempts (so far unsuccessful) to start writing a paper (or two) with the > goal of teasing out those different threads. Peirce himself seems to think > that we can "harmonize" them (his word) by recognizing the *continuity *of > time; in fact, our direct *perception* of the continuous flow of time in > *phenomenology > *is what prompts our retroductive *hypothesis *of a true continuum in > *mathematics*, which we then explicate deductively and evaluate > inductively in other sciences. > > CSP: One opinion which has been put forward and which seems, at any rate, > to be tenable and to harmonize with the modern logico-mathematical > conceptions, is that our image of the flow of events receives, in a > strictly continuous time, strictly continual accessions on the side of the > future, while fading in a gradual manner on the side of the past, and that > thus the absolutely immediate present is gradually transformed by an > immediately given change into a continuum of the reality of which we are > thus assured. The argument is that in this way, and apparently in this way > only, our having the idea of a true continuum can be accounted for. (CP > 8.123n; c. 1902) > > > Logic then provides a plausible explanation for the so-called "arrow of > time." Peirce initially wrote the following in one of his notebooks. > > CSP: 1. A *time *is a determination of actuality independent of the > identity of individuals, and related to other times as stated below. > According to the present proposition we may speak of the state of different > things at the same time as well as of the states of the same thing at > different times and, of course, of different things at different times and > of the same thing at the same time. > 2. At different times a proposition concerning the same things may be > true and false; just as a predicate may at any one time be true and false > of different things. Time is therefore a determination of existents. (NEM > 2:611; c. 1904-5) > > > A few years later, he offered a correction on the opposite page, which is > otherwise blank. > > CSP: I can hardly now see how time can be called a determination of > *actuality*. It is certainly a law. It is simply a unidimensional > continuum of sorts of states of things and that these have an antitypy is > shown by the fact that a sort of state of things and a different one cannot > both be *at the same time*. And in consequence of this antitypy a state > of things varies in one way and cannot turn round to vary the other way. Or > to state it better a variation between state A and state B is limited to > occurrence in one direction, just as the form of a body in space is limited > to one or other of two perverse positions in space. (NEM 2:611; 1908 Aug 13) > > > Peirce here maintains the *mathematical *characterization of time as "a > unidimensional continuum," but describes its parts as "sorts of states of > things" and affirms the *phenomenological *fact that time flows in only > one direction. Turning to *metaphysics*, one thing that occurred to me > just this week is that these different threads at least loosely correspond > to the three main theories about time in the current philosophical > literature. > > 1. Eternalism - past, present, and future all exist. > 2. Presentism - only the present exists. > 3. Growing Block - only the past and present exist. > > If we substitute *reality *for *existence*, these correspond respectively > to Peirce's mathematical, phenomenological, and logical/semeiotic > conceptions of time--a one-dimensional continuous whole, isomorphic to a > line figure (cf. CP 1.273; 1902); an indefinite moment that involves > memory, confrontation, and anticipation (cf. CP 7.653; 1903); and an > ongoing process by which the indeterminate becomes determinate (cf. CP > 5.459, EP 2:357-358; 1905). I have come to believe that #3 is closest to > his overall view and can incorporate the insights of the other two. It is > unfortunate that there is not a more formal name for it; one recent > dissertation suggests "accretivism," but I doubt that this will catch on. > My tentative name for Peirce's version of it is *temporal synechism*. It > seems noteworthy that the basic idea of the "growing block" is that reality > itself is getting "larger," which is reminiscent of a passage in Kelly A. > Parker's book, *The Continuity of Peirce's Thought*. > > KAP: The dynamical object in each successive representation in the > process [of semeiosis] is necessarily different from that of its > predecessor. The dynamical object of the first representation is the real > universe at that time, and the immediate object is an abstraction > consisting of some aspects of this reality. The next representation, > however, cannot have exactly the same dynamical object. The real universe > is at that point populated by at least one additional entity--the first > representamen itself. Every successive representation in the semeiotic > process thus has as its dynamical object not just the universe which the > first representamen represented, but that universe plus the first > representamen itself. (p. 148) > > > The object that determines the sign is different from the object that > determines the interpretant, because the interpretant's object includes the > sign itself. Likewise, the past that determines the present is different > from the past that determines the future, because the future's past > includes the present itself. Moreover, the object affects the sign and > interpretant, but not vice-versa; and likewise, the past affects the > present and future, but not vice-versa. As ongoing and continuous > processes, both semeiosis and time are irreversible because they conform to > Gary R.'s vector of *determination *(2ns→1ns→3ns, > object→sign→interpretant, past→present→future); and once the universe as a > vast quasi-mind becomes *more *determinate, it cannot become *less > *determinate > again. This leads us to the passage that you quoted in your second post. > > CSP: [1] I may mention that my chief avocation in the last ten years has > been to develop my cosmology. This theory is that the evolution of the > world is *hyperbolic*, that is, proceeds from one state of things in the > infinite past, to a different state of things in the infinite future. [2] > The state of things in the infinite past is chaos, tohu bohu, the > nothingness of which consists in the total absence of regularity. The state > of things in the infinite future is death, the nothingness of which > consists in the complete triumph of law and absence of all spontaneity. [3] > Between these, we have on *our *side a state of things in which there is > some absolute spontaneity counter to all law, and some degree of conformity > to law, which is constantly on the increase owing to the growth of *habit* ... > [4] As to the part of time on the further side of eternity which leads back > from the infinite future to the infinite past, it evidently proceeds by > contraries. (CP 8.317; 1891) > > > The *cosmological* basis for the "arrow of time" is Gary R.'s vector of > *process *(1ns→3ns→2ns). The universe is evolving from an absolutely > *indeterminate *state of things at the hypothetical instant corresponding > to "the *commencement *of all time" (NEM 3:1075; c. 1905), when > everything would have been in the *future*, toward an absolutely > *determinate *state of things at the hypothetical instant corresponding > to "the *completion *of all time" (ibid), when everything would be in the > *past*. As I said at the end of my initial post, what is always realized > in the *present *is an indefinitely gradual state of change, and this > terminology conveniently lends itself to another categorial analysis--the > present is an *indefinitely *gradual state of change in its 1ns, an > indefinitely gradual state of *change *in its 2ns, and an indefinitely > *gradual *(i.e., continuous) state of change in its 3ns. > > Returning to mathematics, in a List post > <https://list.iupui.edu/sympa/arc/peirce-l/2019-09/msg00055.html> last > September I proposed five properties that are jointly necessary and > sufficient for a true Peircean continuum. (Incidentally, I am pleased to > report that my essay based on that and several related List discussions, > "Peirce's Topical Continuum: A 'Thicker' Theory," has been accepted for > publication in *Transactions of the Charles S. Peirce Society*.) The > first was *regularity*, which I now prefer to call *rationality*--every > portion conforms to one general law or Idea, which is the final cause by > which the ontologically prior whole calls out its parts (cf. CP 7.535; 1899 > and CP 7.535n6; 1908). I now suggest that time is a *real *Peircean > continuum, and that an indefinitely gradual state of change is the one > general law or Idea to which every lapse of it conforms; i.e., every moment > when it is *present*. > > Since this has gotten quite lengthy, I will try to take up your specific > questions in a later post. > > Regards, > > Jon Alan Schmidt - Olathe, Kansas, USA > Professional Engineer, Amateur Philosopher, Lutheran Layman > www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt > > On Thu, Mar 5, 2020 at 1:56 AM Jeffrey Brian Downard < > jeffrey.down...@nau.edu> wrote: > >> Jon, List, >> >> Consider what Peirce says about his cosmological conception of time in a >> letter to Christine Ladd-Franklin. For the sake of clarity, I'll separate >> and number the points he makes. >> >> 1. I may mention that my chief avocation in the last ten years has >> been to develop my cosmology. This theory is that the evolution of the >> world is *hyperbolic,* that is, proceeds from one state of things in the >> infinite past, to a different state of things in the infinite future. >> >> 2. The state of things in the infinite past is chaos, tohu bohu, the >> nothingness of which consists in the total absence of regularity. The state >> of things in the infinite future is death, the nothingness of which >> consists in the complete triumph of law and absence of all spontaneity. >> >> 3. Between these, we have on *our *side a state of things in which >> there is some absolute spontaneity counter to all law, and some degree of >> conformity to law, which is constantly on the increase owing to the growth >> of *habit.* >> >> 4. As to the part of time on the *further* side of eternity which leads >> back from the infinite future to the infinite past, it evidently proceeds >> by contraries. 8.316 >> >> Focusing on the points made in 3 and 4, how might we understand the >> contrast being made between *our* side of things, and the part of time >> that is on the *further* side of eternity? >> >> A helpful approach, I think, is to start with a mathematical diagram. >> What kind of diagram might we use to clarify the hyperbolic evolution from >> the infinite past to the infinite future? Using this diagram, what is the >> contrast between our side of things and the further side of eternity? >> >> --Jeff >> Jeffrey Downard >> Associate Professor >> Department of Philosophy >> Northern Arizona University >> (o) 928 523-8354 >> ------------------------------ >> *From:* Jeffrey Brian Downard >> *Sent:* Wednesday, March 4, 2020 11:37:06 PM >> *To:* peirce-l@list.iupui.edu >> *Subject:* Re: [PEIRCE-L] The Reality of Time >> >> Hello Jon, List, >> >> At the beginning of the post, you note that Peirce engaged in "mathematical, >> phenomenological, semeiotic, and metaphysical" inquiries concerning time. >> Do you have any suggestions about how we might tease out the different >> threads? Each seems to involve somewhat different methods. >> >> --Jeff >> Jeffrey Downard >> Associate Professor >> Department of Philosophy >> Northern Arizona University >> (o) 928 523-8354 >> >
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