Helmut, List: According to Peirce, we discover (not invent) continuity in phaneroscopy--our conception of it comes from directly observing the flow of time, which he calls "the continuum *par excellence*, through the spectacles of which we envisage every other continuum" (CP 6.86, 1898), so that "to say it is continuous is just like saying that the atomic weight of oxygen is 16, meaning that that shall be the standard for all other atomic weights. The one asserts no more of Time than the other asserts concerning the atomic weight of oxygen; that is, just nothing at all" (CP 4.642, 1908). Here are a few more quotations about this.
CSP: To imagine time, time is required. Hence, if we do not directly perceive the flow of time, we cannot imagine time. Yet the sense of time is something forced upon common-sense. So that, if common-sense denies that the flow [of] time is directly perceived, it is hopelessly entangled in contradictions and cannot be identified with any distinct and intelligible conception. But to me it seems clear that our natural common-sense belief is that the flow of time is directly perceived. (NEM 3:60, c. 1895) CSP: That this element [continuity] is found in experience is shown by the fact that all experience involves time. Now the flow of time is conceived as continuous. No matter whether this continuity is a datum of sense, or a quasi-hypothesis imported by the mind into experience, or even an illusion; in any case it remains a direct experience. (CP 7.535, 1899) 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) Although Peirce acknowledges in the second passage that our direct perception/experience of time might be an illusion, he nevertheless suggests in the other two that its inescapability assures us of its reality, and that this is the only way to account for our having the idea of a true continuum at all. Moreover, right before the statement that I quoted at the end of my last post, he makes the case at greater length that we could not even imagine true continuity unless there were *something *in reality that corresponds to it. CSP: I will submit for your consideration the following metaphysical principle which is of the nature of a retroduction: Whatever unanalyzable element *sui generis* seems to be in nature, although it be not really where it seems to be, yet must really be [in] nature somewhere, since nothing else could have produced even the false appearance of such an element *sui generis*. ... In the same way, the very fact that there seems to be 3ns in the world, even though it be not where it seems to be, proves that real 3ns there must somewhere be. If the continuity of our inward and outward sense be not real, still it proves that continuity there really is, for how else should sense have the power of creating it? Some people say that the sense of time is not in truth continuous, that we only imagine it to be so. If that be so, it strengthens my argument immensely. For how should the mind of every rustic and of every brute find it simpler to imagine time as continuous, in the very teeth of the appearances,--to connect it with by far the most difficult of all the conceptions which philosophers have ever thought out,--unless there were something in their real being which endowed such an idea with a simplicity which is certainly in the utmost contrast to its character in itself. But this something must be something in some sense like continuity. Now nothing can be like an element so peculiar except that very same element itself. ... The extraordinary disposition of the human mind to think of everything under the difficult and almost incomprehensible form of a continuum can only be explained by supposing that each one of us is in his own real nature a continuum. (NEM 4:344-345, 1898) Regards, Jon On Tue, Feb 13, 2024 at 9:18 AM Helmut Raulien <h.raul...@gmx.de> wrote: > Jon, List, > > ontologically, in reality, a continuum cannot be built up from > infinitesimally small points. But infenitesimality can only be infinitely > iterated towards in reality, if there already is a real continuum. So I see > a tautology. Just imagine, that there would not be a real continuum: Then > we nevertheless could get the idea of a continuum out of a line, which in > reality consists of aligned, in this case not infinitesimally small points. > Now we might say: If we are able to have the idea of a continuum, then > there must be one. This argument is similar with Anselm´s proof of God. Ok, > our world may be pixeled or quantized, but God´s realm is continuous. My > Ockham´s-razor-argument in my last post neither is a proof for a real > continuum, and whether Anselm´s proof is a proof, I don´t know. I sense > platonism in the idea, that we cannot get an idea of something that does > not exist. I am not totally convinced anymore about the reality of > continuum. The question seems quasi-theological to me. > > Best, Helmut > *Gesendet:* Montag, 12. Februar 2024 um 20:57 Uhr > *Von:* "Jon Alan Schmidt" <jonalanschm...@gmail.com> > *An:* "Peirce-L" <peirce-l@list.iupui.edu> > *Betreff:* Re: [PEIRCE-L] The Proper Way in Logic (was Peirce's Ongoing > Semiotic Project) > Helmut, List: > > According to Peirce, "Continuity represents 3ns almost to perfection" (CP > 1.337, c. 1882). When we prescind discreteness from continuity, we are > prescinding 2ns from 3ns, and we cannot prescind continuity from > discreteness because we cannot prescind 3ns from 2ns. Since prescission > "consists in supposing a state of things in which one element is present > without the other, the one being logically possible without the other" (EP > 2:270, 1903), the upshot is that 2ns is logically possible without 3ns, but > 3ns is not logically possible without 2ns. Put another way, 3ns always > *involves > *2ns as well as 1ns, and 2ns always *involves *1ns. Nevertheless, 2ns > cannot be *built up* from 1ns, and 3ns cannot be *built up* from 1ns > and/or 2ns. > > For example, a continuous line involves any discrete points within it, but > it cannot be built up from any multitude of such points. The continuous > whole (line) is ontologically prior to any discrete parts (points), which > are indefinite (infinitesimal "linelets") unless and until they are > deliberately marked off within it. Likewise, as I said before, the entire > universe is an inexhaustible continuum (3ns) of indefinite possibilities > (1ns), some of which are actualized (2ns). In Peirce's words, "The whole > universe of true and real possibilities forms a continuum, upon which this > Universe of Actual Existence is, by virtue of the essential 2ns of > Existence, a discontinuous mark--like a line figure drawn on the area of > the blackboard" (NEM 4:345, 1898; see also CP 6.203-209, 1898). > > Regards, > > Jon Alan Schmidt - Olathe, Kansas, USA > Structural Engineer, Synechist Philosopher, Lutheran Christian > www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt > > On Mon, Feb 12, 2024 at 11:01 AM Helmut Raulien <h.raul...@gmx.de> wrote: > >> >> List, I think, we can prescind discreteness from continuity, e.g. by >> supposing the formation of attractors, or coagulation, or reentry (logical >> or actual loops), but we cannot prescind continuity from discreteness. So >> everything including thirdness is at first based on continuity, even if it >> requires discreteness. I think, that thirdness requires discreteness, >> because a relation as part of structure, and a habit too, can and has to be >> prescinded (or discriminated, or dissociated) as something discrete from >> continuity, to logically handle it. >> >> Best, Helmut >> >
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