Erratum: I meant to write at the end of my post "Tom Short in his book on Peire's semeiotic goes no further than to say that "the intentionality of thought is a special case of significance" which hardly equates it with 3ns" (not "intentionality," of course). GR
On Tue, Feb 13, 2024 at 7:31 PM Gary Richmond <gary.richm...@gmail.com> wrote: > John, List, > > JFS: More mathematicians today follow Cantor than Peirce. > > And not only today but in Peirce's day as well. Peirce referred to > Cantor's conception as a "pseudo-continuum," a "bottoms-up" approach. It's > too bad that a contemporary mathematician hasn't written a paper explaining > the virtues of Peirce's top-down approach. Of course on List and in his > *Transactions* paper, "Peirce's Topical Continuum," Jon Alan Schmidt has > argued for Peirce's alternative "top-down" conception. In light of the > current discussion, I reread JAS's paper and can heartily recommend it to > anyone wishing to understand the "top-down" vs "bottom-up" distinction. See: > > Peirce's Topical Continuum: A “Thicker” Theory > <https://philarchive.org/go.pl?id=SCHPTC-2&proxyId=&u=https%3A%2F%2Fphilpapers.org%2Farchive%2FSCHPTC-2.pdf> > Jon Alan Schmidt <https://philarchive.org/s/Jon%20Alan%20Schmidt> > > *Transactions of the Charles S. Peirce Society > <https://philpapers.org/asearch.pl?pub=1106>* 56 (1):62-80 (2020) Copy > BIBTEX > Abstract > Although Peirce frequently insisted that continuity was a core component > of his philosophical thought, his conception of it evolved considerably > during his lifetime, culminating in a theory grounded primarily in topical > geometry. Two manuscripts, one of which has never before been published, > reveal that his formulation of this approach was both earlier and more > thorough than most scholars seem to have realized. Combining these and > other relevant texts with the better-known passages highlights a key > ontological distinction: a collection is bottom-up, such that the parts are > real and the whole is an ens rationis, while a continuum is top-down, such > that the whole is real and the parts are entia rationis. Accordingly, five > properties are jointly necessary and sufficient for Peirce’s topical > continuum: rationality, divisibility, homogeneity, contiguity, and > inexhaustibility. > > I'd also like to take this opportunity to join those on the list who > question your insistence that 3ns = intentionality. I haven't anything to > add to what Edwina, Mike, and now Jon has written except to note that even > Tom Short in his book on Peire's semeiotic goes no further than to say that > "the intentionality of thought is a special case of significance" which > hardly equates it with intentionality. > > Best, > > Gary Richmond > > > > > > On Tue, Feb 13, 2024 at 4:40 PM John F Sowa <s...@bestweb.net> wrote: > >> Jon, >> >> Peirce's observations about the human perception of time as a continuum >> is important. But there are many different ways of talking and thinking >> about time. And there are also many different mathematical ways of >> formulating theories. See my previous note in response to Edwina. >> >> For starters, see the Wikipedia article about Whorf: >> https://en.wikipedia.org/wiki/Benjamin_Lee_Whorf . >> >> The IndoEuropean way of thinking about time is by no means universal, and >> the long-standing puzzle by Zeno shows that the answer by Aristotle is not >> obvious. It's not true that all people everywhere have the same ways of >> thinking about time, continuity, or the relation between time and >> continuity. >> >> And the Peirce-Aristotle theory about the continuum is not the one that >> Cantor formalized. More mathematicians today follow Cantor than Peirce. >> >> JAS> 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 >> >> I admit that this statement is consistent with Peirce's quotations. But >> the languages Peirce knew, although remarkably extensive among 19th century >> philosophers, do not exhaust the full range of thought about time or >> continuity or the relations between them. And the different theories about >> continuity among professional mathematicians does not imply that the way >> people talk about time implies the way they must formulate theories about >> continuity. >> >> The best we can say is that Peirce's views are consistent with views in >> SAE (Whorf's abbreviation for Standard Average European), but they are by >> no means universal. They do not rule out other reasonable human ways of >> thinking about, talking about, and representing time and continuity. >> >> John >> _____________________________________________ >> >> *From*: "Jon Alan Schmidt" <jonalanschm...@gmail.com> >> >> 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 >> >> >> _ _ _ _ _ _ _ _ _ _ >> ARISBE: THE PEIRCE GATEWAY is now at >> https://cspeirce.com and, just as well, at >> https://www.cspeirce.com . It'll take a while to repair / update all >> the links! >> ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON >> PEIRCE-L to this message. PEIRCE-L posts should go to >> peirce-L@list.iupui.edu . >> ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to >> l...@list.iupui.edu with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the >> message and nothing in the body. 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_ _ _ _ _ _ _ _ _ _ ARISBE: THE PEIRCE GATEWAY is now at https://cspeirce.com and, just as well, at https://www.cspeirce.com . It'll take a while to repair / update all the links! ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the body. More at https://list.iupui.edu/sympa/help/user-signoff.html . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
