List: As I noted yesterday, the identification of exactly three kinds of genuine conic sections goes back at least as far as Euclid, so it is not something that Peirce invented or derived from his universal categories. Nevertheless, upon further reflection, there is a sense in which they can be aligned, suggesting that this is another "one of the very numerous phenomena I have met with which confirm this list of categories" (CP 5.121, EP 2:197, 1903). Peirce defines the latter as follows in "A Guess at the Riddle."
CSP: The first is that whose being is simply in itself, not referring to anything nor lying behind anything. The second is that which is what it is by force of something to which it is second. The third is that which is what it is owing to things between which it mediates and which it brings into relation to each other. (CP 1.356, EP 1:248, 1887-8) Again, every conic section is represented as a circle on the projective plane ( https://list.iupui.edu/sympa/arc/peirce-l/2023-04/msg00081/tif7fIZNichwD.tif). The only distinction between the three different kinds is that an ellipse has its being simply in itself, not intersecting the line at infinity; a parabola is what it is by force of its one such intersection, to which it is second; and a hyperbola is what it is owing to its two such intersections, between which it mediates and which it brings into relation to each other. A few paragraphs later, Peirce outlines the corresponding cosmologies, much like he subsequently does in other writings (CP 6.581-585, 1890; CP 6.27, EP 1:294, 1891; R 953, c. 1899). CSP: If you think the measurable is all there is, and deny it any definite tendency whence or whither, then you are considering the pair of points that makes the absolute to be imaginary and are an Epicurean. If you hold that there is a definite drift to the course of nature as a whole, but yet believe its absolute end is nothing but the Nirvana from which it set out, you make the two points of the absolute to be coincident, and are a pessimist. But if your creed is that the whole universe is approaching in the infinitely distant future a state having a general character different from that toward which we look back in the infinitely distant past, you make the absolute to consist in two distinct real points and are an evolutionist. (CP 1.362, EP 1:251) This comes immediately after the sentence that I quoted near the end of my 10-minute presentation--"The starting-point of the universe, God the Creator, is the Absolute First; the terminus of the universe, God completely revealed, is the Absolute Second; every state of the universe at a measurable point of time is the third," which implies that "the universe is a vast representamen [mediating sign], a great symbol of God's purpose [revealing Himself], working out its conclusions in living realities" (CP 5.119, EP 2:193, 1903)--and is accompanied by the following footnote. CSP: The last view [hyperbolic/evolutionist/meliorist cosmology] is essentially that of Christian theology, too. The theologians hold the physical universe to be finite, but considering that universe which they will admit to have existed from all time, it would appear to be in a different condition in the end from what it was in the beginning, the whole spiritual creation having been accomplished, and abiding. Even though the *physical *universe is finite, the two limits of time as a true hyperbolic continuum must be at the *infinite *past and future so that it stretches throughout "the entire universe--not merely the universe of existents, but all that wider universe, embracing the universe of existents as a part" (CP 5.448n, EP 2:394, 1906) along with the universes of possibles and necessitants (CP 6.455, EP 2:435, 1908; EP 2:478-479, 1908). As Peirce says elsewhere, "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 ... 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). On the other hand, Peirce's reference to the one limit in the parabolic/pessimistic cosmology as "Nirvana" might be an allusion to Buddhism and/or Hinduism, and he says elsewhere that the elliptic/epicurean cosmology entails materialism--"The choice of elliptic philosophy, which refuses to acknowledge the ideal, supposes more interest in nature than in reason. The philosophy which sees nothing in nature but the washing of waves on a beach cannot consistently regard mind as primordial, must rather take mind to be a specialization of matter" (CP 6.583). As far as I can tell, both mathematically and categorially, there is no fourth alternative unless thoroughgoing synechism is abandoned in favor of a cosmology that treats time as having "exceptional instants in which it is discontinuous--any abrupt beginning and end" (CP 1.274, 1902), like the posited "Big Bang" and "Big Crunch" singularities. As Peirce points out, the problem with such an approach is that these would be "arbitrary exceptions not warranted by experience." Thanks, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt
_ _ _ _ _ _ _ _ _ _ ► 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] . ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to [email protected] 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.
