Hi Jon S, Gary F, all, Jon, I've read your paper on time, although it was some time ago, so my memory is not fresh.
The diagram of the lines and the circles in figure3 do not appear to show three different types of conic sections. Rather, they show three circles intersecting with a line at two, one and no places. One can give the same sort of diagram for an ellipse, parabola or hyperbola. In order to use the diagrams to clarify points about the relationships between conic sections and a line at infinity in projective space, it would be helpful to supply more than is shown in Figures 3 or 4. In fact, I think a lot more needs to be shown about the character of the absolute in projective geometry for the key points to be made clearer. The points I was emphasizing the passage at CP 6.210 appear to support Gary F's suggestions about the general principle govern the passage from the ideal starting point of inquiry to its ideal ending point. The same holds for the metaphysical hypothesis offered as an explanation of the cosmological evolution of the universe. Yours, Jeff ________________________________ From: peirce-l-requ...@list.iupui.edu <peirce-l-requ...@list.iupui.edu> on behalf of Jon Alan Schmidt <jonalanschm...@gmail.com> Sent: Tuesday, April 25, 2023 5:19 PM To: Peirce-L <peirce-l@list.iupui.edu> Subject: Re: [PEIRCE-L] A question for pragmatists Jeff, List: You and I seem to be more or less on the same page here, along with Martin in light of his helpful clarification that avoiding "originalism" and "endism" simply means recognizing that inquiry has no definite beginning or end--just like the universe in Peirce's cosmology, and consistent with his thoroughgoing synechism that precludes any singularities within a true continuum such as time (CP 1.498, c. 1896; CP 6.210, 1898; CP 1.274-275, 1902). Attached are two relevant diagrams that I included in my "Temporal Synechism" paper--the first (Figure3.tiff) showing the relations between the three different conic sections and the line at infinity in projective geometry, and the second (Figure5.tiff) showing how a hyperbolic continuum is mapped to two parallel lines of infinite length. As Peirce explains ... CSP: I may mention that my chief avocation in the last 10 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. 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. 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. ... 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) Thanks, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt<http://www.LinkedIn.com/in/JonAlanSchmidt> / twitter.com/JonAlanSchmidt<http://twitter.com/JonAlanSchmidt> On Tue, Apr 25, 2023 at 4:10 PM Jeffrey Brian Downard <peirce-l@list.iupui.edu<mailto:peirce-l@list.iupui.edu>> wrote: Gary F., Jon S, all, I take Peirce's argument for the triad of ideals—aesthetic, ethical and logical--to start with an analysis of our ordinary conception of having an end and then asking: what is necessary for an end to be ultimate? In his discussion of the topological character of the relationship between the starting and ending points of inquiry, he appears to be exploring an analogy between the cognitive evolution of intelligent beings like us and the cosmological evolution of the universe. As such, there is an analogy between the logical conceptions of the starting and ending points inquiry and the starting and ending points of the cosmos. How should we understand the conception of what is ultimate as an end? Consider what Peirce is trying to articulate when when offers the topological model at CP 6.581 Philosophy tries to understand. In so doing, it is committed to the assumption that things are intelligible, that the process of nature and the process of reason are one. Its explanation must be derivation. Explanation, derivation, involve suggestion of a starting-point--starting-point in its own nature not requiring explanation nor admitting of derivation. Also, there is suggestion of goal or stopping-point, where the process of reason and nature is perfected. A principle of movement must be assumed to be universal. It cannot be supposed that things ever actually reached the stopping-point, for there movement would stop and the principle of movement would not be universal; and similarly with the starting-point. Starting-point and stopping-point can only be ideal, like the two points where the hyperbola leaves one asymptote and where it joins the other. In regard to the principle of movement, three philosophies are possible. 1. Elliptic philosophy. Starting-point and stopping-point are not even ideal. Movement of nature recedes from no point, advances towards no point, has no definite tendency, but only flits from position to position. 2. Parabolic philosophy. Reason or nature develops itself according to one universal formula; but the point toward which that development tends is the very same nothingness from which it advances. 3. Hyperbolic philosophy. Reason marches from premisses to conclusion; nature has ideal end different from its origin. The aim, I think, is fairly clearly stated. He is using the topological model in an effort to clarify the conception of a principle of movement. Our conception of growth in our understanding—such that progress is really possible--stands in need of clarification both because it is vague and because we are prone to doubt its legitimacy for our logica utens. As such, the aim is to frame a clearer hypothesis about the principle of movement in the philosophical theory of logic (i.e., our logica docens). As Gary F. is pointing out, the ideal stopping point can "only be ideal." At that ideal limit, the "movement would stop and the principle of movement would not be universal." (my emphasis) The same holds for the ideal starting point. My hunch is that Peirce is using the topological model for the theory of logic to help establish the sorts of proportions that are important for the sake of inductively ascertaining the likelihood that a given hypothesis is true or false--within some margin of error. As such, the topological model serves as the basis of a measure of degrees of error for our inquiries generally. Drawing out the connections between the topological, projective (i.e., proportion) and metrical conceptions would take some work. Yours, Jeff
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