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 / twitter.com/JonAlanSchmidt On Tue, Apr 25, 2023 at 4:10 PM Jeffrey Brian Downard < [email protected]> 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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