Jeff, List: I am well aware of Peirce's advocacy of "hyperbolic" philosophy, and used that term myself in the very first post of this thread, stating that it "posits complete indeterminacy in the infinite past and complete regularity in the infinite future; not as *actual *states, but as *ideal *limits." My question remains unanswered, though; if the downward-pointing apex of the triangle is the *beginning*, then what would correspond to the *end*--of cognition, or of inquiry, or of the universe? Is there really a *limit *to the growth of thought, or of knowledge, or of concrete reasonableness, such that this diagram *only *models the (indefinite) beginning? Or is it relevant that the base of the triangle endlessly becomes wider?
Regards, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Thu, Aug 29, 2019 at 10:51 PM Jeffrey Brian Downard < [email protected]> wrote: > Jon S, List, > > Jon: If the downward-pointing apex of the triangle is the *beginning*, > then what would correspond to the *end*--of cognition, or of inquiry, or > of the universe? > > Jeff: See Peirce's remarks about the three frameworks one might adopt with > respect to the beginning and ending points of inquiry: > > 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. CP 6.582 > > In the context of the hyperbolic philosophy, the absolute is conceived to > two parts of a hyperbola. The starting point of inquiry concerning some > general fact is a point on one part of the hyperbola. The ending point of > inquiry concerning that general fact is a point on the other hyperbola. > Just as "reason marches from premisses to conclusion" for the community of > inquirers, so too does nature have an ideal end different from its (ideal) > origin. Unlike other treats of the conception of infinity which takes it to > be a characteristic of a series with no end, the conception of infinity in > projective space is a real (if ideal) part of that space. > > On my reading of Peirce's account of measurement, it is analogous to his > account of classification. Natural classes pick out real general facts. > Similarly, natural forms of measurement pick out real metrical properties > in those facts. > > Here is a more conjectural suggestion that seems to follow from this point > about the reality of metrical properties in the universe at our time. Early > in the evolution of the universe, the cosmos had real topological > characteristics--but probably did not have projective or metrical > properties. There was no dominant system of homoloids in space, just as > lengths and angles were not preserved under movements involving > translation, reflection or rotation in space. Over time, projective > proportions were realized in the real laws governing the universe. Later > on, metrical relations of various kinds (e.g., ordinal and ratio scales) > came to be realized in the governing laws. > > --Jeff > Jeffrey Downard > Associate Professor > Department of Philosophy > Northern Arizona University > (o) 928 523-8354 > >>
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