Jon S, List, Before I try to provide an outline of where I'm heading, let me anchor what I'm trying to do in a specific text. The philosophical points that Peirce is trying to draw from the mathematical examples in RLT are offered, at least in part, in support of the following kind of argument:
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. (CP, 6.582) 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. (CP, 6.582) 3. Hyperbolic philosophy. Reason marches from premisses to conclusion; nature has ideal end different from its origin. (CP, 6.582) 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. Bent on outward studies, it will find the statement that nerve-matter feels, just as carmine is red, a convenient disposition of a troublesome question. Elliptic philosophy is irreconcilable with Spiritualism. (CP, 6.583) He who feels himself and his neighbors under the constraints of overwhelming power, from which they long to take refuge in annihilation – situation little life as rounded with a sleep, readily accepts the idea that the world, too, sprang out of the womb of nothingness to evolve its destiny, and into nothingness back to return. Such life as this philosophy recognizes -- a fatal struggle, a mere death-throe --it should extend throughout nature. Soul should be a mere aspect of the body, not tied to it, therefore, but identical with it. Nothing can be more hostile to Spiritualism than this Parabolic philosophy. (CP, 6.584) Hyperbolic philosophy has to assume for starting-point something free, as neither requiring explanation nor admitting derivation. The free is living; the immediately living is feeling. Feeling, then, is assumed as starting-point; but feeling uncoördinated, having its manifoldness implicit. For principle of progress or growth, something must be taken not in the starting-point, but which from infinitesimal beginning will strengthen itself continually. This can only be a principle of growth of principles, a tendency to generalization. Assume, then, that feeling tends to be associated with and assimilated to feeling, action under general formula or habit less common in this country and age than in other places and times -- viewing this tending to replace the living freedom and inward intensity of feeling. This tendency to take habits will itself increase by habit. Habit tends to coordinate feelings, which are thus brought into the order of Time, into the order of Space. Feelings coordinated in a certain way, to a certain degree, constitute a person; on their being dissociated (as habits do sometimes get broken up), the personality disappears. Feelings over whose relations to their neighbors habit has acquired such an empire that we detect no trace of spontaneity in their actions, are known as dead matter. The hypothesis here sketched, whose consequences, traceable with precision to considerable detail in various directions, appear to accord with observation, to an extent of which I can here give no idea, affords a rational account of the connection of body and soul. This theory, so far as I have been able as yet to trace its consequences, gives little or no countenance to Spiritualism. Still, it is evidently less unfavorable than any other reasonable philosophy. (CP 6.585) He makes these sorts of claims in a number of places (e.g., CP, 8.317). The three types of "philosophies" that Peirce characterizes here are emblematic of three approaches to framing hypotheses about beginning and ending points in a developmental sequence, including those that are more spiritual (i.e., inward) in character as well as those that are more natural (i.e, outward) in character. For the purposes of developing a logical account of the growth of understanding, he is arguing for (3) as a plausible hypothesis and rejecting (1) and (2) because they fail to explain a number of surprising phenomena that are associated with the growth of understanding. What is more, both (1) and (2) have the effect of closing the door to further inquiry in a particularly problematic manner. A parallel argument is made about the growth of order in nature. The mathematical examples in RLT that draw on projective geometry and the relation to metrical geometries as well as the examples that draw on the more fundamental ideas in topology are offered by Peirce for the purposes of getting clearer about a number of key mathematical conceptions that he is putting to use in the development and refinement of the conception of continuity within the logical theory. Many of these conceptions are identified in italics in the text (e.g, completed aggregate, multitude brought to an end, potential, topical singularity, furcation, perissid, artiad, fornix, line, filament, surface, film, space, tripon, chorisis, cyclosis, immensity, ensemble, etc.), and he is applying these mathematical conceptions for the purpose of addressing the problem of how to clarify a logical conception of continuity that will be adequate for a normative theory of semiotics. Peirce focuses on the evolution of more determinate dimensions from a vague potentiality in the account of the logical conception of continuity at 253-4 in RLT because he is trying to articulate an explanation of how the various dimensions of our thought might evolve. Those logical dimensions can be divided, in quite a fundamental way, according to three dimensions of yet further dimensions of possibles, existents and necessitants of signs, objects, interpretants and their relations within a growing system. --Jeff Jeffrey Downard Associate Professor Department of Philosophy Northern Arizona University (o) 928 523-8354 ________________________________ From: Jon Alan Schmidt <[email protected]> Sent: Monday, November 14, 2016 3:17 PM To: Jeffrey Brian Downard Cc: [email protected] Subject: Re: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was Metaphysics and Nothing (was Peirce's Cosmology)) Jeff, List: I am definitely interested, but it would be helpful to me if you could first outline where you see this ultimately going, and then proceed in smaller steps. As you could probably tell, I had trouble making the connection between Desargues' theorem and Peirce's conception of continuity, not to mention the subsequent blackboard diagram; and my own intuition (or perhaps lack thereof) is such that discussing "the projective absolute" and "metrical relations in elliptical, parabolic or hyperbolic geometries" is not (at least so far) helping me understand your/Peirce's point "about the kind of hypothesis that is needed to make sense of ... the growth of order in the cosmos." Also, I still believe that Peirce's "table of contents" in "A Neglected Argument" was for a future book that he had not yet written and never did manage to write, rather than anything specific in his previous material such as RLT. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt<http://www.LinkedIn.com/in/JonAlanSchmidt> - twitter.com/JonAlanSchmidt<http://twitter.com/JonAlanSchmidt> On Mon, Nov 14, 2016 at 3:45 PM, Jeffrey Brian Downard <[email protected]<mailto:[email protected]>> wrote: Jon S, Gary R, Edwina, John S, List, If others are interested, I'd like to continue the discussion of the last lecture on continuity in RLT. The goal, I took it, was to draw on it for the sake of filling in some the details in the "table of contents" for a larger set of inquiries that he sketched in "A Neglected Argument." My proposal is to march through more of the mathematical examples he offers in the hopes of getting more clarity about the logical conception of continuity that he articulates. Then, the aim is to work up to the example of the lines on the blackboard and the way that he uses that example to frame some hypothesis in cosmological metaphysics. Given the fact that my post on Desargues 6-point theorem did not generate much in the way of comments or questions, I am concerned that I overdid it and managed to smother some of the interest in the questions--both interpretative and philosophical--that we were considering. As such, I'm asking for feedback to make see if continued discussion of the mathematical examples is welcome. Late last week, I thought of a way to illustrate Peirce's larger point about how the 6 point theorem is connected to the larger idea that Cayley and Klein make about the character of the projective absolute and how it provides the basis of any system of metrical relations in elliptical, parabolic or hyperbolic geometries. The illustration helps to see, in a more intuitive way, the point Peirce seems to be making about the kind of hypothesis that is needed to make sense of the possibility of progress with respect to the growth of our understanding or, more generally, with the growth of order in the cosmos. So, let me ask if there are any takers for continuing the discussion of RLT along these lines? --Jeff Jeffrey Downard Associate Professor Department of Philosophy Northern Arizona University (o) 928 523-8354<tel:928%20523-8354>
----------------------------- 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 the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
