Jon S, List,
Jon: I take Peirce to be saying that the only real parts of a perfect continuum are potential parts. Any part that is actualized is a topical singularity that interrupts the continuum, rendering it imperfect. The actualized part is still real, of course, but it is no longer a material part of the continuum. Jeff: Consider the following diagrams drawn, let us say, on a 2-dimensional topological space. [cid:b6d8d2cc-e881-4e06-91c3-87ef7742a3af] In saying that points i and j represent discontinuities in A and B, I would not draw the conclusion that those points are no longer parts of the continuous lines A and B. Peirce is making the point that i and j, as points that are now noted on the lower diagram, but not the upper, are now determinate points that are made determinate by the act of making the intersections--and no longer just possible but indeterminate points. Peirce is drawing on the fact that i and j do represent discontinuities in what was once continuous. But it does not follow that, considered in terms of the general rules that are the bases of the generation of the loops, that the loops are no longer continuous lines. There is continuity on A in the lower diagram because there is a continuous path around A passing through i and j. At the same time, there is now an option for a particle tracing a path around A to deviate from the continuous path and to move to a path around B. As far as I can see, Peirce is making the point that the discontinuities are a product of the token diagram with the intersecting loops--considered as existing sorts of things. The same sort of point can be made about the loops in the upper diagram. With respect to the blank sheet on which they were drawn, the token instances of the loops created a discontinuity in the sheet. There is now a part of the surface internal to the loop and a part that is external. Having said that, the underlying sheet is still being generated by a general rule, and that rule gives the sheets its inherent continuity--which is what enables us to move things around on it via processes of transformation (yet further general rules). Well, it is getting too late for me to think very clearly, so I'd better stop here. --Jeff Jeffrey Downard Associate Professor Department of Philosophy Northern Arizona University (o) 928 523-8354 ________________________________ From: Jon Alan Schmidt <[email protected]> Sent: Thursday, August 29, 2019 8:22:43 PM To: [email protected] Subject: Re: Re: Re: [PEIRCE-L] Re: Peirce and the Big Bang Jeff, Gary R., List: Supplementing what I just posted ... JD: On my reading of the last lecture of RLT, I think it is an error to suggest that he is making measurement intrinsic to the definition of those dimensions of either time, space or quality. I said that measurement seems intrinsic to most of the definitions for "dimension," "dimensional," and "dimensionality" that Peirce provided in the Century Dictionary. I then suggested that the familiar notions associated with these words might not apply once we adopt a "top-down" synthetic approach, rather than a "bottom-up" analytic approach. Although Peirce was still very much in his "supermultitudinous" phase in 1898, I think that there are already hints of his eventual shift to the topical theory in that last lecture. JD: In saying that the dimensions of space, time and quality were potential and not actual, I do not take him to be saying that the dimensions were not real. I agree. In fact, I take Peirce to be saying that the only real parts of a perfect continuum are potential parts. Any part that is actualized is a topical singularity that interrupts the continuum, rendering it imperfect. The actualized part is still real, of course, but it is no longer a material part of the continuum. GR: It seems to me that possibles (1ns) are potentially real enough in the ur-continuity (3ns). Continuity as 3ns involves 1ns as those, shall we say, "selected" possibilities which will ultimately be realized as the qualities which can come into existence. That is, they are possibilities which become real qualities when they are embodied in existential things (2ns). I disagree. Peirce clearly affirmed that some possibilities are real, not merely "potentially real"; that is why Max Fisch called him "a three-category realist" as of 1897. In fact, there are real possibilities that never become actualized, such as the resistance to scratching of a diamond that burns up before ever being tested. "Indeed, it is the reality of some possibilities that pragmaticism is most concerned to insist upon" (CP 5.453, EP 2:354; 1905). JD: One thing he is trying to accomplish in clarifying such a limiting idea is to arrive at something that doesn't call out for further explanation. GR: I would question your use of the expression "a kind of limiting idea" here. Beyond limiting "further explanation" (which sounds like a very un-Peircean as Peirce's methodology argues against such a cessation of inquiry). Peirce indeed argued against blocking the way of inquiry by "maintaining that this, that, or the other element of science is basic, ultimate, independent of aught else, and utterly inexplicable" (CP 1.139, EP 2:49; 1898). However, he also recognized that not everything demands an explanation. Jeff is suggesting that "the original vague potentiality" is the kind of thing that does not call for any further explanation. However, my response is that just as a "scriber" is needed to draw the chalk marks on the blackboard, likewise a "creator" is needed to make the blackboard in the first place; and accordingly, I suggest instead that the Reality of Ens necessarium is the kind of thing that does not call for any further explanation. JD: In this case, I think a better analogy than a function in calculus is the conception of the absolute in projective geometry. It is better because the idea of convergence is a matter of proportion involving continuous magnitudes that may have an indeterminate metrical character. Proportions are preserved, but not scalar values. How does this square with Peirce's contention that topical geometry (or Topics) is the proper branch for mathematically investigating continuity, rather than projective geometry (or Graphics)? JD: As Peirce suggests in "Questions Concerning Certain Faculties...", the starting point of a process of cognition can be thought of as triangle touching the surface of water in a glass. The starting point of inquiry--the tip of the triangle--is a kind of limiting idea. I quoted and commented on that entire passage very early in this thread as the sort of reasoning that Peirce might apply to the starting point of the universe, as well. 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? 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 Thu, Aug 29, 2019 at 9:26 PM Jeffrey Brian Downard <[email protected]<mailto:[email protected]>> wrote: Gary R, List, You ask: "Who, besides Peirce (besides some theologians) have mused on how our Universe came into being?" I take most major philosophers to recognize a need to address the question: what is the origin of all things. How will it end? A range of answers have been considered by the likes of Plato and Aristotle, Hume and Kant, Quine to Plantinga. Some say that the history of the cosmos goes back in time with no beginning, and that it will continue without end. Others say that it had a beginning and that it will have an end in time. Empirically minded philosophers have argued that metaphysical questions of this sort have no positive answers--one way or the other--that can be put to the test. Kant considers these opposing answers to be antinomies in the Dialectic of the first Critique. He suggests that we are lead by Reason to address questions concerning the absolute--and that we need to tease out where Reason might be leading us astray. I take Peirce's explorations in the last lecture of RLT to be entirely consonant with what he says here: Chance is First, Law is Second, the tendency to take habits is Third.†4 Mind is First, Matter is Second, Evolution is Third. Such are the materials out of which chiefly a philosophical theory ought to be built, in order to represent the state of knowledge to which the nineteenth century has brought us. Without going into other important questions of philosophical architectonic, we can readily foresee what sort of a metaphysics would appropriately be constructed from those conceptions. Like some of the most ancient and some of the most recent speculations it would be a Cosmogonic Philosophy. It would suppose that in the beginning -- infinitely remote -- there was a chaos of unpersonalized feeling, which being without connection or regularity would properly be without existence. This feeling, sporting here and there in pure arbitrariness, would have started the germ of a generalizing tendency. Its other sportings would be evanescent, but this would have a growing virtue. Thus, the tendency to habit would be started; and from this, with the other principles of evolution, all the regularities of the universe would be evolved. At any time, however, an element of pure chance survives and will remain until the world becomes an absolutely perfect, rational, and symmetrical system, in which mind is at last crystallized in the infinitely distant future. (CP 6.32-33) The idea of our cosmos starting in a condition of absolute chaos of unpersonalized feeling, and then ending in a state of absolutely perfect order seem to be limiting sorts of ideas. As with an asymptotic function in calculus, we can see that the series we are tracing seems to converge as things head off infinitely far in each direction. It is a mistake, however, to think that it actually does converge at some definite point in that series. In this case, I think a better analogy than a function in calculus is the conception of the absolute in projective geometry. It is better because the idea of convergence is a matter of proportion involving continuous magnitudes that may have an indeterminate metrical character. Proportions are preserved, but not scalar values. As far as I can see, Peirce appears to be drawing on the ideas of the beginning and ending points of inquiry--as those are worked out in a speculative rhetoric (methodeutic)--and he is treated them as principles having an objective character in his metaphysical cosmology. The analogy is: (A) the starting point of inquiry is to (B) the origin of all things as (C) the ending point of inquiry is to (D) the end of all things. So, A:B::C:D. Similarly, A:C::B:D. As Peirce suggests in "Questions Concerning Certain Faculties...", the starting point of a process of cognition can be thought of as triangle touching the surface of water in a glass. The starting point of inquiry--the tip of the triangle--is a kind of limiting idea. --Jeff Jeffrey Downard Associate Professor Department of Philosophy Northern Arizona University (o) 928 523-8354 ________________________________ From: Gary Richmond <[email protected]<mailto:[email protected]>> Sent: Thursday, August 29, 2019 4:50 PM To: Peirce-L Subject: Re: Re: Re: [PEIRCE-L] Re: Peirce and the Big Bang Jeff, Jon, List, Jeff concluded: JD: In saying that the dimensions of space, time and quality were potential and not actual, I do not take him to be saying that the dimensions were not real. Possibles may, on Peirce's account, be real things. It seems to me that possibles (1ns) are potentially real enough in the ur-continuity (3ns). Continuity as 3ns involves 1ns as those, shall we say, "selected" possibilities which will ultimately be realized as the qualities which can come into existence. That is, they are possibilities which become real qualities when they are embodied in existential things (2ns). JD: I take this starting point, which is explicated in terms of a conception of vague potentiality, as a kind of limiting idea. One thing he is trying to accomplish in clarifying such a limiting idea is to arrive at something that doesn't call out for further explanation. If someone asks, why does the original vague potentiality have the characteristics it does? His answer is: that doesn't need a further explanation. I would question your use of the expression "a kind of limiting idea" here. Beyond limiting "further explanation" (which sounds like a very un-Peircean as Peirce's methodology argues against such a cessation of inquiry). Would you explain what you mean by "limiting idea" here (unless all you mean is that Peirce wholly uncharacteristically intended to stop further inquiry into the matter)? And the question "why does the original vague potentiality have the characteristics it does" doesn't seem to me to catch the richness of the analogy, the blackboard diagram. In Peirce's presentaiton the blackboard per se represents only what I've termed the ur-continuity upon which these "possibles" will be drawn, chosen, as it were, from an infinite number of possibilities. As Jon has commented, that something is scribed upon the blackboard suggests that there is a scriber (it may not be able to avoid theology in that interpretation, although I don't think it's the only one possible--although it should be recalled that Peirce was a theist), and out of these unlimited possibilities only some were scribed. Peirce writes of our existing world's origins: . . .we must suppose that as a rule the continuum has been derived from a more general continuum, a continuum of higher generality. >From this point of view we must suppose that the existing universe, with all >its arbitrary secondness, is an offshoot from, or an arbitrary determination >of, a world of ideas, a Platonic world. . . CP 6.191- 92 Again, there was "a Platonic world" 'before', so to speak, the existing world came into being: The evolutionary process is, therefore, not a mere evolution of the existing universe, but rather a process by which the very Platonic forms themselves have become or are becoming developed. CP 6.194 And here we are reminded that Peirce has his own "multi-universes" theory: At the same time all this, be it remembered, is not of the order of the existing universe, but is merely a Platonic world, of which we are, therefore, to conceive that there are many, both coordinated and subordinated to one another; until finally out of one of these Platonic worlds is differentiated the particular actual universe of existence in which we happen to be. CP 6.208 JD: Some philosophers might claim that Peirce is wrong to think the original vague potentiality doesn't need a further explanation, but I take that to be the view he is exploring in this last lecture. What sort of "explanations" of "the original vague potentiality" have other philosophers entertained? Who are the philosophers making these claims of the inadequacy of Peirce of Peirce's thinking on the earliest situation of the cosmos? Who, besides Peirce (besides some theologians) have mused on how our Universe came into being? It would appear that most astrophysicists simply accent the singularity of the Big Bang without questioning how something as vast as a cosmos could arise out of nothing (or they posit truly vague and undeveloped ideas, such as "bouncing universes" and "quantum fluctuation" theories). In my view, Peirce's musings of the origin of the universe is sui generis, highly stimulating from both scientific and philosophic (including metaphysical) standpoints, and the furthest any philosopher-scientist (whom I know of at least) has gone into considering the possible situation at our cosmic origin, pre-Big Bang (if one subscribes to that view) While in Peirce's view, the earliest cosmos took form "before time was." Best, Gary R Gary Richmond Philosophy and Critical Thinking Communication Studies LaGuardia College of the City University of New York On Thu, Aug 29, 2019 at 5:58 PM Jeffrey Brian Downard <[email protected]<mailto:[email protected]>> wrote: Jon S, Gary R, List, On my reading of the last lecture of RLT, I think it is an error to suggest that he is making measurement intrinsic to the definition of those dimensions of either time, space or quality. Rather, the thrust of the argument is to start with mathematical conceptions and then use them for the sake of developing hypotheses in metaphysical cosmology. In doing so, he moves from the consideration of metrical geometries, to projective geometry to topology. In doing so, he is setting metrical considerations to the side and focusing primarily on topological matters. It is clear that the topological points--including those about the possible dimensions of a such a malleable space in which such things straigntness, length and degree of angle are not preserved across transformations--are being used to clarify a mathematical conception of continuity. He is then putting that refined notion of continuity to use as he engages with questions about the origins and evolution of the universe. The questions he is trying to answer include the following. How many dimensions of time, space and quality where there early in the history of the universe? How many dimensions of each are there now. How did the number of dimensions change over time? Jon quoted two passages in that last lecture: CSP: A continuum may have any discrete multitude of dimensions whatsoever. lf the multitude of dimensions surpasses all discrete multitudes there cease to be any distinct dimensions. I have not as yet obtained a logically distinct conception of such a continuum. Provisionally, I identify it with the uralt [Ger., ancient], vague generality of the most abstract potentiality. (NEM 3:111, RLT 253-254; 1898) CSP: Let the clean blackboard be a sort of diagram of the original vague potentiality, or at any rate of some early stage of its determination. This is something more than a figure of speech; for after all continuity is generality. This blackboard is a continuum of two dimensions, while that which it stands for is a continuum of some indefinite multitude of dimensions. This blackboard is a continuum of possible points; while that is a continuum of possible dimensions of quality, or is a continuum of possible dimensions of a continuum of possible dimensions of quality, or something of that sort. There are no points on this blackboard. There are no dimensions in that continuum. (CP 6.203, RLT 261; 1898) Consider the following sentence from the second passage: "This blackboard is a continuum of possible points; while that is a continuum of possible dimensions of quality, or is a continuum of possible dimensions of a continuum of possible dimensions of quality, or something of that sort." For the sake of engaging in inquiry in cosmological metaphysics, I would make a distinction between the dimensions of real space at some point in the evolution of the cosmos, and the dimensions of the qualities of the objects in space. As far as I can tell, he is offering a hypothesis about the number of dimensions of (1) time, (2) space and (3) of the various qualities that were present early in the history of the cosmos. It looks to me like he is arguing that each started with a dimensions that were vague in character and not distinctly separated--one from another. Over time, as the cosmos evolved, those dimensions became (a) more determinate and (b) fewer in number. If we go back far enough, we arrive at a vague potentiality as a kind of hypothetical "beginning of all things." This vague conception of potentiality functions as a kind of starting point in the explanations being offered. My assumption is that, in this vague potentiality, there might have been--for instance--potential energy, but there was no kinetic energy. That potential energy might have taken different qualities, such as a particular charge or a particular spin, but there was no actual object having any determinate charge or spin. There might have been a potential for space and time having dimensions, but there were no actual things moving around in space and time. How many dimensions did this potential have? An indefinite vague multitude. The dimensions were continuous. There were uncountable, to say the least. In saying that the dimensions of space, time and quality were potential and not actual, I do not take him to be saying that the dimensions were not real. Possibles may, on Peirce's account, be real things. I take this starting point, which is explicated in terms of a conception of vague potentiality, as a kind of limiting idea. One thing he is trying to accomplish in clarifying such a limiting idea is to arrive at something that doesn't call out for further explanation. If someone asks, why does the original vague potentiality have the characteristics it does? His answer is: that doesn't need a further explanation. It can be illustrated using diagrams. He is offering analogy to the effect that the vague potentiality is like an empty chalkboard before any chalk streaks have been drawn on its surface. Some philosophers might claim that Peirce is wrong to think the original vague potentiality doesn't need a further explanation, but I take that to be the view he is exploring in this last lecture. --Jeff Jeffrey Downard Associate Professor Department of Philosophy Northern Arizona University (o) 928 523-8354
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