Jeff, List: I will try to take a closer look at this later.
Thanks, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Sun, Nov 6, 2016 at 3:36 AM, Jeffrey Brian Downard < [email protected]> wrote: > Jon S, Gary R, List, > > Given our interest in providing a clearer meaning for the conceptions of > order and Super-order, I think that these passages might be helpful. > > Any proposition whatever concerning the order of Nature must touch more or > less upon religion. In our day, belief, even in these matters, depends more > and more upon the observation of facts. If a remarkable and universal > orderliness be found in the universe, there must be some cause for this > regularity, and science has to consider what hypotheses might account for > the phenomenon. One way of accounting for it, certainly, would be to > suppose that the world is ordered by a superior power. But if there is > nothing in the universal subjection of phenomena to laws, nor in the > character of those laws themselves (as being benevolent, beautiful, > economical, etc.), which goes to prove the existence of a governor of the > universe, it is hardly to be anticipated that any other sort of evidence > will be found to weigh very much with minds emancipated from the tyranny of > tradition. (CP 6.395) > > And then, two paragraphs later: > > If we could find out any general characteristic of the universe, any > mannerism in the ways of Nature, any law everywhere applicable and > universally valid, such a discovery would be of such singular assistance to > us in all our future reasoning that it would deserve a place almost at the > head of the principles of logic. On the other hand, if it can be shown that > there is nothing of the sort to find out, but that every discoverable > regularity is of limited range, this again will be of logical importance. > What sort of a conception we ought to have of the universe, how to think of > the ensemble of things, is a fundamental problem in the theory of > reasoning. (CP 6.397) > > So, how should we "think of the ensemble of things"? Peirce provides the > definition for "ensemble" in the Century Dictionary. In the second > definition of the term, he characterizes the mathematical use of the > conception. In that definition, he makes a distinction between an ensemble > of the first genus, the second genus, and a tout ensemble. It is clear, I > think, that he is talking about a tout ensemble at 6.397. What is more, I > believe that he is talking about a tout ensemble in RLT, when he puts the > word in italics on page 259. How should we think of order and Super-order > as they are applied to each of these three sorts of ensembles? > > He explicitly uses "tout ensemble" in the following passage: > > The division of modes of Being needs, for our purposes, to be carried a > little further. A feeling so long as it remains a mere feeling is > absolutely simple. For if it had parts, those parts would be something > different from the whole, in the presence of which the being of the whole > would consist. Consequently, the being of the feeling would consist of > something beside itself, and in a relation. Thus it would violate the > definition of feeling as that mode of consciousness whose being lies > wholly in itself and not in any relation to anything else. In short, a > pure feeling can be nothing but the total unanalyzed impression of the > tout ensemble of consciousness. Such a mode of being may be called simple > monadic Being. CP 6.345 > > Given the fact that Peirce draws this meaning of "tout ensemble" from > mathematics, I'm wondering if some examples from topology, projective > geometry or metrical geometry might help to clarify the differences between > a tout ensemble and ensembles of the first and second genus. Peirce offers > the example of Desargues' theory of Involution and its use in the 6 point > theorem on page 245. How does the conception of an ensemble apply in this > case where we are looking at the intersection of these rays as they are > projected from their origins at Q and R? > > The upshot of this example is made clearer when he says that Cayley showed > that the whole of geometrical metric is but a special problem in > geometrical optic. The point Peirce is making is that the development of > the conception of a projective absolute as a locus in space was central for > thinking about the character of projective space as a whole--i.e., as a > tout ensemble. Taken as a whole, the topological character of the space is > something that we study by a process of decomposition. That is, we cut it > up and see how the parts are connected. In this way, we come to see what > Listing numbers are for the Chorisis, Cyclosis, Periphraxis and Immensity > of such a space. The Periphraxis and Immensity, I take it, are especially > important in understanding the character of the tout ensemble of a > projective space. He says that the Periphraxis of perspective space is 1, > and that the Immensity of any figure in our space is 0, except for the > entirety of space itself, for which the Immensity is 1. > > These kinds of exercises in mathematics are essential, I believe, for > understanding the points he is illustrating using the diagram involving > blackboard on pages 261-3. How might we draw them out? > > --Jeff > > Jeffrey Downard > Associate Professor > Department of Philosophy > Northern Arizona University > (o) 928 523-8354
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