Jeff, List: As we resume discussion of this topic, I am renaming the thread and leaving out the quoted posts from November; I hope you do not mind.
Your diagram below is very interesting, but I would appreciate some further elaboration of what it represents. 1. You refer to the starting and ending points of inquiry, but then represent them as hyperbolic curves. Is the idea that each point on the left curve is the start (in the indefinite past) of a distinct line of inquiry, some of which eventually converge (in the indefinite future) at a single point on the right curve? 2. Is there a connection between these curves and points with the concepts of continuity and discontinuity, respectively, within Peirce's synechism? 3. Does semeiosis fit into the picture somehow--in particular, the progression of immediate, dynamic, and final interpretants? 4. What exactly does it mean to say that "inquiry seeks to enlarge the circumference of the circle," given that multiple lines meeting at one point is the ultimate goal? 5. How does Peirce's notion of measuring the amount of a proposition's or reasoning's falsity come into play (if at all)? Thanks, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Fri, Mar 17, 2017 at 10:19 AM, Jeffrey Brian Downard < [email protected]> wrote: > Jon A, John S, Jon S, Clark, List, > > I'd like to refer back to an earlier discussion of the last lecture in RLT > in order to take up the question of how we try to supply a diagram for > better understanding the relationship between truth and the starting and > ending points of inquiry. The diagram below is a sketch of how I would like > to develop the philosophical implications of what Peirce says about the > mathematics of projective relations. Let me know if you have suggestions > for making things clearer. > > Peirce argues that, in regard to the principle of movement from these two > points, only three types of philosophical positions are possible. Here > are the passages I'm trying to interpret: > > 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, 6.581-2) > > Pierce argues that the conception of the absolute in philosophy “fulfills > the same function as the absolute in geometry. According as we suppose the > infinitely distant beginning and end of the universe are *distinct*, > *identical*, or *nonexistent*, we have three kinds of philosophy. What > should determine our choice of these? Observed Facts. These are all in > favour of the first.” [W 8.22; 1890], [CP 4.145; 1893]) Drawing on > the series of mathematical examples copied below, let's construct a diagram > to illustrate Peirce's claim that “[j]ust as geometry has its descriptive > and its metrical portions, the former considering whether points coincide > or not, the latter measuring how far distant from one another they are... > so logic has first to decide whether a proposition or reasoning to be true > or false, and secondly in the latter case, to measure the amount of its > falsity” [W 4.241; 1881], [W 5.166; 1885]) > > > While I'm not able to fit it into this diagram, one idea I'd like to > capture is that of the relations of proportion in quantitative inductive > inferences between what has been observed and what might observed in the > future. In order to understand the significance of picturing the horizon as > hyperbolic lines, see the discussion below. > > --Jeff > Jeffrey Downard > Associate Professor > Department of Philosophy > Northern Arizona University > (o) 928 523-8354 <(928)%20523-8354> >
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