Hi Jon, List,
In response to your remarks about points and lines on the horizon. Let's focus on the case of perspective geometry and leave projective geometry to the side for the time being. I recommend thinking of the points on the horizon I have drawn in several figures that use the idea of railroad tracks running off to distant points as examples of what all of the possible parallel lines would look like that run through every part of the space. All of those possible parallel lines form a line on the horizon. That is what I am trying to illustrate with the diagrams having larger set of parallel lines going to the same two points. Every possible point on the horizon has an unlimited number of possible parallels line that could run through it from every possible part of the larger two dimensional space. That is what one is able to see quite readily when one alters the diagrams by processes of continuous transformation. --Jeff Jeffrey Downard Associate Professor Department of Philosophy Northern Arizona University (o) 928 523-8354 ________________________________ From: Jon Alan Schmidt <[email protected]> Sent: Tuesday, March 28, 2017 6:43 PM To: Jeffrey Brian Downard Cc: [email protected] Subject: Re: Diagramming Inquiry (was Super-Order and the Logic of Continuity) Jeff, List: JBD: As in projective geometry, the points on the horizon form lines. I am not very familiar with projective geometry, and that is probably why I am having a hard time understanding how points on the horizon can form lines, hyperbolic or otherwise. Is it a change in perspective that facilitates this transformation? Is it a limitation of your two-dimensional diagram that you have to show multiple points along each line? JBD: Inquiry starts with surprising phenomena that are a source of doubt. As such, the points on the far left where the lines originate are meant to pick out the sources of those doubts, It is likely that they will need to be represented in a way that better captures the vagueness that is part and parcel of such doubts (as a kind of grey area on the line, and not a definite point). In that case, should each group of parallel lines of inquiry perhaps originate from the same vague region of the line on the left, rather than discrete points? Maybe the lines of inquiry themselves should also be fuzzy at first. Or is the idea that distinct lines of inquiry that ultimately converge are initially prompted by different sources of doubt? JBD: In a way, the collection of meeting points at the infinitely distant horizon that form the hyperbolic curves are a kind of origin from which the continuity of the larger space gets its ultimate shape. This is nitpicking, but obviously Peirce would not accept a collection of points as constituting a continuum. Again, maybe I am just not understanding how projective geometry works. Normally we think of only one horizon, but your diagram has two curves that are separate. I understand that this represents how the end is different from the origin, but it is not very intuitive for most people (myself included). JBD: In effect, our understanding of the aims and principles of reasonable inquiry grows as our beliefs and theories grow. That makes sense, but it still seems contrary to the idea that the lines of inquiry converge. My thought was that the number and variety of beliefs and theories being considered shrinks over time, until the final opinion consists of "the truth, the whole truth, and nothing but the truth." JBD: As such, the converging lines of inquiry are supposed to represent the manner in which, over the course of time, inquiry makes incremental improvements in the proportions ... Right, so my thought is that maybe the circles should represent the measurement of total falsity in the collection of all believed propositions, which would cause it to get smaller rather than larger, until it disappears at the end of inquiry. 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 Tue, Mar 28, 2017 at 11:15 AM, Jeffrey Brian Downard <[email protected]<mailto:[email protected]>> wrote: Jon S, List, Thanks for your questions about the sketch of a diagram I've offered as part of an interpretation of Peirce's remarks about conceiving of the starting and ending points of inquiry in terms of a conception of the absolute drawn from projective geometry. Here are some initial responses to the first four questions you've asked. I will need to think a bit more about the 5th question before responding in greater detail. Having said that, let me offer these initial responses to your thought provoking questions. 1. With respect to the sketch of a diagram, I refer to the starting and ending points of inquiry, but then represent them as hyperbolic curves. As in projective geometry, the points on the horizon form lines. In this diagram, the lines are hyperbolas, and they are meant to represent in iconic form what Peirce says about a hyperbolic philosophy in the passage quoted. 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? Inquiry starts with surprising phenomena that are a source of doubt. As such, the points on the far left where the lines originate are meant to pick out the sources of those doubts, It is likely that they will need to be represented in a way that better captures the vagueness that is part and parcel of such doubts (as a kind of grey area on the line, and not a definite point). 2. Is there a connection between these curves and points with the concepts of continuity and discontinuity, respectively, within Peirce's synechism? Yes, in a quite a keep way. The absolute is, within projective geometry, a very special part of the space, especially when it is represented by a hyperbolic curve. In a parabolic system (e.g., Euclidean geometry) parallel lines never meet. In a hyperbolic system, they do meet and in a real place within the space. In a way, the collection of meeting points at the infinitely distant horizon that form the hyperbolic curves are a kind of origin from which the continuity of the larger space gets its ultimate shape. That is, every possible point in the space is characterized in its relation to every other point by the way they and their relations ultimately relate to the infinitely distant horizon--and the rays extending from one horizon to the other makes this something that we can observe in the diagram. 3. Does semeiosis fit into the picture somehow--in particular, the progression of immediate, dynamic, and final interpretants? Yes, looking back in the past, we can see that subsequent sheets of assertion would contain the expression of observations that have caused us surprise, and then the expression of our doubt, and then the formulation of question, hypotheses, deductions from hypotheses, tests, inductive conclusions drawn on the basis of data gathered as part of the tests--and so on through the cycle of inquiry. All of these would be expressed as books on each sheet of assertion, where the various pages in the gamma book represent what is found in the past sheets of assertion and what we expect to find in the future. 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? Over time, as our understanding expands, there are more positive assertions that have, up to that point, met the test of experience. As such, we have observed more, and there is more that we can explain. In this respect, I am drawing on Emerson's essay "Circles" to explain some points Peirce is making about the growth of our understanding. I suspect that Peirce is drawing on this essay quite self consciously, largely because Peirce is making the same sort of points about Kant's discussion of the ever-expanding horizon of our experience that Emerson is making. Part of that ever expanding horizon is the growth of our beliefs and theories--but it also includes the growth of our ability to feel, to observe, to infer and to guide ourselves. In effect, our understanding of the aims and principles of reasonable inquiry grows as our beliefs and theories grow. 5. Let me offer some initial remarks about your last question. Note that I am using multiple circles (titled a bit) to represent past, present and future stages of our understanding. As such, we might image one stage containing a statement of some surprising phenomena, and then subsequent circles containing questions, hypotheses, consequences that are drawn from the hypotheses, tests, and the results of tests. The inductive inferences that we draw as part of conducting the tests and evaluating the data connect our assertions through so many observations--both actual and future possible. As such, the converging lines of inquiry are supposed to represent the manner in which, over the course of time, inquiry makes incremental improvements in the proportions that are represent in our general explanations based on the observations we've made thus far the inductive inferences one can permissible draw on the basis of such data. Hope that helps, 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 .
