tag:blogger.com,1999:blog-4987609114415205593.post2521574527211178971..comments2024-03-28T13:40:26.497+00:00Comments on M-Phi: Reductio arguments from a dialogical perspective: final considerationsJeffrey Ketlandhttp://www.blogger.com/profile/01753975411670884721noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-4987609114415205593.post-35418718783572871002023-08-13T16:49:16.249+01:002023-08-13T16:49:16.249+01:00Greatt blogGreatt blogLiam Noblehttps://liamnoble68.blogspot.com/noreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-56168852350506688942015-08-11T23:01:02.888+01:002015-08-11T23:01:02.888+01:00it's clear to me now that (insofar as geometry...it's clear to me now that (insofar as geometry is concerned) I never successfully enter into that hypothetical realm which may or may not be absurd, remaining in the same world I had attempted to leave after every attempt. I have to disagree with the phenomenological account you offered, insofar as it seemed to suggest we had been invited into an impossible realm and asked to destroy it from within, even according to its own rules, as Maria intuits. But indeed, the thing presents itself to me as if I had been barred access, or more accurately, rerouted back to the place I began. If every time I attempted to draw a line at right angles to the extremity of the diameter of a circle, my purpose was either deflected and it was not the thing I desired to draw, or I succeeded and the tangent was outside the circle, why should I not feel justified that tangents may only exist outside the shape they are tangent to? Moreover, I had not once come into contact with that realm where the tangent falls inside the circle, my will to do so being deflected each time.<br /><br />And while its obvious that my powerlessness to bring about a state of affairs does not, ipso facto, declare that state of affairs as impossible, (not being able to actualize some potential), the above seems different: to bring about a state of affairs where something becomes possible, that wasn't possible before. (to actualize a potential which previously had no such potency). The latter is pretty rock-solid definition of what's impossible. The particular details of what happens when I fail may be enough to distinguish between my lack of capacity, and the object's lack of receptivity. There may or may not be relevant differences between conceiving the impossible, and attempting to do the impossible. <br /><br />For similar reasons I've at times felt that Lobachevskian geometry should, strictly speaking, be considered false, unless demonstrated on a saddle-shaped surface, because in every case past the first few theorems, I was asked to demonstrate an impossibility (like parallel lines that met and weren't in perspective), I actually ended up demonstrating its absurdities up on the blackboard, and then was congratulated on proving the thing that was to be demonstrated. I've read somewhere that Kant was the last person who seriously adhered to the idea that diagrams had specific epistemological content that the same proof in mere logic didn't.<br /><br /><br />P.S.<br />It seems that you're considering the dual-agent aspect of the dialogical perspective literally, perhaps because of your interest in the pedagogy of reductios. But my suspicion is that the adversarial component does not necessarily lead to two agents. Goethe and, I think, Galileo are on record as seeing Natural Philosophy/science (and its mathematization) as an interrogation of Nature, putting her under duress to reveal her secrets. I think Darwin or some early geneticist is on record as well regarding the difficulty of breeding some animals in captivity as Nature's way of resisting such interrogations into her methods. It may be all anthropomorphized hogwash, but I do think it agrees with much of what a phenomenological approach to intellectual discovery would offer.<br />Kevin Ringeisennoreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-56982940326442710832015-08-11T23:00:01.957+01:002015-08-11T23:00:01.957+01:00Sorry for the length, this is continued in another...Sorry for the length, this is continued in another comment but reductios have always interested me.<br /><br />Regarding the difficulty of representing the impossible:<br /><br />I've always thought that that difficulty was one of the great virtues of (geometrical) reductios. In studying Euclid and Appolonius, it struck me that unlike regular propositions, some reductios didn't seem to be able to be reduced to the definitions/common notions/postulates.<br /><br />For example, Euclid's Elements Book III, Proposition 16: The line drawn at right angles to the extremity of the diameter of a circle will fall outside said circle. If not, let it fall within while remaining at right angles to the extremity of the diameter. An absurd situation arises no matter how you draw the line, resulting in a triangle greater than two right angles (!) and therefore, not inside; and not on the circumference either which results in a lesser triangle (putatively) larger than the larger triangle which contains the lesser. Therefore the tangent falls outside the circle.<br /><br />This example demonstrates the culprit issue you discussed: had our beliefs regarding parallel lines been different, this wouldn't have been absurd at all (leading us to Lobachevskian geometry). Appolonius in his Conics, Book 1, Proposition 17 demonstrates the same: that the tangent must fall outside the parabola.There the parallel postulate's implications are far less discernible.<br /><br />But in either case, the impossibility of doing the thing asked: of passing a tangent inside the shape, always felt like good evidence for doing that "leap of faith." Every attempt to represent the impossible always resulted in failure, and it could always be shown that all possible types of situation were covered. Hand someone a cone, and a stick (better if its telescopic), and it becomes very easy to corroborate that a line with both extremities within the cone, if extended must at some point pass beyond at least one boundary of any conic section (reductio, Conics, I.18). Very quickly, they'll determine the exercise can't be completed, and I don't think they'd share the same worry about not knowing what they don't know. In as little as a few seconds they will have exhaustively tried the issue and believe it exhaustively tried. <br /><br />This of course raises an important question regarding geometry's independence from experience, but classical, geometrical reductios always felt like they were utilizing space in a different way than your typical proposition, using the impossibility of doing the task as a way of demonstrating the impossibility of anything that might come out of it: "It's impossible! Go ahead and try it! Therefore, etc. QED." The very paper seemed to resist in a reductio, refusing to allow you to draw the thing you wanted to.<br /><br />Kevin Ringeisennoreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-25260597689874905422015-08-11T11:47:26.219+01:002015-08-11T11:47:26.219+01:00I think reductios can also be used in dialogical s...I think reductios can also be used in dialogical situations of one person arguing against the other, as long as the assumptions I outlined are in place (e.g. that the enumeration of cases is exhaustive). As for your suggestion of a proof applying across the population of logicians, check out Malink's paper in Phronesis this year, which makes a very similar point wrt the differences between the Topics and the Prior Analytics.Catarinahttps://www.blogger.com/profile/03277956118114314573noreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-61368938350123221282015-07-22T22:10:50.493+01:002015-07-22T22:10:50.493+01:00One question is: What is the benefit of the reduct...One question is: What is the benefit of the reductio argument over their genealogical ancestors?<br /><br />I take it that dialectical refutation is generally an argument between two people. Even if the argument is meant to be general, it is still only employed against an actual opponent.<br /><br />By formalizing such arguments using logic, we are able to argue more generally. In terms of the dialogical approach, we are arguing against the Prover or Skeptic, a proxy for a (n idealized) real person. This gives much more power to the argument, since it now applies generally across the population of logicians.<br /><br />But this benefit comes with logical formalization, and is not specific to the reductio. I have to think that there is some other special reason for the reductio's widespread use and characteristics.<br /><br />Here is one suggestion:<br /><br />Since we are arguing against an idealized opponent in the dialogical approach, we have to assume that all the steps in their argument are unassailable. Hence the only thing that could have poisoned their reasoning is the assumption for the reductio, and this is why we are able to reject that one premise. noahnoreply@blogger.com