Peircers, We can describe how science works. We cannot prove that it works.
Regards, Jon http://inquiryintoinquiry.com > On Dec 12, 2015, at 2:49 AM, John Collier <colli...@ukzn.ac.za> wrote: > > Clark, List, > > Just a couple of points to take up something that Clark says within the more > general context of logic and formal mathematics, and, in this case, its > relation to physics, but still very Peircean I think. See below. > > John Collier > Professor Emeritus, UKZN > http://web.ncf.ca/collier > > From: Clark Goble [mailto:cl...@lextek.com] > Sent: Friday, 11 December 2015 19:41 > To: Peirce-L > Subject: Re: [PEIRCE-L] in case you were wondering > > I tend to see “in the long run” as more a regulatory concept rather than > something actual. For a long time I did worry about how the “in the long run” > worked and raised concerns similar to yours. The question of whether it > really functions the way Peirce needs it to function if it’s not potentially > actual in some sense is still a big issue I think gets neglected too much. So > don’t think I’m brushing that aside. I do share some of your concerns there. > I’ve just come to think that for Peirce the fundamental issue is the meaning > of truth which then brings in the issues I raised as regulatory concepts. > > [JDC] Agreed. There are a number of counter-examples to convergence that are > worrisome, such as counter-induction, sets that show arbitrarily long > patterns for finite stages that aren’t reflected in the overall statistics of > the whole set, and so on. > > All that said, I’m not sure infinity works quite the way you suggest simply > because Peirce is not dealing with a normal potentially countable infinity. > That is his continuity ends up dealing with higher order infinities - even if > he does differ from the typical cardinal/ordinal sets we deal with in > mathematics. Now I’ll confess it’s been more than 10 years since I last > studied Peirce on these particular issues or where he differs from Cantor and > company. So my memories are a tad fuzzy. Forgive me for errors. I think > however that if there’s a potential countable infinity of the sort > <image001.png> that Peirce’s in the long run in his semiotics allows this to > be dealt with by semiotics running in higher orders like or so on. I’m > curious as to what others thing here. > > My logic professor, George Boolos, dreamed up a being he called Zeus > (so-called as to not pre-empt contemporary religious concerns) that got > better at processes if it repeats them. The idea is that in calculating an > infinite series, Zeus could do each step twice as fast as the previous one, > and be able to complete a series in finite time. Obviously, neither we nor > any other finite system could be a Zeus demon, but it does give a way to > interpret infinite convergence. I see this as a case of going from > <image001.png> to . The relevant set becomes the cross-product. I came up > with a somewhat similar demon I called the Hermes demon, which can make every > increasingly accurate measurements in the same way. It can achieve accuracy > in measurement. Combine the two, and you have a Laplacean demon, making some > sense of an otherwise somewhat mysterious idea. We could carry this to higher > levels by calculating over all functions possible on an sized set, and so > on, if necessary. Is this outside of the range of semiotics because it uses > infinite methods and assumes creatures that could not exist (Peircean sense)? > I think not, since it is an extension of ideas in the finite realm to the > continuous in a fairly straight-forward way that is already pretty well > understood. > > The second issue is whether we really need this. The concern ends up being > more or less a common critique of convergence theories. That is you might > test out to Tx but that the pattern completely shifts at Tx+1. I think > Peirce’s conception works simply because in the long run is regulative as I > mentioned but also because what is doing the testing is an infinite community > rather than a finite one. That is the way Peirce attempts to get out of this > is via his Hegelian/neoPlatonic like conception of the universe as an > argument working itself out. So when we talk about truth it’s this universe > that counts. That is we can maintain Peirce’s notion without having to deal > with a practical knowing community. > > I think we need it. Testing the infinite community of functions seems to me > to require at least two levels past <image001.png>, with the set of possible > functions, as I mentioned above. The order, in this case, becomes > irrelevant, because all orderings are included if the demon is carefully > rendered. As someone who doesn’t find the Hegelian/neo-Platonic outlook very > perspicuous (though for a time I thought it solved all outstanding > metaphysical problems). In any case, from my current perspective to > understand even the problem requires going to higher order infinities, let > alone to understand how we might deal with actual cases. I am pretty sure > that the Axiom of Choice, or one of many equivalent forms (well-ordering, > basically) is required for bringing the abstract Laplacean demon I outlined > down to earth. It doesn’t help a lot to know there are suitable functions to > describe any pattern if one can’t find them. > > For any finite community then (i.e. any practical community we worry about) > we’re always fallible from Peirce’s conception. What I sense you wanting > isn’t a point of relative stability in our beliefs through continued inquiry. > Rather I think you’re looking for something more akin to what Putnam takes up > against Peirce. A kind of warranted assertability ala Dewey’s change from > Peirce. If we’re looking for that sort of strong warrant then I’d probably > agree we may not get it. I’m not sure we need that but I can completely > understand why many might find Peirce ultimately unsatisfactory relative to > these finite groups. He can offer inquiry but not certainty. (I’m not sure in > practice Dewey/Putnam can do better mind you) > > I think it is obvious that we cannot meet Putnam’s requirement. It is also > not necessary unless we assume some version of verificationism, however > weak. Fallibilism undermines verificationism as a determiner of meaning. The > result of Putnam’s (very weak – “meaning is something that we determine if > anything does”) verificationism is the Quine-Duhem Thesis (see chapter 1 of > my PhD thesis). I really should write this up. > > Best, > John
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