Hi Rex, Thank you for bringing this paper to our attention. I would like to point out two problems that I see in Meillassoux’ argument.
So to minimize arguing against a straw man I will quote specific passages from the paper. “ if laws were contingent, they would change so frequently, so fre- netically, that we would never be able to grasp anything whatsoever, because none of the conditions for the stable representation of objects would ever obtain. In short, if causal connection were contingent, we would know it so well that we would no longer know anything. As can be seen, this argument can only pass from the notion of contingency to the notion of frequency given the presupposition that it is extraordinarily improbable that the laws should remain constant rather than being modified in every conceivable way at every moment.” Here we have what appears to be a well reasoned argument until we inquire as to the definition of the term “to know” that is used. If an entity exists in a universe subject to frequent and contingent change what is to allow the mind of that entity the ability to have the ability to know anything at all? The entity and its brain/mind would be subject to the very same capricious randomness that the rest of that universe undergoes and thus the notion of knowing becomes null and void. “...thinkable worlds, which could only reinforce the conviction that the constancy of just one of them is extraor- dinarily improbable. But it is precisely on this point that the unacceptable postulate of our `probabilist sophism' hinges, for I ask then: of which infinity are we speaking here? We know, since Cantor, that infinities are multiple, that is to say, are of different cardinalities - more or less `large', like the discrete and continuous infinities - and above all that these infinities constitute a multiplicity it is impossible to foreclose, since a set of all sets cannot be supposed without contradiction. The Cantorian revolution consists in having demonstrated that infinities can be differentiated, that is, that one can think the equality or inequality of two infinities: two infinite sets are equal when there exists between them a biunivocal correspondence, that is, a bijective function which makes each element of the first correspond with one, and only one, of the other. They are unequal if such a correspondence does not exist. Further still, it is possible to demonstrate that, whatever infinity is considered, an infinity of superior cardinality (a `larger' infinity) necessarily exists. One need only construct (something that is always possible) the set of the parts of this infinity. From this perspective, it becomes impossible to think a last infinity that no other could exceed. But in that case, since there is no reason, whether empirical or theoretical, to choose one infinity rather than another, and since we can no longer rely on reason to constitute an absolute totality of all possible cases, and since we cannot give any particular reason upon which to ground the existence of such a universe of cases, we cannot legitimately construct any set within which the foregoing probabilistic reasoning could make sense. This then means that it is indeed incorrect to infer from the contingency of laws the necessary frequency of their changing. So it is not absurd to suppose that the current constants might remain the same whilst being devoid of necessity, since the notion of possible change - and even chaotic change, change devoid of all reason - can be separated from that of frequent change: laws which are contingent, but stable beyond all probability, thereby become conceivable.” The bold and italics are my highlighting of a statement within this passage. end quote Does Meillassoux not understand anything about calculus, analysis, computational complexity theory or other higher mathematics? These infinities within the Cantorian tower are not just some abstraction that has no relation with other abstract structures. There is a long line of careful reasoning that allow us to understand what Cardinality of infinity a set belongs to and thus this part of Meillassoux’ argument is contradicted by mathematics. Additionally, Meillassoux seems to also gloss over the assumption of well-foundedness in his logic... Failure to understand what infinities are has plagued many and a failure to understand them by some persons is a sad fact in our world. OTOH, to wonder which infinity the set of all possible worlds belongs to is not trivial matter so I can forgive this obvious 1004 error (of using jargon to hide a fallacy), we can point to Max Tegmark’s meandering thoughts on this question if we want to, we need to find a firm foundation upon which we can leverage the notion of “contingent yet stable”laws. Over all I think that Meillassoux is asking the right kinds of questions but I just wish that he would venture away from the Streetlight. I will continue to read and think about this papers ideas. Please also see http://www.cosmosandhistory.org/index.php/journal/article/view/118/272 for more detailed discussion of Meillassoux’ ideas. Onward! Stephen From: Rex Allen Sent: Tuesday, November 02, 2010 8:24 PM To: firstname.lastname@example.org Subject: Probability, Necessity, and Infinity Somewhat related to Stephen's post on Srednicki and Hartle's paper. Quentin Meillassoux, "Potentiality and Virtuality": "We have at our disposal the means to reformulate Hume's problem without abandoning the ontological perspective in favour of the epistemic perspective largely dominant today. Beginning to resolve the problem of induction comes down to delegitimating the probabilistic reasoning at the origin of the refusal of the contingency of laws. More precisely, it is a matter of showing what is fallacious in the inference from the contingency of laws to the frequency (and thus the observability) of their changing. This amounts to refusing the application of probability to the contingency of laws, thereby producing a valuable conceptual distinction between contingency understood in this radical sense and the usual concept of contingency conceived as chance subject to the laws of probability. Given such a distinction, it is no longer legitimate to maintain that the phenomenal stability of laws compels us to suppose their necessity." (pdf attached) -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-l...@googlegroups.com. 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