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: everything-list@googlegroups.com
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)
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