The excerpts are
from After Finitude of Quentin Meillassoux (page numbers are from the
ebook version.). Disclaimer: Fair use – In the purpose of critique
/Answering a question: text analysis
(Not very clean formatting. Pardon me)
This absolute lies at the
furthest remove from the absolutization we sought: the one that
would allow mathematical science to describe the in-itself. We
claimed that our absolutization of mathematics would conform to
the Cartesian model and would proceed by identifying a primary
absolute (the analogue of God), from which we would derive a
secondary absolute, which is to say, a mathematical absolute (the
analogue of extended substance).
(p 105)
Note: Absoulutization of mathematics (derivation of a
secondary mathematical absolute) is a requirement to establish a
Cartesian in-itself. No problem, he does not say he did it.
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We are not
claiming that the non-totalizing axiomatic is the
only possible
(i.e. thinkable) one. Consequently, we are not
claiming that the
possible is always untotalizable, even if this is
the case in the
standard axiomatic of sets. For we cannot deny a
priori the
possibility that it could also be thinkable that the
thinkable
constitutes a totality. The fact that the untotalizable is
thinkable within a
given axiomatic does not prevent anyone from
choosing another
axiomatic, in which the frequentialist
implication would
still be valid. There is always more than one
axiomatic, and
despite its eminence, that of standard set-theory is
only one among many.
Thus, we cannot rule out a priori the
possibility of
selecting an axiomatic in which the realm of possible
worlds would
constitute an ultimate and determinate numerical
totality. But
this at least must be accorded to us: we have at our
disposal one
axiomatic capable of providing us with the resources
for thinking that
the possible is untotalizable.
However, the mere
fact that we are able to assume the truth of this axiomatic
enables
us to disqualify the necessitarian inference, and with it
every
reason for continuing to believe in the existence of the necessity of
physical laws - a necessity that is mysteriously superimposed onto
the fact of the stability of these same laws.
(169)
Note:
Meillassoux does not necessitate the possible (or the
physical/possible world) to be untotalizable. Ok. He knows that
there are alternative axioms. In the case of physical world nobody
has ruled out any of those axioms (untotalizable or other). Hence
world may be untotalizable.
To prove stability of the world in this way, there are two steps.
Step 1. Prove that the physical world (possible worlds) is
non-totalizable, in the means of deriving it from the thesis of
factiality/contingency.
Step 2: Prove the stability of the world starting from
non-totalizable.
Step 1 is yet to
be done. Ok. Nobody has
disproved it even. OK. (It
is to be proved or disproved.) Step 1 is a conjecture.
Questions:
1. What is it
about step 2, is it completed? (Is it completed when the step 1 is
done?)
2. Is step 1 is
required to get the
conclusion of step 2?
(Should one proves
step 1 first to prove possibility of stability?)
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What the set-theoretical axiomatic demonstrates is at the very
least a fundamental uncertainty regarding the totalizability
of the
possible.1 But this uncertainty alone enables us to
carry out a
decisive critique of the necessitarian inference by destroying one
of the latter's fundamental postulates2: we can
only3 move
immediately3 from the stability of laws
to their necessity so long as
we do not question3 the notion that the
possible is a priori
totalizable3. But since this totalization is
at best only operative
within certain axiomatics, rather than in all of them, we can
no
longer continue to claim that the frequentialist implication is
absolutely valid. We have no way of knowing whether the
possible can be totalized in the same way as the faces of a set of
dice can be totalized.
(170)
Note:
This
is a part of Step 2.
1.
Non-totalizability is a valid
conjecture. OK.
2.
Assuming Step 1 we can complete Step 2. (N.B. enables
us, destroying)
3.
Answer to Question 2.
Step 1 is required: If this
world is totalizable we can
immediately conclude that the stability of laws guaranties the
necessity of laws. Therefore we must question
totalizability of the world. Best case we should this world or all
possible physical worlds are non-totalizable. It is required
to complete the proof. At
least we should
grasp about the validity of
the conjecture. Hence, non-totalizability which is a
requirement to grasp our experience of stable history in a
factual/contingent world and which is also mathematical is an elegant
and necessary secondary absolute to complete this project. But the
derivation is yet to be done.
My opinion: This
not OK. This is the part I disagree. One
cannot move immediately from the stability
to necessity even if the events are totalizable. Ensemble
probabilities and ergodicity does not constitute a necessary
relation. Zero probability does not mean impossibility and
probability of one does not mean necessity. Other probabilities does
not mean any requirement of actualization.
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But
how is Kant able to determine the actual frequency of the
modification of laws,
assuming
the latter to be contingent? How does he know that this
frequency
would be so extraordinarily significant as to destroy the
very
possibility of science, and even of consciousness? By what
right
does he rule out a priori the possibility that contingent laws
might
only very rarely change - so rarely indeed that no one
would
ever have had the opportunity to witness such a
modification?
It can only be by the right
which he derives from
applying
the calculus of probability to our world as a whole,
rather
than to any phenomenon given within the world,
and
hence
from an a priori totalization of the possible,
which we
know,
since Cantor, can no longer lay claim to any logical or
mathematical
necessity - which is to say, to any sort of a priori
necessity
(172)
Note:
Not OK. A priori
totalization is not needed for probability and there is no impact on
actualization argument from the constraints of assigning numbers to
events. Concept of probability is one thing, assigning numbers to
probability is another.
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We
then noticed that at the root of this
presupposition
lay an instance of probabilistic reasoning applied
to the laws of
nature themselves; a piece of reasoning which there
was no reason to
accept once its condition - the claim that
conceivable
possibilities constitute a totality
- was revealed to be
no
more than a hypothesis, as opposed to an indubitable truth.
In
doing so, although we have not positively demonstrated
that
the possible is untotalizable, we have identified an alternative
between
two options - viz., the possible either does or does not
constitute
a totality -with regard to which we have every reason to
opt
for the second - every reason, since it is precisely the second
option
that allows us to follow what reason indicates - viz., that
there
is no necessity to physical laws - without wasting further
energy
trying to resolve the enigmas inherent in the first option.
(173)
Note :
Not Ok. Previously explained.
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But
what is most fundamental in all this
- and this was
already
one of the guiding intuitions of Being and Event - is
the
idea
that the most powerful conception of the incalculable and
unpredictable
event is provided by
a thinking that continues to be
mathematical
- rather than one
which is artistic,
poetic, or
religious.
It is by way of mathematics that we will finally
succeed
in thinking that
which, through its power and beauty, vanquishes
quantities and
sounds the end of play.
(175)
Note:
Not Ok. This answers Question 2. Here Meillassoux says it is
required to complete step 1 to get the conclusion of stability. One
has to go through mathematics to grasp it, not any other way.
Meillassoux has not completed the Step 1 but that step is required.
According to him his incomplete proof recruits mathematics rather
than any other thought to establish stability. Remaining task is to
derive it.
I disagree. This second step is flawed. There is no guarantee that
first step is required.
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Most importantly:
However,
we must return to our proposed resolution of
Hume's
problem, for the former cannot wholly satisfy us. As
we
saw,
this resolution is fundamentally non-Kantian insofar as it
aims
to establish the conceiv-ability of the actual contingency of
the
laws of nature. Yet it
would not be quite right to assert that
our
resolution itself is unequivocally speculative, just because it is
anti-transcendental
in intent. For although the thesis we advanced
was
ontological, and did indeed assert something about the in-
itself
rather than phenomena in maintaining the detotalization of
the
possible, nevertheless, it was only advanced as an ontological
hypothesis.
We have not established whether this non-totalization
actually obtains,
we have merely supposed it, and drawn the
consequences of
the fact that such a supposition is possible.4 In
other
words, although our
proposed resolution of Hume's
problem
gives us grounds for not immediately giving up on the
idea
of factial speculation,
it has not itself been engendered as a
truth by means of
speculative reasoning.5
For a
properly factial
resolution of Hume's problem would require that
we derive the
non-totalization of the possible from the principle of
factiality itself.
In order to
elaborate such a solution, we would have to derive the
non-whole as a
figure of factiality6,
just as we sketched the
derivation
of consistency and of the 'there is'. This
would entail
absolutizing
the transfinite6
in the same way in which we
absolutized
consistency - which is
to say that we would have to
think the former
as an explicit condition of contingent-being7,
rather than
merely construing it as a mathematically formulated
hypothesis7
that can be
advantageously supported by the
speculative.
But it is clear that such resolution of the problem
would
require that we be in a position to do for mathematical
necessity
what we tried to do for logical necessity. We
would have
to
be able to rediscover an in-itself that is Cartesian,
and no
longer
just Kantian - in other words, we would
have to be able to
legitimate
the absolute bearing of the mathematical
- rather than
merely
logical - restitution of a reality that is construed as
independent
of the existence of thought. It would be a question
of establishing
that the possibilities of which chaos - which is the
only in-itself -
is actually capable cannot be measured by any
number, whether
finite or infinite, and that
it is precisely this
super-immensity of the chaotic virtual that
allows the impeccable
stability of the visible world.
(178-179)
Note:
4. He is saying step 2 is completed.
5. He is saying step 1 is yet to be done.
6. He is saying step 1 is required to conclude that a factual
universe can be stable.
7.
He says it required to prove that transfinite is not just another
mathematical axiom but the only mathematical axiom applicable to the
physical world. Therefore some sort of mathematics absolutely govern
the world.
My opinion: I
disagree. Non-totalizability
or any other axiom does not prevent ergodicity and simply we can
reject applicability of ergodicity (which is mathematical). Simply we
can move further saying there is no absolute mathematics. Step 2 is
easily resolved. There is no requirement for
step 1.
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But
it is clear that such a derivation would not only have to be
far
more complex, but also more adventurous than that of
consistency,
since it would have to demonstrate how a specific
mathematical
theorem, and not just a general rule of the logos, is
one of the
absolute conditions of contingency8.
Accordingly, it
might
seem wiser
to confine9
ourselves to our
hypothetical
resolution9
of Hume's problem, since the latter seems sufficient to
vanquish the
objection from physical stability10,
which provided
the
only 'rational' motive
for not simply abandoning
every variant
of
the principle of reason.
However, there is another problem that
rules
out such caution, and it is precisely the problem of
ancestrality.
For as we saw, the resolution of the latter demanded
an
unequivocal demonstration of the absoluteness of mathematical
discourse.
We begin to see then, albeit dimly, that there
now seem to be two problems tied to the issue of the absolute scope
of
mathematics
- the problem of the arche-fossil and the problem
of
Hume.
It remains for us to connect them in such a way as to
provide a precise
formulation of the task for non-metaphysical
speculation.
(179)
Note:
8. Step 1 is yet to prove and it is required.
9. Wow! Now he is saying it is wise to say this is THE PROOF
although it is not completed. Why?
10. Meillassoux: “Why? I proved the second step, right! When stage
1 is done the game is over. Right!”
දැන් මාක්ස්ට අනුව සියලු ශ්රම-අධික හා ප්රාග්ධන-අධික කර්මාන්ත සඳහා ලාභ රේට්ටු සමාන වන ලෙස පරිණාමනයක් සිදු වේ. 
