**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?)**

**------------------------------------------------------------------------------------------------------------------------**

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 postulates^{2}: we can
**only**^{3}** **move

i**mmediately**^{3} *from the stability of laws
to their necessity* so long **as**

**we do not question**^{3} the notion that the
possible is **a** **priori**

**totalizable**^{3}. 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.

------------------------------------------------------------------------------------------------------------------

**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 factiality ^{6}**,

__just as we sketched the__

__derivation
of consistency and of the 'there is'. __This
would entail

*absolutizing
the transfinite*^{6}
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-being ^{7}**,

*rather than*

**merely construing it as a mathematically formulated**

**hypothesis ^{7}**

*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 contingency ^{8}**.
Accordingly, it

might
*seem *__wiser
to confine__^{9}*
*ourselves to our
**hypothetical**

**resolution ^{9}**
of Hume's problem,

__since the latter seems sufficient to__** vanquish the
objection from physical stability^{10}**,
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!”