The title is bizarre because it is really "finitude" which makes such  
sort of construction coherent and non ad hoc, through the constructive  
Some people could object, also, that in the transfinite, there are  
model where the "totality of thinkable" is thinkable.
But in general, with the most shared conception of set, usually the  
totality escapes comprehension and even naming. Cf my usual critics of  
Tegmark: the whole of mathematics cannot be a mathematical object, or  
even: the whole physical reality cannot be physical, etc. Set theories  
with "universal object" can temperate such critics, but the comp  
hypothesis temperate it naturally: "computerland" is the only "whole"  
which represents itself without ad hoc axiomatics. I hope this will be  
clearer when the universal machine (and dovetailler) will be explained  
in the "seventh" thread.


On 20 Sep 2009, at 21:28, wrote:

> Possibly of interest.  I haven't read it, but it sounds intriguingly
> Brunoesque.  Perhaps Bruno could comment.
> After Finitude: An Essay on the Necessity of Contingency,
> Quentin Meillassoux
> Particularly:
> By claiming that physical laws are contingent, Meillassoux proposes in
> chapter 4 a speculative solution to Hume's problem of primary and
> secondary qualities. The author's treatment of what at first could
> have passed for an innocuous metaphysical non-problem is implemented
> in order to transform our outlook on unreason. A truly speculative
> solution to Hume's problem must conceive a world devoid of any
> physical necessity that, nevertheless, would still be compatible with
> the stability of its physical laws. Here contingency is the key
> concept that, insofar as it is extracted from Humean-Kantian
> necessitarianism and thus distinguished from chance, enables
> Meillassoux to explain how and why Cantor's transfinite number could
> constitute a condition for the stability of chaos. Here we find the
> transition from the primary absolute to the secondary or
> mathematically inflected absolute. The demonstration thus consists in
> implementing the ontological implications of the Zermelo-Cantorian
> axiomatic as stipulated by Alain Badiou in his Being and Event. This
> axiomatic enables Meillassoux to show that for those forms of aleatory
> reasoning to which Hume and Kant were subservient, what is a priori
> possible can only be conceived as a numerical totality, as a Whole.
> However, this totalization can no longer be guaranteed a priori, since
> Cantor's axiomatic rules out the possibility of maintaining that the
> conceivable can necessarily be totalized. Thus Cantor provides the
> tool for a mathematical way of distinguishing contingency from chance,
> and this tool is none other than the transfinite, which Meillassoux
> translates into an elegant and economical statement: "the
> (qualifiable) totality of the thinkable is unthinkable." (104) This
> means that in the absence of any certainty regarding the totalization
> of the possible, we should limit the scope of aleatory reasoning to
> objects of experience, rather than extending it to the very laws that
> rule our universe (as Kant illegitimately did in the Critique of Pure
> Reason), as if we knew that the these laws necessarily belong to some
> greater Whole.
> >

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