> On 26 Jan 2019, at 08:36, Philip Thrift <cloudver...@gmail.com> wrote:
> 
> 
> 
> Varieties of finitism
> http://www.mbph.de/Logic/Finitism.pdf
> Manuel Bremer
> http://www.mbph.de
> 
> Annotated bibliography of strict finitism
> http://jeanpaulvanbendegem.be/home/papers/strict-finitism/
> Jean Paul Van Bendegem
> http://jeanpaulvanbendegem.be
> 
> Apparently, strict finitism requires a (likely) paraconsistent modality 
> (implying there may be inconsistencies). If one takes strict finitism 
> seriously (Tegmark would have to be a strict finitist, if he isn't kidding 
> people about what he said) then of course physics (and mathematics, of 
> course) would be radically different.


Computationalism (digital mechanism) is consistent with strict finitisme, but 
rather unsound.

Mechanism is a finitisme, but it keeps the potentially infinite of the 
classical and intuitionist thinkers. 

But with mechanism, we cannot put the induction axioms in the ontology, so we 
cannot prove that there is no biggest natural numbers in the ontology. From 
outside, we know that this is consistent only because we believe in some 
infinite objects, making strict finitisme consistent, but rather arithmetically 
unsound.

Nothing in Tegmark suggests that he would espouse anything like “strict” 
finitisme, but when he moved to computationalism, he might become a finitist.

The best book (beside my work :) ) on the subject of mechanism and finitism is 
the book by Judson Webb, 1980. 

WEBB J. C., 1980, Mechanism, Mentalism and Metamathematics : An essay on 
Finitism, D. Reidel Pub. Company, Dordrecht, Holland.

Bruno

> 
> - pt
> 
> 
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