On Monday, January 28, 2019 at 5:46:12 AM UTC-6, Bruno Marchal wrote:
> On 26 Jan 2019, at 08:36, Philip Thrift <cloud...@gmail.com <javascript:>> 
> 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

Max Tegmark writes that the mathematics of physics in the future needs to 
be "infinity-free".


(Almost like it's a sin to have infinities around.) That sounds like strict 
finitism to me.

As Manuel Bremer's paper above shows, a strictly-finite arithmetic is 
(likely) inconsistent, which is OK, since "inconsistent mathematics can 
have a branch which is applied mathematics".


- pt

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