Not it is not. It is finitism, not strict finitism. Actually you need sting actual infinities to make sense of strict finitism. Finitism need only potential infinite to be define, but strict finitism needs actual infinities at the metalevel. To define what is a machine, or what is “finite", you need potential infinite. Strict finitisme makes sense … thanks to big infinities at the meta-level. Absolute strict finitism cannot be Turing universal. > > As Manuel Bremer's paper above shows, a strictly-finite arithmetic is > (likely) inconsistent, It is not valid. RA can be strictly finitist, but again, at the semantical level this is made possible by the existence of a non standard natural number which are bigger than all standard numbers. > which is OK, since "inconsistent mathematics can have a branch which is > applied mathematics”. Inconsistency treatment I useful for natural language, and human psychology, but in most applied math, we need consistent theories. In metaphysics, paraconsitency is a red herring. It hides the problems instead of solving them. But now, self-reference makes inconsistency consistent, and G/G* has a small quasi-para-consistent part, useful indeed for the embedded machine (in sheaves of arithmetical computations). Bruno > > https://plato.stanford.edu/entries/mathematics-inconsistent/ > > - pt > > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to everything-list+unsubscr...@googlegroups.com > <mailto:everything-list+unsubscr...@googlegroups.com>. > To post to this group, send email to firstname.lastname@example.org > <mailto:email@example.com>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > For more options, visit https://groups.google.com/d/optout > <https://groups.google.com/d/optout>. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to firstname.lastname@example.org. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.