> On 8 Apr 2018, at 19:42, [email protected] wrote: > > http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHAL.pdf > > On 3,) Arithmetic Realism (AR), why is the statement "1+1=2", equivalent to > the Goldbach conjecture, or the inexistence of a bigger prime, or the > statement that some digital machine will stop? > Please take each item in list separately? Goldbach conjecture? Inexistence? > Why stopping? And why can't the statement "1+1=2", just mean the symbols on > the left should be taken to mean the symbol on the right? TIA, AG
I did not claim that those statement are equivalent, I state only that they are true of false independently of me. Then when and if proved they will be automatically equivalent in the weak sense of classical mathematical logic, where all (known) truth are equivalent. The arithmetical realism is just the idea that a (closed) proposition is either false or truth in the standard model (N, 0, +, *). We can limit realism to the sigma_1 sentences, which can be shown equivalent with the statements saying that a digital machine stops or does not stops in arithmetic. 99,9 % of the mathematicians are mathematical realist, which means that they believe that the excluded middle principle is valid in very large part of math, like set theory, analysis, etc. Arithmetical realism is doubted only by ultra-finitist, who believe that there is no infinities at all, not even at the meta-level. Then “1+1 = 2” does not talk about symbols, so your suggestion does not make much sense. You confuse un number, like s(0) with a sequence of sign. Bruno > > -- > 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 [email protected] > <mailto:[email protected]>. > To post to this group, send email to [email protected] > <mailto:[email protected]>. > 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
