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On 4/9/2018 7:10 AM, Bruno Marchal wrote:

On 8 Apr 2018, at 19:42, agrayson2...@gmail.com<mailto:agrayson2...@gmail.com> wrote:http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHAL.pdf<http://iridia.ulb.ac.be/%7Emarchal/publications/SANE2004MARCHAL.pdf>On 3,) Arithmetic Realism (AR), why is the statement "1+1=2",equivalent to the Goldbach conjecture, or the inexistence of abigger 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", justmean the symbols on the left should be taken to mean the symbol onthe right? TIA, AGI did not claim that those statement are equivalent, I state only thatthey are true of false independently of me.Then when and if proved they will be automatically equivalent in theweak sense of classical mathematical logic, where all (known) truthare equivalent.The arithmetical realism is just the idea that a (closed) propositionis either false or truth in the standard model (N, 0, +, *).

`But that depends on what "true" means. Whether it refers to fact, a`

`theorem, or a convention of language.`

We can limit realism to the sigma_1 sentences, which can be shownequivalent with the statements saying that a digital machine stops ordoes not stops in arithmetic.99,9 % of the mathematicians are mathematical realist, which meansthat they believe that the excluded middle principle is valid in verylarge part of math, like set theory, analysis, etc.

`But valid =/= true. It means it prevserves a presumption of true in the`

`premises...but not that it is the only possible inference rule that does so.`

Arithmetical realism is doubted only by ultra-finitist, who believethat there is no infinities at all, not even at the meta-level.

`No. It is doubted by many mathematicians. My mathematician friend Norm`

`Levitt used to say, "Mathematicians are Platonists Monday thru Friday`

`and Nominalists on the weekends."`

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