> On 18 Dec 2018, at 01:14, Bruce Kellett <[email protected]> wrote: > > On Tue, Dec 18, 2018 at 6:15 AM Bruno Marchal <[email protected] > <mailto:[email protected]>> wrote: > On 17 Dec 2018, at 08:50, Bruce Kellett <[email protected] > <mailto:[email protected]>> wrote: >> >> What I am curious to know is how how many of these statements you agree with: >> >> "2+2 = 4" was true: >> 1. Before I was born >> 2. Before humans formalized axioms and found a proof of it >> 3. Before there were humans >> 4. Before there was any conscious life in this universe >> 5. As soon as there were 4 physical things to count >> 6. Before the big bang / before there were 4 physical things >> >> "2+2=4" is a tautology, true because of the meanings of the terms involved. >> So its truth is not independent of the formulation of the question and the >> definition of the terms involved. > > What about ExEyEz (x^3 + y^3 +z^3 = 33) ? > > What about it? Not all syntactically correct formulae are either true or > false; some are undecidable.
A is undecidable means ~[]A & ~[]~A. It does not mean ~A & ~~A. That A (= ExEyEx(x^3 + y^3 + z^3)) is either true or false is a direct consequence of the excluded middle. Either such numbers exists or they don’t. If it is undecidable in PA, it means that PA cannot decide it, but it does not mean that ZF or ZF+kappa could not decide it. And even if they couldn’t, it is still does not mean that A is not true, or false, which it is, certainly. > Unless and until you find some x,y,z that satisfy this relationship, the > statement is neither true nor false. In intuitionist logic. I have made clear that I use classical logic (indeed, in mathematical theology, we can expect many statement to be undecidable by the finite creatures/theories). Same already in theoretical computer science. The notion of totality is non constructive, “halting” is non constructive, in fact all attribute of programs can be shown to be necessarily non constructive. I recursion theory, constructive is equivalent to limiting research in the security zone of some RE subset of TOT. Machines have no right to search for a number which might not exist. > Unperformed experiments have no results! Even in physics, this is doubtful and indeed contradict Einstein’s physical realism. No problem, as we know it has to be tampered with the Mechanist assumption. Bruno > > Bruce > > -- > 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.
