> On 2 Jul 2018, at 04:22, John Clark <[email protected]> wrote: > > On Sun, Jul 1, 2018 at 8:00 AM, Bruno Marchal <[email protected] > <mailto:[email protected]>> wrote: >> >>> If “0 things exist” is true, I don’t see how “0 things exist” can >> exist. >> >> >>If if “0 things exist” is true then “0 things exist” exists, > >That does not follow. If the universe is empty, i.e. u = { }, > > The null set is something, my nothing does not contain a set of any sort. > > >So you agree with Jason that the “nothing theory” is inconsistent? I am > not sure it is inconsistent, but I am sure it is false. > > So you think "nothing" could be a grammatically correct fictional story with > no plot holes written in the language of mathematics. You could be right. > >> >>> I think we should distinguish well between “being true” and existence. >> >> >>If there is a difference between “being true” and existence then >> either: >> >> 1) Some things are true but don't exist. In other words some things are >> logically consistent but are self contained and have nothing to do with >> physics or physical reality in general. > > >Assuming Aristotle's theology. > > Sometimes i have the feeling I'm debating with a chatbot that has been > programmed to throw in the word Aristotle, theology, Plato or Greek at least > once every 250 words. > > >>Or in still other words some mathematical stories are fictional and much > of modern abstract mathematics has no deeper meaning than a Harry Potter > novel and the fanfiction stories that spawn off from it. > > >That is inconsistent with mechanism, > > I see no reason to to think that must be true.
Because you claim to have an algorithm able to predict what anyone could live after a self-duplication. But you have never given that algorithm, except “W & M” which is refuted immediately by both copies. So, it is hardly astonishing you can get this point. > You can write a story in the English language that is grammatical and > contains no logical plot holes but that never happened, why can't the same > thing be done in the mathematical language? Because if the story is consistent and based on some computation, some computation in arithmetic will emulate it, and no Turing machine can see immediately the difference. > > >but also pretty ridiculous. > > I'm just trying to follow the consequences of your statement "we should > distinguish well between “being true” and existence". > > If 1+1 = 2 is fiction, then, [...] > > I didn't say every consistent mathematical statement was fiction! I'm sure > 1+2=2 is nonfiction, You worry me.I guess it is a typo. > I'm less sure that Cantor's Theorem on transfinite sets is. With mechanism, it is. That is the whole difference between cantor Diagonal and Kleene diagonal, which I did explain many times here. > And physics doesn't care if the Continuum hypothesis is true or not, because > all the mathematics that physicists use would remain unchanged either way. That is not obvious. Some key theorem on knots, which have been used in quantum gravitation were based on some studies on large cardinals (until someone found more “elementary” proof). It is hard to tell in advance if some math will or not been applicable in some other science. Hardy was “proud” that number theory did not have application and he thought it would never add, but he was wrong. > > >In logic, logicians have tools to delineate precisely the difference > between truth and existence. Existence os when an existential proposition is > true, > > So logicians have concluded that existence exists when its true that > existence exists? Not at all. Logicians said that a theory proves an existence when they can prove with the theory some formula F(t), where t is a closed term of the theory. They use the inference rule F(t) —— (or some others, more sophisticated to be valid in the intuitionist frame). ExT(x) And, as they don’t do metaphysics, they add nothing. Obviously in metaphysics, the situation if far more complex, and we have to distinguish between ontological or primitive existence and phenomenological appearance of existence. Incompleteness already imposes such nuances all by itself. Bruno > > John K Clark > > > > > -- > 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.
