> On 11 Jan 2019, at 21:04, Brent Meeker <[email protected]> wrote: > > > > On 1/11/2019 3:24 AM, Bruno Marchal wrote: >> Anyway, the question is if it is true or false. In mathematics, mechanism >> restricts realism only to finite mathematics, or arithmetic. This is >> basically the idea that 2+2=4, and that this is true independently of me. > > But "true"and "exist" are different things.
Yes. True in a model, means satisfied in that model. Now “Ex(x = k)” is true in a model, if k exists in the model. For exemple “Ex(x = s(s(0))” is true in all models of arithmetic, and is true in particular in the standard model of arithmetic. The structure/model (N, 0, +, x) satisfies “Ex(x = s(s(0))”. > Mathematics uses "exist" to mean "satisfies some predicate” Satisfies some formula (build with some predicate or legality). Yes, OK. > . But we don't think Waston existed because he satisfied "the companion of > Homes”. It exists in the model satisfying the “axioms” of the “theory”, which we take as granted when, for entertaining purpose, we want do some awake dreaming, like TV and Novels make possible. Is our reality a model of that theory? Of course we know that this is fewly possible. But we do assume that the reality/model in which Watson and Holmes do exist is enough similar to us so that we can be sure that Holmes will not loss his pipe all along the history we follow. Bruno > > Brent > > -- > 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. -- 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.
