> On 11 Jan 2019, at 21:04, Brent Meeker <meeke...@verizon.net> 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
> 
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