> On 30 Oct 2018, at 12:01, Tomas Pales <litewav...@gmail.com> wrote:
> On Tuesday, October 30, 2018 at 10:36:59 AM UTC+1, Bruno Marchal wrote:
> Any object can be inconsistently defined. I can define the moon by the set of 
> squared circles.
> The set of squared circles is the empty set. The moon is not an empty set, it 
> has a complex internal structure.
> Anyway, the word "define" has two meanings which need to be distinguished. 
> "An object is defined" may mean:
> 1) "An object is described" (this usually means that there must be someone 
> who defines/describes the object)
> 2) "An object is constituted/formed" (this doesn't require anyone to define 
> the object, just as the fact that an object is composed of parts doesn't 
> require a composer)
> When I say that an object is consistently or inconsistently defined, I mean 
> defined in the second sense. That's the existential/ontological sense. An 
> inconsistently defined object is not identical to itself, it is not what it 
> is, it does not have the properties it has. Such an object is nonsense, it 
> cannot exist, it is not really an object, it is nothing. The definition of an 
> object in the first sense is true/accurate iff it corresponds to the 
> definition of the object in the second sense. 
>> - and this I mean in the absolute sense, regardless of theory: an object 
>> that is not identical to itself is inconsistent in any theory. Such an 
>> object cannot exist. All other objects can exist somewhere.
> You are not using the (logical) terms in their standard meaning. It is hard 
> to follow. I don’t undersetand what you mean by object.
> Sorry, by "object" I mean anything that exists. Not nothing.
> With mechanism, the axiom of infinity leads to an inflation of predictions, 
> which is not what we are experiencing
> That may mean that we live in a finite mathematical structure. Still, that 
> doesn't rule out the existence of infinite mathematical structures. If they 
> are consistent, why wouldn't they exist?

The elegance of mechanism is that it explains, by assuming only very simple 
rule, why the numbers eventually discover the infinities in their own mind, and 
correctly so. 

We get an explanation why the finite number can dispense themselves of using 
infinities to throw some light on themselves. With a simple ontology (any 
universal system will do) we get the phenomenological reality of matter and 
analysis, and beyond.

And it can be tested, and perhaps completed in case we are not machine, but 
actual gods, which I doubt. That would not change much in the approach, only 
make it technical more demanding. But let us not put the complexity in the 
start. We can add it if it is needed.


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