On Wednesday, March 10, 2021 at 4:12:21 PM UTC+1 Bruno Marchal wrote:

> On 10 Mar 2021, at 00:03, Tomas Pales <litew...@gmail.com> wrote:
>
> The law of identity determines what can possibly exist, namely that which 
> is identical to itself. But what is the difference between a possibly 
> existing object and a "really" existing object? I see no difference, and 
> hence all possible objects exist, necessarily.
>
>
> But what is an object? 
>

Good question. Whatever an object is, it seems it must necessarily have 
these two kinds of relations to other objects: 

1) composition relation (the relation between a part and a whole, or 
between an object and a collection (combination, set) of objects that 
includes this object)
2) instantiation relation (the relation between an object and its property)

Having a composition relation means being a part or having a part (all 
objects are parts of a greater object, and some objects also have parts). 
Having an instantiation relation means having a property or being a 
property (all objects have a property, and some objects are also 
properties). Wouldn't you agree that every possible object must have these 
two kinds of relations?

The composition relation generates all possible collections (combinations, 
sets), down to empty collections (non-composite objects) and maybe even 
without bottom as long as there is no contradiction. And the instantiation 
relation generates all possible properties and objects that have these 
properties, down to collections (which are not properties of anything else) 
and maybe even without bottom as long as there is no contradiction.

So, there are two kinds of objects: collections and properties (roughly 
synonymous with concrete and abstract objects, respectively). Actually, we 
might count relations as a third kind of object because, after all, they 
are something too. Abstract relations are also properties of concrete 
relations (for example the abstract/general composition relation is a 
property of any concrete composition relation).
 

> I agree that Unicorn can exist, in the mind of some people, or in a dream, 
> but most would say that Unicorn do no exist, because being fictional is 
> part of their definition.
>

Minds are parts of reality, so parts of minds (like unicorns) are parts of 
reality too. Like every object, unicorns exist in the way in which they are 
defined, in this case as parts of minds. And maybe in some other world also 
outside of minds, as long as there is no contradiction.
 

> Or take a square circle, or a dog which is also a cat…
>

These are not possible objects because their definition violates the law of 
identity. What is a circle that is not a circle? Nothing.

Why? A red can which is blue can be identical with itself. All odd natural 
> number solution to 2x = x + 1 are equal to itself, despite not existing. 
> Your self-identity criteria is too weak for being a criteria of existence.
>

A red car that is blue is a red car that is not red. Violation of law of 
identity, therefore nothing.


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