On Friday, March 12, 2021 at 1:30:55 PM UTC+1 Bruno Marchal wrote:
I translate this by “an object is an element of a set together with some
> structure or laws. OK? So vectors, numbers, maps, can all be seen as
> (mathematical) object.
>
Yes.
(And with mechanism, we can then deduce that there is no physical object,
> although the mind can easily approximate them by some “object” (build by
> the mind).
>
Not sure what you mean by "physical". I regard as physical those
mathematical objects that are in spacetime (and spacetime itself is a
mathematical object too, a 4-dimensional space with one dimension somewhat
different that the other three).
OK. In math we use often set theory, intuitively (or formally) to define,
> or better to represent, the different object we want to talk about.
>
> It is known that arithmetic (the natural numbers) can be used too, for
> most of the usual mathematics (including a lot of constructive real
> objects, and more, but not all real numbers)
>
Reality may be bigger than arithmetic and then we need set theory to
capture it, no? Well, we may never know if reality is bigger than
arithmetic because it's impossible to prove that even arithmetic is
consistent, let alone something bigger.
> “Concrete” is a tricky term which does not survive Mechanism, which
> reverse not just physics and psychology-theology, but also abstract and
> concrete. Just 0, s0, … are concrete, but a physical object like a table
> becomes abstract. It looks concrete phenomenologically, but that is because
> we have millions of neurons making us feel that way.
>
By "concrete" object I mean an object that is not a property. For example,
the general triangle (an abstract object) is a property of all concrete
triangles such as ones I can draw on a piece of paper. But a concrete
triangle is not a property of anything. Same with tables; the concrete
table in your room is not a property of anything but the abstract table
("table in general") is a property exemplified in all concrete tables.
We cannot really invoke “reality” as its very nature is part of the inquiry.
>
I regard as reality all objects (that are identical to themselves, of
course).
A red car that is blue is a red car that is not red. Violation of law of
identity, therefore nothing.
Fair enough, at least with a content relative to the metaphysics, or basic
> ontology we assume at the start.
>
Without respecting law of identity, logical explosion will erase all
differences between object and non-object, existence and non-existence,
turning everything into nonsense. Paraconsistent logics arbitrarily deny
law of identity in some circumstances and arbitrarily block explosion in
some circumstances. They are meaningful and corresponding to reality only
to the extent they affirm the law of identity.
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