On 21 Jul 2011, at 17:54, meekerdb wrote:

On 7/21/2011 2:27 AM, Bruno Marchal wrote:
But I think you beg the question by demanding an axiomatic definition and rejecting ostensive ones.

The point is that ostensive definition does not work for justifying an ontology.

That seems to be a non-sequitur. How can any kind of definition justify an ontology?

Because a definition or an axiomatization refer to an intended model, of a theory which handle existential quantifier. The theory of group requires the existence of a neutral elements, for example. The theory of number requires zero, etc.

Definitions are about the meaning of words. If I point to a table and say "Table." I'm defining "table", not justifying an ontology.

OK. And then what? You are just pointing on some pattern.

That's what the dream argument shows. Being axiomatic does not beg the question. You can be materialist and develop an axiomatic of primitive matter. The whole point of an axiomatic approach consists in being as neutral as possible on ontological commitment.

But what you demanded was a *physical* axiomatic definition. Which seems to be a demand that the definition be physical, yet not ostensive. I think that's contradictory.

I did not asked for a physical axiomatic definition, but for an axiomatic definition of physical (and this without using something equivalent to the numbers, to stay on topic).

Axiomatics are already in Platonia so of course that forces computation to be there.

The computations are concrete relations.

If the are concrete then we should be able to point to them.

Either by concrete you mean "physical", and that beg the question.
If not, I can point on many computations is arithmetic. This needs Gödel's ariothmetization, and so is a bit tedious, but it is non- controversial that such things exist. Indeed RA and PA proves their existence.

They don't need axioms to exist. Then the numbers relation can be described by some axiomatic.

And one can regard the numbers as defined by their relations. So the "fundamental ontology" of numbers is reduced to a description of relations. The is no need to suppose they exist in the sense of tables and chairs.


This means only that we *can* agree on simple (but very fertile) basic number relations. For primitive matter, that does not exist, and that is why people recourse to ostensive "definition". They knock the table, and say "you will not tell me that this table does not exist". The problem, for them, is that I can dream of people knocking tables. So for the basic fundamental ontology, you just cannot use the ostensive move (or you have to abandon the dream argument, classical theory of knowledge, or comp). But this moves seems an ad hoc non-comp move, if not a rather naive attitude.

What "dream argument"? That all we think of as real could be a dream? I think that is as worthless as solipism.

This is the recurring confusion between subjective idealism and objective idealism. Objective idealism is not a choice, but a consequence of the comp assumption and the weak Occam razor.



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