Re: My talk about Godel to the post-grads.

Mitch wrote:
On Jul 18, 11:07 pm, John Jones <jonescard...@xxxxxxx> wrote:
So a major point of distinction between us so far, I think, is that you
argue that objects have properties, and I argue that objects have tags.

Yeah, that seems right. (I remember you mentioning tags briefly once,
with little or no explanation) but very loosely that seems about the
same as properties.

This disagreement may not have been identified earlier, and I do not
know who ought to be right. But there are consequences for each of our
positions;

hm...disagreement? they actually seem the same to me, but maybe I'm
assuming too much.

the consequences are that
1) for your position - which is that objects (or elements, etc) are
distinguished by their 'properties',

yes that sounds right. if a has exactly the same properties as b then
a = b.

it must follow that each object has
a fixed ontology.

I don't follow that inference.

If this were not so, then all objects would be alike
in having indeterminate or unlimited properties.

OK (if given the previous). But they might be alike in being similarly
indeterminate but not identical.

Now, a fixed ontology
of objects has at least one consequence for set theory. This consequence
is that we cannot create sets ad hoc. For if objects are identified by
the properties they gain by virtue of being in sets, AND if objects have
a fixed ontology, then we cannot create sets ad hoc. Creating sets
arbitrarily, which is what set theorists do, makes the ontology of the
objects variable when it ought to be fixed!

I'm not really sure about the fixed vs variable ontology. I don't
think it matters. Maybe you're confusing ad hoc with hypothetical or
variables


2) for my own position - that objects are distinguished by their tags,
the ontology of an object is not fixed. It is not fixed because we can
append any number of tags to an object. This also has consequences for
set theory. The consequence is that sets have no subsets because the
tags are always 'tagged' to the object, and not appended to another tag.
But an advantage of 'tags' over 'properties', is that only tags allow an
indeterminate number of set creations.

How do properties not allow an indeterminate # of set creations?
Whatever your line of reasoning before, When presented like that, I
don't see any difference between properties and tags.

At the end of the day, I do not think that either of our positions are
tenable - whether objects are distinguished by their properties or by
their tags, neither account can fulfill the requirements of set theory.

What are the requirements of set theory?

So what I am missing and what, I think, is ultimately the source of my
difficulties with the proposal "AuB", is a satisfactory account of set
formation. Is there such an account?

That -does- seem like a reasonable question. And yes there is a
satisfactory account. Zermelo-Fraenkel set theory is pretty much it.
(there are other possibilities but the questions you have in mind are
handled pretty much the same among them)

Mitch

I will rework the definitions, as I see it, with some errors possibly:
i might start a new post with. In fact I will, just to polish off some last contributions I am making. So see new post.

.

Relevant Pages

  • Re: My talk about Godel to the post-grads.
    ... So a major point of distinction between us so far, I think, is that you ... and I argue that objects have tags. ... of objects has at least one consequence for set theory. ... a fixed ontology, then we cannot create sets ad hoc. ...
    (sci.logic)
  • Re: My talk about Godel to the post-grads.
    ... But I used the term 'tags'. ... So a major point of distinction between us so far, I think, is that you argue that objects have properties, and I argue that objects have tags. ... a fixed ontology of objects has at least one consequence for set theory. ...
    (sci.logic)