Re: An uncountable countable set

Tony Orlow wrote:
I didn't say that you said that all objects in a class are equal. In
fact that is why it is imporatant to keep clear the difference between
equality and equivalence.

Ugh. You keep missing the point. It must be deliberate.

Yes, I do it because it makes my dog happy.

but given some
criterion for distinguishing objects, one can form CLASSES where a given
property is the same for all members of any given class, ignoring all
other properties.

That's pretty much what we do in set theory. Except we don't "ignore"
other properties; rather, we just have only a finite number of
primitives. And we don't need to refer to classes; rather sets x and y
are the same set.

Yep. You're doing it on purpose. There is no other explanation for you
ignoring that I have already said that finite theories with a finite
number of primitives can only address a finite number of properties.

I don't know what you mean by a 'finite theory', since every theory,
being a set of sentences closed under entailment,is infinite. But YOU
missed MY point again. A finite number of primitives does not limit us
to finitely many properties, since properties are compound.

I understand that it is your postulate. But it is not the same
statement as the symmetry of identity. And apparently that IS difficult
for you to understand.

Ugh again. Is is = = ???? Is IS =. = = is. Got it?

No. I don't know what you mean by those strings. But I can tell you
that you'd profit by reading something on the subject of identity
theory.

x IS the set S of property values defining it.

Now a different formulation from you. Okay, your postulate is that x is
the set of properties that define x. Now you just need a logistic
system, axioms, primitives, and defintions to go along with that.

x=S <-> S=x.

Comprende? Dios mio!

What in the world is wrong with you? Of course I understand symmetry of
equality.

Sorry for not reading your mind when you mentioned, in your own scare
quotes, "subjective". As to your point, I don't want to comment at this
time since I see some philosophical complexities here I couldn't
address properly within only a paragraph. Anyway, my original point is
that a theory such as set theory avoids having the identity of objects
depend upon DISCOVERY (which is epistemological) of properties.


Of course not. It IGNORES any other properties besides those explicitly
defined within the theory. There is no room for other possibilities
within the theory. That's what I'm saying.

No theory accounts for all properties. And of course any theory does
not allow what is not possible in the theory.

See, that is what is subjective (or epistemological). We don't define
equality by "way to distinguish" but rather by FORMULAS.
Formulas are a fine way to distinguish objects. For instance, I
distinguish a vastly greater number of different infinities than
cardinality simply by ordering formulas on a unit infinity. Good suggestion.

As usual, you seem not to recognize my point.

I believe I do, but if you would like to clarify your point, here's your
chance.

Requote what I said to which you were in response and I'll consider
your offer.

No, we may do better than that in theories in which there are only
finitely many primitive predicate symbols, such as set theory. I told
you all about that already.
If there are only finitely many primitive predicate symbols, then there
are only finitely many properties being addressed by the theory.

No, because properties are not just primitive but are also compound.

Unless you compound them infinitely,

It's not a process such as that.

you still have a finite set of
compound properties. Perhaps yuo could give an example you think
contradicts that statement.

The set of definining formulas of Z set theory is countably infinite.
There's your example.

When I specifically distinguished it in my first mention (after the
initial one-liner comment) from deductive logic and inductive proof
(which is deductive), and then get further confusion, then I start to
wonder a little.

No, at THAT time, in that other thread, I said that if you are talking
about inductive logic as opposed to induction in mathematics, then my
remarks would have to be adjusted for that. I posted that immediately
upon your saying that you had inductive logic in mind.

Now, if I were you, I'd say you don't know the difference merely from
the fact that you misspoke. But I'm not you, so I don't resort to that
kind of cheap tactic.

It's not that you misspoke. That's Virgil's gig, anyway. It's that,
after specific clarification you still seemed not to understand what I
was saying, and still don't. Any clue as to why I would bring up
inductive logic, as opposed to inductive proof?

Since the incident I just mentioned, please show exactly where you
mentioned "inductive logic" and I posted as if otherwise.

Number the objects in the universe starting from
0. Every unique set is therefore a unique bit string representing which
elements are members.

If that's your axiom, fine. But it contradicts set theory. So, again,
we need to be clear what theory we're talking about. But you don't have
a theory, so it's nugatory anyway. You just keep announcing disparate
axioms without stating a logistic system, primitives, or definitions.

You say it contradicts set theory, but I imagine that depends on how you
define the universe.

No it doesn't. I just contradicts set theory.

If it's "the set of all sets", sure, that leads to
contradictions.

The contradiction has nothing to do with that.

If it's "the set of all objects, properties, and
relations between them", perhaps that a different story? Is there a
universe in ZFC. Ross says not. It makes one wonder how a statement
about the universe could contradict ZFC then.

I'm not paid to sort out such utter confusions as in the above
paragraph.

You may define words however you like. However, you should at least be
aware when your definitions and meanings depart from those of most of
the other people in a converstation.

Which is most of the time, but that's the point of the conversation here.

An odd point then.

But those don't ential that, for example, b = {P | P is a defining
property of b}.
Really, they do.
Because you say so. But you couldn't demonstrate that entailment in a
system.
I'll have to think about that. What makes you so sure?

Because YOU present yourself as so sure that you don't need to bother
with understanding what is involved in such things. But, of course, as
we recognize, appearences could be deceiving and it's possible you've
already digested an entire graduate library of mathematical logic, set
theory, and mathematics but are only pretending to know virtually
nothing about them.

Oh. Another insult. You had me fooled for a second. I thought you might
have some reasonable stance as to why it could not be accomplished in
theory. Never mind. You got me. Good one.

In WHAT theory?

What dismissal? YOU won't read even a SINGLE book from the ENTIRE
history of HUMAN THOUGHT on the subject.

You don't know what I've read or studied, and can't even get most of my
points, and try to cover it up by accusing me of ignorance. I'm not an
expert steeped for years, but I know enough to see transfinitology is
misguided, and enough now to see a clear alternative on the horizon.

You haven't read a single book in mathematical logic or set theory.

MoeBlee

.

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