Where is your logic and evidence for your claim? — Corvus

I posted the links. That's the evidence. The logic is pretty much inferring that what is posted at the links says just what it says.

Still speaking on behalf of Banno? — Corvus

No, I don't speak on his behalf. I speak on my own behalf to say that it is a plain fact that Banno did not exaggerate by saying 'hundreds' but that you exaggerated by saying that he did say 'hundreds'.

Again it's in the plain record of the posts.

I posted the links. That's the evidence. The logic is pretty much inferring that what is posted at the links says just what it says. — TonesInDeepFreeze

That is not logic. Logic must have premises and conclusions. The premises must be backed up by the evidence. You don't seem to know even what Logic means.

Why would A=A imply that the order of the elements in B would need to be the same as A? — Banno

Jesus Banno, if A is the same as B, as implied by "A=B", (if "=" signifies identity, or "the same"), then the order of A's elements is the same as the order of B's elements, necessarily, as this is a part of "being the same"..

Order has nothing to do with this.

An ordering is a certain kind of relation on a set.

The axiom of extensionality pertain no matter what orderings are on a set. — TonesInDeepFreeze

That is the first, and most obvious piece of evidence which indicates that the axiom of extensionality does not state identity. Clearly "identity" by the law of identity includes the order of a thing's elements, as it includes all aspect of the thing, even the unknown aspects. So the ordering of the thing's elements is therefore included in the thing's identity, unlike the supposed (fake) "identity" stated by the axiom of extensionality.

No, I don't speak on his behalf. I speak on my own behalf to say that it is a plain fact that Banno did not exaggerate by saying 'hundreds' but that you exaggerated by saying that he did say 'hundreds'.

Again it's in the plain record of the posts. — TonesInDeepFreeze

Yes, he made his post sounding like that. Do you still not understand any simile or metaphor expressions in English?

Hey look, if you don't have any meaningful philosophy to write down, please remain silent. We want to discuss philosophy here.

See your ad hominem attacks on other interlocutors from the beginning of your posts? That is not a good manner at all. Please just discuss the philosophy. Have some respect. Don't throw insults to the other interlocutors. — Corvus

First, you lied that earlier I began with ad hominems.

Second, you skipped my reply about that my arguments are not ad hominem, but rather I give arguments that are not ad hominem but also add the needed observation that the interlocuter is indeed ignorant, confused, and dishonest, as at a certain point it deserves remarking that he is ignorant, confused and dishonest.

Indeed, you can see that my first posts in this thread, and others like it, are devoid of personal remarks, and my first posts to new interlocuters are devoid of personal remarks. But, eventually stubbornly ignorant, confused and dishonest posting deserves to be pointed out for being what it is.

Meanwhile, as you take such umbrage to disparaging remarks, you're free to cut them out of your own posting. I think it's your prerogative to make them, but yours happen to be quite inapposite, which is putting it mildly.

Yes, he made his post sounding like that. Do you still not understand any simile or metaphor expressions in English? — Corvus

That is ridiculous. You accused him of exaggeration. That's not simile or metaphor. So you exaggerated, not him.

Look at the links and my remarks about them.

First, you lied that earlier I began with ad hominems. — TonesInDeepFreeze

At least, I presented the logic that I have never lied. And I have now the evidence of your post quote, you starting your post with ad hominem insults to the other interlocutors.

You, have no logic, no evidence, no ground for your claims. But just make up false statements and claims on the others.

Now I am only asking you to stop your nonsense, and let us get on with the philosophical discussions with the basic manners, respects and rationality.

Again for the crank:

There are different orderings on sets.

There is no such thing as "THE" ordering for sets with at least two members. There are often what we call 'standard orderings' but still there is not just "THE" ordering of a set with at least two members.

Again for the crank:

The axiom of extensionality pertains no matter what orderings are on a set.

{0 1 } = {1 0}

{<0 1>} is an ordering on {0 1}
and
{<1 0>} is an ordering on {0 1}

{<0 1>} not= {<1 0>}

{<0 0> <1 1>} is a sequence whose range is {0 1}
and
{<0 1> <1 0>} is a sequence whose range is {0 1}

{<0 0> <1 1>} not= {<0 1> <1 0>}

The treatment of orders and sequences is rigorous in set theory. And the axiom of extensionality is not inconsistent with the theorems about them.

Of course, you can't deal with the plain fact of the record of posts, which document not only that you've been lying (which itself is insulting) but which also includes relatively detailed remarks by me about mathematics and philosophy.

if you don't have any meaningful philosophy to write down — Corvus

See above post.

Did someone say that the axiom of extensionality "states identity"?

Jesus Banno, if A is the same as B, as implied by "A=B", (if "=" signifies identity, or "the same"), then the order of A's elements is the same as the order of B's elements, necessarily, as this is a part of "being the same".. — Metaphysician Undercover

Christ, Meta, sets are not order.

Clearly "identity" by the law of identity includes the order of a thing's elements, as it includes all aspect of the thing, even the unknown aspects. — Metaphysician Undercover

The order of the elements is not part of what a set is. See

But we are at the point where further discussion is without purpose. Again, you have shown that there is no value in discourse with you.

I am here to read and discuss philosophy. — Corvus

You havn't posted anything of philosophical merit for page after page; just bitchin'.

Here's the link that proves it.

But we are at the point where further discussion is without purpose. Again, you have shown that there is no value in discourse with you. — Banno

You havn't posted anything of philosophical merit for page after page; just bitchin'.

Here's the link that proves it. — Banno

Your posts are biased and full of distortion of the facts as usual. I don't see a point in philosophical discourse with you either. You claim that you care for philosophy, but in reality you distort the truths with your bias, prejudice and false judgement.

distortion [...] bias, prejudice and false judgement. — Corvus

That is not an insult but "ignorant and confused" is?

That is not an insult but "ignorant and confused" is? — TonesInDeepFreeze

I am not sure what planet you live, and say that. But it is an insult, and definitely needless thing to say to your interlocutors without valid reasons.

If someone came on, and replied to your post starting "You are ignorant and confused ... intellectually incompetent" without any evidence or ground, then I am sure you wouldn't feel pleasant.

I don't see a point in philosophical discourse with you either. — Corvus

Then, please, don't feel any need to reply to my posts. For page after page. :wink:

But if you do want to get back into a conversation that is on topic, you might re-phrase whatever your position is, taking into account the various responses hereabouts.

I wonder what makes of this. They haven't responded at all, but that seems to be their way; they are in the unusual position of having less comments (8) than Discussions (11)...

I think I've had enough of this. There's been no progress for days. Thanks for sharing your insights.

There is no such thing as "THE" ordering for sets with at least two members. — TonesInDeepFreeze

Exactly, the ordering of the elements which make up "a thing" is essential to the identity of the thing. Therefore "identity" in set theory is not consistent with "identity" as stated by the law of identity, which is a statement about things.

We might go on and consider the supposed identity of an empty set as well. What type of "thing" has no elements in its composition? Well, that's not a thing at all, and it has no identity, because "identity" by the law of identity is a statement about things.

Further, we might consider whether a thing with infinite elements could really have an identity. That's a difficult philosophical question, which you might just take the answer for granted, because there's a serious lack of rigour in your concept of "identity".

The order of the elements is not part of what a set is. See ↪TonesInDeepFreeze — Banno

I know, and that's exactly the point, because order of a thing's elements is an essential aspect of identity. That's why if two sets are said to be "the same", they are not the same by the conditions of the law of identity, because the order of the elements is not included in that supposed (fake) identity..

How do you suppose that there is a thing which has an identity, yet that thing has no order to its elements? That's not a thing at all. And if it's not a thing it has no identity, by the law of identity, which is a statement about things.

Again, you have shown that there is no value in discourse with you. — Banno

Yes, as usual, I prove you to be wrong in your belief, and then you go off and ignore me for a period of time. The problem though, is that you never learn, and will come back later to argue what has already been demonstrated to you as wrong. Oh well, its no loss to me.

As usual, you evaded the point. Again:

"distortion [...] bias, prejudice and false judgement."

That is not an insult but "ignorant and confused" is?

As to what is not pleasant, it is not pleasant to have one's posts misrepresented, strawmanned and outright lied about, as you regularly do, and to confront supposed arguments against them that skip their key points, as you regularly skip the key points.

You can look back in this thread to see that I posted back and forth with you with my not saying anything remotely personal, until I pointed out that you were skipping the points.

And copious evidence and argument have been given showing that the main crank in this thread is ignorant and confused about this subject - including right up to this very moment.

the ordering of the elements which make up "a thing" is essential to the identity of the thing. — Metaphysician Undercover

...unless it isn't, as is the case with sets...

That's why if two sets are said to be "the same", they are not the same by the conditions of the law of identity, because the order of the elements is not included in that supposed (fake) identity.. — Metaphysician Undercover

No; and that's why the order is irrelevant when determining if two sets are the same...

Fucksake.

I sincerely regret having entered into a direct discussion with you. I will try not to make the same error again.

No; and that's why the order is irrelevant when determining if two sets are the same... — Banno

Yes, "the order is irrelevant when determining if two sets are the same". But the order of the elements is essential to determining the identity of a thing. And the law of identity is a statement about the identity of things. Therefore the identity of sets is not consistent with the law of identity. Understand?

The main crank continues to argue by mere assertion about the ordering, repeating over and over and over his dogma, without even taking a peek at the information provided him that explains his confusion.

/

Set theory is an axiomatic system with one non-logical primitive. From the axioms we prove there is a unique object such that there is no x such that x bears the relation denoted by 'e' to said object. If the nickname 'the empty set' does' comport with one's notions about set, then it can be called 'the zempty zet' or 'the-thing-that-has-no-things-on-the-left-of-it'. The nicknames would not alter the formal theory.

Generally as to what things don't have members other than the empty set: urelements.

As usual, you evaded the point. Again:

"distortion [...] bias, prejudice and false judgement." — TonesInDeepFreeze

This is truth. He just comes along says that the others interpretations are wrong, and there is no arguments or logical ground for that judgement. No one can think differently from him.

That is not an insult but "ignorant and confused" is? — TonesInDeepFreeze

If you call someone ignorant and confused from the start of your posts, when it is you who are ignorant and confused, then that is an insult to the person. You may not know that, because he is not saying anything, but just thinking about it. It is also unnecessary to say things like that in philosophical discussions.

I am sure if someone said that to you, it would be because you said it to him first. I know you said something like that first to me, and wasn't pleasant.

You can look back in this thread to see that I posted back and forth with you with my not saying anything remotely personal, until I pointed out that you were skipping the points.

And copious evidence and argument have been given showing that the main crank in this thread is ignorant and confused about this subject - including right up to this very moment. — TonesInDeepFreeze

I have not been replying to all of your walls and walls of off topic posts to me. I don't see a point in ad hominem posts. I have no time or inclination for getting involved in non-philosophical quibbles with you. I was just pointing out problems in your posts for the inaccuracies and personal comments you were putting out.

The issue I'm discussing is identity. It's only indirectly related to the op, so if you do not want to discuss this, that's fine. What you can "prove from the axioms" is irrelevant, when it is the acceptability of the axioms which is being questioned.

This is truth. — Corvus

First, it's not. Second, it is also truth that the main crank here is ignorant and confused about the subject.

So it seems you think that ""distortion [...] bias, prejudice and false judgement" is not an insult, because you think it is true, but "ignorant and confused" is an insult.

As to start of posts, there are different starting points: The start of a single post, the entry posts in a thread, and the first posts between posters in this forum. In the start of this thread, I did not make personal remarks. Over time, as the main cranks misrepresents, strawmans, posts in ignorance and confusion on the subject in this thread, then I remark on that. And this is in context of a MASSIVE amount of that kind of insulting dishonesty in many other threads in this forum.

It's not a question of replying to all of what poster writes, but it deserves remarking when you criticize posts while skipping their key points and misrepresent what they say.

~~

But the order of the elements is essential to determining the identity of a thing. — Metaphysician Undercover

So an hourglass changes its identity as each sand grain drops.

A few pages back I said:

So the reply will consist in an obfuscation of the law of identity by confusing it with an "ontological" principle. Mistaking a language act for a thing in the world. — Banno

...and here it is. Thanks.

I have no time or inclination for getting involved in non-philosophical quibbles with you. — Corvus

You're free not to!

I don't see a point in ad hominem posts. — Corvus

You don't see a point in them, but that doesn't stop you from posting insults.

And, again, it is very important to distinguish between an ad hominem ARGUMENT and, on the other hand, stating an non-ad hominem argument but in addition remarking that a poster is confused, ignorant and dishonest, especially when detailed explanation is given the poster as to what his ignorance, confusion and dishonesty are.