If a set consists of concrete objects, then it has the order that those concrete objects have, and no other order — Metaphysician Undercover

Set consisting of three balls colored red, white and blue. They also have differing weights. What is THE order? Just curious.

If a set consists of concrete objects, then it has the order that those concrete objects have, and no other order — Metaphysician Undercover

And exactly what order is that?

No, Tones was referring to the principle called "the identity of indiscernibles", which is completely different from the law of identity. The law of identity makes a thing's identity the thing itself, the identity of indiscernibles associates a thing's identity with the thing's properties. These are fundamentally different principles. — Metaphysician Undercover

Yes I understand that. I didn't realize @TonesInDeepFreeze was talking about IofI. Actually I just learned there's an identity of indiscernibles and an indiscernibility of identicals.

No, you simply fell for the sophistry. Tones is very good at it, and apt to convince others, earning the title "head sophist". — Metaphysician Undercover

Ok this is interesting. My quote was, "Sets are subject to the law of identity." So that if X is a set, I can say X = X without appealing to any principle of set theory.

Tones convinced me of that. Now you say that he only sophisted me. How so please? If X is a set, how is X = X not given by the law of identity? You have me curious.

You think I'm a victim of Tones's sophistry. That is an interesting remark.

So, a set is a mathematical structure. — Metaphysician Undercover

Set theory is a mathematical structure. The analogy is:

Set theory is to group theory as a particular set is to a particular group.

But a set is a mathematical structure too, since the elements of sets are other sets.

How do you make this consistent with the head sophist's claim that the members of The Beatles is a set, and the particles which make up a rock is a set? The sophist says "the set whose members are all and only the bandmates in the Beatles has 24 orderings". Notice that this is not stated as possible orderings, it is stated as the "orderings" — Metaphysician Undercover

I take no responsibility for anyone else's posts. I barely take responsibility for my own. You've already told me you don't like real world examples about playgrounds so I don't use those anymore with you.

Remember your schoolkid example? — Metaphysician Undercover

Yes. I agreed with you that this was only a casual analogy, and once you told me that you don't like it, I stopped using it.

You recognized that the objects which bear that name have what you called SOME order, and this is an expression of the condition which they are actually in, at any point in time. I would call this their "actual order". — Metaphysician Undercover

This is true about kids in playgrounds, NOT mathematical sets. You have informed me that you don't like real-world analogies so I no longer use them. Mathematical sets have no inherent order.

No, Tones was referring to the principle called "the identity of indiscernibles", which is completely different from the law of identity. The law of identity makes a thing's identity the thing itself, the identity of indiscernibles associates a thing's identity with the thing's properties. These are fundamentally different principles. — Metaphysician Undercover

Yes I understand that. I didn't realize @TonesInDeepFreeze was talking about IofI. Actually I just learned there's an identity of indiscernibles and an indiscernibility of identicals.

No, you simply fell for the sophistry. Tones is very good at it, and apt to convince others, earning the title "head sophist". — Metaphysician Undercover

Ok this is interesting. My quote was, "Sets are subject to the law of identity." So that if X is a set, I can say X = X without appealing to any principle of set theory.

Tones convinced me of that. Now you say that he only sophisted me. How so please? If X is a set, how is X = X not given by the law of identity? You have me curious.

You think I'm a victim of Tones's sophistry. That is an interesting remark.

So, a set is a mathematical structure. — Metaphysician Undercover

Set theory is a mathematical structure. The analogy is:

Set theory is to group theory as a particular set is to a particular group.

But a set is a mathematical structure too, since the elements of sets are other sets.

How do you make this consistent with the head sophist's claim that the members of The Beatles is a set, and the particles which make up a rock is a set? The sophist says "the set whose members are all and only the bandmates in the Beatles has 24 orderings". Notice that this is not stated as possible orderings, it is stated as the "orderings" — Metaphysician Undercover

I take no responsibility for anyone else's posts. I barely take responsibility for my own. You've already told me you don't like real world examples about playgrounds so I don't use those anymore with you.

Remember your schoolkid example? — Metaphysician Undercover

Yes. I agreed with you that this was only a casual analogy, and once you told me that you don't like it, I stopped using it.

You recognized that the objects which bear that name have what you called SOME order, and this is an expression of the condition which they are actually in, at any point in time. I would call this their "actual order". — Metaphysician Undercover

School kids and physical objects in general do. Mathematical sets don't. You explained to me that you don't like physical examples so I no longer use them. Mathematical sets have no inherent order. The purpose of defining things that way is so that we may study the abstract notion of order.

Can you see what the head sophist has done? The sophist has removed any distinction of an actual order, to say that the group, or set, has 24 orderings, and all these orderings are equal, or the same, being in each case a different presentation of the same set. But you and I recognize, that in reality there is "SOME order", an actual order, which is the order that the objects are actually in, at any given point in time. The sophist might talk about 24 orderings, but you and I recognize that if these 24 account for all the possibilities, only one of those possibilities represents the very special "actual order", and, that since these elements are physical objects, there must be an actual order which they are in, at any given time. — Metaphysician Undercover

I can't comment on what anyone else has said. This has nothing to do with the conversation you and I are having.

The law of identity is very important to recognize the actual existence of a thing, and its temporal extension. — Metaphysician Undercover

A temporal extension. You are saying it only applies to things that exist in time? Meaning not sets? I don't think that's right. Any set is identical to itself and also equal to itself by virtue of the law of identity.

Tones did explain that to me, but not via sophistry. He asked me to prove the transitivity of set equality. Once I attempted to do that, I realized that I needed not the axiom of extensionality, but its converse. And that converse is true by way of the law of identity from the underlying predicate logic. This I discovered for myself when Tones pointed me to it.

Through time a thing changes, and the law of noncontradiction stipulates that contradicting properties cannot be attributed to the same thing at the same time. So if a specific group has ordering A at a specified time, that is a property of that group, and it surely cannot have ordering B at the same time. The head sophist claims that the specified group has 24 orderings, all the time (as time is irrelevant in that fantasy land of sophistry). Obviously the head sophist has no respect for the law of noncontradiction, and is just making contradictory statements, in that sophistic fantasy. — Metaphysician Undercover

That may or may not be true about physical objects. You say the kids in height order is not identical to the kids in alphabetical order. I say the set of kids is the same. But I do not argue this point and od not care about it.

I tell you that a set has no inherent order; and that the set of natural numbers in its usual order; and the set of natural numbers in the even-odd order say -- 0, 2, 4, 6, ...; 1, 3, 5, 7, ... is exactly the same set. It is a different ordered set, because in an ordered set, the order is part of the identity of the set. In a plain set, it's not. This is how mathematicians play their abstraction game.

That is what happens when we allow that abstractions such as mathematical structures have an identity. Inevitably the law of noncontradiction and/or the law of excluded middle will be violated. Charles Peirce did some excellent work on this subject. It's a difficult read, and you've already expressed a lack of interest in this subject/object distinction, so you probably don't really care. Anyway, here's a passage which begins to state what Peirce was up to. — Metaphysician Undercover

On the contrary, I've expressed great interest in the ideas of Pearce when members of this forum have mentioned them to me.

The relevance of all this to the principles of excluded middle and contradiction is as follows. Peirce wrote that “anything is general in so far as the principle of excluded middle does not apply to it,” e.g., the proposition “Man is mortal,” and that “anything” is indefinite “in so far as the principle of contradiction does not apply to it,” e.g., the proposition “A man whom I could mention seems to be a little conceited” (5.447-8, 1905). If we take Peirce to have meant LEM and LNC, then it appears that he wanted to deny the principle of bivalence (according to which all propositions are true or else false) with regard to universally quantified propositions, and that he meant to claim that existentially quantified propositions are both true and false. But why think that “Man is mortal,” which seems to be straightforwardly true, is neither true nor false? And why think that one and the same proposition, “A man whom I could mention seems to be a little conceited,” is both true and false? Once we see what Peirce meant by “principles of excluded middle and contradiction,” we see that this is not what he was claiming.
— Digital companion to C. S. Peirce — Metaphysician Undercover

Yes, well, discussions of denying LEM don't interest me much. I'll agree with that. But I've come by it honestly. I've made a run at constructivism and intuitionism more than once. I've read Andrej Brauer's "Five Stages of Accepting Constructive Mathematics." It doesn't speak to me. The paragraph you quoted is a little above my philosophical pay grade. Perhaps you can explain its relevance to the topic at hand.

http://www.commens.org/encyclopedia/article/lane-robert-principles-excluded-middle-and-contradiction — Metaphysician Undercover

I'll take a look as the spirit moves me, but I don't think this is a particularly productive line of conversation for me. I don't know what you are trying to tell me.

This is blatantly untrue, and as demonstrated above, if we assign "identity" to a set, the law of non-contradiction will be violated. — Metaphysician Undercover

I don't see why. If X is a set, then X = X by identity.

Now if you are trying to say that the order properties might differ or whatever, I say you are just being your usual anti-abstraction self. I don't understand your aversion to mathematical abstraction. But it doesn't effect my mathematical ontology in the least.

Or maybe you're saying something else. If so, please explain.

The law of identity enables us to understand an object as changing with the passing of time, while still maintaining its identity as the thing which it is. — Metaphysician Undercover

There is no time in set theory. Mathematics is outside of time, or talks about things that are outside of time.

Sets have distinct formulations existing all the time, which would cause a violation of the law of noncontradiction if we allow that a set is subject to the law of identity. Therefore we must conclude that sets are not subject to the law of identity. The type of thing which the law of identity applies to is physical objects. And there is obviously a big difference between physical objects and sets, despite what head sophist claims. — Metaphysician Undercover

You are just wrong about this. But give me a more specific example, if you would, so that I may understand you better.

You also have no problem with contradiction, it seems. — Metaphysician Undercover

I can always tell when you can't defend your point. The insults come out. You can do better, can't you?

This tells me nothing until you explain precisely what ∈ means. [/math]

$\in$ is an undefined primitive of set theory. Its behavior is defined by the axioms.
— Metaphysician Undercover

To me, you are simply saying that x is an element of y if x is an element of y. What I am asking is what does it mean "to be an element". — Metaphysician Undercover

It doesn't "mean" anything. It's an undefined primitive in set theory, as point, line, and plane are undefined primitives of Euclidean geometry. Its behavior and usage are defined by the axioms.

If we go with this definition, you ought to se very clearly that sets, as categories, abstract universals, do not have an identity according to the law of identity. A category is not a thing with an identity. — Metaphysician Undercover

I have no problem with that. If you want to say that set theory, as the universal, is not subject to identity, that's fine. I can' say that "set theory equals set theory." I'm perfectly fine with that. Nobody ever says it.

But given particular instances of set theory; that is, sets; we can ask if they are equal to each other or not.

So I promise not to say that the universe of sets is equal to the universe of sets. Though the category theorists will probably disagree with you.

Obviously this does not work. As you said already, elements are often sets. Therefore you cannot characterize the set as an abstract universal, and the element as an abstract particular, because they're both both, and you have no real distinction between universal and particular. — Metaphysician Undercover

You are distorting what I said. ANY particular set is a particular instance of the concept of set, as any particular apple is an instance of the concept (or category) of apple. That causes no problem.

You are willfully obfuscating this point. It's a very clear point. The set of integers is a particular. Sets in general, or the concept of sets, are generalities or a category or a universal.

There's no point in trying to justify the head sophist's denial of reality. — Metaphysician Undercover

It's pointless to keep referring to conversations you've had that I haven't seen, with people who aren't me.

If "Cinderella" refers to a particular, an instance of the category "fairy take characters", then that is a physical object. — Metaphysician Undercover

Clearly Cinderella is not a physical object. That's exactly why I used a fictional character as an example.

If "Cinderella" refers to a further abstract category, like in the case of "red is an instance of colour", then it does not refer to a particular. The head sophist seems to have convinced you that you can ignore the difference between a physical object and an abstraction, but you and I both know that would be a mistake. — Metaphysician Undercover

Knock it off, will you please? Take your complaints WITH the other party, TO the other party.

I have long ago agreed that physical objects and mathematical objects are not the same.

Cinderella refers to the individual fictional character of Cinderella, as Captain Ahab refers to the fictional character of Captain Ahab.

If a set consists of concrete objects, then it has the order that those concrete objects have, and no other order. — Metaphysician Undercover

And exactly what order is that? — tim wood

‘Set’ and ‘order’ are very interesting concepts that I discussed in other threads, and it is not always clear what we can include in them. If I am not mistaken, I guess MU refers to those objects that are logically attached to an order and, therefore, make a set. For example, ground, bricks, walls, ceiling, windows, and a door altogether make a set, which is the house. 
Please keep in mind that I am not arguing about whether those are necessary order objects or not. However, it is evident that they create the order and set.

Set consisting of three balls colored red, white and blue. They also have differing weights. What is THE order? Just curious. — jgill

The order is how items are organised with one another based on a specific attribute. The only distinguishing feature is that they are spherical. The weight and colours are only accessories. The set would be spheres, and the order would be the three balls. Right?

Then the crank, in his usual manner of self-serving sophistry, misconstrues fishfry. fishfry didn't contradict that the law of identity is different from the identity of indiscernibles. — TonesInDeepFreeze

cc: @Metaphysician Undercover

You guys get a room! LOL. FWIW you convinced me that X = X for sets follows from the definition of = in the underlying predicate logic. How the = of logic relates to the law of identity, I have no idea.

It is not any more a contradiction for a set to have more than one ordering than it is a contradiction for a person to own more than one hat. — TonesInDeepFreeze

Having X hat does not exclude having Y hat, that's obvious. The two do not contradict. But if X order contradicts Y order (e.g. John is closer to the front of the stage than Paul, contradicts Paul is closer to the front of the stage than John), then X order excludes Y order.

Your analogy is not relevant because having one property clearly does not exclude the possibility of having another property, but having the property of one order clearly contradicts having the property of the contradictory order.

I think it's time for you to go back to grade school and learn some fundamentals of logical thinking.

Set consisting of three balls colored red, white and blue. They also have differing weights. What is THE order? Just curious. — jgill

Show me your balls and I will tell you their order.

And exactly what order is that? — tim wood

However those objects relate to other objects, the context, or environment they are in, dictates their order.

Ok this is interesting. My quote was, "Sets are subject to the law of identity." So that if X is a set, I can say X = X without appealing to any principle of set theory.

Tones convinced me of that. Now you say that he only sophisted me. How so please? If X is a set, how is X = X not given by the law of identity? You have me curious.

You think I'm a victim of Tones's sophistry. That is an interesting remark. — fishfry

What is the case, is that "X=X" is an ambiguous and misleading representation of the law of identity. This is because "=" must mean "is the same as", to represent that law, but it could be taken as "is equal to". Notice that in the axiom of extensionality it is taken to mean "is equal to". Therefore when Tones takes "X=X" to be an indication of the law of identity there is most likely equivocation involved.

Set theory is a mathematical structure. The analogy is:

Set theory is to group theory as a particular set is to a particular group.

But a set is a mathematical structure too, since the elements of sets are other sets. — fishfry

So, do you recognize, and respect the fact that group theory is separate from, as a theoretical representation of, the objects which are said to be members of a specified "group"? And, I'm sure you understand that just like there is a theoretical representation of the group, there is also a theoretical representation of each member of the group. In set theory therefore, there is a theoretical "set", and also theoretical "elements".

So when Tones says that a set may consist of concrete objects, this is explicitly false, because the set is the theoretical representation, and the elements of the set are theoretical representations as well. Through such false assertions, Tones misleads people and earns the title of sophist.

When Tones speaks about the set "George, Ringo, John, Paul", these names signify an abstract representation of those people, as the members of that set, the names do not signify the concrete individuals. You, Fishfry, have shown me very clearly that you know this. So there is an imaginary "George", "Ringo" etc., which are referred to as members of the set. The imaginary representation is known in classical logic as "the subject". We make predications of the subject, and the subject may or may not be assumed to represent a physical object. Comparison between what is predicated of the subject, and how the object supposedly represented by the subject appears, is how we judge truth, as correspondence.

What is important to understand in mathematics, is that the subject need not represent an object at all. It may be purely imaginary, like your example Cinderella. This allows mathematicians to manipulate subjects freely, without concern for any "correspondence" with objects. Beware the sophist though. I believe that when the sophist says that the members of a set may be abstractions, or they may be concrete objects, what is really meant if we get behind the sophistry, is that in some cases the imaginary, abstract "element", may be assumed to have a corresponding concrete object, and sometimes it may not. Notice though, that in all cases, as you've been insisting in discussions with me, the elements of the sets are abstractions, as part of the theory, and never are they the actual physical objects. Failure to uphold this distinction results in an inability to determine truth as correspondence. And that is the effect of Tones' sophistry

This is true about kids in playgrounds, NOT mathematical sets. You have informed me that you don't like real-world analogies so I no longer use them. Mathematical sets have no inherent order. — fishfry

I'll return to the schoolkids example briefly to tell you why I didn't like it. Using that example made it unclear whether "schoolkids" referred to assumed actual physical objects, or imaginary representations. That's why "real-world analogies" are difficult and misleading. The names, "George", "Paul", etc., appear to refer to real-world physical objects, and Tones even claims that they do, but within the theory, they do not, they are simply theoretical objects. If we maintain the principle that the supposed "schoolkids" are simply imaginary, then they have no inherent order unless one is stipulated as part of the rules for creating the imaginary scenario. Set theory ensures that the elements have no inherent order, but this also ensures that the elements are imaginary.

A temporal extension. You are saying it only applies to things that exist in time? Meaning not sets? I don't think that's right. Any set is identical to itself and also equal to itself by virtue of the law of identity. — fishfry

This is wrong, and where Tones mislead you in sophistry. A set is not identical to itself by the law of identity. The set has multiple contradictory orderings, and this implies violation of the law of identity. We allow that "a thing", a physical object has contradictory properties with the principle of temporal extension. At one time the thing has a property contradictory to what it has at another time, by virtue of what is known as "change", and this requires time. But set theory has no such principle of temporality, and the set simply has multiple (contradictory) orderings.

Tones did explain that to me, but not via sophistry. He asked me to prove the transitivity of set equality. Once I attempted to do that, I realized that I needed not the axiom of extensionality, but its converse. And that converse is true by way of the law of identity from the underlying predicate logic. This I discovered for myself when Tones pointed me to it. — fishfry

As I said, the reference was to the identity of indiscernibles, not the law of identity. You recognize that these two are different. The proof was not by way of the law of identity. If you still believe it was, show me the proof, and I will point out where it is inconsistent with the law of identity.

I tell you that a set has no inherent order; and that the set of natural numbers in its usual order; and the set of natural numbers in the even-odd order say -- 0, 2, 4, 6, ...; 1, 3, 5, 7, ... is exactly the same set. It is a different ordered set, because in an ordered set, the order is part of the identity of the set. In a plain set, it's not. This is how mathematicians play their abstraction game. — fishfry

We agree on this very well. The principle we need to adhere to, is that this is always an "abstraction game". If we start using names like "Ringo" etc., where it appears like the named elements of the set are concrete objects, then we invite ambiguity and equivocation. And if we assert that the elements are concrete objects, like Tones did, this is blatantly incorrect.

Yes, well, discussions of denying LEM don't interest me much. I'll agree with that. But I've come by it honestly. I've made a run at constructivism and intuitionism more than once. I've read Andrej Brauer's "Five Stages of Accepting Constructive Mathematics." It doesn't speak to me. The paragraph you quoted is a little above my philosophical pay grade. Perhaps you can explain its relevance to the topic at hand. — fishfry

The three fundamental laws of logic, identity, noncontradiction, and excluded middle, are inextricably tied together. Therefore one cannot discuss identity without expecting some reference to the other two. There has been some philosophical discussion as to which comes first, or is most basic. Aristotle seemed to believe that noncontradiction is the most basic, and identity was developed to support noncontradiction.

What C.S. Peirce noticed, is that if we allow abstract objects to have "identity" like physical objects do, as Tones seems to be insisting on, then necessarily the validity of the other two laws is compromised. Instead of denying identity to abstract objects, as I do in the Aristotelian tradition of a crusade against sophistry, Peirce sets up a structure outlining the conditions under which noncontradiction, and excluded middle ought to be violated.

I don't see why. If X is a set, then X = X by identity. — fishfry

You are missing the point. The law of identity refers explicitly to things, "a thing is the same as itself". A "set" is explicitly a group of things. Therefore when you say X = X, and X is a set, rather than a thing, then "=" does not signify identity by the law of identity.

There is no time in set theory. Mathematics is outside of time, or talks about things that are outside of time. — fishfry

Right, this is the point. "Time", or temporal extension allows that a thing may have contradictory properties, at a different time, yet maintain its identity as the same thing, all the while. This is fundamental to the law of identity. Without time (as in mathematics), the multiple orderings of a set, which Tones referred to, are simply contradictory properties. That is a good example of the issue Peirce was looking at.

But given particular instances of set theory; that is, sets; we can ask if they are equal to each other or not.

So I promise not to say that the universe of sets is equal to the universe of sets. Though the category theorists will probably disagree with you. — fishfry

Fine, but can you respect the fact that "equal" does not imply "identical", despite the sophistical tricks that Tones is so adept at.

You are distorting what I said. ANY particular set is a particular instance of the concept of set, as any particular apple is an instance of the concept (or category) of apple. That causes no problem. — fishfry

No, that's simply wrong. A particular apple is a physical object. A set is an abstraction. An instance of an apple is a physical object. Your supposed "instance" of a set is an abstraction, a concept. The two are not analogous, and I argue that this is a faulty, deceptive use of "instance".

An instance is an example, and understanding of concepts or abstractions by example does not work that way. Assume the concept "colour" for example. If I present you with the concept "red", this does not provide you with an instance of the concept "colour". An instance of the concept "colour" would be the idea of colour which you have in your mind, or the idea of colour which I have in my mind, expressed through the means of definition. Each of those would provide you with an example of the concept of "colour", an instance of that concept. The concept "red" does not provide you with an example of the concept of "colour". Nor does a specific "set" provide you with an example or instance of the concept "set".

What you are saying in this case is completely mixed up and confused.

If a set consists of concrete objects, then it has the order that those concrete objects have, and no other order
— Metaphysician Undercover

And exactly what order is that? — tim wood

However those objects relate to other objects, the context, or environment they are in, dictates their order. — Metaphysician Undercover

It appears, then, that one and no other is actually a many. Hard to make sense of that.

@fishfry
I think you and I agree substantially on the difference between abstractions and physical objects, and that the elements of a set are always abstractions and never physical objects. So you might avoid a long reply on that subject. It's only the head sophist who disagrees with us on this, claiming that the elements of a set may be concrete objects.

We do have significant disagreement concerning your claim to a proof that "X=X", when X signifies a set, means that X is the same as itself by virtue of the law of identity. You have not provided that proof in any form which I could understand.

It appears, then, that one and one and no other is actually a many. — tim wood

Sorry tim, I'm not picking up what you're putting down.

It appears, then, that one and one and no other is actually a many.
— tim wood

Sorry tim, I'm not picking up what you're putting down. — Metaphysician Undercover

Very nice. How toxic of you, MU. But note that what I "put down" is just what you put down, I merely asking you to make sense of it.

Show me your balls and I will tell you their order. — the crank

Yikes.

Very nice. How toxic of you, MU. But note that what I "put down" is just what you put down, I merely asking you to make sense of it. — tim wood

I never spoke about "one and one", nor about "many". I have no idea what you are making reference to, or how you draw the conclusion that "one and one" are a requirement for "many".

I'm not trying to be toxic, only I have no idea of what you are trying to express. What I said was an expression meaning that I am not understanding what you are saying.

I'm not trying to be toxic, only I have no idea of what you are trying to express. — Metaphysician Undercover

Your words

If a set consists of concrete objects, then it has the order that those concrete objects have, and no other order
— Metaphysician Undercover

And exactly what order is that?
— tim wood

However those objects relate to other objects, the context, or environment they are in, dictates their order.
— Metaphysician Undercover — tim wood

You say, a set of objects has an order and no other order. I ask what that order is, and you say, however they relate to other things. As they can relate in multiple ways, it would seem, according to you, they can have more than one order. Thus you say they have one order and no other, and yet many. And then when asked about that, you play dumb. Not the first time. And that is why I call you toxic.

Your views and opinions become nonsensical and self-contradictory, a waste of time. And maybe your views and opinions always have been. Or in short you play a dishonest and toxic game.

Yikes. — TonesInDeepFreeze

The sense of humour leaves the head sophist exposed, revealing no control over the inclination to equivocate.

As they can relate in multiple ways, it would seem, according to you, they can have more than one order. Thus you say they have one order and no other, and yet many. — tim wood

This is not more than one order, it is just different aspects of one order, like one object has numerous properties, but the properties are all just different aspects of the one object. That we say a thing has volume, weight, colour, etc., is just a feature of how we describe the thing. For example, saying B is prior to A in the smallness scale, and A is prior to B in the largeness scale, does not mean that the two objects have more than one order, it's just a feature of the way we describe things, i.e. our way of imposing a conceptual order.

You appear to be mixing up the natural order which things have by being the things which they are, in the circumstances which they are in, and the conceptual order which we artificially impose on the thing in abstract understanding. That is the same mistake the head sophist makes, failing to distinguish the concrete thing itself, from the conception of it.

Judging by what you argued in the other thread on "purpose", you believe that the only kind of order is conceptual order. Until you realize that this idea is faulty, you will never understand the natural order that things have simply by being the things that they are, in the circumstances that they are in. Discussion seems pointless right now.

Your words, MU:

However those objects relate to other objects, the context, or environment they are in, dictates their order. — Metaphysician Undercover

There is either one order or there are many. Which?

As I said, the context dictates their order, and context is singular. An object does not exist in a multitude of distinct contexts at the same time, despite the fact that the context may change over time. I covered change and temporality in my reply to fishfry. You might go back and read that.

An object does not exist in a multitude of distinct contexts at the same time, — Metaphysician Undercover

Of course it does. Or, if you are quite sure it doesn't, which one is right and how do you know?

Sorry tim, I have no interest in engaging with you here in the Lounge. You have demonstrated that you are very steadfast with an extremely closed mind. Banter with TIDF is at least somewhat amusing. That sophist actually has a sense of humour and some degree of conscience, which you seem to be fully and completely lacking in. Furthermore, Tones actually listens to what I say, and sometimes makes an attempt at understanding, whereas you simply dismiss it as "toxic", "dishonest", and "a waste of time". No point in wasting time if it doesn't come with entertainment.

Ugh, the crank drags me into his personal dispute by dissing me with passive aggressive faint praise as a way to diss the other poster. What a snake.

and the order would be the three balls. Right? — javi2541997

Seems like a peculiar use of the word "order".

This is not more than one order, it is just different aspects of one order — Metaphysician Undercover

Deep stuff, here. :roll:

I believe that's what The Lounge is for. The deep stuff gets booted off the main page, being for most, undistinguishable from shit.

dissing me with passive aggressive faint praise as a way to diss the other poster — TonesInDeepFreeze

I agree, it's no compliment to say that you're higher in the order of virtue than tim is. I should have just spoke the truth, tim is even lower down than you are. And both of you make a snake appear like an angel.

You appear to be mixing up the natural order — Metaphysician Undercover

Three billiard balls on a billiard table: what is their "natural" order? Three battleships at sea, what is their "natural" order? Three horses in a field, what is their "natural" order? Or, one billiard ball, one battleship, one horse, what is their "natural" order? What is "natural" order? And if there is one only and no other order, and that order depends upon their "context," their "relation" to other objects, or their "environment," what exactly are "context" and "environment," and "relation" that they are so singularly determinative? How do these disparate things establish one and one only order? And how do you know?

The substance of these questions has been before you repeatedly and you make no substantive answer.

Frame that.

The crank says, "The deep stuff gets booted off the main page, being for most, undistinguishable from shit."

The crank can't discern irony, even when it is declared with an emoji.

/

The crank says, "tim is even lower down than you are. And both of you make a snake appear like an angel."

That's lower than lame.

@fishfry

The converse of extensionality is not provided by the law of identity. It is provided by the indiscernibility of identicals.

The crank's latest posts are again a welter of blatant sophistry. If only one's time were infinite to write out out all that should be said about his confusions, illogic, self-contradictions, and lies.

I came to this topic hoping to learn anything about set, order, infinite, and so on, but the responses seem like a shootout among the users. Just calm down a bit, folks. Your positions and answers are quite good; it is not necessary to reach personal animosity. :up:

I came to this topic hoping to learn anything about set, order, infinite — javi2541997

There's plenty of detailed information and explanation posted in this thread.

If you have any questions, or wish to learn more, then it's as simple as asking (and not asking someone who doesn't know anything about the subject).

Your positions and answers are quite good — javi2541997

Which positions? You think it's a good position to deny that a set with more than one member has more than one ordering?

There's plenty of detailed information and explanation posted in this thread.

If you have any questions, or wish to learn more, then it's as simple as asking. — TonesInDeepFreeze

I know. This long thread is very informative. I just didn’t want to ask because it is obvious that I don’t have the same high level of math and/or logic as you do, and my posts would interrupt the debate. But it is dreary to read such negative comments loaded with animosity. 

Questions are not interruptions. And no level is required to ask questions.

When someone lies about your posts and incessantly posts disinformation about the subject, then it is appropriate to comment on that and it is pertinent too to comment on the modus operandi behind it. After correcting a crank over and over and over, with the crank still continuing to post the disinformation and indeed adding even more, the more salient subject becomes not the topic but the deleterious effects of the crank. The point is to not normalize cranks. I see forums ruined by being inundated by cranks, not ruined by informed people posting back against cranks. Then, also, search engines include posts with disinformation from cranks near the top of search results on various subjects. And that is added to the disinformation and confused presentations about mathematics on Wikipedia. And that's along with the outrageous disinformation and confusion transmitted at the speed of light by AI answer bots. Thus the torrent of effluvia from which the Internet spirals down and down into a cesspool of disinformation.