he teacher insisted no, the numeral is not the number. So it took me very long to figure out that the numeral was not the "number" which the teacher was talking about, and that the number was just some fictitious thing existing in the teacher's mind — Metaphysician Undercover

I didn't need a teacher to make me aware that numerals are not numbers. '2' and 'two' refer to the same thing. But '2' is not 'two'. So whatever they refer to is something else, which is a number, which is an abstraction. Rather than be a benighted bloviating ignoramus (such as you), I could see that thought uses concepts and abstraction and our explanations, reasoning and knowledge are not limited to always merely pointing at physical objects.

Meanwhile, you're not even familiar with the distinction between semantics and syntax and the notion of model theoretic truth. — TonesInDeepFreeze

That's not true. I simply don't accept it as a realistic notion of "truth", and don't want to waste my time discussing it.

In any event, can you please respond to my point about chess? Surely if you learned to play chess, or any other artificial game -- monopoly, bridge, checkers, baseball -- you were willing to simply accept the rules as given, without objecting that they don't have proper referents in the real world or that they make unwarranted philosophical assumptions. If you could see math that way, even temporarily, for sake of discussion, you might learn a little about it. And then your criticisms would have more punch, because they'd be based on knowledge. I wonder if you can respond to this point. Why can't you just treat math like chess? Take it on its own terms and shelve your philosophical objections in favor of the pleasure of the game. — fishfry

I didn't answer, because it's not relevant. Philosophy is not a game in which you either accept the rules of play or you don't,, neither is theoretical physics such a game, nor is what you call "pure mathematics" (or as close to "pure" as is possible). In these fields we determine, and create rules which are deemed applicable. So your analogy is not relevant, because the issue here is not a matter of "will you follow the rules or not", it's a matter of making up the rules. And there's no point to arguing that people must follow rules in the act of making up rules because this is circular, and does not account for how rules come into existence in the first place.

It makes no sense to anyone else either. This is well known. Especially in terms of quantum fields being "probability waves." That makes no sense to me. Physics has perhaps lost its way. Many argue so. You and I might well be in agreement on this. — fishfry

Ok, we've found a point of agreement, physics has lost it's way. Do you ever think that there must be a reason for this? And, since physics is firmly based in mathematics, don't you see the implication, that perhaps the root of the problem is actually that mathematics has lost its way.

Ok. I get that. And I've asked you this many times. You don't want to play the game of math. So then why the energetic objection to it? After all if someone invites me to play Parcheesi and I prefer not to, I don't then go on an anti-Parcheesi crusade to convince the enthusiasts of the game that they are mis-allocating their time on a philosophically wrong pursuit. So there must be more to it than that. With respect to a perfectly harmless pastime like Parcheesi or modern math, one can be for, against, or indifferent. You have explained why you are indifferent; but NOT why you are so vehemently against. — fishfry

Physicists, engineers, and others, applying mathematics in the world have a huge impact on the world in which I live, unlike Parcheesi players. Despite arguments that mathematical objects exist in some realm of eternal truth where they are ineffectual, non-causal, I think it is undeniable, that the mathematical principles which are applied, have an impact on our world. I believe it is inevitable that bad mathematics will have a bad effect.

That people vehemently support and defend fundamental axioms which may or may not be true, refusing to analyze and understand the meaning of these axioms, simply accepting them on faith, and applying them in the conventional way, in new situations, with little or no understanding of the situation, or the axioms, to me is a clear indication that bad results are inevitable.

Makes no sense. It's perfectly clear that you can order a random assemblage of disordered points any way you like, and that no one order is to be preferred over any other. — fishfry

You do not seem to be making any effort to understand this fundamental principle, which is the key to understanding what I am arguing. A group of particles, or dots (we cannot really use "points" here because they are imaginary) existing in a spatial layout, have an order by that very fact that they are existing in a spatial arrangement. Yes, they can be "ordered any way you like", but not without changing the order that they already have. The order which they have is their actual order, whereas all those others are possible orders.

Do you understand and accept this? Or do you dispute it, and know some way to demonstrate how a spatial arrangement of dots or particles could exist without any order? It's one thing to move to imaginary points, and claim to have a specific number of imaginary points, in your mind, which have no spatial arrangement, but once you give them a spatial arrangement you give them order. Even if we just claim "a specific number of points", we need to validate that imaginary number of points without ordering them. This is what Tones and I discussed earlier. How can we count a specific number of points without assigning some sort of order to them? To count them we need to distinguish one from the other by some means or else we do not know which ones have been counted and which have not been counted. So even to have "a specific number of points", imaginary, in your mind, requires that they have an order, or else that specific number cannot be validated.

Well yes, the random number generator I used was actually determined at the moment of the big bang, if one believes in determinism. But you're making a point about randomness, not about the order of the points. You are not persuading me with your claim that a completely random collection of points has an inherent order. — fishfry

Yes, I'm making a point about "randomness" because you are using the term "random" to justify your claim that a bunch of dots in a spatial arrangement could have no order. You simply say, the points are "randomly distributed" and you think that just because you say "randomly", this means that there actually could be existing dots in a spatial assemblage, without any order. But your use of the term does not support your claim. There was a process which placed the dots where they are, therefore they were ordered by that process, regardless of whether you call that process "random" or not.

You don't want to read the Wiki piece on order theory. — fishfry

I looked at the Wikipedia entry, and it does not appear to cover the issue of whether existing things necessarily have an order or not. So it seems to provide nothing which bears on the point which I am trying to get you to understand.

Actually it doesn't make initial sense. Moving from one letter to the next is always a whole step, except from B to C and from E to F. And then double flats move you down a letter except from C to Cbb and from F to Fbb, and double sharps move you up a step except from B to B## and from E to E##. — TonesInDeepFreeze

All this, what you say, comes later, it's not "initial". What is "initial" is that you learn a specific fingering, and it sounds good, therefore it makes sense. The part that doesn't make sense is when you move deeper into the theory. This is just like mathematics. The initial practice makes sense, learning addition, multiplication, pi, Pythagorean theorem, etc.. All these simple procedures make perfect sense, you learn a procedure, apply it, and it works. However, then there is layers of theory piled on after the fact, and this is where the sense gets lost, because the theory doesn't necessarily follow what is actually the case.

You could see the quantity of objects but not the number of objects? — Luke

Right, I don't look at two chairs and see the number 2 there.

You must have already understood that the number is not the numeral in order to do simple arithmetic. Otherwise, the addition of any two numbers (i.e. numerals) would always equal 2 (numerals). — Luke

No, the numeral represents a quantity, and a quantity must consist of particulars, or individual things. So "2"" represents a quantity, or number of individuals, two, and "1" represents a quantity of one individual. What is added or multiplied is the quantity or number of individuals. The number is of the individual, a predication, and what is added or subtracted is the individuals, not the number. Have two individuals, add two more individuals, and you have four individuals. See, the operation is a manipulation of individuals, not a manipulation of some imaginary "numbers". And, the fact that we can make the individuals imaginary, such that the manipulation of individuals involves imaginary individuals, does not change the reality that the individuals are what is manipulated, not the numbers.

I didn't need a teacher to make me aware that numerals are not numbers. '2' and 'two' refer to the same thing. But '2' is not 'two'. So whatever they refer to is something else, which is a number, which is an abstraction. Rather than be a benighted bloviating ignoramus (such as you), I could see that thought uses concepts and abstraction and our explanations, reasoning and knowledge are not limited to always merely pointing at physical objects. — TonesInDeepFreeze

When I was seven years old I had no idea what an abstraction is, or what a concept is. I didn't understand this until much later when I studied philosophy. This is why mathematics really is like religion. We are required just to accept the rules, on faith, follow and obey, without any real understanding. 'There really is a number two there, accept and obey'. 'There really is a God there, accept and obey'.

Right, I don't look at two chairs and see the number 2 there. — Metaphysician Undercover

Right, so numbers are not objects?

No, the numeral represents a quantity, and a quantity must consist of particulars, or individual things. So "2"" represents a quantity, or number of individuals, two, and "1" represents a quantity of one individual. What is added or multiplied is the quantity or number of individuals. The number is of the individual, a predication, and what is added or subtracted is the individuals, not the number. — Metaphysician Undercover

You said your teacher insisted that "the numeral is not the number" and that you couldn't understand it. But you also said that you had no problem with basic arithmetic. My point was that you must have understood that "the numeral is not the number" in order to do basic arithmetic.

In order to do basic arithmetic you must have already understood what you say here - that ""2" represents a quantity, or number of individuals"; or that "2" represents something other than the symbol itself. What I don't understand is why you had a problem with the distinction between numeral and number if you already understood basic arithmetic.

Have two individuals, add two more individuals, and you have four individuals. See, the operation is a manipulation of individuals, not a manipulation of some imaginary "numbers". — Metaphysician Undercover

"Two" and "four" do not refer to numbers? How many is an "individual"?

You want to say that an individual is 1, and add another one to get 2. Therefore, the objects are themselves numbers, or numbers are their objects, right? But "1" or "2" are the number of individuals, not the individuals. You want to pretend that you don't need the abstract concept of number, but you are still using it. Also, you are still vacillating between numbers being objects and numbers not being objects.

What is added or multiplied is the quantity or number of individuals. The number is of the individual, a predication, and what is added or subtracted is the individuals, not the number. — Metaphysician Undercover

That's just a plain contradiction from one sentence to the next.

I simply don't accept it as a realistic notion of "truth", and don't want to waste my time discussing it. — Metaphysician Undercover

Dollars to donuts that, without copy/paste from Wikipedia, you could not in your own words state the distinction bewteen syntax and semantics and the notion of truth in a model.

Physicists, engineers, and others, applying mathematics in the world have a huge impact on the world in which I live [...] bad mathematics will have a bad effect. — Metaphysician Undercover

The computer you're typing on and the science and technology that makes your world better are enabled by mathematics. What is an example of a bad effect from mathematics?

That people vehemently support and defend fundamental axioms which may or may not be true, refusing to analyze and understand the meaning of these axioms, simply accepting them on faith — Metaphysician Undercover

But in the philosophy of mathematics, which includes many mathematicians themselves, people do investigate, question, and debate the axioms - giving reasoned arguments for and against axioms. It's just that you are ignorant of that.

The order which they have is their actual order, whereas all those others are possible orders. — Metaphysician Undercover

That is one of the best, most risible, evasions of a challenge I've ever read. What is "the order they actually have" as opposed to all the others? Saying that they have the order they "actually" have is not telling us what you contend to be the order nor how other orderings are not the "actual" ordering. You are so transparently evading and obfuscating here.

When confronted with the challenge of points in a plane, a reasonable response by you would be "Let me think about that." But instead you reflexively resort to the first specious and evasive reply that comes to you and post it twice with supposed serious intent. That indicates once again your lack of intellectual curiosity, honesty or credibility.

the term "random" — Metaphysician Undercover

'random' in this context need not have anything other than an informal sense. One could just as well say 'unstated'. You're harping on the word 'random' to evade the heart of the argument against you.

You were presented with points in a plane, without being given a stated particular ordering. You were asked to say what is the "inherent order". You reply by saying, essentially, that their order is the postions they have. But that is not ordering. Ordering, such as a linear order, is a relation in which each object is determined to be before or after another object. And not necessarily temorally or physically. And you can't say what is the "inherent order" even temporally or physically! You fail.

I looked at the Wikipedia entry — Metaphysician Undercover

And you comprehended nothing from it.

The part that doesn't make sense is when you move deeper into the theory. This is just like mathematics. — Metaphysician Undercover

I want to understand: Are you saying that music theory is wrong just as you say mathematics is wrong? And, by the way, do you know any music theory?

When I was seven years old I had no idea what an abstraction is, or what a concept is. I didn't understand this until much later when I studied philosophy. — Metaphysician Undercover

When I was seven I didn't know about abstraction, but I used abstraction. Later, I didn't have to wait until studying philosophy to know about abstraction. You seem to have a condition that prevents you from grasping the notion of abstraction and therefore to revile it.

This is why mathematics really is like religion. We are required just to accept the rules, on faith, follow and obey, without any real understanding. — Metaphysician Undercover

That is false. It's the opposite. That describes the grade school memorization and regurgitation of tables and rules for basic addition, subtraction, multiplication, and division that you find so suitable. Mathematics though provides understanding of the bases for those rules.

Meanwhile, your own presentation is not by reason but from your own very personal and subjective misundertstandings and dogma. And your use of even common language terms is wildly personal and impossible to negotiate with common meanings. You insist on confused, incoherent, illogical, and self-contradictiory concepts, meanings, and flat out unsupported assertions, expecting that others should accept them while you are ignorant of even the basics of the subject as it has been developed and offered to open scrutiny in a rich peer-reviewed literature.

/

And aside from you specious (essentially vacuous) argument about the points in plane, here are some of the other points still unanswered by you (and these are just the most recent):

What else could demonstrate falsity other than a reference to some form of inconsistency?.
— Metaphysician Undercover

Falsity is semantic; inconsistency is syntactical.

Given a model M of a theory T, a sentence may be false in M but not inconsistent with T. — TonesInDeepFreeze

An axiom is expressed as a bunch of symbols, so it must be interpreted.
— Metaphysician Undercover

Formulas don't have to be interpreted, though usually they are when they are substantively motivated. — TonesInDeepFreeze

If in interpretation, there is a contradiction with another principle then one or both must be false.
— Metaphysician Undercover

It might not be a matter of principles but of framework. Frameworks don't have to be evaluated as true or false, but may be regarded by their uselfulness in providing a conceptual context or their productivity in other ways. — TonesInDeepFreeze

Notice there is an exchange of "equal" and "same"
— Metaphysician Undercover

Even though there is nothing wrong with taking 'equal' to mean 'same', the axiom of extensionality doesn't require such mention.

Az(zex <-> zey) -> x=y.

"=' is mentioned, but not "same". — TonesInDeepFreeze

energy is finite in quantity but infinite in quality as it is the action of change, of transformation. Nothing is infinite in a specific moment, only when given time.

What is added or multiplied is the quantity or number of individuals. The number is of the individual, a predication, and what is added or subtracted is the individuals, not the number.
— Metaphysician Undercover

That's just a plain contradiction from one sentence to the next. — Luke

That's a beauty.

P.S.

The order which they have is their actual order — Metaphysician Undercover

It's ironic that if you knew any mathematics, you could have given an answer:

<b c> is before <d f> if and only if (b < d or (b = d and c < f)).

That is a linear ordering.

(But it can be called the 'standard ordering' only by convention. It is no more "inherent" than any other ordering.)

I have a hunch about cranks in logic and mathematics. It's not something I can prove, but it seems to me to be a plausible narrative:

The crank is not necessarily unintelligent. He (it seems that virtually all cranks have male names if their username does suggest gender) may be adept at peforming complicated mathematical operations, computer programming, applied mathematics, engineering and physics. Some cranks got good grades in high school math and even into college. This was a point of pride for the crank. But when the crank was confronted by more abstraction, there was a breakdown. He cannot understand such things as the empty set, material implication (with the FT and FF truth table rows mapping to T), infinite sets, diagonalization, uncountability, incompleteness, and the unsolvability of the halting problem. So when the crank sees other people understanding what he cannot understand, to avoid feeling inadquate, he lashes out with sour grapes that logic and math are all a bunch of nonsense. And the more you try to help him with information and explanation, the more entrenched he becomes in his own world of "they're all wrong; I'll show them who is right!" Then, for him, not only are logicians and mathematicians wrong, but they are knaves and scoundrels (one crank on another forum didn't just want to defund and abolish univerersity mathematics, but he (seriously) advocated mass executions). Internet discussion forums are where the crank lives out his pathetic agenda, and once he claims his perch, he will howl from it forever.

without any order — Metaphysician Undercover

You are obfuscating by sliding between adressing "order" and "actual order" (or "inherent order"). That's typical of your intellectual sloppiness.

It is not the case that there are not orderings. The point though is that there is not a single ordering that is "THE actual ordering". There are many orderings and they are actual even though 'actual' is gratuitious.

This is what Tones and I discussed earlier. How can we count a specific number of points without assigning some sort of order to them? To count them we need to distinguish one from the other by some means or else we do not know which ones have been counted and which have not been counted. — Metaphysician Undercover

You are mentioning me yet again, without quotation or context. This is about the fifth time you've done it.

I never claimed that we can count things that are not distinguishable.

There was a process which placed the dots where they are, therefore they were ordered by that process — Metaphysician Undercover

First, of course, is that we may take a collection of dots as given, without stipulating that a particular person placed the dots herself.

Second, let's even suppose that "actual order" is a function of a person placing the dots. Say that Joe places the dots in temporal succession and Val places the dots in a different temporal succession. But that both collection of dots look exactly the same to us. So there's "Joes actual (temporal) order" and "Val's actual (temporal) order", but no one can say which is THE actual order of the collection of dots we are looking at without Joe and Val there to tell us (if they even remember) the different order of placement they used.

This is the magical ideation of crank mathematics. That for all the possible formulas, statements, objects, and states-of-affairs, there are actual people running around creating each of them individually. It's so ludicrous that even a child would know it makes no sense; and it surely does not "correspond to reality".

You said your teacher insisted that "the numeral is not the number" and that you couldn't understand it. But you also said that you had no problem with basic arithmetic. My point was that you must have understood that "the numeral is not the number" in order to do basic arithmetic. — Luke

No, as I explained. The numeral 2 represents how many objects there are. We could also call that symbol the number 2, which represents how many objects there are. There is no need to assume that the number 2 is distinct from the symbol, to do basic arithmetic..

But "1" or "2" are the number of individuals, not the individuals. — Luke

If that were the case, I'd be fine with it, but it's not what I was told. I was told that "1" and "2" are numerals, symbols, and there is also something else, called the numbers 1 and 2. The numbers are distinct from the numerals, as what is represented by the numerals. So, I was told that "1" and "2" are symbols, which represent the numbers 1 and 2, and the number represent how many individuals there are. Why not just say that the symbols "'1" and "2" represent how many individuals there are, directly?

That is one of the best, most risible, evasions of a challenge I've ever read. What is "the order they actually have" as opposed to all the others? Saying that they have the order they "actually" have is not telling us what you contend to be the order nor how other orderings are not the "actual" ordering. You are so transparently evading and obfuscating here. — TonesInDeepFreeze

Fishfry posted the order, it's right here:

What more do you want?

When confronted with the challenge of points in a plane, a reasonable response by you would be "Let me think about that." But instead you reflexively resort to the first specious and evasive reply that comes to you and post it twice with supposed serious intent. That indicates once again your lack of intellectual curiosity, honesty or credibility. — TonesInDeepFreeze

Look, if the dots exist on a plane, they have positions on that plane, and therefore an exact order which is specific to that particular positioning. They do not have any other order, or else they would not be those same dots on that plane. Take a look at that posting of fishfry's and see the order which the dots have, on that plane, and tell me how they could have a different order, or no order at all, and still be those same dots on that same plane.

If you cannot apprehend this simple fact, then tell me what is so difficult for you.

You were presented with points in a plane, without being given a stated particular ordering. — TonesInDeepFreeze

How can you not see that 'points in a plane without a particular ordering' is a blatant contradiction? If the points exist on a plane, then they each have a particular position on that plane, as demonstrated in fishfry's post, and it is impossible that they have no particular order, because the particular order has been posted. Can you grasp this fact?

One could just as well say 'unstated'. — TonesInDeepFreeze

The problem is, that it is stated. It is stated that they exist on a plane. Therefore each point has a position on that plane unique to itself. Not one of these points makes a line, nor occupies a section of the plane, they each have a specific position. Therefore there is necessarily an order to these points, their positions on that plane, according to what is stated. To give them no order you'd have to remove them from their positions on the plane.

Suppose we just assume a multitude of points, without any spatial reference, no dimensions or anything, just points. Then we have the question of what distinguishes one point from another. It is stipulated that there is a multitude of points. If there is no spatial reference, therefore no space separating one point from another, what makes them distinct from one another? How can we assume a multitude of points when we posit no principle whereby one point is distinguished from another point? And if we posit a principle of separation other than space, (suppose one is later in time than another, or something like that), then isn't this a principle of order. it is impossible to posit a multitude of points without implying order.

It isn't I who is evading the issue. All those people who simply assume that it is possible for a multitude of points to exist without any order, are the one's evading the issue, because such a scenario is logically impossible.

It is not the case that there are not orderings. The point though is that there is not a single ordering that is "THE actual ordering". There are many orderings and they are actual even though 'actual' is gratuitious. — TonesInDeepFreeze

Again, look at fishfry's post:
Do you not see that there is an actual order to those dots on the plane? How could there be "many orderings" if to give them a different order would be to change their positions? Then it would no longer be those dots on that plane. And if your intent is to abstract them, remove them from that plane, then they are no longer those dots on that plane. Why is something so simple so difficult for you to understand?

First, of course, is that we may take a collection of dots as given, without stipulating that a particular person placed the dots herself. — TonesInDeepFreeze

OK, but do you agree that something must have caused those dots to be where they are, i.e. given them that order?

Second, let's even suppose that "actual order" is a function of a person placing the dots. Say that Joe places the dots in temporal succession and Val places the dots in a different temporal succession. But that both collection of dots look exactly the same to us. So there's "Joes actual (temporal) order" and "Val's actual (temporal) order", but no one can say which is THE actual order of the collection of dots we are looking at without Joe and Val there to tell us (if they even remember) the different order of placement they used. — TonesInDeepFreeze

I am talking about their spatial ordering, their positioning on the plane, like what is described by a Cartesian system. Do you not apprehend spatial arrangements as order?

First thing I really want to know what are the bad things that you think mathematicians and scientists are going to cause to happen? What bad things do you think are going to happen if mathematicians contnue to regard numerals and numbers as not the same, as mathematicians have for a very long time? Why haven't these bad things already happened? What do you think are the bad things that are going to happen if mathematicians continue to recognize that sets have many different orderings that there is no "THE actual ordering"?

There is no need to assume that the number 2 is distinct from the symbol, to do basic arithmetic.. — Metaphysician Undercover

Suppose the number 2 is not distinct from the numeral '2'. Suppose also that the number 2 is not distinct from the Hebrew numeral for 2. Then both the numeral '2' and the Hebrew numeral for 2 are the same. But they are not.

The numerals are not the numbers. If they were, then anybody who used different numerals would be naming different numbers. But they're not. Everybody is naming the same number 2 whether they use the numeral '2' or the Hebrew numeral of the Roman numeral or the word 'two' or any of many other names for the number 2. A child can understand that.

Why not just say that the symbols "'1" and "2" represent how many individuals there are, directly? — Metaphysician Undercover

We can, and we do. But also we wish to mention in particular that the number of individuals is 1 or 2 as may be the case.

Fishfry posted the order, it's right here:
↪fishfry — Metaphysician Undercover

You are totally confused. That's a picture of dots in a disk. It's not an ordering.

What more do you want? — Metaphysician Undercover

For you to state what you claim to be the "actual ordering of the dots" - as I asked about five times already. And to give reason why that is the "actual ordering" as opposed to other orderings. That means for you to state which dots come before other dots, for each dot. And then say why that ordering you chose is "actual" while other orderings we can choose are "not actual".

How can you not see that 'points in a plane without a particular ordering' is a blatant contradiction? — Metaphysician Undercover

A contradiction is a statement and its negation.

One things virtually all cranks have in common is claiming to point out a contradiction when all they're doing is pointing out something that they happen to disagree with. There should be a name for that fallacy.

Anyway, you cannot see that there are many orderings of that finite set of points, but no one of those many ordefings is "THE actual ordering". They ALL are actual orderings. And "actual" is gratuitious anyway.

One more time: There are many different orderings. But not one of them is privileged as being more "actual" or "inherent" than the others. Do really still not understand that?

The rest of your post is just different ways of you repeating your misunderstanding sourced in your not knowing what an ordering is.

Again, you use the word 'ordering' or 'order' in a way that is neither their use in mathematics nor even in everday speech. You assert an entirely personal notion and usage. And your own usage is not even coherent onto itself nor consistently applied by you. Yet you expect everyone else to come around to adopt your personal usage and then also to revise their clear and common notions about basic mathematics to conform to your ignorant, uneducated, and incoherent concept of mathematics. Classic crank to the core.

Reminding again, more of the recent points you have failed on:

What else could demonstrate falsity other than a reference to some form of inconsistency?.
— Metaphysician Undercover

Falsity is semantic; inconsistency is syntactical.

Given a model M of a theory T, a sentence may be false in M but not inconsistent with T.
— TonesInDeepFreeze — TonesInDeepFreeze

An axiom is expressed as a bunch of symbols, so it must be interpreted.
— Metaphysician Undercover

Formulas don't have to be interpreted, though usually they are when they are substantively motivated.
— TonesInDeepFreeze — TonesInDeepFreeze

If in interpretation, there is a contradiction with another principle then one or both must be false.
— Metaphysician Undercover

It might not be a matter of principles but of framework. Frameworks don't have to be evaluated as true or false, but may be regarded by their uselfulness in providing a conceptual context or their productivity in other ways.
— TonesInDeepFreeze — TonesInDeepFreeze

Notice there is an exchange of "equal" and "same"
— Metaphysician Undercover

Even though there is nothing wrong with taking 'equal' to mean 'same', the axiom of extensionality doesn't require such mention.

Az(zex <-> zey) -> x=y.

"=' is mentioned, but not "same".
— TonesInDeepFreeze — TonesInDeepFreeze

/

And new ones:

What is added or multiplied is the quantity or number of individuals. The number is of the individual, a predication, and what is added or subtracted is the individuals, not the number.
— Metaphysician Undercover

That's just a plain contradiction from one sentence to the next. — Luke

That people vehemently support and defend fundamental axioms which may or may not be true, refusing to analyze and understand the meaning of these axioms, simply accepting them on faith
— Metaphysician Undercover

But in the philosophy of mathematics, which includes many mathematicians themselves, people do investigate, question, and debate the axioms - giving reasoned arguments for and against axioms. It's just that you are ignorant of that. — TonesInDeepFreeze

The part that doesn't make sense is when you move deeper into the theory. This is just like mathematics.
— Metaphysician Undercover

I want to understand: Are you saying that music theory is wrong just as you say mathematics is wrong? And, by the way, do you know any music theory? — TonesInDeepFreeze

This is why mathematics really is like religion. We are required just to accept the rules, on faith, follow and obey, without any real understanding.
— Metaphysician Undercover

That is false. It's the opposite. That describes the grade school memorization and regurgitation of tables and rules for basic addition, subtraction, multiplication, and division that you find so suitable. Mathematics though provides understanding of the bases for those rules. — TonesInDeepFreeze

without any order
— Metaphysician Undercover

You are obfuscating by sliding between adressing "order" and "actual order" (or "inherent order"). That's typical of your intellectual sloppiness.

It is not the case that there are not orderings. The point though is that there is not a single ordering that is "THE actual ordering". There are many orderings and they are actual even though 'actual' is gratuitious. — TonesInDeepFreeze

/

Also, you continue to mention me sometimes without quote or context, placing me in certain roles in the dialectic that I have not taken.

The numeral 2 represents how many objects there are. We could also call that symbol the number 2, which represents how many objects there are. — Metaphysician Undercover

The numeral/symbol represents the number, or “how many”. The symbol is not the number, it is the numeral.

Similarly, the word “tree” represents a tree but the word/symbol is not a tree. The symbol is not the tree, it is the word.

Why not just say that the symbols "'1" and "2" represent how many individuals there are, directly? — Metaphysician Undercover

The symbols do represent how many individuals there are. What do you mean by “directly”?

Do you recognize that the word 'tree' is not a tree?

That the word 'Chicago' is not the city of Chicago?

That the word 'courageousness' is not the atrribute courageousness?

That the word 'Ahab' is not a fictional character?

That the word 'liberty' is not liberty itself nor the concept of liberty?

Yes?

But you fail to recognize that the word 'two' or the symbol '2' are not the number 2.

So, I was told that "1" and "2" are symbols, which represent the numbers 1 and 2, and the number represent how many individuals there are. — Metaphysician Undercover

I overlooked this.

The number does not represent how many individuals there are.

The number is how many individuals there are.

First thing I really want to know what are the bad things that you think mathematicians and scientists are going to cause to happen? — TonesInDeepFreeze

Come on TIDF, don't you see that as a ridiculous question? If one could predict the bad things that were going to happen, before they happened, then we could take the necessary measures to ensure that they don't happen. It's like asking me what accident are you going to have today. It's a matter of risk management. If the mathematics employed in any given situation is faulty, the risk is increased. The biggest problem, I think, is the complete denial of the faults, from people like you. This creates a false sense of certainty. That's why it's like religion, you completely submit to the power of the mathematics, with your faith, believing that your omnibenevolent "God", the mathematics would never mislead you.

Suppose the number 2 is not distinct from the numeral '2'. Suppose also that the number 2 is not distinct from the Hebrew numeral for 2. Then both the numeral '2' and the Hebrew numeral for 2 are the same. But they are not. — TonesInDeepFreeze

The symbols are not the same, nor ought they be said to be the same, or to say the same thing. They ought not be said to say the same thing, because different cultures have different ways of looking at the world. Where's the problem with that? If someone translates a passage of philosophy from ancient Greece, we ought not say that the translation says the same thing as the original. Something is always lost in translation. Likewise, we ought not say that the numeral 2 says the same thing as the Hebrew symbol. This would be very clear to you if you would consider all the different numbering systems discussed on this forum, natural, rational, real, cardinals, ordinals, etc.. The same symbol has a different meaning depending on the system. If we do not keep these distinguished, and adhere to the rules of the specific system, we have equivocation.

That's a picture of dots in a disk. It's not an ordering. — TonesInDeepFreeze

If you refuse to acknowledge that there's an order to those dots, then I don't see any point in proceeding with this discussion.

. That means for you to state which dots come before other dots, for each dot. — TonesInDeepFreeze

Order is not necessarily temporal. And, modern physics looks at time as the fourth dimension of space. So if you cannot see order in an arrangement on a two dimensional plane, I don't see any point in discussing "order" with you.

The symbols do represent how many individuals there are. What do you mean by “directly”? — Luke

If you follow what is taught in math, the symbol "2" represents a mathematical object which is called a number. The number represents how many individuals there are.

Do you recognize that the word 'tree' is not a tree? — TonesInDeepFreeze

Of course, the word "tree" might be used as a symbol, to represent a tree.

But you fail to recognize that the word 'two' or the symbol '2' are not the number 2. — TonesInDeepFreeze

You misunderstand. What I am asking is why can't the symbol "2" be used to represent a quantity of two individuals, just like the word "tree" is used to represent a tree? Why must the symbol "2" represent a mathematical object, the number two, and the number two represents a quantity of two individuals? We don't say that the word "tree" represents a conceptual object, tree, and this concept represents the individual tree.

In reality we simply use the word "tree" to represent a tree, and we use the symbol "2" to represent a quantity of two individuals. There is no conceptual object, or mathematical object in between. So if someone states as a premise, that "2" represents a mathematical object, the number two, this would be a false premise.

The number does not represent how many individuals there are.

The number is how many individuals there are. — Luke

Well no, this is not true. The number is how many individuals it is said that there are. The number is supposed to be what the numeral stands for. It is conceptual, and a representation of a particular quantity of individuals. Being universal, we cannot say that it is actually a feature of the individuals involved, but a feature of our description, therefore a representation. That's why the OED defines "number" as "an arithmetical value representing a particular quantity and used in counting and making calculations." If the number is not a representation of how many individuals there are, but actually "how many individuals there are", there would be no possibility of error, or falsity. If I said "there are 2 chairs", and the supposed mathematical object, the number 2 which is said to be signified by the numeral "2" was "how many individuals there are", rather than how many there are said to be, how could I possibly lie?

And, modern physics looks at time as the fourth dimension of space — Metaphysician Undercover

A bit of vaudeville relief :lol:

We don't say that the word "tree" represents a conceptual object, tree, and this concept represents the individual tree. — Metaphysician Undercover

We don't? To which particular object does the word "tree" refer, then?

The number is how many individuals there are.
— Luke

Well no, this is not true. The number is how many individuals it is said that there are. The number is supposed to be what the numeral stands for. It is conceptual, and a representation of a particular quantity of individuals. Being universal, we cannot say that it is actually a feature of the individuals involved, but a feature of our description, therefore a representation. — Metaphysician Undercover

We seem to have been using "individuals" differently. I was trying to explain to you the concept/meaning of number, and I was considering "individuals" as abstract units, e.g. the (number of) individuals/units represented by the numeral "2". You seem to be using "individuals" to refer to individual objects, or in the application of numbers to particular objects.

Regardless, haven't you answered your own question:

What I am asking is why can't the symbol "2" be used to represent a quantity of two individuals, just like the word "tree" is used to represent a tree? Why must the symbol "2" represent a mathematical object, the number two, and the number two represents a quantity of two individuals? — Metaphysician Undercover

You've been asking why a number must represent objects, yet here you are telling me why a number must represent objects.

If the number is not a representation of how many individuals there are, but actually "how many individuals there are", there would be no possibility of error, or falsity. If I said "there are 2 chairs", and the supposed mathematical object, the number 2 which is said to be signified by the numeral "2" was "how many individuals there are", rather than how many there are said to be, how could I possibly lie? — Metaphysician Undercover

Your concern is that if you say that there are 2 chairs, even if there are not 2 chairs, then the world will somehow magically become whatever you say? And, therefore, you will be unable to lie or make any errors because whatever you say will always become true? Oh no. Luckily, that's not how language or the world works.

I didn't answer, because it's not relevant. Philosophy is not a game in which you either accept the rules of play or you don't,, neither is theoretical physics such a game, nor is what you call "pure mathematics" (or as close to "pure" as is possible). In these fields we determine, and create rules which are deemed applicable. So your analogy is not relevant, because the issue here is not a matter of "will you follow the rules or not", it's a matter of making up the rules. And there's no point to arguing that people must follow rules in the act of making up rules because this is circular, and does not account for how rules come into existence in the first place. — Metaphysician Undercover

This was in reference to my question, Why don't you treat math like chess, and accept it on its own terms? And I see no answer here. Math is a game that has standard rules, and many varieties of nonstandard rules. The essence of creativity in math is to make up new rules. That's the history of math, the creation of new rules that violated the old. Because you won't put aside your naive objections long enough to understand math, your objections have no force, because they come across as petulant rather than informed. As far as how the rules came into being in the first place, there is a huge, extensive literature on the subject from Frege and Russell and Zermelo through the modern philosophers of math. A history you have no interest in, because you prefer to remain ignorant. The problem is that you can't make a good case, because your ignorance of the subject shines through above all.

Ok, we've found a point of agreement, physics has lost it's way. Do you ever think that there must be a reason for this? — Metaphysician Undercover

Yes, primarily two. One, we have reached the point where experiments are so expensive as to command a large share of the public treasury. Bill Clinton came into office in 1993 and killed the Superconducting Supercollider. a project that would have reached far higher energies than the Large Hadron collider at CERN. And the next generation of particle accelerators is estimated to come in at over $20B. The expenditures have become a matter of politics, and there are always more worthy and immediate causes to be funded.

Secondly, just as there were a couple of thousand years between Aristotle and Newton, and 250 or so years between Newton and Einstein, it may well be that physics needs to tread water for another couple of centuries before the next breakthrough. We can't hope to have a major revolution every year or even every century.

And, since physics is firmly based in mathematics, don't you see the implication, that perhaps the root of the problem is actually that mathematics has lost its way. — Metaphysician Undercover

Not in the least. Math stands on its own. Just as math invented non-Euclidean geometry 70 years before Einstein had any use for it, math today as always is full of meaningless and useless curiosities that may or may not find practical application in the future. Math stands on its own and needs no applicability or practicality to justify itself. This is your fundamental conceptual error. It's not the fault of math that physics is lost. That's the physicists' problem. The mathematicians are doing just fine; and for that matter, are in the midst of a great period of revolutionary turmoil and development in its foundations, to wit category theory, homotopy type theory, computerized proof assistants, and neo-intuitionism. Developments far ahead of anything the physicists care about or even know about.

Physicists, engineers, and others, applying mathematics in the world have a huge impact on the world in which I live, unlike Parcheesi players. — Metaphysician Undercover

Then your complaint is with the physicists, engineers, and others; and not the mathematicians, who frankly are harmless. This is your core error. You have no idea what math is about, so you think it's engineering.

Despite arguments that mathematical objects exist in some realm of eternal truth where they are ineffectual, non-causal, I think it is undeniable, that the mathematical principles which are applied, have an impact on our world. I believe it is inevitable that bad mathematics will have a bad effect. — Metaphysician Undercover

Again, your complaint is with those mis-applying math or applying math to bad ends. The mathematicians themselves do work that is so far out there that the only reason you think it has any applicability to the real world is that you have no idea what modern math is or does. If you're upset with applications of math, then your complaint is with those applying it. The math exists on its own, and must be understood and comprehended on its own terms. If you can't do that, your ire is greatly misdirected.

That people vehemently support and defend fundamental axioms which may or may not be true, refusing to analyze and understand the meaning of these axioms, simply accepting them on faith, and applying them in the conventional way, in new situations, with little or no understanding of the situation, or the axioms, to me is a clear indication that bad results are inevitable. — Metaphysician Undercover

Again, your ignorance betrays you and makes talking to you tedious. There's been 170 years of intensive research into mathematical foundations, starting with the revolution of non-Euclidean geometry. I could point you to Zermelo, or Mac Lane, or Maddy, but what good would it do? You'd rather be ignorant than learn anything. You say that people have accepted the axioms on faith "with little or no understanding," which betrays an ignorance that would deeply embarrass you, if you had any self-awareness of your mathematical and philosophical ignorance.

You do not seem to be making any effort to understand this fundamental principle, which is the key to understanding what I am arguing. A group of particles, or dots (we cannot really use "points" here because they are imaginary) existing in a spatial layout, have an order by that very fact that they are existing in a spatial arrangement. — Metaphysician Undercover

Particles? Dots? What are those? In math, the elements of sets are other sets. There are no particles or dots. Again, you confuse math with physics.

Yes, they can be "ordered any way you like", but not without changing the order that they already have. The order which they have is their actual order, whereas all those others are possible orders. — Metaphysician Undercover

The very conception of a mathematical set does not include any inherent order. You're just making that up and I'm supposed to sit here several times a week and argue with you about it. It's pointless and tedious. Why don't you learn something about sets instead of showing off your ignorance?

Do you understand and accept this? — Metaphysician Undercover

Your delusions about mathematics? Of course not.

Or do you dispute it, and know some way to demonstrate how a spatial arrangement of dots or particles could exist without any order? — Metaphysician Undercover

I have no idea what you could possibly mean by dots or particles. A set is defined by the axioms of set theory. The axiom of extensionality says that a set is entirely characterized by its elements. Period. That's all anyone needs to know about sets, but you prefer to live in your own fantasy world of dots and particles. You're making it up.

It's one thing to move to imaginary points, and claim to have a specific number of imaginary points, in your mind, which have no spatial arrangement, but once you give them a spatial arrangement you give them order. — Metaphysician Undercover

There is no spatial arrangement. You're just throwing an ignorant tantrum about things you refuse to learn.

Even if we just claim "a specific number of points", we need to validate that imaginary number of points without ordering them. — Metaphysician Undercover

Validate the imaginary number of points? What does that mean? I have no idea.

This is what Tones and I discussed earlier. — Metaphysician Undercover

I'm not reading much of this thread, only my mentions.

How can we count a specific number of points without assigning some sort of order to them? — Metaphysician Undercover

I can't argue with the fantasies in your head. Set theory is what it is.

To count them we need to distinguish one from the other by some means or else we do not know which ones have been counted and which have not been counted. So even to have "a specific number of points", imaginary, in your mind, requires that they have an order, or else that specific number cannot be validated. — Metaphysician Undercover

Counting is a much more sophisticated operation than merely positing the existence of a set. To count, we must have the cardinal or ordinal numbers. To have the cardinal or ordinal numbers, we must conceptually build them up from the basic concept of set, which is as I've tried to describe to you.

Yes, I'm making a point about "randomness" because you are using the term "random" to justify your claim that a bunch of dots in a spatial arrangement could have no order. — "Metaphysician

There are no dots. I don't know what dots are. I tried to give you a visual example but perhaps that was yet another rhetorical error. I should just refer you to the axiom of extensionality and be done with it, because in truth that is all there is to the matter.

You simply say, the points are "randomly distributed" and you think that just because you say "randomly", this means that there actually could be existing dots in a spatial assemblage, without any order. But your use of the term does not support your claim. There was a process which placed the dots where they are, therefore they were ordered by that process, regardless of whether you call that process "random" or not. — Metaphysician Undercover

Forget the visual analogy. Now you're just arguing with the analogy and not with the concept of set. A set is entirely determined by its elements. That's rule one of the game. Take it or leave it. I don't care.

I looked at the Wikipedia entry, — Metaphysician Undercover

You surely did not engage with it.

and it does not appear to cover the issue of whether existing things necessarily have an order or not. So it seems to provide nothing which bears on the point which I am trying to get you to understand. — Metaphysician Undercover

https://en.wikipedia.org/wiki/Axiom_of_extensionality

A contradiction is a statement and its negation. — TonesInDeepFreeze

Contradiction may be implied. Here's Wikipedia's opening statement:
'In traditional logic, a contradiction consists of a logical incompatibility or incongruity between two or more propositions."

The problem is that you refuse to recognize that an arrangement of points on a plane, logically implies order, therefore "an arrangement of points on a plane without order" is contradictory.

This was in reference to my question, Why don't you treat math like chess, and accept it on its own terms? — fishfry

Don't you see that I said math is not like chess. Therefore I do not treat math like chess. I answered your question.

Then your complaint is with the physicists, engineers, and others; and not the mathematicians, who frankly are harmless. — fishfry

Obviously not, as you've already noticed,

Again, your complaint is with those mis-applying math or applying math to bad ends. — fishfry

No, my complaint is with the fundamental principles of mathematicians, As explained already to you, violation of the law of identity, contradiction, and falsity. You, and Tones alike (please excuse me Tones, but I love to mention you, and see your response. Still counting?), are simply in denial of these logical fallacies existing in the fundamental principles of mathematics, and you say truth and falsity is irrelevant to the pure mathematicians.

Particles? Dots? What are those? In math, the elements of sets are other sets. There are no particles or dots. Again, you confuse math with physics. — fishfry

In case you forgot, you posted a diagram with dots, intended to represent a plane with an arrangement of points without any order. This is what I argued is contradictory, "an arrangement... without order". And this was representative of our disagreement about the ordering of sets. You insisted that it is possible to have a set in which the elements have no order. You implied that there was some special, magical act of "collection" by which the elements could be collected together, and exist without any order. What you are in denial of, is that if the elements exist, in any way, shape, or form, then they necessarily have order, because that's what existence is, to be endowed with some type of order.

You tell me, just imagine a plane, with points on the plane, without any order, and I tell you I can't imagine such a thing because it's clearly contradictory. If the points are on the plane, then they have order. And you just want to pretend that it has been imagined and proceed into your smoke and mirrors tricks of the mathemajicians. I'm sorry, but I refuse to follow such sophistry.

I can't argue with the fantasies in your head. Set theory is what it is. — fishfry

Why not give it a try? I can argue with the fantasies in your head, demonstrating that they are contradictory. So please explain to me how you think you can have a collection of elements, points, or anything, and that collection has no order. Take this fantasy out of your head and demonstrate the reality of it.

There are no dots. I don't know what dots are. I tried to give you a visual example but perhaps that was yet another rhetorical error. I should just refer you to the axiom of extensionality and be done with it, because in truth that is all there is to the matter. — fishfry

The dots. I believe, were supposed to be a representation of points on a plane. The points on a plane, I believe, were supposed to be a representation of elements in a set. And you were using these representations in an attempt to show me that there is no inherent order within a set. So, are you ready to give it another try? Demonstrate to me how there could be a set with elements, and no order to these elements.

I've explained to you the problem. You describe the set as a sort of unity. And you want to say that the parts which compose this unity have no inherent order. Do you recognize that to be a unity, the parts must be ordered? There is no unity in disordered parts. Or are you going to continue with your denial and refusal to recognize the fundamental flaws of set theory?

Demonstrate to me how there could be a set with elements, and no order to these elements. — Metaphysician Undercover

Hopefully others will correct me if I'm wrong but, as I understand it, the point iof the diagram of "dots" is that the elements of the set have no inherent numerical order or sequence. Otherwise, you should be able to number the elements from 1 to n and explain why that is their inherent order.

We still have this list of corrections, challenges, and questions that Metaphysician Undercover has not answered: https://thephilosophyforum.com/discussion/comment/544630

And now we have another installment of ignorance, confusion, illogic, dishonesty, and trolling from him.

Let's start with the dishonesty:

You [fishfry], and Tones alike [...], are simply in denial of these logical fallacies existing in the fundamental principles of mathematics, and you say truth and falsity is irrelevant to the pure mathematicians. — Metaphysician Undercover

I don't speak for fishfry, but the second 'you' above appears to include both of us. But I have never said, implied, or remotely suggested, that truth and falsity are irrelevant to pure mathematics. So you are lying to suggest that I did.

the complete denial of the faults, from people like you. — Metaphysician Undercover

I have never claimed that mathematics, or classical mathematics, is exempt from criticisms. Indeed I have said at least a few times that I am interested in discussion of criticisms, including from such tenets as predicativism, constructivism, finitism, formalism, relevance logic, and even paraconsistent logic. Also, the question of infinite regress in meta-theory. Also, objections that set theory is too rococo and overshoots the target of mathematics for the sciences. Also, reverse mathematics. And I have not opined that all these critiques are incorrect and especially I have not opined that they are not worthwhile. So you are lying about me.

Next, Metaphysician Undercover's trolling:

I love to mention you, and see your response. — Metaphysician Undercover

I pointed out that continually you mention me without stating the context or quotes, thus making it seem that I have played a certain role or taken a certain position in an unspecified exchange with you. And above you admit that you do this to provoke my response regarding that. That is the very definition of 'trolling'. And you admit it. You're an obnoxious bane.

Next, a break to repeat a question:

The part that doesn't make sense is when you move deeper into the theory. This is just like mathematics.
— Metaphysician Undercover

I want to understand: Are you saying that music theory is wrong just as you say mathematics is wrong? And, by the way, do you know any music theory? — TonesInDeepFreeze

Now more of the ignorance and confusion of Metaphysician Undercover:

If one could predict the bad things that were going to happen, before they happened, then we could take the necessary measures to ensure that they don't happen. — Metaphysician Undercover

I'm not asking you what particular bad things you think will happen, but what kind of bad things. At least you could say what is the general nature of the bad things you think will happen (you do below, I'll get to it).

It's like asking me what accident are you going to have today. — Metaphysician Undercover

No it's not. That's a strawman argument by you. I'm not asking you to predict that Joe Blow in Paducah will burn his toast tomorrow. Obviously, that would be ridiculous. So obviously it's not what I'm asking. I'm asking what is the general category of bad things you are warning against (you do below, I'll get to it). .

The biggest problem, I think, is the complete denial of the faults, from people like you. — Metaphysician Undercover

I mentioned in a post above that I don't have such a denial. But at least you do mention a general kind of bad effect you have in mind.

(1) The most present example is your denial of the utter ludicrousness of you your ignorant, confused, illogical, and deceptive ideas about mathematics. No matter how clearly those are pointed out to you, you evade and deny.

(2) Any subject can have people in denial about its faults. If we deleted intellectual work on the basis that there are certain people that have too rigid adherence, then we'd have virtually no intellectual work to refer to for all human history.

(3) So when you said "bad things", it turns out that for the most part, these bad things are that people explain to you how mathematics actually works so that they may disabuse you of your ignorant and confused imaginings about it.

This creates a false sense of certainty. That's why it's like religion, you completely submit to the power of the mathematics, with your faith, believing that your omnibenevolent "God", the mathematics would never mislead you. — Metaphysician Undercover

I have addressed the "religion" claim in detail in other posts. You ignore what I said. That is your favorite argument tactic: Don't recognize the points others make and instead just keep repeating your false and confused claims.

Also, you are virtually lying about me again by claiming that I believe that mathematics is an omnibevolent "God" that would never be misleading.

we ought not say that the numeral 2 says the same thing as the Hebrew symbol. — Metaphysician Undercover

We sure better say that '2' and 'bet' name the same number. Otherwise, translation would be impossible. If 2' and 'bet' named different numbers then English speakers and Hebrew speakers could never agree on such ordinary observations as that the quantity (you like the word 'quantity') of apples in the bag is the same whether you say it in English or in Hebrew.

This would be very clear to you if you would consider all the different numbering systems discussed on this forum, natural, rational, real, cardinals, ordinals, etc.. — Metaphysician Undercover

Ah, red herring.

The point is whether the English numeral and the Hebrew numeral name the same number. That is unproblematic. It is not a contradiction or illogical for an object to have different words denoting it.

It is an unrelated point that there are different kinds of numbers.

(By the way, for naturals, ordinals and cardinals, they are the same.)

The same symbol has a different meaning depending on the system. If we do not keep these distinguished, and adhere to the rules of the specific system, we have equivocation. — Metaphysician Undercover

You have it reversed, as you often do.

Yes, by making clear that certain symbols are used differently in different contexts, we avoid equivocation. Using a symbol in more than one way is one-to-many: one (one symbol) to many (many different meanings). And one-to-many is a problem if we don't make clear contexts.

But with the English numeral and Hebrew numeral, we're not talking about one-to-many. Rather, we are talking many-to-one: many (two symbols) to one (one number).

Either you are actually so confused that you can't help but reversing or you are dishonest trying to make the reversal work for you as an argument. I'm guessing the former, since, even though you are often dishonest, more often it is apparent that you are just pathetically confused.

.That means for you to state which dots come before other dots, for each dot.
— TonesInDeepFreeze

Order is not necessarily temporal — Metaphysician Undercover

YOU were the one harping on temporality and saying that things were place in order temporally by people. I don't rely on temporality. I didn't say that 'before' is 'before' only in a temporal sense.

Still you are evading the challenge: What is "THE INHERENT" order you claim that the dots have?

Whatever you like - temporal or not - you claim that sets have "AN INHERENT" order. So what is the inherent order of those dots?

So if you cannot see order in an arrangement on a two dimensional plane, I don't see any point in discussing "order" with you. — Metaphysician Undercover

STOP

Stop driving right past the point I have told you over and over.

Just read this. Take a moment. And try to understand:

I have said several times that there ARE orderings. There are MANY orderings. So there is not a single ordering that can be called "THE INHERENT" ordering.

Indeed, for a finite set of cardinality n, the number of (total linear) orderings of is n factorial ('n!' in math notation). And when n>1, n!>1, so there are MORE THAN ONE orderings of the set.

And stop trying to make it seem that I deny that there are no orderings of a set.

What I am asking is why can't the symbol "2" be used to represent a quantity of two individuals, — Metaphysician Undercover

It is used to denote the quantity two.

Why must the symbol "2" represent a mathematical object, the number two, and the number two represents a quantity of two individuals? We don't say that the word "tree" represents a conceptual object, tree, and this concept represents the individual tree. — Metaphysician Undercover

Because 'tree' is not a proper noun.

In reality we simply use the word "tree" to represent a tree, and we use the symbol "2" to represent a quantity of two individuals. — Metaphysician Undercover

The number does not represent how many individuals there are.

The number is how many individuals there are.
— Luke

Well no, this is not true. — Metaphysician Undercover

Well yes, it is true.

Start with what people say in everyday language. Jack says, "What is the number of students in the class?" and Sue says, "The number of students in the class is two".

The number IS the number of students. That is everyday language.

And mathematics captures that thinking.

You want for us to regard everyday language working differently, working according to your own nut-case confusions.

1. For any moment in time, we can always ask what the time was before that.

2. If for any moment in time, we can always ask what the time was before that then, the past is infinite

Ergo,

3. The past is infinite [1, 2 MP]

4. If the past is infinite and we're in the present then, the infinite past is an actual infinity

5. We're in the present

6. The past is infinite and we're in the present [3, 5 Conj]

7. The infinite past is an actual infinity [4, 6 MP]

8. If the infinite past is an actual infinity then, there are actual infinities

9. There are actual infinities [7, 8 MP]

Metaphysician Undercover with the same dishonest claim:

Contradiction may be implied. Here's Wikipedia's opening statement:
'In traditional logic, a contradiction consists of a logical incompatibility or incongruity between two or more propositions."

The problem is that you refuse to recognize that an arrangement of points on a plane, logically implies order, therefore "an arrangement of points on a plane without order" is contradictory. — Metaphysician Undercover

(1) Again, I have said at least a few times already that sets have orderings. Sets of cardinality greater than 1 have more than one ordering.

You even put in QUOTE MARKS "an arrangement of points on a plane without order", which is something I never said. You are lying about me.

(2) A set of statements is inconsistent if and only if it implies a contradiction. A contradiction is a statement and its negation.

You claim that I have advanced a contradiction. So, you should be able to show that anything I've said implies a contradiction. But these two statements are not a contradiction:

* For every set, there are orderings of the set.

* For sets of cardinality greater than 1, there is no single ordering that is "THE INHERENT ORDERING".

(I'll add that if one want to define 'the inherent ordering' for certain sets, such as the ordering by membership for ordinals, or the standard ordering of the reals, etc., then that's okay with me. But the point is that there is not such a definition for sets in general.)