The apparent order is made up, a created order, assigned to the group of things, so it is not perceived, it is produced by the mind. — Metaphysician Undercover

Apparent order is not perceived? Do you know what "apparent" means?

If apparent order is not perceived, then your earlier distinction between "internal" and "external" perspective is irrelevant; it's not a matter of perspective at all. So why did you introduce the distinction between "internal" and "external" perspective?

Yes, you see the object along with the order which inheres within, meaning you see the order, you just do not apprehend it. Consider the dots, we see them, we must see the order because it's there — Metaphysician Undercover

Do we perceive both the apparent order and the inherent order? Is there a difference between the apparent order and the inherent order? If so, what is the difference between them?

If there is no difference between the apparent order and the inherent order, then why did you draw the analogy with Kant's phenomena-noumena distinction, and why did you state:

We are talking about "inherent order". This is the order which inheres within the group of things. It is not the perspective dependent order, — Metaphysician Undercover

If there is a difference between the apparent order and the inherent order, then why did you state:

The inherent order is the exact spatial positioning shown in the diagram. — Metaphysician Undercover

As I said, the order is right there, in the object, as shown by the object, and seen by you, as you actually see the object, along with the order which inheres within the object, yet it's not apprehended by your mind. — Metaphysician Undercover

Are these both the inherent order (bolded)? If so, then why do you say "along with the order"?

If you see now, that the entire time, I was talking about the order which inheres within the thing itself, as "inherent order", rather than some perceived, apprehended, or creatively imagined order, you can go back and reread the entire section and clear up your misunderstanding. — Metaphysician Undercover

If you were talking about the inherent order the entire time, and if the inherent order is not perceived or apprehended, then why did you say:

The inherent order is the exact spatial positioning shown in the diagram. — Metaphysician Undercover

Take a look at that posting of fishfry's and see the order which the dots have — Metaphysician Undercover

It can only be because you were not talking about the inherent order the entire time. You have contradicted yourself.

Furthermore this:

the entire time, I was talking about the order which inheres within the thing itself, as "inherent order", rather than some perceived, apprehended, or creatively imagined order — Metaphysician Undercover

contradicts this:

The order is right there in plain view — Metaphysician Undercover

I don't use that distinction as the basis for my argument, I gave that distinction as an example which i thought you might be able to understand. — Metaphysician Undercover

That's odd. When I asked you what the "internal perspective" of an arrangement of objects was, you said:

Are you aware of Kant;s distinction between phenomena and noumena? As human beings, we do not know the thing itself, we only know how it appears to us. Kant seems to describe the noumena as fundamentally unknowable. — Metaphysician Undercover

And only a day ago you said:

Right, inherent order, which I classed as noumenal, appears to be spatial-temporal. — Metaphysician Undercover

But now you say that Kant's phenomena-noumena distinction is not the basis for your argument. How do you expect me to understand your argument about inherent order if one day you say that inherent order is noumenal, and the next day you say that Kant's phenomena-noumena distinction is not the basis for your argument?

Come on Luke, use some intelligence. Kant did not have to name every instance of what contributes to phenomena for us to place things in that category. If you think I am wrong, and intention ought not be placed in that category, then just tell me. But please give reasons. Simply saying Kant didn't explicitly say it therefore, you're wrong in your analogy, is pointless. — Metaphysician Undercover

You've now told me that you don't use Kant's distinction as the basis for your argument, so I don't know what analogy you're referring to. Either inherent order is noumenal or it isn't. Maybe you meant indirect realism instead of noumena? I don't know.

You claimed a contradiction when I said I couldn't describe something which was shown. — Metaphysician Undercover

False. I claimed a contradiction between your position and statements before you introduced Kant, and your position and statements after you introduced Kant.

Thanks for all the quotes removed from context. — Metaphysician Undercover

What context is lacking? Feel free to use the links provided to find the context.

To be shown, or demonstrated does not mean to be stated, I went through that in the last post, and again above. — Metaphysician Undercover

Yes, but in the posts before you introduced Kant, you were clearly saying that the appearances were the reality (i.e. direct realism), as demonstrated by the quotes. Again:

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 — Metaphysician Undercover

You asked us here (prior to your introduction of Kant) to take a look at the diagram and see the order the dots have, and that they could not have any other order. Yet now (after your introduction of Kant) you are trying to convince us of the opposite: that there must be another order - the inherent order - which is different to the order we can see in the diagram. Moreover, you have claimed that the appearance of order and the inherent order could not be the same just by chance, despite your admission that you don't know whether or not they could be the same.

The contradiction is more stark here:

The inherent order is the exact spatial positioning shown in the diagram. — Metaphysician Undercover

To return to my recent point, you have conceded that there are "many other types" of order which are not "temporal-spatial", therefore your references to phenomena-noumena (or indirect realism or whatever) do not apply to these many other types of order. Therefore, you cannot claim that there is some hidden order to these other types. While that might be irrelevant to your claims, it is not irrelevant to the criticisms of your claims made by the other posters here. You are the only one arguing that order must involve spatio-temporal phenomena (and/or noumena).

I don't know if Kant ever said, but it's pretty obvious how intention must fit in. — Metaphysician Undercover

So you don't know whether intention has anything to do with Kant's phenomena-noumena distinction?
And yet you still use this distinction as the basis of your argument regarding inherent order?

You tried to draw an analogy between your supposed inherent order and Kant's noumena. When I pointed out that you had already conceded that "many other types" of order are not spatio-temporal and therefore not noumenal, you said that one other type (best to worst) "is relevant to intention, therefore phenomenal". If you don't know whether intention has anything to do with Kant's phenomena-noumena distinction, as you now admit, then you cannot claim that best-to-worst order is "relevant to intention, therefore phenomenal".

No, sorry I must have made a mistake, or perhaps you just misunderstood. — Metaphysician Undercover

There has been no misunderstanding. It's clear to everyone that you continually change your position and argue out of both sides of your mouth.

I'm very well acquainted with your strawman interpretations designed at creating the appearance of contradiction. — Metaphysician Undercover

What strawman interpretation? Instead of empty accusations, go ahead and explain how or what I have misinterpreted.

There is no contradiction in saying that I am showing you an order which I cannot describe. — Metaphysician Undercover

That's different to what you were saying earlier in the discussion. Earlier, you were saying that the inherent order can be seen and described. For example:

The inherent order is the exact spatial positioning shown in the diagram. — Metaphysician Undercover

If there are points distributed on a plane, or 3d space, the positioning of those points relative to each other is describable, therefore there is an inherent order to them. — Metaphysician Undercover

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. — Metaphysician Undercover

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

I specified the order. It is a spatial order, the one demonstrated by the diagram. Why is this difficult for you to understand? When a diagram shows us an arrangement of dots, it shows us the spatial order of those dots, where the dots must be on a spatial plane to fulfill the order being demonstrated. — Metaphysician Undercover

Only recently did you invoke Kant's phenomena-noumena distinction, changing your position entirely:

We are talking about "inherent order". This is the order which inheres within the group of things. It is not the perspective dependent order — Metaphysician Undercover

The "inherent order" is the order that the things have independently of the order that we assign to them. — Metaphysician Undercover

The inherent order is the true order, which inheres in the arrangement of objects. If I stated an order, this would be an order which I assign to those objects, from an external perspective, and therefore not the inherent order. — Metaphysician Undercover

if I stated an order, it would be a representation, imposed from my perspective, and therefore not the order which inheres within the object, the inherent order. — Metaphysician Undercover

I cannot tell you the order which inheres within the group of things, because iIwould just be giving you an order which I impose on that group from an external perspective. — Metaphysician Undercover

Contrary to the claims of your earlier posts, we can no longer simply look and see the inherent order which is demonstrated by the diagram. You now claim that what we see is a mere phenomena, and that the true, inherent order cannot be seen, described or known. Pure contradiction.

Intention is an integral part of the phenomenal system — Metaphysician Undercover

Where does Kant say this?

Also, do you have any intention of accounting for your latest blatant contradiction:

The inherent order is the exact spatial positioning shown in the diagram. — Metaphysician Undercover

The inherent order is the true order, which inheres in the arrangement of objects. If I stated an order, this would be an order which I assign to those objects, from an external perspective, and therefore not the inherent order. — Metaphysician Undercover

Before your claim was that the inherent order is what's shown. Now you claim that the inherent order is what's hidden. It can't be both.

Right, inherent order, which I classed as noumenal, appears to be spatial-temporal. But the type of ordering which fishfry demonstrated to me, ordering by best, or better, cannot be inherent order because it is relative to intention, therefore phenomenal.

I don't see the problem. — Metaphysician Undercover

How is intention phenomenal (in the relevant Kantian sense)? Or are you no longer talking about Kantian concepts, just like you are no longer talking about the "dots" diagram having the inherent spatial order that it has?

The inherent order is the exact spatial positioning shown in the diagram. — Metaphysician Undercover

That doesn’t work and you’ve misunderstood.

You are trying to draw an analogy between order/inherent order and phenomena/noumena. However, phenomena and noumena are both temporal-spatial, which makes order and inherent order also temporal-spatial by analogy.

You have already conceded that there are “many other types” of order besides temporal-spatial.

If there are “many other types” of order besides temporal-spatial, then order is not necessarily phenomenal or noumenal, so your argument fails.

If order is not limited to temporal-spatial order, then you can no longer hide behind your claim that true order is unknowable. So how do you account for any order which is not temporal-spatial?

Temporal/spatial was just one type of order, fishfry and Lluke gave examples of many other types. — Metaphysician Undercover

Are you aware of Kant;s distinction between phenomena and noumena? As human beings, we do not know the thing itself, we only know how it appears to us. — Metaphysician Undercover

If order is not restricted to "temporal/spatial", then order is not restricted to unknowable noumena.

The inherent order is the true order, which inheres in the arrangement of objects. If I stated an order, this would be an order which I assign to those objects, from an external perspective, and therefore not the inherent order. — Metaphysician Undercover

If the true order cannot be assigned from an external perspective, then what is the "internal perspective" of an arrangement of objects? Will I know the "true order" of its vertices if I stand in the middle of a triangle?

In other words, how could the inherent order be known? If it cannot be known then how do you know there is one?

Wittgenstein might have not said this, and I mistakenly said that he did; but, isn't it a feature of language that this does actually happen normally? — Shawn

That what does actually happen normally? That people follow norms? Yes, that is (statistically) normal.

All criticisms aside, I still think there's merit to mentioning that ethics consists, at least extensionally by my own reasoning from Wittgenstein, to an adherence to those very norms in society. — Shawn

To borrow your own example, do you think it was unethical:

for blacks in the use [U.S.?] the refusal to accept social norms in the 1950's onwards. — Shawn

Well, yes, by the very fact of how bias and norms create quasi-rules of how language is used in a society. I understand that terms become reified with time as these tendencies abate or are pressured due to how social norms progress. — Shawn

In what sense does Wittgenstein advocate an adherence to these norms?

That's just another undefined term by you as is 'inherent order'. — TonesInDeepFreeze

From earlier in the discussion, “inherent” is being used to mean “non-arbitrary”.

When a diagram shows us an arrangement of dots, it shows us the spatial order of those dots, where the dots must be on a spatial plane to fulfill the order being demonstrated. What is the diagram? An arrangement of dots. What does it demonstrate to us? An ordering of those dots. — Metaphysician Undercover

You continue to assert that the elements have an order without specifying what that order is. "What is that order? An arrangement. And what is that arrangement? The order it has."

Someone could proceed with that diagram to lay out the same pattern with other objects, with the ground, or some other surface as the plane. — Metaphysician Undercover

What algorithm might someone use to re-create the same pattern?

Just because fishfry called it a "random" arrangement doesn't mean that it does not demonstrate an order. Fishfry used "random" deceptively, as I explained already. — Metaphysician Undercover

"It's not random because it has an order and it has an order so it isn't random." Empty words.

There was a process which put those dots where they are, a cause, therefore a reason for them being as they are and not in any other possible ordering. — Metaphysician Undercover

"They have that order and not some other order because there was a cause of that order."

Seriously? That does not explain why the elements must have this particular order instead of some other order. Why wasn't some other order or arrangement caused instead?

It's a spatial order, each dot has its own specific position on the plane. To change the position of one would change the order — Metaphysician Undercover

There are two issues here: "order" and "inherent".

You claim that the elements of the diagram have a "spatial order". Effectively, this is to say that the elements "have the order they have" without specifying what that order is.

You also presume that the elements of the diagram have an inherent order. You have provided no explanation as to why the diagram has the spatial order it has instead of any other possible spatial ordering of the the same elements.

"Order" is defined as "the condition in which every part, unit, etc., is in its right place". — Metaphysician Undercover

A more suitable definition in the context of this discussion might be “the arrangement or disposition of people or things in relation to each other according to a particular sequence, pattern, or method.”

There is no need to specify a start and end. After giving me examples of order which is not a temporal order, you cannot now turn around and insist that "order" implies a known start and end. — Metaphysician Undercover

Those "start" and "end" points would be non-temporal. That was the point of the counterexamples.

Nearly all of those counterexamples have elements which can be ordered first to last, lowest to highest, worst to best, etc. Those orderings (e.g. poker hands, military ranks, letters of the alphabet) therefore have "start" and "end" points in terms of the arrangement of their elements.

So we really haven't agreed on any specific type of order yet. — Metaphysician Undercover

That’s a cop out. You claimed that the diagram has an inherent order. Specify that order. Which dots are the start and end points of that order? This needn’t imply a temporal start and end. For example, winning poker hands have a rank from lowest to highest; from a pair to a royal flush. This is not a spatial or temporal order of rank.

It was my suggestion that "order" is fundamentally temporal — Metaphysician Undercover

How does this account for the order of rank of military officers, or of suits in a game of bridge? Or the order of values of playing cards in Blackjack? Or the order of the letters of the alphabet? Or monetary value?

I really don't see how the qualification "numerical" is relevant , or even meaningful in the context of dots on a plane. So I don't see why you think it was implied. Fishfry is not sloppy and would not have forgotten to mention a special type of order was meant when "no inherent order" was said numerous times. — Metaphysician Undercover

Perhaps “numerical” wasn’t the right word. The context of the post and the preceding discussion indicates that a “before and after” ordinality was implied, of the sort Tones recently mentioned:

If there is a certain ordering that you think is "the inherent ordering" then tell us what it is. Point to each dot and tell us which dots it comes before and which dots it comes after. That is what is meant by an ordering in this discussion (a total linear ordering). — TonesInDeepFreeze

Your assertion that the diagram has an inherent order which can be discerned simply by looking at the diagram does not specify what that order is.

Actually "numerical order" (whatever that is supposed to mean in reference to a diagram of dots) was not specified. It was simply asserted that the elements have no inherent order. — Metaphysician Undercover

If not specified, then at least strongly implied in the same post:

What is the inherent order of the points in this set? Can you see that the points are inherently disordered or unordered, and that we may impose order on them arbitrarily in many different ways? Pick one and call it the first. Pick another and call it the second. Etc. What's wrong with that? — fishfry

Did you not read this when you went on to argue that the diagram has the order it has?

Just another example of your wilful ignorance and dishonest argumentation.

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 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.

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.

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”?

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.

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.

Where are these "numbers" that the teacher kept trying to tell us about, I thought. All I could see is the numerals, and the quantity of objects referred to by the numeral. But the 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, so I shouldn't even bother looking for it because I have to make up that fiction in my own mind, for there to be a number for me to "see". — Metaphysician Undercover

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

Even learning the numerals, how to count, and simple arithmetic, addition, subtraction multiplication, division made sense to me right from the start. It was only later, when they started insisting that there existed a number, distinct from the numeral, that things started not making sense. — Metaphysician Undercover

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).

My view is physical matter exists only in the present and that leads to the question of why and how we perceive past, present and future. — Mark Nyquist

We perceive in the present, remember the past, and anticipate the future.

If I remember correctly, until now, physical matter has always been found to exist in the future.

Notice, the quoted passage says numbers are assumed when "you" count. And, it's your count that I argue is false. . — Metaphysician Undercover

I'm sure you meant the impersonal pronoun. This is more obvious with the preceding sentence provided for context:

Your "ascending order" is based on quantity, therefore your supposed "count" of ascending order means nothing unless it is determining a quantity. This is why "numbers" as objects are assumed, so that when you count up to ten you have counted ten objects, (numbers). — Metaphysician Undercover

You assert your stipulation/argument that "ascending order" is based on quantity, and then "This is why "numbers" as objects are assumed" by you. It's your argument and your assumption.

Otherwise, if you were arguing that "my" count is false, then it would also be false that "when you count up to ten you have counted ten objects, (numbers)." This would be odd, since it's the antithesis of your argument in earlier posts. But you are no stranger to contradiction, since you said in the very same post:

And, if numbers are not true objects, as I argue is the case, then this is not a true act of counting at all. — Metaphysician Undercover

Keep blowing smoke trying to hide your contradiction. You clearly cannot account for it.

Do you understand the meaning of the word "if"? — Metaphysician Undercover

As in, if you were arguing that numbers are not objects? But you already told us that you were. You also told us that you assume numbers are objects.

For someone so rabid about logic, you seem quite content with your contradiction.

I explained this already. Your "ascending order" is based on quantity, therefore your supposed "count" of ascending order means nothing unless it is determining a quantity. — Metaphysician Undercover

I explained this already. Your “quantity” is based on ascending order, therefore your supposed “count” of quantity means nothing unless it is reciting an ascending order.

This is why "numbers" as objects are assumed, so that when you count up to ten you have counted ten objects, (numbers). — Metaphysician Undercover

And, if numbers are not true objects, as I argue is the case, then this is not a true act of counting at all. — Metaphysician Undercover

You assume that numbers are objects but argue that numbers are not objects? Sounds about right given your confusion.

In a logical proceeding, it is imperative that the symbol employed maintains the same meaning, to avoid the fallacy of equivocation. If "beating" means something different when used to describe beating eggs, from what it means when used to describe beating drums, and we proceed with a logic process, there could be a fallacious conclusion. For example, after the eggs are beaten, the internal parts are all mixed up into a new order, therefore if I beat the drums the internal parts will become all mixed up into a new order. — Metaphysician Undercover

I welcome you to provide a non-circular reason for why "determining a quantity" is (true) counting and why "reciting the natural numbers in ascending order" is not (true) counting.

It is my opinion that there is no such thing as numbers which serve as a medium between the numeral (symbol) and its meaning, or what it represents. — Metaphysician Undercover

I have no idea what this is supposed to mean or how you think it relates to anything I've said.

To say that a particular order is "ascending order", is simply to make a reference to quantity. — Metaphysician Undercover

To determine a quantity is equally to make reference to an ascending order. Counting in one sense is no different to counting in the other sense. They are both the same sense of "counting".

In plain terms, your argument is like saying that there is a difference in meaning between beating a drum and beating eggs, therefore we shouldn’t use the same word “beating” for both of these, and eggs are not genuinely beatable. But of course you can “beat” both eggs and a drum despite the difference in meaning, and despite your protestations, and attempts to restrict language, to the contrary. We don’t “beat” eggs the same way that we “beat” a drum, but neither do we “beat” a drum the same way that we “beat” eggs. One meaning is not superior to the other.

You might argue that “counting” in the sense of reciting the natural numbers in ascending order is not the proper meaning of the word, but why is it not? Why is “counting” in the sense of determining a quantity the only proper meaning of the word? These are both counting.

I think you need to reread my post. I have no desire to respond to your misinterpretation. — Metaphysician Undercover

I see. Allow me to try again.

If you give the number 2 meaning, a definition, to validate its existence as a conceptual object, you might say that it means a quantity of two, but then you justify my argument, that counting is counting a quantity of objects, and "2" refers to two objects, not one object, the number 2. — Metaphysician Undercover

If you give the number 2 meaning, a definition, to validate its existence as a conceptual object, you might say that it means the number which comes after 1, but then you justify my argument, that counting (e.g counting the natural numbers) is expressing an order, and “2” refers to one of the numbers in that order, the number 2.

If you give the number 2 meaning by saying that it is the number which comes after 1, then you justify my argument that what you are doing is expressing an order, rather than counting. — Metaphysician Undercover

If you give the number 2 meaning by saying that it means a quantity of two, then you justify my argument that what you are doing is measuring, rather than counting.

If you give the number 2 meaning, a definition, to validate its existence as a conceptual object, you might say that it means a quantity of two, but then you justify my argument, that counting is counting a quantity of objects, — Metaphysician Undercover

If the number 2 means "a quantity of two", then how could counting the natural numbers be "expressing an order", as you claim?

If you give the number 2 meaning by saying that it is the number which comes after 1, then you justify my argument that what you are doing is expressing an order, rather than counting. — Metaphysician Undercover

If you give the number 2 meaning by saying that it is the number which comes after 1, then you justify my argument that what you are doing is measuring (determining a quantity), rather than counting.

That is, 2 comes after 1 in either case.

Right, and the reason why I argued this is that we ought not have two distinct activities going by the same name in a rigorous logical system, because equivocation is inevitable. So, one ought to be called "counting" and the other something else. I propose the obvious, for the other, expressing an order. — Metaphysician Undercover

I propose instead that we reserve the term "counting" for counting the natural numbers and counting imaginary things, and that we should use the term "measuring" (instead of "counting") for "determining a quantity".

I trust you will have no problem with this as it avoids any equivocation.

The point is to avoid equivocation which is a logical fallacy. — Metaphysician Undercover

That's not your point, though. Your point is not merely to avoid equivocation; your point in drawing the distinction between the two senses of "counting" is to discount the sense of "counting the natural numbers", "counting from one to ten", or "counting imaginary things" as not a true sort of counting. You have attempted to argue that the only true sort of counting is "determining a quantity" and/or counting "actual objects". For example:

numbers are not even countable objects in the first place, they are imaginary, so such a count, counting imaginary things, is a false count. Therefore natural numbers ought not be thought of as countable. — Metaphysician Undercover

And we described counting as requiring objects to be counted. I distinguished a true count from a false count on this basis, as requiring objects to be counted. Clearly, if the objects counted are not actual objects, but imaginary objects, it is not a true count. — Metaphysician Undercover

Look, I think it's very important for a rigorous mathematics to distinguish between counting real things, and counting imaginary things. This is because we have no empirical criteria by which we can determine what qualifies as a thing or not, when the things are imaginary. Therefore we can only count representations of the imaginary things, which exist as symbols. So we are not really counting the imaginary things, but symbols or representations of them, and we have empirical criteria by which we judge the symbols and pretend to count the imaginary things represented by the symbols. But this is not really counting because there are no things being counted. — Metaphysician Undercover

Since one sense of "counting" involves counting real things, then why not call this "real counting"? — Metaphysician Undercover

You have not been using the term "real counting"; I have. My use of "real counting" does not denote "counting real things". "Real counting" denotes genuine counting, as opposed to non-genuine counting.

You have attempted to argue that counting natural numbers, or counting imaginary things, is not true counting, and that to call this "counting" is a misnomer. Your only "argument" has been that true counting must involve "determining a quantity" and/or counting "actual objects". However, you have still provided no justification for this so-called "argument" (i.e. stipulation).

Yes, i call it "counting" — Metaphysician Undercover

You call it "counting" even though you consider it a misnomer to call it "counting" (since there is "nothing being counted")?

but the point is that there's two very distinct senses of "counting" and to avoid ambiguity and equivocation we ought to have two distinct names for the activity, — Metaphysician Undercover

You introduced this distinction solely to make the point that one side of the distinction is not real counting. But sure, let's avoid ambiguity and equivocation over the two distinct types of counting (P.S. you think one of them isn't real counting).

If it is the case, that when a person expresses the order of numerals, one to ten, and the person calls this "counting", it is interpreted that the person has counted a quantity of objects, a bunch of numbers, rather than having expressed an ordering of numerals, then the interpretation is fallacious due to equivocation between the distinct meanings of "counting". — Metaphysician Undercover

You're repeating yourself. This is just another way of saying that real counting must involve "determining a quantity". But what is the justification for your stipulation that counting natural numbers is not real counting or that real counting must involve "determining a quantity"?

To count, in the sense of determining a quantity, is an act of measuring. To "count" in the sense of counting up to ten, is a case of expressing an order, two comes after one, three comes after two, etc.. To call this "counting the natural numbers" is a misnomer because this is nothing being counted, no quantity being determined. — Metaphysician Undercover

You're the only one who thinks it's a misnomer. Everyone else considers "counting up to ten" to be counting (you also called it "counting", by the way). Why should we care about your unjustified stipulation that counting the natural numbers is not real counting or that real counting must involve "determining a quantity"?

Counting is not "the same as measuring", it's a form of measuring. What is required for measuring is a standard, The standard for counting is "the unit", which is defined as an individual, a single, a particular. — Metaphysician Undercover

You have it backwards.

The standard for counting is "the unit".
The standard for measuring is "the unit of measurement".

What unit of measurement is required for counting the natural numbers? Metres? Litres? Hours? Bananas? Obviously, no unit of measurement is required. You can count to ten without having to determine any unit of measurement. Therefore, counting is independent of measuring. Counting is not a "form of" measuring.