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

There are numerous philosophers who argue against the law of identity as stated by Aristotle, Hegel opposed it, as is evident here: https://thephilosophyforum.com/discussion/9078/hegel-versus-aristotle-and-the-law-of-identity/p1 — Metaphysician Undercover

Appreciate the reference.

What I see as an issue which arises from rejecting the idea that each particular object has its own unique identity (law of identity), is a failure of the other two interrelated laws, non-contradiction, and excluded middle. Some philosophers in the Hegelian tradition, like dialectical materialists, and dialetheists, openly reject the the law of non-contradiction. When the law of identity is dismissed, and a thing does not have an identity inherent to itself, the law of non-contradiction loses its applicability because things, or "objects" are imaginary, and physical reality has no bearing on how we conceive of objects.

There are specific issues with the nature of the physical world that we observe with our senses, which make aspects of it appear to be unintelligible. There must be a reason why aspects of it appear as unintelligible. We can assume that unintelligibility inheres within the object itself, it violates those fundamental laws of intelligibility, or we can assume that our approach to understanding it is making it appear.as unintelligible. I argue that the latter is the only rational choice, and I look for faults in mathematical axioms, and theories of physics, to account for the reason why aspects appear as unintelligible. I believe this is the only rational choice, because if we take the other option, and assume that there is nothing which distinguishes a thing as itself, making it distinct from everything else (aspects of reality violate the law of identity), or that the same thing has contradictory properties at the same time (aspects of reality violate the law of non-contradiction), we actually assume that it is impossible to understand these aspects of reality. So I say it is the irrational choice, because if we start from the assumption that it is impossible to understand certain aspects of reality, we will not attempt to understand them, even though it may be the case that the appearance of unintelligibility is actually caused by the application of faulty principles. Therefore it is our duty subject all fundamental principles to skeptical practices, to first rule out that possibility before we can conclude that unintelligibility inheres within the object.

Aristotle devised principles whereby the third fundamental law, excluded middle would be suspended under certain circumstances, to account for the appearance of unintelligibility. Ontologically, there is a very big difference between violating the law of excluded middle, and violating the law of non-contradiction. When we allow that excluded middle is violated we admit that the object has not been adequately identified by us. When we allow that non-contradiction is violated we assume that the object has been adequately identified, and it simply is unintelligible. — Metaphysician Undercover

Not a word of this is even on topic relative to whether 2 + 3 and 5 are identical. Since mathematically they are, and as a mathematical expression it must necessarily be interpreted in terms of mathematics, nothing you say can make the slightest difference. Excluded middle? Did Aristotle anticipate intuitionism? That's interesting.

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? — Luke

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.

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

Why not? The order which we assign to things is clearly not the same as the "exact" order which inheres within things or else we'd have an absolutely perfect understanding of the order of the universe.

Not a word of this is even on topic relative to whether 2 + 3 and 5 are identical. Since mathematically they are, and as a mathematical expression it must necessarily be interpreted in terms of mathematics, nothing you say can make the slightest difference. Excluded middle? Did Aristotle anticipate intuitionism? That's interesting. — fishfry

As I've explained to you already, the idea that 2+3 is mathematically the same as 5, is simply a misunderstanding of the difference between equality and identity. They are equal, but equal is distinct from identity. I've told you this numerous times before, but you do not listen. Nor do you seem to pay any attention to my references, only repeating your misunderstanding in ignorance.

However, I'll reproduce for you the opening lines from the Wikipedia entries on both "equality" and "identity" below, just to remind you of how bad your interpretation really is.

In mathematics, equality is a relationship between two quantities or, more generally two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object.

In philosophy, identity, from Latin: identitas ("sameness"), is the relation each thing bears only to itself.

As I've explained to you already, the idea that 2+3 is mathematically the same as 5, is simply a misunderstanding of the difference between equality and identity. — Metaphysician Undercover

On the contrary. 2 + 3 and 5 are mathematically identical. There is not the slightest question, controversy, or doubt about that.

They are equal, but equal is distinct from identity. I've told you this numerous times before, but you do not listen. — Metaphysician Undercover

I listen very well, but the problem is that you are factually wrong. Wrong on the facts. 2 + 3 and 5 are mathematically identical. They represent the same thing. The identical thing. There is one single thing, and it has two names, 2 + 3 and 5. It has many other names as well, such as, "The cardinality of the vertices of a pentagon." If you kept telling me the sun rises in the west and I disagreed and you accused me of not listening, that would be an unfair statement on your part, would it not? Likewise 2 + 3.

Nor do you seem to pay any attention to my references, only repeating your misunderstanding in ignorance.[/quote = 5. — Metaphysician Undercover

You did in fact give me a reference, the very first one you've given me in three years, after I've asked you many times for references. And it turned out to be only a reference to another thread on this board, and not a reference to the work of any reputable or even disreputable philosopher. And when I read the reference, I did not find anything that shows that 2 + 3 is anything at all other than 5.

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?

I don't want to distract from this fascinating and delightfully lengthy discussion, but to return to the title of the thread: Physicists and infinity

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

In that context, "apparent" must mean "seems". If you used "apparent" to mean "perceived by the senses", I would say that you had stated an oxymoron. We apprehend order with the mind, we do not perceive it with the senses.

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? — Luke

I don't believe I said anything about an internal perspective. I distinguished between the order which inheres within the thing itself (which we assume must be real to account for the consistency we note from observations), and the order which we assign to things, from our external perspective of them. This is the reason why our knowledge of the order of things is fallible, the order which we say something has is not the same as the order which it actually has. The best we can say is that we have created a representation of the order that things have. We create the representations through the means of analysis of empirical observations, which do not provide us with the inherent order, in conjunction with theorizing, hypotheses. So there is a separation, a medium consisting of observation and theory, which lies between the apparent order (the order which things seem to have), and the true order which inheres within the things themselves.

The reason why I introduced this distinction is because fishfry claimed that there is a sort of thing, "a set", which has no inherent order at all. I said that such a thing does not exist, because to exist is to have some sort of inherent order. Fishfry scoffed at this. So I proceeded to ask fishfry to explain this type of unity of parts, within which the parts have no order. How could there be such a unity? The point being, that this is simply an imaginary thing stated, 'parts without order', which doesn't correspond to any reality, which is really a logical inconsistency representing falsity, because it is impossible to have parts without order. To be a part of something implies an order in relation to a whole, without that order it cannot be said to be a part. We would have to call it something other than a "part". The point being, that the whole, which the so-called part is said to be a part of, "the set", is not a true whole because it provides no order relations to the so-called parts. Things existing with absolutely no relations of order cannot be said to form a whole, or unity of any kind.

Fishfry will argue fervently that "pure mathematics" is not influenced by physics. Perhaps some mathematicians actually have no respect for physical principles, and that's why infinities have become the norm, rather than the abnormal.

Interesting. Thanks.

I don't believe I said anything about an internal perspective. — Metaphysician Undercover

You spoke of an "external perspective", which implies an internal perspective. You might recall I asked you about it and you responded:

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?
— Luke

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

It was when I asked you about the implied "internal perspective" of an arrangement/order that you drew the analogy with Kant's distinction between phenomena and noumena, saying of a thing that "we only know how it appears to us".

In that context, "apparent" must mean "seems". If you used "apparent" to mean "perceived by the senses", I would say that you had stated an oxymoron. We apprehend order with the mind, we do not perceive it with the senses. — Metaphysician Undercover

Bullshit. You are trying to pretend you were never talking about sense perception? Sense perception is exactly what Kantian phenomena is about, and clearly what you meant when you said that we can only know how a thing "appears to us".

If we apprehend order with the mind and not with the senses, then perhaps you could finally explain this:

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

Your current argument is that we do not perceive order with the senses, and that we cannot apprehend inherent order at all. Therefore, how is it possible that the inherent order is the exact spatial positioning shown in the diagram?

On the contrary. 2 + 3 and 5 are mathematically identical. There is not the slightest question, controversy, or doubt about that. — fishfry

As per the quotes above, from Wikipedia, the mathematical notion of identical , as equal, is not consistent with the philosophical notion of identity, described by the law of identity. In other words, mathematicians violate the law of identity to apply a different concept of identity, making two things of equal value mathematically identical. You might accept this, and we could move on to visit the possible consequences of what I believe is an ontological failure of mathematics, or you could continue to deny that mathematicians violate this principle. The latter is rather pointless.

You spoke of an "external perspective", which implies an internal perspective. You might recall I asked you about it and you responded: — Luke

If all perspectives are external to the object, then "perspective" is necessarily external, and saying "external perspective" just emphasizes the fact that perspective is external. Internal perspective is not implied, just like saying "cold ice" doesn't imply that there is warm ice. That's why I referred to Kant, to show how our perspective of the thing in itself is external to the thing.

Your current argument is that we do not perceive order with the senses, and that we cannot apprehend inherent order at all. Therefore, how is it possible that the inherent order is the exact spatial positioning shown in the diagram? — Luke

Why not? I don't understand your inability to understand. Let me go through each part of your question. 1) We do not perceive order with the senses. No problem so far, as we understand order with the mind, not the senses. 2) We cannot apprehend the inherent order. Correct, because the order which we understand is created by human minds, as principles of mathematics and physics, and we assign this artificially created order to the object, as a representation of the order which inheres within the object, in an attempt to understand the inherent order. But that representation, the created order is inaccurate due to the deficiencies of the human mind. 3)The inherent order is the exact positioning of the parts, which is what we do not understand due to the deficiencies of the human mind.

Does that help? You have emboldened the word "shown". Why? Do you understand that something can be shown to you which you do not have the capacity to understand? The physical world shows us many things which we do not have the capacity to understand. For example, the theologians used to argue that the physical world shows us the existence of God. Most people would claim that the physical world is not evidence of God, and in no way does the physical world show us God. The theologian would say that you just do not understand what is being shown to you. the exact order is being shown to us but we do not understand it.

As per the quotes above, from Wikipedia, the mathematical notion of identical , as equal, is not consistent with the philosophical notion of identity, described by the law of identity. — Metaphysician Undercover

You're factually wrong.

Is the set {0,1,2,3,4} identical to the set {0,1,2,3,4}? I have to assume you'd say yes.

But 2 + 3 and 5 are both representations of the set {0,1,2,3,4}. So they're identical.

In other words, mathematicians violate the law of identity to apply a different concept of identity, making two things of equal value mathematically identical. — Metaphysician Undercover

I just showed (as I have probably a hundred times before) that you are wrong about this. Mathematicians call two things identical when those things are identical.

Now I will concede that there are subtle counterexamples. For example the natural number 5 and the real number 5 are distinct as sets. Nevertheless they are identical when viewed structurally. If you wanted to say they are equal but not identical that would be arguable, but it's a subtle point, and could be argued either way.

You might accept this, and we could move on to visit the possible consequences of what I believe is an ontological failure of mathematics, or you could continue to deny that mathematicians violate this principle. — Metaphysician Undercover

Well, math does not violate this principle. 2 + 3 and 5 are identical. They are both representations of the set represented by {0,1,2,3,4}, which of course is not actually "the" set, but is rather yet another representation of that abstract concept of 5.

The latter is rather pointless. — Metaphysician Undercover

Only to the extent that you don't seem to think a thing is identical to itself. Because when mathematicians use equality, they mean identity, and this is provable from first principles. They either mean identity as sets; which is easy to show; or, they often mean identical structurally. This is a more subtle philosophical point.

3)The inherent order is the exact positioning of the parts, which is what we do not understand due to the deficiencies of the human mind. — Metaphysician Undercover

You said that "1) We do not perceive order with the senses" and that "2) We cannot apprehend the inherent order". Therefore, how do you know that what's shown in the diagram is the exact positioning of the parts (i.e. the inherent order)?

Isn't the positioning of the dots that I perceive the "perspective dependent order" which you earlier stated was not the inherent order? So how can the diagram show the inherent order to anybody?

The inherent order cannot be perceived by the senses and we can't apprehend it, anyway.

2) We cannot apprehend the inherent order. Correct, because the order which we understand is created by human minds, as principles of mathematics and physics, and we assign this artificially created order to the object, as a representation of the order which inheres within the object, in an attempt to understand the inherent order. But that representation, the created order is inaccurate due to the deficiencies of the human mind. — Metaphysician Undercover

If "We cannot apprehend the inherent order", then how do you know that our representations are inaccurate?

If the inherent order is unintelligible to the human mind by definition, then what makes inherent order preferable to (or distinguishable from) randomness?

You're factually wrong.

Is the set {0,1,2,3,4} identical to the set {0,1,2,3,4}? I have to assume you'd say yes.

But 2 + 3 and 5 are both representations of the set {0,1,2,3,4}. So they're identical. — fishfry

The way you described sets in this thread, a set is something which cannot have an identity because it has no inherent order. Therefore I cannot agree that the set {0,1,2,3,4} is identical to the set {0,1,2,3,4}. It seems like a set is an abstraction, a universal, rather than a particular, and therefore does not have an identity as a "thing". It is particulars, individual things, which have identity according to the law of identity. Notice that the law of identity says something about things, a thing is the same as itself.

The law of identity is intended to make that category separation between particular things, and abstractions which are universals, so that we can avoid the category mistake of thinking that abstractions are things. "The set {0,1,2,3,4}" refers to something with no inherent order, so it does not have an identity and is therefore not a thing, by the law of identity, To say that it is a thing with an identity is to violate the law of identity.

Well, math does not violate this principle. 2 + 3 and 5 are identical. They are both representations of the set represented by {0,1,2,3,4}, which of course is not actually "the" set, but is rather yet another representation of that abstract concept of 5. — fishfry

This is the whole point of the law of identity, to distinguish an abstract concept from a thing, so that we have a solid principle whereby we can avoid the category mistake of thinking of concepts as if they are things. A thing has an identity which means that it has a form proper to itself as a particular. To have a form is to have an order, because every part of the thing must be in the required order for the thing to have the form that it has. So to talk about something with no inherent order, is to talk about something without a form, and this is to talk about something without an identity, and this is therefore not a thing.

Only to the extent that you don't seem to think a thing is identical to itself. Because when mathematicians use equality, they mean identity, and this is provable from first principles. They either mean identity as sets; which is easy to show; or, they often mean identical structurally. This is a more subtle philosophical point. — fishfry

The problem is not that I don't think a thing is the same as itself. That is the law of identity, which I adhere to. The problem is that you make the category mistake of believing that abstract conceptions are things. Because you will not admit that a concept is not a thing, you make great effort to show that two distinct concepts, like what "2+3" means, and what "5" means, which have equal quantitative value, refer to the same "thing". Obviously though, "2+3" refers to a completely different concept from "5".

If you would just recognize the very simple, easy to understand, fact, that "2+3" does not mean the same thing as "5" does, you would understand that the two expressions do not refer to the same concept. So even if concepts were things, we could not say that "2+3" refers to the same thing as "5", because they each have different associated concepts. And it's futile to argue as you do, that the law of identity is upheld in your practice of saying that they refer to the same "mathematical object", because all you are doing is assuming something else, something beyond the concepts of "2+3", and "5", as your "mathematical object". This supposed "object" is not a particular, nor a universal concept, but something conjured up for the sake of saying that there is a thing referred to. But there is no basis for this object. It is not the concept of "2+3" nor is it the concept of "5", it is just a fiction, a false premise you produce for the sake of begging the question in your claim that the law of identity is not violated.

You said that "1) We do not perceive order with the senses" and that "2) We cannot apprehend the inherent order". Therefore, how do you know that what's shown in the diagram is the exact positioning of the parts (i.e. the inherent order)? — Luke

It is a fundamental ontological assumption based in the law of identity, that a thing has an identity. In Kant we see it as the assumption that there is noumena, which is intelligible, just not intelligible to us. In Descartes we see skepticism as to whether there even is external objects.

So we assume that there is something, the sensible world, and we assume it to be intelligible, it has an inherent order. To answer your question of how do we "know" this, it is inductive. We sense things, and we conclude that there is reality there. Also, we have some capacity to understand and manipulate what is there, so we conclude that there is intelligibility there, intelligibility being dependent on ordering. We have some degree of reliability in our understanding of the ordering therefore there must be some ordering.

Isn't the positioning of the dots that I perceive the "perspective dependent order" which you earlier stated was not the inherent order? So how can the diagram show the inherent order to anybody?

The inherent order cannot be perceived by the senses and we can't apprehend it, anyway. — Luke

Yes, you perception provides for you, the basis for a perspective dependent order, which your mind produces. What the object is showing you, its inherent order, and the order which you are producing towards understanding the inherent order, are two distinct things. As I described, there is some degree of inconsistency, constituting a difference, between what is shown to you, and what you apprehend from that showing. The claim of difference is justified by our failures. The inherent order is shown. It is not perceived by the senses. If you try to understand the inherent order, your mind will produce an order which you think best represents that which inheres in the object.

Consider, that in seeing objects we do not see the molecules, atoms or other fundamental particles, we have to figure those things out as a representation of the order which inheres within. But we cannot completely apprehend that order because our minds are deficient. This doesn't mean that sentient beings will never be able to apprehend it, or that there isn't an omniscient being which already can apprehend it. And even if it is impossible that human beings or any sentient beings will ever be able to understand it in perfection, like an omniscient being is supposed to be able to, we can still improve our understanding, i.e. get a better understanding, and decrease our failures.

If "We cannot apprehend the inherent order", then how do you know that our representations are inaccurate? — Luke

I think we judge the accuracy of our understanding mostly by the reliability of our predictions. But reliability is perspective dependent and subjective. So where some people see reliability, I see unreliability. It all depends on what type of predictions you are looking for the fulfillment of.

If the inherent order is unintelligible to the human mind by definition, then what makes inherent order preferable to (or distinguishable from) randomness? — Luke

Order is fundamentally intelligible. So assuming order is to assume the possibility of being understood, which is to inspire the philosophical mind which has the desire to understand. To assume randomness is to assume unintelligibility which is repugnant to philosophical mind which has the desire to understand.

So, as I explained. If the object appears (seems) to be unintelligible (without inherent order), we need to determine why. Is it our approach (are we applying the wrong principles in our attempt to understand), or is it the reality, that the object truly has no inherent order? The latter is repugnant to the philosophical mind, and even if it were true, it cannot be confirmed until the possibility of the former is excluded. Therefore, when the object appears to be unintelligible (without inherent order), we must assume that our approach is faulty (we are applying the wrong principles in our attempt to understand), and we must subject all principles to extreme skepticism, before we can conclude that this object is truly unintelligible (without inherent order). The rational approach is to assume that we are applying the wrong principles, and to assume that the object has no inherent order is irrational.

So we assume that there is something, the sensible world, and we assume it to be intelligible, it has an inherent order. To answer your question of how do we "know" this, it is inductive. — Metaphysician Undercover

This is irrelevant to my question. I did not ask you about the history of philosophy or why there must be inherent order; I asked you specifically about your statement regarding @fishfry's diagram:

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

Given that (1) we do not perceive order via the senses and that (2) we cannot apprehend inherent order, then how can the inherent order be the exact spatial positioning shown in the diagram? Even if I grant you that there is an inherent order to the universe, how can you say that the inherent order of the diagram is the same as the order that we perceive via the senses, or "the exact spatial positioning shown"?

But we cannot completely apprehend that order because our minds are deficient. — Metaphysician Undercover

I note your change in position. You are no longer arguing that the inherent order cannot be apprehended. You have now adopted the weaker claim that the inherent order cannot be completely apprehended.

Is it our approach (are we applying the wrong principles in our attempt to understand), or is it the reality, that the object truly has no inherent order? The latter is repugnant to the philosophical mind, and even if it were true, it cannot be confirmed until the possibility of the former is excluded. — Metaphysician Undercover

No, it cannot be confirmed at all. Assuming that the world is random (or not) makes no difference to our ability to find patterns and order in the world. More importantly, as far as I can tell, inherent order is not the kind of order that mathematicians are concerned with.

Given that (1) we do not perceive order via the senses and that (2) we cannot apprehend inherent order, then how can the inherent order be the exact spatial positioning shown in the diagram? — Luke

I think I've answered this about three times, so either I don't understand your question, or you don't understand my answer, or both.

Even if I grant you that there is an inherent order to the universe, how can you say that the inherent order of the diagram is the same as the order that we perceive via the senses, or "the exact spatial positioning shown"? — Luke

I told you, we don't perceive order with the senses, we create orders with the mind. Judging by this statement, I'm thinking it's you who is the one not understanding.

I note your change in position. You are no longer arguing that the inherent order cannot be apprehended. You have now adopted the weaker claim that the inherent order cannot be completely apprehended. — Luke

Again, you're looking for hidden meaning to make unjustified inferences. The inherent order cannot be apprehended by us. I can't even imagine what it would mean to partially understand an order. If my use of "completely" misled you, I retract it as a mistake, and apologize.

More importantly, as far as I can tell, inherent order is not the kind of order that mathematicians are concerned with. — Luke

Maybe, but fishfry claimed that a set has no inherent order. So if mathematicians are making such assumptions in their axioms, then they are concerned with it; concerned enough to exclude it from the conceptions of set theory. The issue I'm concerned with is the question of whether a thing without inherent order is a logically valid conception.

I told you, we don't perceive order with the senses — Metaphysician Undercover

Exactly, so why did you identify/equate "the inherent order" with "the exact spatial positioning shown in the diagram"?

It sounds very much as though the inherent order is identical with what is apprehended as the "exact spatial positioning shown". Otherwise, why specify the "exact spatial positioning shown"? You have not merely said that the diagram has an inherent order which we are unable to apprehend despite what we see; you have identified the inherent order with the "exact spatial positioning" that we do see. Otherwise, to whom is the exact spatial positioning "shown", and from which perspective?

Sorry Luke, now it's me who can't understand what you're saying. Do you think that we sense location?

Do you think that we sense location? — Metaphysician Undercover

Do you think that location can be shown to someone without it being sensed?

Anyway, that's not what I said.

Do you think that location can be shown to someone without it being sensed? — Luke

Of course, location is intelligible, conceptual, so it's not actually sensed it's something determined by the mind, just like meaning. When you tell someone something, they do not sense the meaning. This is "showing" in the sense of a logical demonstration. And the point is that upon seeing, or hearing what is shown, the mind may or may not produce the required conceptualization, which would qualify for what we could call apprehending the principle. More specifically, the conceptualization produced in the mind being shown the demonstration is distinct and uniquely different from the conceptualization in the mind which is showing the demonstration, therefore they are not the same. That is why people misunderstand each other..

I now see why we have such a hard time understanding each other, we seem to be very far apart on some fundamental ideas, which form the basis for our conceptualizing what is shown by the other. I thought you were intentionally misreading me, in order to say that I contradict myself. But now I see that this is the way you actually understand those words. My apologies for the accusation.

Do you think that location can be shown to someone without it being sensed?
— Luke

Of course, location is intelligible, conceptual, so it's not actually sensed it's something determined by the mind, just like meaning. When you tell someone something, they do not sense the meaning. This is "showing" in the sense of a logical demonstration. And the point is that upon seeing, or hearing what is shown, the mind may or may not produce the required conceptualization, which would qualify for what we could call apprehending the principle. More specifically, the conceptualization produced in the mind being shown the demonstration is distinct and uniquely different from the conceptualization in the mind which is showing the demonstration, therefore they are not the same. That is why people misunderstand each other.. — Metaphysician Undercover

You avoid the question instead of answering it. How can location be shown to someone without it being sensed?

"Shown" in the sense of a logical demonstration is different to "shown" in the sense of your statement: "the exact spatial positioning shown in the diagram". That's obvious.

You avoid the question instead of answering it. How can location be shown to someone without it being sensed? — Luke

I answered the question, it's just like a logical demonstration. Like when one person shows another something, and the other makes a logical inference. All instances of being shown something intelligible, i.e. conceptual, bear this same principle. We perceive something with the senses and conclude something with the mind. The things that I sense with my senses are showing me something intelligible, so I produce what serves me as an adequate representation of that intelligible thing, with my mind.

"Shown" in the sense of a logical demonstration is different to "shown" in the sense of your statement: "the exact spatial positioning shown in the diagram". That's obvious. — Luke

Sorry, you've lost me. You appear to be making up a difference in the meaning of "shown", for the sake of saying that I contradict myself. I take back my apology, I'm going back to thinking that you do it intentionally.

The issue I'm concerned with is the question of whether a thing without inherent order is a logically valid conception. — Metaphysician Undercover

Sorry, I haven't kept up. Are you speaking of inherent order or inherent ordering?

We perceive something with the senses and conclude something with the mind. — Metaphysician Undercover

I'm glad that you finally acknowledge the role played by the senses in "showing". Only a couple of posts ago, you stated:

I told you, we don't perceive order with the senses — Metaphysician Undercover

But you now concede that sense perception is involved in showing.

You appear to be making up a difference in the meaning of "shown", for the sake of saying that I contradict myself. — Metaphysician Undercover

I'm not making anything up; the word has more than one meaning. Google's definitions of the verb "show" include:

1. allow or cause (something) to be visible.
2. allow (a quality or emotion) to be perceived; display.
3. demonstrate or prove.

In the context of your statement:

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

I would say that the word "shown" here means what is visible in, or displayed by, the diagram; not what is demonstrated or proved by the diagram.

Regardless, I never claimed that there is no apprehension or awareness involved in showing. It was immediately before you began on this detour that I said:

It sounds very much as though the inherent order is identical with what is apprehended as the "exact spatial positioning shown". Otherwise, why specify the "exact spatial positioning shown"? You have not merely said that the diagram has an inherent order which we are unable to apprehend despite what we see; you have identified the inherent order with the "exact spatial positioning" that we do see [and apprehend]. — Luke

Hopefully, this now clarifies my original intent. My omission of "[and apprehend]" seems to be what sent you off on a tangent. But I'm glad you now concede that sense perception is involved in "the exact spatial positioning shown in the diagram" (even if you refuse to concede that you intended "shown" in the seemingly more obvious sense that I outlined above).

All that remains for you to explain is your contradictory pair of claims that (i) the inherent order is the exact spatial positioning that we do apprehend in the diagram; and that (ii) we are unable to apprehend the inherent order.

If we are unable to apprehend the inherent order (in any case), then how can the inherent order possibly be (demonstrated or proved by) the exact spatial positioning shown in the diagram?

There are numerous philosophers who argue against the law of identity — Metaphysician Undercover

A = A is false must necessarily be a conversation stopper...awkward pause.

The way you described sets in this thread, a set is something which cannot have an identity because it has no inherent order. — Metaphysician Undercover

Well this is just nonsense, but it relates to the reason I didn't reply to the last post you wrote to me regarding the subject of order. It finally became clear that by order you mean "where everything is in time and space," so that for example a collection of spatial points or a collection of school kids does have an inherent order.

But this is a total equivocation of the way I defined mathematical order to you, as a binary relation on a set that is reflexive, antisymmetric, and transitive.

Now I gave you that definition several times. So you could (and should) have said something like,

"I don't understand what the words reflexive, antisymmetric, and transitive mean," or "I don't know what you mean by binary relation," or, "I see you're giving the mathematical definition, but I am using the more general definition of "where things are in time and space,"".

But you didn't say any of those things. Instead you just accepted the mathematical definition I repeatedly gave you, and then kept arguing from your own private definition. When I finally figured out what you were doing, I was literally shocked by your bad faith and disingenuousness. I'm willing to have you explain yourself, or put your deliberate confusion-inducing equivocation into context, but failing that I no longer believe you are arguing in good faith at all. You have no interest in communication, but rather prefer to waste people's time by deliberately inducing confusion.

I'm perfectly willing to have you explain yourself. But once I repeatedly gave the mathematical definition of order, and instead of saying, "Oh that's not how I define order," but rather kept arguing from your own private definition without acknowledging that you were doing so, I believe you were arguing in bad faith and I have lost interest in conversing with you further. Like I say I'm perfectly willing to hear your side of this, but I can't tell you how dismayed I was to finally realize what you meant by order, and to realize that you deliberately didn't bother to explain that you were ignoring the mathematical definition. You never said, "No that is not the definition I use." My frustration with this your conversational style is terminal at this point.

Therefore I cannot agree that the set {0,1,2,3,4} is identical to the set {0,1,2,3,4}. — Metaphysician Undercover

Yeah right, whatever.

It seems like a set is an abstraction, — Metaphysician Undercover

Uh ... what the hell else could it be? I've told you a dozen times a set is a mathematical abstraction.

a universal, rather than a particular, and therefore does not have an identity as a "thing". — Metaphysician Undercover

Yeah ok. We could have a conversation around this, but I don't believe you're interested in communication, only obfuscation.

It is particulars, individual things, which have identity according to the law of identity. Notice that the law of identity says something about things, a thing is the same as itself. — Metaphysician Undercover

You just denied a set is equal to itself.

The law of identity is intended to make that category separation between particular things, and abstractions which are universals, so that we can avoid the category mistake of thinking that abstractions are things. "The set {0,1,2,3,4}" refers to something with no inherent order, so it does not have an identity and is therefore not a thing, by the law of identity, To say that it is a thing with an identity is to violate the law of identity.[/quote

I'm sorry, this is just no longer of interest to me.
— Metaphysician Undercover

This is the whole point of the law of identity, to distinguish an abstract concept from a thing, so that we have a solid principle whereby we can avoid the category mistake of thinking of concepts as if they are things. A thing has an identity which means that it has a form proper to itself as a particular. To have a form is to have an order, because every part of the thing must be in the required order for the thing to have the form that it has. So to talk about something with no inherent order, is to talk about something without a form, and this is to talk about something without an identity, and this is therefore not a thing. — Metaphysician Undercover

Word salad. Which I don't mind. But you've convinced me you're not conversating in good faith.

The problem is not that I don't think a thing is the same as itself. That is the law of identity, which I adhere to. The problem is that you make the category mistake of believing that abstract conceptions are things. Because you will not admit that a concept is not a thing, you make great effort to show that two distinct concepts, like what "2+3" means, and what "5" means, which have equal quantitative value, refer to the same "thing". Obviously though, "2+3" refers to a completely different concept from "5". — Metaphysician Undercover

When you put those in quotes of course that is correct, but that has never been the subject of the conversation. More obvious bad faith and sophistry.

If you would just recognize the very simple, easy to understand, fact, that "2+3" does not mean the same thing as "5" does, you would understand that the two expressions do not refer to the same concept. — Metaphysician Undercover

I think any reader following this thread can perfectly well see that the quotation marks have never been the subject of the conversation. I think you genuinely argue in bad faith and like to waste people's time. You're a troll.

So even if concepts were things, we could not say that "2+3" refers to the same thing as "5", because they each have different associated concepts. And it's futile to argue as you do, that the law of identity is upheld in your practice of saying that they refer to the same "mathematical object", because all you are doing is assuming something else, something beyond the concepts of "2+3", and "5", as your "mathematical object". This supposed "object" is not a particular, nor a universal concept, but something conjured up for the sake of saying that there is a thing referred to. But there is no basis for this object. It is not the concept of "2+3" nor is it the concept of "5", it is just a fiction, a false premise you produce for the sake of begging the question in your claim that the law of identity is not violated. — Metaphysician Undercover

I'd be more inclined to respond if you hadn't been deliberately obfuscatory about your different use of the word order, after I'd given you the mathematical definition several times. Absent a clear explanation of why you did that, knowing how much confusion you were causing, I don't want to play.

Sorry, I haven't kept up. Are you speaking of inherent order or inherent ordering? — jgill

I think I said "inherent order", but I don't quite understand the point to making the difference.

But you now concede that sense perception is involved in showing. — Luke

Of course sense perception is involved! Where have you been? We've been talking about seeing things and inferring an order. My point was that we do not sense the order which inheres within the thing, we produce an order in the mind. I never said anything ridiculous like we do not use the senses to see the thing, when we produce a representation of order for the thing.

I would say that the word "shown" here means what is visible in, or displayed by, the diagram; not what is demonstrated or proved by the diagram. — Luke

But we went through this already. I explained that this is not what I meant by "shown"., and the reason why, being that order is inferred by the mind, it is not visible. I went through a large number of posts explaining this to you. It seemed to be a very difficult thing for you to grasp. And now, when you finally seemed to grasp the meaning associated with the way I used the term, you've gone right back to assuming that this is not the way I used it, despite all those explanations. Why? We just go around in circles, it's stupid. You pretend to have understood my explanation as to what I meant by "shown", then all of a sudden you say but obviously that's not what you meant. It's ridiculous. It' like you're saying 'I would not have used "shown" that way, therefore you did not'. And when i go through extreme lengths to explain that this is actually how I used the term, to the point where you seem to understand, you turn right back to the starting point, claiming but I would not have used it that way, therefore obviously you didn't. What's the point?

All that remains for you to explain is your contradictory pair of claims that (i) the inherent order is the exact spatial positioning that we do apprehend in the diagram; and that (ii) we are unable to apprehend the inherent order. — Luke

I stated repeatedly that we do not apprehend the exact spatial positioning, so you have a strawman here.. You don't seem to be capable of understanding any of what I am saying, we're just going around in circles of misunderstanding. it's pointless.

I explained that this is not what I meant by "shown"., and the reason why, being that order is inferred by the mind, it is not visible. — Metaphysician Undercover

By "shown" you do not mean "displayed". After all, "it is not visible". Therefore, you must not be making the argument - as you did earlier - that we see the order but do not apprehend it.

By "shown" you mean "logically demonstrated". If something is logically demonstrated then it is apprehended, right?

I stated repeatedly that we do not apprehend the exact spatial positioning — Metaphysician Undercover

You are saying that the "exact spatial positioning" is logically demonstrated by ("shown" in) the diagram, but it is not apprehended? If the exact spatial positioning is not (or cannot be) apprehended, then how has it been logically demonstrated by the diagram?

I think I said "inherent order", but I don't quite understand the point to making the difference. — Metaphysician Undercover

Inherent order is a wider concept, applying in particular to biological systems and natural phenomena. Ordering is more specific having to do with listing. I think you are discussing the latter.

If the universe is endlessly expanding forever and ever isnt that an infinite scenario? Will it stop expanding? If not then the universe is infinite. If it does stop expanding could it have expanded forever if circumstances allowed it to.