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
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 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
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
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
If there is a difference between the apparent order and the inherent order, then why did you state: — Luke
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. — Metaphysician Undercover
They are equal, but equal is distinct from identity. I've told you this numerous times before, but you do not listen. — Metaphysician Undercover
Nor do you seem to pay any attention to my references, only repeating your misunderstanding in ignorance.[/quote = 5. — Metaphysician Undercover
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? — Luke
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. — 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?
— 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
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
The inherent order is the exact spatial positioning shown in the diagram. — Metaphysician Undercover
On the contrary. 2 + 3 and 5 are mathematically identical. There is not the slightest question, controversy, or doubt about that. — fishfry
You spoke of an "external perspective", which implies an internal perspective. You might recall I asked you about it and you responded: — Luke
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
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
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
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
The latter is rather pointless. — Metaphysician Undercover
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
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
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
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
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
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
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
If "We cannot apprehend the inherent order", then how do you know that our representations are inaccurate? — Luke
If the inherent order is unintelligible to the human mind by definition, then what makes inherent order preferable to (or distinguishable from) randomness? — Luke
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
The inherent order is the exact spatial positioning shown in the diagram. — Metaphysician Undercover
But we cannot completely apprehend that order because our minds are deficient. — Metaphysician Undercover
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
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
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 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
More importantly, as far as I can tell, inherent order is not the kind of order that mathematicians are concerned with. — Luke
I told you, we don't perceive order with the senses — Metaphysician Undercover
Do you think that we sense location? — Metaphysician Undercover
Do you think that location can be shown to someone without it being sensed? — Luke
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? — Luke
"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
The issue I'm concerned with is the question of whether a thing without inherent order is a logically valid conception. — Metaphysician Undercover
We perceive something with the senses and conclude something with the mind. — Metaphysician Undercover
I told you, we don't perceive order with the senses — Metaphysician Undercover
You appear to be making up a difference in the meaning of "shown", for the sake of saying that I contradict myself. — Metaphysician Undercover
The inherent order is the exact spatial positioning shown in the diagram. — Metaphysician Undercover
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
There are numerous philosophers who argue against the law of identity — Metaphysician Undercover
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
Therefore I cannot agree that the set {0,1,2,3,4} is identical to the set {0,1,2,3,4}. — Metaphysician Undercover
It seems like a set is an abstraction, — Metaphysician Undercover
a universal, rather than a particular, and therefore does not have an identity as a "thing". — Metaphysician Undercover
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
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
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
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
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
Sorry, I haven't kept up. Are you speaking of inherent order or inherent ordering? — jgill
But you now concede that sense perception is involved in showing. — Luke
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
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 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
I stated repeatedly that we do not apprehend the exact spatial positioning — Metaphysician Undercover
I think I said "inherent order", but I don't quite understand the point to making the difference. — Metaphysician Undercover
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