I think what makes a rule a rule, is to be explicitly stated.
— Metaphysician Undercover

There is no rule (used my way) for the use of "rule".
— Metaphysician Undercover

Which is it, MU? — Luke

Both it is. What makes a rule a rule is to be explicitly stated (my opinion, notice "I think"). But there is no rule which states that "rule" must be used in this way.

It sounds profound to talk of the Law of Identity; we need to keep in mind that what we are talking about is just a=a. — Banno

No, I'm not talking about a=a. What I'm talking about is the law of identity, which states that a thing is the same as itself. Look it up if you don't already know it. If you represent the law of identity as "a=a", then we must respect the fact that you are using a=a to express "a thing is the same as itself.", that is the defined meaning of a=a.

As it stands it is impossible to confirm its validity, let alone that it is cogent. It mixes terms - mind, necessity, dependency - that need considerable work to be understood. — Banno

I know that the validity of the law of identity cannot be proven, and that's irrelevant. You can accept it or not, but I think like any other fundamental proposition, it's best to understand it before rejecting it. And understanding it requires recognizing that a thing and its identity are one and the same. Therefore to be a thing is to have an identity, and to have an identity is to be thing. Clearly there is no stipulated dependence on a mind required for a thing to be a thing, and no reason to think that a mind is required, therefore a thing is mind independent.

It is also clear that a=a is a relationship, contrary to what you claim; all you have done is stipulate that relationships are between different individuals. — Banno

This is equivocation on the meaning of "a=a", and so you've provided a fallacious argument. As indicated above "a=a" must represent "a thing is the same as itself" to represent the law of identity. And, being one and the same as, is not a relation. "Relation" indicates what one has to do with another, and that's something completely different from being the same thing.

What makes a rule a rule is to be explicitly stated (my opinion, notice "I think"). But there is no rule which states that "rule" must be used in this way. — Metaphysician Undercover

Therefore, rules do not have to be explicitly stated.

That's right, you can use "rule" however you please.

I know that the validity of the law of identity cannot be proven... — Metaphysician Undercover

I wasn't questioning the validity of a=a; I was questioning the validity of your argument.

No, I'm not talking about a=a. What I'm talking about is the law of identity, which states that a thing is the same as itself. — Metaphysician Undercover

Yep. And this is where I walk away.

That's right, you can use "rule" however you please. — Metaphysician Undercover

You can believe that or you can believe that a rule must be explicitly stated. You can't have both. So I trust you've given up on your opinion that rules must be explicitly stated.

Yes, there is always more reading to do. — Fooloso4

I wonder why most people read instead of figuring these things out for themselves. I mean, I don't wonder, it's obvious why. I just wanted to make others aware that their minds are an excellent source material, too, should they choose to employ it for that purpose.

Yeah. The products of those minds that have read neither widely nor deeply are unfortunately easily found hereabouts.

Yeah. The products of those minds that have read neither widely nor deeply are unfortunately easily found hereabouts. — Banno

Yeah. I so totally agree. I may add that there are some extremely well-read minds around here, who hide behind jargon and throwing about big names but which minds nevertheless succeed to show very little original thought.

You, Banno, at least apply your knowledge appropriately. And my favourite contributor on these forums, Fooloso4, combines the two: a solid background knowledge and an ability to employ his or her agile mind to not only question and interpret the readings, but also to creatively build on its learned knowledge base.

Yes, Fooloso4's contribution has been noted.

we can imagine the concept of empty space, but we cannot imagine the concept of there being no space. — RussellA

I have a clear idea of what dimensions are; and I understand what zero-dimensional space would be. like. Saying I can't imagine it - so what? — Banno

“...We never can imagine or make a representation to ourselves of the non-existence of space, though we may easily enough think that no objects are found in it. It must, therefore, be considered as the condition of the possibility of phenomena, and by no means as a determination dependent on them, and is a representation a priori, which necessarily supplies the basis for external phenomena....” (A24/B39)

Why bring up dimensions or zero-dimensional space, when those are mere euphemisms for the terms given in the text? Do you see that thinking objects in space (from the text) does not give you a coordinate system, which makes dimensions (from your statement) irrelevant? And space is itself zero-dimensional anyway, so amending space with that qualifier adds nothing whatsoever to the significance of the term.

Do you see there’s no congruency between your “I understand what zero-dimensional space would be like”, and, “we may easily enough think that no objects are found in it”? You will say they amount to the same thing, they have the same truth-value or some such nonsense, because you’re submerged in language games, but I shall nonetheless point out you’ve treated space as the subject in your statement, but space is in the predicate of the statement you’ve claimed, for all intents and purposes, to not understand. But that just sets the ground. In effect, you’ve merely stated you understand what space would be like, which is altogether quite impossible, while I...and even yourself...can imagine holding our hands out with no object resting in their respective palms. I mean....what is space like, really? Compared to.....what?

Finally, that which you can’t imagine, re: Russell’s “concept of there being no space”, is not the same as what the text says can’t be imagined, re: “the representation to ourselves of the non-existence of space”. But, herein in your defense, because I acknowledge your tacit rejection of Kantian epistemology as being left behind by those finding precious little value in anything a few years older than themselves, I grant you won’t accept the theoretical subtleties which sustain the difference.

Oh. And your “so what?”? It is answered, if I may poach from the illustrious Paul Harvey.....in the rrEESSSTTT of the story!!

Cheers(?)

Yep. And this is where I walk away. — Banno

Wise move. Educate yourself on the law of identity, and prepare yourself with some principles before you attempt to argue that identity is a relation. I think such an argument only demonstrates a lack of understanding of the difference between what a relation is, and what an absolute is.

I will refer you back to Wittgenstein's "Philosophical Investigations", 253-256. If you understand these passages you will apprehend the need for an explicit criterion of identity. Without that law of identity we might use "same" in the ordinary, customary way, such as to say that this chair is the same as that chair, or even my sensation is the same as your sensation.

You can believe that or you can believe that a rule must be explicitly stated. You can't have both. — Luke

"Must" is normative here, it does not imply logical necessity, so your argument is not logical, it is fallacious by equivocation. And I believe that people are free to act contrary to the norms. So I see no problem with believing that you use "rule" differently from me, and also believing that a rule must be explicitly stated to qualify as being a "rule". You are doing what I think you ought not do, and this type of thing is a common occurrence. So I believe that you use "rule" in an incoherent way which renders logical procedure impossible. I believe that to proceed logically we need to distinguish between what is stated and what is not stated, and only what is stated qualifies as a rule.

But you believe that there could be premises (rules governing the use of a word) which are not stated, and this foils logical procedures by enabling equivocation. I've tried to persuade you to see things my way, so we could proceed together logically, but to no avail . Since I have no inclination to join you in your incoherency, and you appear to have no desire to proceed logically, discussing this issue is fruitless..

"Must" is normative here — Metaphysician Undercover

It is your belief or opinion that a rule must be explicitly stated. What's normative about that?

So I see no problem with believing that you use "rule" differently from me, and also believing that a rule must be explicitly stated to qualify as being a "rule". — Metaphysician Undercover

The problem is not with your belief that you and I use the word "rule" differently. The problem, as I have pointed out, is that you contradict yourself with your pair of beliefs that "you can use "rule" however you please", and that "you use "rule" in an incoherent way."

Either I can use "rule" however I please or I cannot. Which is it?

The obvious implication here is that if you want to use the word "rule" in a coherent way, then you cannot use the word "rule" however you please.

So it looks as though language is a game consisting of rules after all.

I have extensive knowledge of language; language is mind code.

The strict definitions outlined in the dictionary are only guidelines to what is a more mechanical impulse.

The word 'and' is used in this way:

• There one apple and one banana.
• There we were, and suddenly there she was too.
• And it.
• And plus.

And - derivative. Is the mind code usage of the word 'and'.

Try another, 'if':

• If I say this, do this.
• If we come to a crossroad, go left.
• If the river is blue in your eyes, what exactly is this red substance I see?
• If tomorrow never comes...

If - simulation. Is the mind code usage of the word 'if'.

Thus, truly they are not word games and we are not playing; if the dictionary has perplexed your view of language, try fixing that error so you can see how serious and permanent language is.

When I use the word 'and' or 'if', I do so in the manner of machine code; which isn't following phrasing norms as outlined by the dictionary, but sensible phrasing: and - do this - (this) if X occurs, ledge all sense data as English Language, if X does not occur, work on defining ledged data - until dictionary is complete. If random shutdown, do not reboot.

Kantian epistemology — Mww

Kant — Banno

The impossibility of imagining something that cannot be imagined
Kant's proposal of a priori pure intuitions is at the core of my philosophical beliefs. Although Kant in Critique of Pure Reason only specifically mentioned space, time and objects, in my opinion, other concepts can be included a priori. For example, the colour red, a bitter taste, an acrid smell, a velvety touch and a grating noise.
A26, A33 - "Space and time are merely the forms of our sensible intuition of objects. They are not beings that exist independently of our intuition (things in themselves), nor are they properties of, nor relations among, such beings"
A239 - "We can only cognize objects that we can, in principle, intuit. Consequently, we can only cognize objects in space and time, appearances. We cannot cognize things in themselves".
IE, such a priori pure intuitions, concepts, explains to me how the mind relates to that which is outside the mind.

I can imagine zero dimension, but not no dimensions
I can imagine a cube of 1cm sides. I can imagine a cube of 1mm sides. I can imagine a cube having sides of zero dimension. But I can only imagine this cube of zero dimensions within my ordinary everyday space of tables, chairs, etc. For the mind to be able to imagine no space would be as if the mind could imagine not existing, as the concept of space is a fundamental building block from which the mind is constructed.

Colour as a tractable example
As regards colour, my position is that of eliminativist projectivist, where we project a colour, which is purely a mental phenomena, onto objects in our environment. A post-box isn't red, but emits light at a wavelength of 700nm which the mind interprets as the colour red. Stephen Palmer wrote in 1999 "colour is a psychological property of our visual experiences when we look at objects and lights, not a physical property of those objects and lights". In a similar fashion, the concept of space is a mental phenomena which the mind projects onto what it perceives as an outside world.

Galileo, for example, thought that physical science had shown that objects are not really coloured, but inside the mind.

For the mind to be able to imagine no space, would be as if a person born colour blind
could experience the colour red by being described it by others, even allowing for the possibility of an "inverted spectrum".

Kant postulated that the mind intuits sensory experience which it processes in the faculty of understanding in order to produce an ordered predictable world, Consequently, we must already have knowledge of what space and time are in order to recognize the intuition of time and space. Similarly, we must already have knowledge of the colour red in order to recognize the intuition of the colour red.

As with the question, do objects in the world have the property of colour that the mind perceives them to have or is the property only a mental phenomenon. Is what the mind perceives as "space" a property of what is external to the the mind or a property only of an internal mental phenomenon.

As in order to be conscious of the colour red we must have an a priori innate ability to
be conscious of the colour red, in order to be conscious of space and time we must have an a priori innate ability to be conscious of space and time.

Synergism of the brain with the world through evolution
The mind today, ie, the brain, is the product of 3.7 billion years of evolution within the world. The Synergism Hypothesis of 1983 addressed the evolution of cooperative phenomena in nature and increased complexity in living systems. I am not saying that space and time don't exist, but that the mind is not directly aware of space and time. What the mind perceives as space and time is a projection by the mind of innate concepts that have evolved over billions of years onto sense impressions it receives through sight, sound, etc. As the concepts of space and time are an innate part of the mind, it is beyond the ability of the mind to imagine their non-existence.

The mind is not separate to a priori pure intuitions, the mind "is" a priori pure intuitions
As the concept of space and time is an innate physical part of the structure of the brain, it would as impossible for the brain to imagine the non-existence of space and time as it would be for the brain to imagine the non-existence of pain when touching a hot stove.

As it would be impossible for the mind to think about what it would be like to not think, it would be impossible for the brain to contemplate the non-existence of space and time, as the concept of space and time is innate within the brain, and a part of the physical structure of the brain.

The brain is not separate to its innate a priori concepts - space, time,etc - rather, the brain "is" its innate a priori concepts, and therefore cannot contemplate the non-existence of something that makes up its very nature.

Pretty good synopsis, I must say. There are some fundamental contentions, but they don’t detract from the general picture, and certainly wouldn’t matter in the least, to someone rejecting the system itself.

While that was written with great passion, it was very hard to follow. "... space is itself zero-dimensional anyway"?

Here's the quote:

As Kant wrote in Critique of Pure Reason, "Space and time are merely the forms of our sensible intuition of objects. They are not beings that exist independently of our intuition (things in themselves), nor are they properties of, nor relations among, such beings". (A26, A33) — RussellA

Prima facie, this is at odds with General Relativity. But that's not what is of import here...

It's just that our understanding of space has moved on considerably since Kant. — Banno

But I'll read on...

Yep. And this is where I walk away.
— Banno

Wise move. — Metaphysician Undercover

Indeed.

Kant's proposal of a priori pure intuitions is at the core of my philosophical beliefs. — RussellA

What a shame.

I can imagine zero dimension, but not no dimensions — RussellA

...imagine...

It's unclear to me what imagination has to do with dimensions. The dimensionality of an object is, roughly, the number of coordinates needed to specify a point on the object.

One cannot imagine eleven-dimensional space, but one can do the maths.

The maths for zero-dimensional space is considerably simpler.

But then topology was developed after Kant, so we can't blame him for not being able to imagine it.

It is your belief or opinion that a rule must be explicitly stated. What's normative about that? — Luke

It's my opinion and belief. It's my opinion that if it hasn't been stated in some form it cannot be a rule, and I believe this. This "must" in your statement, "must be explicitly stated" is normative, because it's a standard of behaviour that I believe in. For example, suppose you think of something which you believe is a rule, but it has never been explicitly stated. Then I break this so-called "rule" and you accuse me of breaking the rule. I would argue that I didn't break any rule because what you thought was a rule was never stated and therefore it did not exist as a rule.

The problem, as I have pointed out, is that you contradict yourself with your pair of beliefs that "you can use "rule" however you please", and that "you use "rule" in an incoherent way." — Luke

I don't see how this is contradictory. People use words in incoherent ways quite often. This is just a matter of describing reality. I believe the word "rule" ought to be used in a way which avoids contradiction, but I know, and respect the fact that freely choosing human beings such as yourself, can use words however you want. It's no different from saying that I believe people ought to act morally, but they freely choose to act in immoral ways. It's my opinion, and I firmly believe that one ought to do what is right (use "rule" in a logically rigorously defined way), yet I have respect for the reality that people are free to do what I believe is wrong. Furthermore, I might even do what I believe is wrong in some instances.

Either I can use "rule" however I please or I cannot. Which is it? — Luke

I've told you many times, you are free to use that word however you want. However, I will not necessarily agree with the way that you use it. There is no contradiction here. Until we have a rigorous definition (a rule dictating how we must use "rule"), I cannot accuse you of breaking any rules. I can however say that your use appears incoherent (inconsistent) to me. This was the case the last time we discussed this, I believe you were equivocal in your use.

The obvious implication here is that if you want to use the word "rule" in a coherent way, then you cannot use the word "rule" however you please. — Luke

What we want, and what we are actually free to do, are two distinct things. That's reality. And that I am free to do something which I do not want to do, does not amount to contradiction. Even when I end up doing something which I didn't want to to, this is generally a mistake, it is not a contradiction. But when I say I will not do something, yet I do it intentionally rather than by mistake, this is lying or hypocrisy.

I can imagine zero dimension, but not no dimensions
I can imagine a cube of 1cm sides. I can imagine a cube of 1mm sides. I can imagine a cube having sides of zero dimension. But I can only imagine this cube of zero dimensions within my ordinary everyday space of tables, chairs, etc. For the mind to be able to imagine no space would be as if the mind could imagine not existing, as the concept of space is a fundamental building block from which the mind is constructed. — RussellA

I don't understand any of this. How is it possible to imagine a zero dimension cube? Why is it impossible for the mind to imagine spacelessness, or non- spatial existence? If we imagine that the mind might have temporality only, and is prior to spatial existence, then spatial presence becomes unlimited. That is to say, if space is conceived of as coming into existence from no space, as time passes, and the mind itself is prior to spatial existence, then the mind is free to appear in many different spatial points at the same time. Isn't this how free willing locomotion works? The mind has freedom to determine spatial location.

It's my opinion and belief. It's my opinion that if it hasn't been stated in some form it cannot be a rule, and I believe this. This "must" in your statement, "must be explicitly stated" is normative, because it's a standard of behaviour that I believe in. — Metaphysician Undercover

There is no such "standard"; it is merely your own personal opinion. You don't set the standards or norms all on your own.

Otherwise, where can I find this standard of behaviour? Where is it written? By your own reckoning, a rule cannot exist unless it is explicitly stated, so where is it explicitly stated that a rule must be explicitly stated?

I've told you many times, you are free to use that word however you want. — Metaphysician Undercover

You cannot use that word however you want if you want to be coherent. Your argument is analogous to saying: I can move any chess piece to wherever I like on the board because it's physically possible, therefore chess has no rules. But you can't move the pieces just anywhere if you want to play the game, or if you want to make moves in the game that are permissible/coherent/understood. You seem to think you're making an interesting point about the freedom to make any moves whatsoever, but all we're really interested in are possible moves within the game. This is where the line is drawn between coherent and incoherent. But this line cannot be drawn by you alone. Who told you that?

Your argument is analogous to saying: I can move any chess piece to wherever I like on the board because it's physically possible, therefore chess has no rules. — Luke

Yep.

There is no such "standard"; it is merely your own personal opinion. You don't set the standards or norms all on your own. — Luke

You ought to recognize, that in my context of usage, a "standard" is an example or model used for judgement, like a criterion. That any specific standard is the one which ought to be applied is a matter of judgement and therefore opinion. However, there may be a rule which states which standard or criterion is applicable in a specific type of situation. Such rules can greatly assist in one's application of standards. So standards are things which you hold on your own, as opinions, and they may or may not be consistent with the rules. But if I used an unacceptable word here, that's my mistake and I apologize if it was taken as an offence .

Otherwise, where can I find this standard of behaviour? Where is it written? By your own reckoning, a rule cannot exist unless it is explicitly stated, so where is it explicitly stated that a rule must be explicitly stated? — Luke

Since when is "standard" necessarily exchangeable with "rule"? The reason why a language has many different words is to provide us with the capacity to say many different things. If you make all the different words mean the same thing, how could you ever say anything meaningful? Obviously, judging by the context, I do not use "standard" to mean the same thing as "rule". That would mean I was intentionally contradicting myself. So your behaviour of exchanging "standard" for 'rule" so that you might ridicule me, is not only unsupported with any logic, but is downright mean.

You cannot use that word however you want if you want to be coherent. Your argument is analogous to saying: I can move any chess piece to wherever I like on the board because it's physically possible, therefore chess has no rules. But you can't move the pieces just anywhere if you want to play the game, or if you want to make moves in the game that are permissible/coherent/understood. You seem to think you're making an interesting point about the freedom to make any moves whatsoever, but all we're really interested in are possible moves within the game. This is where the line is drawn between coherent and incoherent. But this line cannot be drawn by you alone. Who told you that? — Luke

You are just providing evidence here that the "game" analogy fails. Instead of looking at the reality of language use, and seeing that the "game" analogy is incapable of capturing all the aspects of language, you argue against the truth about language, by applying the game analogy. This is a very important point to understand about the use of things like analogies, similes, metaphors, hyperboles, parables, and allegories. These tools are only capable of bringing us a limited understanding, and if we adhere to every aspect of them, as if they are a literal description, they will surely mislead us, ending up with misunderstanding rather than understanding.

You could create an analogy that a computer is just like a car, they both are mass produced artificially, and have electronics. And anytime I tried to show you that there are no wheels on the computer, so the analogy fails at this point, you keep denying the reality of what I am showing to you, by referring to the analogy and insisting that there must be wheels on the computer, because it's just like a car.

So referring to the game analogy, intending to disprove the facts about language which I am showing you, when I am showing you this for the sake of demonstrating the failings of the analogy, really doesn't help your case.

So standards are things which you hold on your own, as opinions, — Metaphysician Undercover

Equivocation. These are different "standards" to those in the context of norms and normativity.

You are just providing evidence here that the "game" analogy fails. — Metaphysician Undercover

How does the analogy fail? Moving pieces wherever you want, irrespective of the rules of the game, is not playing the game.

These are different "standards" to those in the context of norms and normativity. — Luke

There was no equivocation. The first line in the Wikipedia entry on "Normative": "Normative generally means relating to an evaluative standard." Isn't that just what I said about how I used "standard"?

The problem which you seem to have, is accepting that there is a difference between a publicly stated "rule", and a principle which an individual applies in one's mind when making a decision or judgement. In order to have a proper understanding of language use, we need to maintain this distinction. The reality of this difference is what allows one to know the rule, yet act in a way which is inconsistent with the rule. When I explained this reality to you, you insisted that it's contradiction. But that's only because you do not heed the distinction, rather dissolving it and creating confused ambiguity.

How does the analogy fail? Moving pieces wherever you want, irrespective of the rules of the game, is not playing the game. — Luke

Right, in playing a game we must adhere to the rules with all moves. But in language we see competing rules which makes such a thing impossible, so we ought to drop the analogy right there. Instead, a multitude of games is proposed. However, a closer look at language use would reveal that it is shaped not by rules, but by freely chosen activities of free willing beings. Hence, what is basic or fundamental to the form which language takes, is not a rule governed structure, but the very opposite of this, activities which are free from rules. Therefore, if we adhere to the game analogy when trying to describe, or represent language use, our models will be completely backward. The game analogy represents language use evolving from fundamental rules (hinge propositions or whatever), building more and more rules on top of foundational rules, instead of modeling the reality of language, as a fundamentally free and lawless activity, free from foundational rules, from which rule structured activities may emerge.

How we employ an analogy, as a tool, is that we apply it until the point where it fails. Its failure, and how it fails, tells us something new, which we didn't already know, about the thing that it is applied to. We take a well known thing, and compare it to a lesser known thing, something we are trying to understand. Of course the two things will not be exactly the same. So when we get to the point where the comparison fails, and it can be carried no further, we have exposed the aspects of the lesser known thing which we do not understand. Now we can proceed toward understanding these mysterious aspects. But at this point we can no longer apply the analogy, so we must apply other principles.

Prima facie, this is at odds with General Relativity. But that's not what is of import here... — Banno

No, it isn’t important at all:

“...If we confine the application of the theory to the case where the gravitational fields can be regarded as being weak, and in which all masses move with respect to the co-ordinate system with velocities which are small compared with the velocity of light, we then obtain as a first approximation the Newtonian theory. Thus the latter theory is obtained here without any particular assumption, whereas Newton had to introduce the hypothesis that the force of attraction between mutually attracting material points is inversely proportional to the square of the distance between them. If we increase the accuracy of the calculation, deviations from the theory of Newton make their appearance, practically all of which must nevertheless escape the test of observation owing to their smallness...”
(Relativity: The Special and General Theory, Pt 2, Sec. 29, 1916)

It's just that our understanding of space has moved on considerably since Kant. — Banno

Yeah, no biggie. Calling space a gravitational field is merely another language game, innit? Proving gravitational fields are warped by massive bodies doesn’t prove space is a property of objects, which is sufficient reason to permit Kant’s exposition of space as a pure intuition “...by which the experience of objects is possible....” to stand unmolested. That the coordinate system for the location of objects must be relative to something, and that something being called space, is not refuted or even impinged upon, by GR. Notice as well, if you will, Kant made time, itself a “pure a priori intuition”, just as necessary for the experience, therefore the relation, of objects, as did Einstein, albeit not necessarily Euclidean, with his “spacetime continuum” (ibid, Sec. 27)

Not denigrating progress in science, mind you, just defending its metaphysical origins.

the reality of language, as a fundamentally free and lawless activity — Metaphysician Undercover

Right, in playing a game we must adhere to the rules with all moves. But in language we see competing rules which makes such a thing impossible, so we ought to drop the analogy right there. — Metaphysician Undercover

Does language have no rules or does it have "competing rules"? What "competing rules" does language have?

However, a closer look at language use would reveal that it is shaped not by rules, but by freely chosen activities of free willing beings. — Metaphysician Undercover

How is this different to the game of chess? It is not as though people are forced to play chess against their will by the deterministic laws of nature, or that they are physically unable to make illegal moves. Chess is also "shaped...by freely chosen activities of free willing beings", yet it is still a game for all that, and has rules too.

and the mind itself is prior to spatial existence — Metaphysician Undercover

As I believe in reductive physicalism, in that I believe that the mind and body are ontologically indiscernible, for me, the mind cannot be prior to spatial existence

One cannot imagine eleven-dimensional space, but one can do the maths. — Banno

I agree that there are two aspects to imagining either an eleven-dimensional space or there being no space, dependent on whether mathematics was a discovery or an invention. My belief is that mathematics was invented.

If mathematics was discovered, then points of "no dimension" exist in the world independent of the existence of any observer. I would then agree that in geometry, where the dimension of any space is defined as the minimum number of coordinates needed to specify any point, and a point has no dimensions, then I don't need to imagine what "no dimensions" means. I only need to understand how it is used, as Wittgenstein might have said.

If mathematics was invented, then a point of "no dimension" is a mental construct, and therefore mathematics cannot be used to determine existence independently of the existence of the mind.

It depends on whether one is in Plato's or Aristotle's camp.

You made the claim, after Kant, that space does not have properties. General Relativity treats space as having the properties - being curved to calculable extents; those calculations are use din your phone to find your location using GPS.

Kant is so yawnsome.