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One for the Metaphysicians - Kant's 'Left Hand/Right hand Paradox!'

I think you're underthinking this. Or maybe overthinking.

Just because there's no one there to classify it or because there's nothing to act as the opposite is irrelevant.

A left hand is intrinsically different than a right hand. Take your hands and you try to position them so that they're sitting on top of eachother identically.

You cannot accomplish this- mirror images they may be, but they are different.

It was either a left or right hand, but it's impossible to answer which.
 
you know this hammilton guy is freaking genius, I so agree with him. YOU DON'T? Too bad!
 
Ham-milton said:
I think you're underthinking this. Or maybe overthinking.

Just because there's no one there to classify it or because there's nothing to act as the opposite is irrelevant.

A left hand is intrinsically different than a right hand. Take your hands and you try to position them so that they're sitting on top of eachother identically.

You cannot accomplish this- mirror images they may be, but they are different.

It was either a left or right hand, but it's impossible to answer which.


Who said anything about disagreeing? If you are a genius then I applaud you, I hope you apply your skills to the constructive advancement of the content, or form, of the human knowledge-base.

You are correct in your observation that I am perhaps under-thinking this, would that I had the time to indulge the topic further. You are also right about over-thinking the concept, but the two are not mutually exclusive.

This is not a problem seeking some solution, but rather points to the solution of a problem we have yet to encounter.

Are incongruent counterparts really intrinsically different? In what way? This is not about actual hands, but rather handidness. Left- and right-handidness are fundamental properties of the universe, spin, polarity, black-holes, galaxy-clusters...all describe a certain handedness. Understanding if this is illusory, or as you say ‘intrinsic’...I’m assuming meaning objectively-existant – is a question worthy of contemplation. You state that it’s impossible to know – that could be the solution, but until you prove to me why, I will continue to explore the various possible answers, to test them rigorously until they either fall, or are accepted as new axiomatic principles...then the real work begins, insofar as what do such axioms deliver to our understanding of either relative, or absolute space.

I cannot pretend to even know the first thing in such matters, I am a dunce, I know only one thing, and it's the same 'thing' that Socrates knew.


AN
 
Alephnul said:
Unobserved, objects’ ‘qualia’ have little meaning (hence the heckneyed philosophical question: ‘If a tree falls down in the forst, with no one to hear it, doe it make a noise?’

Yep. I've always noticed this, and tend to stress it when I talk philosophy with people. Your experience of what you observe is a crucial ingredient OF what you observe. Sentience is a meeting of a world within with a world without.
 
Right and left is still a label that assumes that a right exists for your left. Using some generic object that doesn't have a recognisable difference in relative position, there is no reason to believe that a right even exists. Nor does it consider that the same generic object would likely have more then one meta-mirror image, making definition by simply right or left insufficient.
 
Re OP:

It wouldn't have a label, because language and symbols would do not yet exist without the consciousness to conceive them. But say it did have a label, it couldn't be left or right, because there is no body attached to it, nor a body that was ever been witnessed attached to such a shape, and so no conclusion could be made that it was a right or left hand. So "neither".
 
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Alephnul said:
So, to summaries, if we posit a theoretical 4th dimension to resolve Kant's paradox, we must also, by logical necessity accept the existence of negative dimensions of space. Most empiricists would say 'I told you so, dreaming up non-exeriential geometries to solve some of the problems of space as experienced by the senses (3d) gets you in a whole heap of trouble' whilst the rationalist is left with a choice, approach Kant's paradox some other way (accepting that positing super-experiential dimensions through analogy is not valid) or, accept the negative dimensions and start trying to work out what they are, and what they do.

There's many problems with this reasoning. Correct me if I'm wrong, this is how the argument runs:
1) Some proposition P is true for 2d figures in 3d space.
2) P is also true if we increase all the dimensions involved by 1. (3d figures in 4d space)
3) Therefore P must be true if we increase or reduce the dimensions involved by any natural number!

I think when it's put plainly like that, this is clearly nonsense. If you want a demonstration, though, just note that we can derive all sorts of ridiculous things with this reasoning: n=2 is a positive number. If we increase n by 1, then n=3 is also positive. By your reasoning above, then, we can keep decreasing n and it will always still be positive!

In reality, what you're trying to do is of course an argument by induction. What you need to get it to work is to show the induction step in the right direction. If you can show that for any positive integer D, given a space of dimension D, you can create a bigger viable space of dimension D+1 -- then you've shown that spaces of all positive integer dimension exist. To get negative dimensions, though, you need to do the induction step in the opposite direction: you need to show that you can always construct a space of lower dimensions. That's a very different thing, and it's not possible in any sensible way.** (You might try "taking off" an orthogonal direction, but then you of course stop when you get to 0 dimensions; there's no more orthogonal directions to remove.)

Note that your own little dialogue about boundaries give you a hint you can't get negative dimensions! A 3d cube has 6 squares bounding it; a 2d square has 4 lines bounding it; a 1d line has 2 points bounding it. Following the pattern, a 0d point would have 0 (ie no) lower-dim objects bounding it.


Incidentally, let me also add that "analogy" is not an acceptable way of demonstrating the existence of higher-dimensional spaces. The 2d to 3d analogy is useful in giving you clues as to what 4d space might be like, but it's only a guess until you actually construct 4d space and explore its properties. For example: there are no knots in 2d, while there are a number of classes of knots in 3d. By analogy you might expect even more types of knots in 4d; but in reality there are no knots in 4d, either! In any case, all this wanking around with "analogy" is completely pointless -- higher-dimensional spaces are well-understood. What you're talking about here is R^3 (ordinary 3d Euclidean space) and R^4 (4d Euclidean space.) Indeed it's trivial to actually construct them.

It would truly be disappointing if this supposed argument gets taken seriously in the philosophy literature.

---

Going back a bit, this isn't really a "solution" to the original issue (which is silly in itself.) All it does is invent a scenario (3d hand in 4d universe) where the supposed problem doesn't exist. But that's easy -- we can imagine a 3d universe containing just a single perfect sphere. Or a 3d universe containing just two hands, one right and one left. So what? If you think it's a "paradox" that we can imagine a 3d hand in a 3d universe, then what difference does it make that we can invent a different scenario without the supposed paradox?

As to the original question, well, it's just one of many equally 'paradoxical' questions. For example: If the first thing in the universe were a cup of coffee, would it be espresso or brewed? If there were indigenous Martians and they had invented a written language, would they write left-to-right or right-to-left? If I were a marsupial, would I be platypus or a wallaby?




** In fact, if you have an ordinary positive dimensional space but where some of the coordinates are anticommuting rather than commuting, these can in a limited sense be considered as having negative dimensions. But this isn't a "real" negative dimension (in the way that e.g. R^6 really has 6 dimensions).... it's more like the non-integer "fractal dimension" that people ascribe to fractals. That is, a few particular formulae that apply to ordinary spaces also apply to these (the fractal or the anticommuting space) if you replace the dimension with a negative/noninteger number.
 
Alephnul said:
'If a human hand, was the first thing to exist in th universe, is it a left hand, or a right hand'?

this is pretty simple. if you're looking at it palm-side, is the thumb on the left or right side relative to the other fingers? if its on the left, then its a lefty, otherwise a righty. If you're still not sure, why not ask the hand?
 
|ZORN
There's many problems with this reasoning. Correct me if I'm wrong, this is how the argument runs:
1) Some proposition P is true for 2d figures in 3d space.
2) P is also true if we increase all the dimensions involved by 1. (3d figures in 4d space)
3) Therefore P must be true if we increase or reduce the dimensions involved by any natural number!

Thanks for your detailed and informed input. Few little corrections.
<<there's many problems with this reasoning. Correct me if I'm wrong, this is how the argument runs:>>

I have no desire to correct you, but IN MY OPINION

<<There's many problems with this reasoning.>> With yours, as you present it, or with mine? – your premise/conclusion rigidity doesn’t reflect my thoughts on the issue.

Some proposition P is true for 2d figures in 3d space.
This formulation ignores the distinction between qualia-type proposition, relative propositions, and belies a logical-positivist bias, (limiting formal logic toc’truth value probabilities– ‘ the King of France is bald, disucss.), a bias that has neglected Metaphcsics altogether, for the abstract nature of the discipline is not suited to P1, p2|| C strictures of metalinguistics.closes the more open
a
Some proposition P is true for 2d figures in 3d space
2) P is also true if we increase all the dimensions involved by 1. (3d figures in 4d space)
3) Therefore P must be true if we increase or reduce the dimensions involved by any natural number!

I think when it's put plainly like that, this is clearly nonsense. If you want a demonstration, though, just note that we can derive all sorts of ridiculous things with this reasoning: n=2 is a positive number. If we increase n by 1, then n=3 is also positive. By your reasoning above, then, we can keep decreasing n and it will always still be positive!

I would agree, the arument you outline above is nominally weak (though not invalid) - but this is your argument, as such any criticism of it + or -, are self-criticism I like the humility :)

quote, this is clearly nonsense quot

Nonsense is a word I usually reserve for an argument without merit, or empirical or rational foundation. You are clearly aware of some of the issues raised here, but I’m disappointed you lack the ability to form ideogenetic responses beyond – this is nonsense (I feel you writing the words is in itself nonsensical, but that would raise an argument on meta-language and language – not what this thread is about.

In your opinion perhaps. As you have presented the argument, one might, as you have, conclude that it is nonsense (which I take to mean that the argument is problematic, or do you insist it's invalid?
. But it doesn’t represent a structure I would use, nor fealt I pursued. And subtely expresses autologous contradictions that you may derive from this thread. Labelling it ‘clearly nonsense’ undermines your assertian of verisimilitude with the syllogisms buried in this thread.


ALEPHNUL -

P1: A premise is proposed, that the congruity of entiamorphic pairs, can be affirmed to represent the illusion of differentiation and allow for their ‘rotation’ through n+1 dimensions.
P2. That given P1, when applied to 2d incongruous counterparts, the incongruous nature of these objects can be dismissed as representing ‘qualia’ not things ‘ in themselves, observers bounded by 2d space must accept axiomatically that incongruous counterparts, reveal differet qualia through their incongruity.

)Gardner , The ambidextrous Universe: Moebius , that posited a 4th dimension of space. To give some pointers on what the issues are here.

P3. Incongrous counterparts (ICs) in 3d space (eg – enantiomorphic polyhedrons) could be made to ‘inteleginbly’ collapse into, congruent similitude, and therefore share (all except absolute space-vector) qualia, While remaining entirely unchanged to the 3d observer, for whom left and right are fundamental properties of the localised space they inhabit, I do not by induction, expect their broken right thumb, to diplace itself into a broken left thumb simply becuse the latest Metaphsics colloquim has posited a 4th dimension of space wherein left and right, up and down, mysteriously disappear as qualia leading to the inevitable debate of differentiation, and arguably persude through logic that spatial extension, is in fact an illusion (of the Bererkleyian type (solipcism, a lonely mode of thought (to be expanded in a future thread explicating the likelihood that we are all living in a computer generated simulation predicated preferably to accept some P1, P2, Pn probabilities on quantum computing’s processing limits - , and our ability and willing ness to generate artificial-reality ancestor simulations (I digress = post-humanism and simulation paradoxes to come soon though.)

P4, the process of rotating a 3d object through 4d space is not a ‘simple’ abstract process that empirically-derived perception can engage with, an extended 4th dimension of space that allows for 3d enantiomorphicity to be revealed as illusory, is not readily acceptable to the imagination. Many apparently necessary features of extended 3d space require symmetry and handidness.

P5 – positing non-experiential features of reality, though acceptable theoretically, makes ‘relational ‘assumptions that can but be based on experiential experience of relational features observed between empirical datum.
------------------------------------------------------------------------------
C – The assumption that the relationship of theoretical 4d to experiential 3d, is not equivalent, nor even similar to that which exists between 3d and 2d, or if it is, and we proceed to make truth statements about 4d space, we accept an additional premise neccessarily

P6 – that dimensions are qualatitively related, such that truth statements about theoretical dimensions below 0, hold equi-ideoglyphic reality as positive integer dimension of space above 3
-------------------------------------------------------------------------------------
C2 - truth values that describe 4d space, are etiher as equally valid as truth statements made about -1D, IFF such statements derive their logic by super-imposing the interdimensionally-relative, empirically-derived Euclidian-geometric epistemology.

That is a fairer representation of once of the various hypotheses I suggest in this thread.


[QUOTE
]In reality, what you're trying to do is of course an argument by induction.

Of course? Somewhat presumptious?

Nice try, the value of statements that critique, by deferrering to Humian induction, leads me to believe that you are 'closed' to the methodologies of rationalism. If you truly mistrust induction, you're life must be quite daunting. Believig in the possibility of a non-rational supervention of the laws of physics,logic etc by a new, unrelated order beset by hyper-contra-chronological realities, should instill a suspiscion of inductive reasoning, not a rejection.

What you need to get it to work is to show the induction step in the right direction. If you can show that for any positive integer D, given a space of dimension D, you can create a bigger viable space of dimension D+1 -- then you've shown that spaces of all positive integer dimension exist. To get negative dimensions, though, you need to do the induction step in the opposite direction: you need to show that you can always construct a space of lower dimensions. That's a very different thing, and it's not possible in any sensible way.** (You might try "taking off" an orthogonal direction, but then you of course stop when you get to 0 dimensions; there's no more orthogonal directions to remove.)

These are your criteria, orthogonal axsese to our experienced three are no more ‘real’ or logically describable than the negative dimensions that necessarily accompany truth claims about super-tertiary space. I am not, and have not argued for the non-existence of super-tertiary dimensions, but rather what truth claims can be made of them. You have already ascribed an orthogonal relationship with >3D, which must be accompanied by the existence of at least -1d.

I see no reason why 4d, 5d, nd etc must be inductively reasoned before any disucussion on the problems of absolute vs relative space can begn.

Note that your own little dialogue about boundaries give you a hint you can't get negative dimensions! A 3d cube has 6 squares bounding it; a 2d square has 4 lines bounding it; a 1d line has 2 points bounding it. Following the pattern, a 0d point would have 0 (ie no) lower-dim objects bounding it.

Read that back to yourself and think about what you’re saying.
Descent of dimensional relationships.
3d cube = 6 2d ‘limits’
2d plane = 4 1d limits
1 dimensional line = 2 x 1d limit
0 d = 1 x -1 limit
You have simply inserted an arbitrary conclusion to the pattern, as have I


It would be nice to
Incidentally, let me also add that "analogy" is not an acceptable way of demonstrating the existence of higher-dimensional spaces

Nice opinion, much dikos, little episteme. Acceptable to whom?


. The 2d to 3d analogy is useful in giving you clues as to what 4d space might be like, but it's only a guess until you actually construct 4d space and explore its properties. For example: there are no knots in 2d, while there are a number of classes of knots in 3d.By analogy you might expect even more types of knots in 4d; but in reality there are no knots in 4d, either
So you’ve measured this 4d, and decided it is knotless? (????????????)

! In any case, all this wanking around with "analogy" is completely pointless -- higher-dimensional spaces are well-understood. What you're talking about here is R^3 (ordinary 3d Euclidean space) and R^4 (4d Euclidean space.) Indeed it's trivial to actually construct them.

Your’re the boss. I’m glad you’re here to put us all straight, I’ve seen much opinion, little fact, and no references. You may have missed the point of this thread, I’m not trying to ‘prove’ anything, I am introducing a metaphysical concept of interest to some. But seems you’ve got it all worked out:
“higher-dimensional spaces are well-understood.”, really, by whom, I’m assuming no epistemological understanding is possible, your theoretical super-tertiary dimensions are as real as my possible negative ones.
Would you like to hazard a guess at an answer? Provide some arguments with more than simple opinion?

I’ve made no claims to knowing the answer.
Left or right?
I’m assuming (presuming) you’re a scientist of some sort, and I’m sure I could learn much from you, the reason being I only know one thing, whilst you pupport to know it all.

It would truly be disappointing if this supposed argument gets taken seriously in the philosophy literature. – really, why, have you, or could you entertain the possibility that yu have underestimated the question?

I agree I should have posted in context. Please enlighten me with your clearly more valid research, perhaps you’re right, maybe Kant was not in fact the greatest thinker of the Western Modern canon

I’m tired and wish to avoid being rude, but do you know what this question is actually about?

Happy to discuss at length.

AN

---
Going back a bit, this isn't really a "solution" to the original issue (which is silly in itself.)

Yes, silly-billy question! Note to self, don't be silly, and adopt silly as a truly mordascious invective.


All it does is invent a scenario (3d hand in 4d universe) where the supposed problem doesn't exist. But that's easy -- we can imagine a 3d universe containing just a single perfect sphere. Or a 3d universe containing just two hands, one right and one left. So what? If you think it's a "paradox" that we can imagine a 3d hand in a 3d universe, then what difference does it make that we can invent a different scenario without the supposed paradox?

Hmmm, No it doesn't, no its not eay, so what? Fine, not you cup of tea, why don't you go and talk i-phones and RGPs in science and tech :-)

I think I'd rather discuss with the more open-minded than explain the importance of the question. You don't care, fine. Its import in history and phil. of sciene is huge, and puzzled newton, leibniz, kant, einstein, through to modern cosmology, epistemelogical theories, and M-theory to inflation, dark matter etc - shame, as I assumed you'd find interest in that

As to the original question, well, it's just one of many equally 'paradoxical' questions. For example: If the first thing in the universe were a cup of coffee, would it be espresso or brewed? If there were indigenous Martians and they had invented a written language, would they write left-to-right or right-to-left? If I were a marsupial, would I be platypus or a wallaby?

I give up, non of these questions have any intellectual parity to the one 'at hand'. Yous sort of saying 'why existence' is an equivalid question to 'I (ie you) exist to didactically tell these morons what's what, I doubt you're out of college.

Get some action, chill, learn.

Gnothi Seauton

AN:| :|
Ad-hom removed. - Jamshyd
---

Going back a bit, this isn't really a "solution" to the original issue (which is silly in itself.) All it does is invent a scenario (3d hand in 4d universe) where the supposed problem doesn't exist. But that's easy -- we can imagine a 3d universe containing just a single perfect sphere. Or a 3d universe containing just two hands, one right and one left. So what? If you think it's a "paradox" that we can imagine a 3d hand in a 3d universe, then what difference does it make that we can invent a different scenario without the supposed paradox?

As to the original question, well, it's just one of many equally 'paradoxical' questions. For example: If the first thing in the universe were a cup of coffee, would it be espresso or brewed? If there were indigenous Martians and they had invented a written language, would they write left-to-right or right-to-left? If I were a marsupial, would I be platypus or a wallaby?


[/QUOTE]
 
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Jamshyd said:
^ Holy crap!

Ok, Aleph... I think you took way too much offence at Zorn's post. Let's cool it down.

Sincerest apologies, not sleapt in 48hrs ad seeing doc today. I thought I remained polite, just vigorously disagree with his dismissiveness and the large section of opinion dressed as fact. He seems like nice guy, but read his post, don't mind sound academic wrangle, but I'm not an undergrad parvenu.

Xanax, then i'll be better :-)
 
I should clarify, because it's driving me bonkers, forget the hand (its representative), its simple absolute vs relational space, absolute = observer could discern what direction thumb was in. Relationsal space, can't say, nothing to relate it to.
I dug it up as its being re-debated by cosmologists, that'sall. SOrry for any offence, I'm to passionate about what I do.
Apologies.
walks off, takes Xany, much better. Got to teach, so not in this frame of mind. Zorn, sorry, I'm sure we can have a good debate about this, and other phil of science topics, I'm sure Iwill learn much.

PAX VOS LIBERTANS
 
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