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

All Cretan's are liars and n-dimensional space

^^ I’m not quite sure how you are rephrasing the question, rather than perhaps posing s similar, yet ultimately different one the theone athand (that is not to say that your questions is not very interesting, and would be the good start of a new thread.

To clarify: In Kant’s Prolegommena to all Future Metaphysics he stated

“What can more resemble my hand […] and be in all points more alike, than its image in the looking glass? And yet I cannot put such a hand as I see in the glass in the place of the original”

To rephrase it so one doesn’t get tied up in hands, human or mannequin
(it is handedness, left or right that is at issue), imagine instead any two enantiomorphic shapes, as basic as you like. What struck Kant is that in every way these pairs were the same (congruous:same length, same internal geometry, identical in every way) except one element, that you can’t take one of the shapes, and fit it into the space of the other (the simpler the polyhedron one chooses, the more obvious this becomes) through rotation etc.

The context for Kant was that he realised this beared upon the raging argument of the time between Newton and Leibniz, the former believed space to be ‘transcendentally ideal’ as ebola put it, that is it exists independently of matter, put more simply – if there were no universe, space would still exist.

Leibniz disagreed, and believed that space was a property of matter, ie – non universe (no matter), then literally NO UNIVERSE.


To try and examine the problem, Kant posited the problem of incongruous counterparts, in his own life-time unresolved. Though Kant thought about why there are only 3 dimensions of space, rather than 4, it was Ferdinand Moebius, basing his work on Kant, who developed a theory of n-dimensional space


Just as 2 dimensional p and q (n=2 type incongruous counterparts) can be ‘the same’ if rotated to match each other through 3 dimensional space, perhaps a general rule existed that incongruous counterparts in n-dimensional space could be rotated tomatch, to become congruous through n+1 space. Moebius posited the idea that the left hand/right hand universe paradox/problem could be solved by stating that it existed in 4 dimensional space as simply ‘a hand’ that appeared in 3 dimensional space to be left or right handed.


So as B9 said the hand could be both left and right handed (but only if 4 dimensional space is a reality). Problem solved? Not quite, because modern Metaphysicians revisiting the problem argued that to accept 4 dimensional space, is to accept negative dimensions of space, with all the problems that creates.


So what?

Quite!


PS – ebola, you’re set-theory paradox, a new version of Epimendides’ ‘liar paradox’, which from a logical-positivist perspective (though I don’t agree) is not a paradox, but rather a confusion between language and meta-language.
 
mc.jpg
 
Alephnul said:
I’m not quite sure how you are rephrasing the question, rather than perhaps posing s similar, yet ultimately different one the theone athand
Click to expand...

What I meant was that by applying new physcial theories, you still end up with the same fundamental problem.

Perhaps Kant was mistaken about the similarity of the left and right hands? That it is just a trick of the mind that makes us think they are more similar than they really are?

?selur eht egnahc uoy fi ylno ro ,ti fo esnes ekam llits uoy nac ,sdrawkcab ecnetnes a etorw I fI
 
Okay

I see what you mean now. I think we’re looking at the same problem from two perspectives (pertinently), it’s the same issue that unites such seemingly epistemologically-disparate concepts as varied as Augistine’s theodicy, Plato’s cave-dwellers, Ouspensky’s flatlanders, and this hand, which may appear to me as having left-ness, but in fact viewed through’ 4th-dimension’ glasses would collapse into a (left-right) hand.

However this in itself creates further questions, as what one might term ‘handedness’ is a vital character of our empirical senses, and in fact once you’ve accepted a 4th dimension, you must accept an n-th dimension (and all those negative dimensions of n which we mentioned earlier) which would collapse all symmetry into logically posited limit, which itself would leave little of meaning left to say about anything.

I think I’ve now pulled a ligament in my brain muscle, and must apply some ointment, in the form of a beer!!
 
Ah, now that you clarified what you were asking about (and, more importantly, put it within a context), I understand what you're trying to achieve. When you said that this was "one for the Metaphysicians", you weren't using the latter term loosely - you are actually looking for a response that incorporated the (primitive, IMO - no offense intended) western Metaphysical tradition (Academic, that is).

On that note, I will back out, because I have not delved deep enough into that tradition to give you an answer. I'd be stating the obvious if I mention that I doubt you'll find many who have ;)
 
In relationistic (Leibnitian) way two hands are similar, and in two dimensional space.
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...

look at the palm, if clockwise you get first the thumb and then the forefinger and so on, it's a left hand

if you get the little finger, the annular and so on, it's a right hand
Click to expand...
 
Good discusssion, and thanks Jamshyd for pointing out the lexical ambiguity of the title. I'm a philosopher of the Western canon and therefore take the strictly academic definition of Metaphysics (NOT primitive to my mind), I placed Kant's (really Moebius's) paradox out of context presumptiously. There's still acre of room for debate on this, if anyone's intereted PM me for some recent papers on the topic.

cheers - AN
 
>>
So as B9 said the hand could be both left and right handed (but only if 4 dimensional space is a reality). Problem solved? Not quite, because modern Metaphysicians revisiting the problem argued that to accept 4 dimensional space, is to accept negative dimensions of space, with all the problems that creates.
>>

Now I see the import. I don't see, however, how it follows that we need accept negative dimensions. We might need accept all possible positive spatial dimensions, but why need the paradox generalize to n-1?

My solution to this problem is to abolish a priori truths while allowing for non-empirical a posteriori guiding axioms (see the Pragmatist tradition).

>>PS – ebola, you’re set-theory paradox, a new version of Epimendides’ ‘liar paradox’, which from a logical-positivist perspective (though I don’t agree) is not a paradox, but rather a confusion between language and meta-language.>>

I thought that, in lieu of having a genuine creative moment, I'd bring up a classic. I also concur. The logical positivists sacrifice adequacy (not that complete adequacy is attainable) for consistency, but they lose sight of this fact.

>>you are actually looking for a response that incorporated the (primitive, IMO - no offense intended) western Metaphysical tradition (Academic, that is).>>

;)
Then again, there is a good bit of speculation that Heraclitus was influenced heavily by encounters with "Eastern" philosophers. In this way, the whole "Western" tradition exists as an interchange with "outsiders" (I have quickly used up my quota of buffering quotation marks). I would refer you to Said on Orientalism, but I know that I needn't do so. ;)

ebola
 
^ Oh indeed, I am actually aware of such interactions.

It is the very nature of the Academic institution of Philosophy that I've got grief with.
 
Can a hand draw a distinction (ie between itself and the rest of the universe) without a mind?

If not then there is also a mind present to observe it.
 
ebola? said:
>>

>>you are actually looking for a response that incorporated the (primitive, IMO - no offense intended) western Metaphysical tradition (Academic, that is).>>

;)
Then again, there is a good bit of speculation that Heraclitus was influenced heavily by encounters with "Eastern" philosophers. In this way, the whole "Western" tradition exists as an interchange with "outsiders" (I have quickly used up my quota of buffering quotation marks). I would refer you to Said on Orientalism, but I know that I needn't do so. ;)

ebola
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^^ Couldn’t agree more with that last comment. Western Philosophy is historiographically the fusion of Abrahamic (particularly Mesopatamic and Persian) theologies, fused with Vedic, Egypto-Ethiopic, Cosmic, Slavic […](the list is too long!!) etc elements to form a mono-myth, upon which Greek (or rather Hellenic) philosophies were grafted, then drawn through the exegetical strictures of the ‘Scriptures’ from which it was not let loose entirely until the late Renaissance/early Enlightenment. The geographical limits of ‘the West’ wax and wane. Said is a vital counterpoint to works like ‘the arab mind’, Patai – and to my mind the majority of Context Group-linked historiographers and Anthropologists.

Re: Negative dimensions – it’s a long but fairly complex logical outcome [If you really want the details PM me], the ‘4D=Negative D’ is a fairly contemporary Metaphysical debate, and provides a nexus of debate between theoretical cosmologists and contemporary philosophy.

The cosmologists are still returning to the Leibniz vs Newtonian space (I am certainly no scientist so please don’t ask me for the details, perhaps any cosmologists out there can help. Negative dimensions of space isn’t so weird when you think M-Theory has 11-13 dimensions of space, apparently all curled up in the 3 dimensions we see – they need it for their vibrating strings :-)n
I’m not up on the Pragmatists – can you recommend a book?

Can a hand draw a distinction (ie between itself and the rest of the universe) without a mind?

If not then there is also a mind present to observe it.
Click to expand...

Quite true, and a valid point, but as this is meant as a thought experiment, though your comment one lead one to think about whether a ‘point of observation’ could exist outside the hand/polygon, or simply within it: That was an implicit part of the question Kant was asking, Newton would have said yes, Leibniz, no.




MENS AGITAT MOLEM
 
>>It is the very nature of the Academic institution of Philosophy that I've got grief with.>>

Ah yes. Here, I am very ambivalent.
1. I think that it's pretty silly that "philosophy" is something done in the ivory tower, quartered off from external insights, read by a few specialists. Everyone is an armature philosopher (aren't we?).
2. My personality is frighteningly suited to academia (often to my detriment). If I weren't institutionalized as one, I'd likely still act and think like one.

>>Re: Negative dimensions – it’s a long but fairly complex logical outcome [If you really want the details PM me], the ‘4D=Negative D’ is a fairly contemporary Metaphysical debate, and provides a nexus of debate between theoretical cosmologists and contemporary philosophy.>>

I am indeed interested. Perhaps others are too.

>>The cosmologists are still returning to the Leibniz vs Newtonian space (I am certainly no scientist so please don’t ask me for the details, perhaps any cosmologists out there can help. Negative dimensions of space isn’t so weird when you think M-Theory has 11-13 dimensions of space, apparently all curled up in the 3 dimensions we see – they need it for their vibrating strings :-)n>>

Well, positive spatial dimensions, while hardly intuitive when superseding 3, are not so exotic, as I have analogies with the jump between 1 and 2 and then 2 and 3. Also, it is my (limited) understanding that these >3 spatial dimensions aren't quite curled up into our 3, but are rather quite small in terms of how far objects may extend within them and have severe curvature in comparison to our 3, which are currently estimated to be pretty flat. Hence, we can navigate our world without reference to them (so it would seem).

>>I’m not up on the Pragmatists – can you recommend a book?>>

Experience and Nature - Dewey: this is his metaphysics. It's great, but not easy.

William James - Principles of Psychology...I wish I had selections to point you towards.

The collective works of Mead. This puts a more social spin on things. Watch out though...a lot of it is collected lecture notes, so it's hardly coherent.

On the two dogmas of empiricism - Quine. The logical positivists are finally damned on their own terms.

Various by Lakeoff and/or Johnson - connecting pragmatism to cognitive psychology. I studied under Johnson.

I've also read a smattering of stuff by Royce (arguably pragmatist) and Pierce. Drawing a blank on the titles.

Pierre Bourdieu - He's rolling in his grave. This is where the line from Marx, through the phenomenologists and existentialists...Foucault too, ends up at a synthesis which expresses a pragmatist metaphysics. Finally, this weird split between Europe and the US is reconciled.

ebola
 
Many thanks for the book suggestions. I'm currently tied up in one of those ivory towers whose strictures are forcing me back to my own field of research! :-)

We are all philosophers - absolutely, and academia's categorisation can, I agree, be too strict. The contributors to this forum are all philosophers, which is simply the love of Wisdom, and she is not confined to the lecture theatre, but dwells in the most unexpected places. Seek, and you will find Her :)

I will write a reply to the 4D= negatve D when time allows (the analogy of jumping from 1 to2, or 2 to 3 should logically work the other way around, 3 to2, and 0 to -1)? I promise a fuller reply as soon as time allows
 
Long post, Skip to last section for summary.


Sorry for the delay, real life interceded.

So we got as far as (I think?) agreeing that Kant’s left hand – right hand paradox could be overcome by imagining a 4th dimension of space through which the ‘mirror-image’ of a hand, could be flipped, through such a dimension to fit perfectly with its incongruent couterpart.

The example I used is a common one, think of p and q next to each other on a 2 dimensional plane, no amount of turning or rotating will make p sit atop q such that they are rendered congruent. However we can all imagine flipping the p (through 3 dimensional space) so that it could become congruent.

By analogy of how the relationship between spatial objects can be radically assimilated if we take the perspective of n + 1 dimensions. (where n= the dimension in which the objects exist). With p and q their apparent difference in n=2 dimensional space, is removed if we move the object through 3 dimensional space.

The logical problem is that analogy – that the relation between 2 and 3 dimensional space is the same as that between 3 and our theoretical 4th dimension. If we accept this, then we must also accept that the relation of the n=3 to n=2 ( three dimensional space to 2 dimensional space) is the same as that between n=2 and n=1, and n=1 to n=0 so far nothing unusual, we can imagine (sort of) 2d and 1d and even 0d, they are used in maths all the time. But just as above we use the analogy of 2d to 3d to posit a theoretical 4th dimension, so must we accept a theoretical dimension of –1, whose relationship to 0d is by analogy the same as that between 0d and 1d.

The nub is that by using analogies of dimensional relationships within our 3 dimensional space (the space of experience) to imagine theoretical ‘other dimensions’ beyond the three of perceptual experience, we open a can of worms that allows for theoretical negative dimensions, the latter seem less acceptable to logical reason.

Summary

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.

As a die-hard Platonist I favour the latter, that non-experiential dimensions of space exist, both positive and negative – the question for me is not do negative dimensions exist, but rather, what are they like? It would be great to hear from you all what you think, agree, disagree, hazard a guess at what negative dimensions are like?8) 8)

I dug out some old metaphysics texts which seemed to leave the problem unresolved, maybe it is not even a problem!

AN
 
>>
The logical problem is that analogy – that the relation between 2 and 3 dimensional space is the same as that between 3 and our theoretical 4th dimension. If we accept this, then we must also accept that the relation of the n=3 to n=2 ( three dimensional space to 2 dimensional space) is the same as that between n=2 and n=1, and n=1 to n=0 so far nothing unusual, we can imagine (sort of) 2d and 1d and even 0d, they are used in maths all the time. But just as above we use the analogy of 2d to 3d to posit a theoretical 4th dimension, so must we accept a theoretical dimension of –1, whose relationship to 0d is by analogy the same as that between 0d and 1d.>>

Not necessarily. We could say axiomatically that the dimensions in a system only make sense for natural numbers of dimensions.

Or we could do something more elegant:
When we say that something is 3 dimensional, we actually mean that there are 3 orthogonal directions in which one could travel. So a system of dimensional space (or hypothetical universe, whatever you wanna call it) is built of these orthogonal "modes of position".

It doesn't make a whole lot of sense to build a system of space out of a negative number of orthogonal dimensions. This would be like putting a negative number of papers in a binder before going off to school.

Or...the solution a I like, would be to say that dimensionality is an a posteriori, non-empirical axiom. We do well operating with 3. It's wired in our brains to be intuitive. Higher-order dimensions work well within more restricted domains, like some theoretical physics. Oddly enough, so do fractional dimensions, when it comes to fractal geometry. So maybe negative dimensions are useful for something that I've never heard of... :)

But this requires us to accept that our investigative efforts are part of the universe, and they in-form its structure.

>>I'm currently tied up in one of those ivory towers whose strictures are forcing me back to my own field of research! :-)>>

Out of curiosity, what's your field? Analytic philosophy?
I was all over the place in undergrad, currently a sociologist.

ebola
 
So a negative hand would not grasp an object but instead release the rest of the universe?
 
^^ very interesting tought, but that could happen within 3 dimensions without us knoking :-)

Not necessarily. We could say axiomatically that the dimensions in a system only make sense for natural numbers of dimensions.

Or we could do something more elegant:
When we say that something is 3 dimensional, we actually mean that there are 3 orthogonal directions in which one could travel. So a system of dimensional space (or hypothetical universe, whatever you wanna call it) is built of these orthogonal "modes of position".

It doesn't make a whole lot of sense to build a system of space out of a negative number of orthogonal dimensions. This would be like putting a negative number of papers in a binder before going off to school
Click to expand...

The question in upon what are these axioms founded, it can't be empirical data as we are using a purely intelligibe concept (the 4th dimension of space) to explain a problem bounded by the three dimensions of space. THe expiricist could respond that one is no less able to posit 'the nartural umber axiom' than one might it's counterpart, 'the negative imensions do exist' axiom.


Again the critical factir is that we are proceeding by analogy to describe what the 4th dimension could do, which mens that the reverse analogy is equally valid (note this is not an argument that excludes the existence of spatial diensions above 3, but rather what we can say about them. As soon as we adduce qualities through analogy wih empirically predicated 3d space w cannot avoid the same logic as working back down the other way. An example would be
Socrates: You accept that a three domensional object, (a prefect square for instance) is bounded by six 2 dimensional planes?
Hume: Yes, I can agree that
Socrates: And furethermore that these 2 dimensional planes are in turn bounded four 1 dimensional lines.
Hume: I can imagine such a thing, but this is nothing new....
Socrates: Bear with me, can you now imagine these four one dimesional lines, are bounded by 0 dimensional points?
Hume: that would be the natrual order of euclidian geometry.
Socrates: then by analogy could we not expect these zero dimensional points to be bounded by ‘limits’ in -1 dimensions?

I agree ebola we can work from a posteori qualities of space, but cannot arbitrate on what they should be.

As for our inquiry infoming the universe, there’s nothing new in this, ineed theoretical particle physics accepts, whilst the rationslists of the late enlightenment required it. 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?’

I apologise to all for ahving dragged this out, but I hoped for more than a poll on the issue, but rather a debate, it’s certainly made me return to the issue to rethink it, hope it has served some value to everyone else

Out of curiosity, what's your field? Analytic philosophy?
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No, I have studied philosophy and my research ties in late-classical philosophy but analytical philosophy os not my thing. If you're a sociologist you'd get on with the Idler who in another forum described then as buffoons (not quite his words but you get the gist) - But given he's still at school one can forgive the youthful ignorace :-)

GNOTHI SEAUTON
 
>>
The question in upon what are these axioms founded>>

Well, what are axioms founded on in general? As far as I can tell, they are things that we assume, either through habit or deliberation, and then we build a logical system out of them, and then we connect this system to empirical content, and then we see if it "works". To what end to negative dimensions "work"?

>>
Again the critical factir is that we are proceeding by analogy to describe what the 4th dimension could do, which mens that the reverse analogy is equally valid (note this is not an argument that excludes the existence of spatial diensions above 3>>

Well, we could translate into algebraic equaltions the necessary descriptors of a 4+ dimensional euclidian system. The we'd use analogies to visualize things, but we can use the math to see if negative dimensions would make and sense / do any work for us.

>>
Socrates: then by analogy could we not expect these zero dimensional points to be bounded by ‘limits’ in -1 dimensions?
>>

Or it could be that boundedness as such ends at "0". Wouldn't a zero-dimensional point be bounded at all sites regardless...as its a point?

>>No, I have studied philosophy and my research ties in late-classical philosophy but analytical philosophy os not my thing. If you're a sociologist you'd get on with the Idler who in another forum described then as buffoons (not quite his words but you get the gist) - But given he's still at school one can forgive the youthful ignorace :-)>>

Neat. Philosphy exerts the pull regardless. I've actually only dabbled in it, having a Marxist and pragmatist bent.

ebola
 
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