wu :: forums
        (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi)
      

        riddles >> general problem-solving / chatting / whatever >> Platonism
        
(Message started by: ThudanBlunder on Sep 21st, 2008, 8:43am)
Title: Platonism
Post by ThudanBlunder on Sep 21st, 2008, 8:43am
Among other things, Platonism claims that mathematical objects such as triangles and squares have their own objective reality and exist independently of anything else.

However, I would say that as a mental conception they require a sufficiently sophistocated consciousness in order to be said to exist.

What do you think?
Title: Re: Platonism
Post by towr on Sep 21st, 2008, 9:42am
I think I rather like the idea of planets moving in ellipses even before there was anyone around to know what an ellipse was.
On the other hand I'm not quite sure what Plato means with an objective reality/existence of such abstract concepts. (Especially considering he had such ideas about things like "beauty", "goodness" etc as well.)
Title: Re: Platonism
Post by rmsgrey on Sep 22nd, 2008, 8:25am
Planets don't move in mathematically precise ellipses even today...
Title: Re: Platonism
Post by towr on Sep 22nd, 2008, 8:38am

on 09/22/08 at 08:25:40, rmsgrey wrote:
Planets don't move in mathematically precise ellipses even today...
Close enough, though.
And I'm sure they move along some curve that constitutes a mathematical object.
Title: Re: Platonism
Post by Grimbal on Sep 22nd, 2008, 8:50am
I like to think even the number 2 doesn't exist in real life.  Because there are no 2 identical things in the Universe.  You can not say with mathematical precision that there are 2 of something.
To me mathematical concepts are our way to deal with a world that is way too complicated for us to understand.  It is easier to think of 10 chairs rather than to think of each chair separately, each a bit different from the others in shape, color, solidity, history, etc.
I think I already said that in a previous thread.
Title: Re: Platonism
Post by SMQ on Sep 22nd, 2008, 9:11am

on 09/22/08 at 08:50:47, Grimbal wrote:
I like to think even the number 2 doesn't exist in real life.  Because there are no 2 identical things in the Universe.

Perhaps not on a macro scale, but the process of stimulated emission (http://en.wikipedia.org/wiki/Stimulated_emission) (the SE of LASER) results in two identical photons, and I think photons are well-enough studied that they can be said to exist "in the real world" -- arguably unlike many other quantum-physical entities.

--SMQ
Title: Re: Platonism
Post by towr on Sep 22nd, 2008, 9:25am

on 09/22/08 at 08:50:47, Grimbal wrote:
I like to think even the number 2 doesn't exist in real life.  Because there are no 2 identical things in the Universe.
Why would they need to be identical? If I have an apple and an orange, I have two pieces of fruit.
Title: Re: Platonism
Post by Grimbal on Sep 22nd, 2008, 12:56pm
If you take a bite from the apple, do you still have 2 fruits?


on 09/22/08 at 13:12:07, towr wrote:
I'm not even sure what I just responded to. Clearly you couldn't have made two posts in this thread.  ::)

Is this still the 2nd post? ;)
Title: Re: Platonism
Post by towr on Sep 22nd, 2008, 1:05pm

on 09/22/08 at 12:56:48, Grimbal wrote:
If you take a bite from the apple, do you still have 2 fruits?
Almost. Regardless it'd still be precisely two objects. Three if you spit out and count the bite you took.
Title: Re: Platonism
Post by towr on Sep 22nd, 2008, 1:12pm
I'm not even sure what I just responded to. Clearly you couldn't have made two posts in this thread.  ::)
Title: Re: Platonism
Post by Grimbal on Sep 22nd, 2008, 1:17pm
But it is just your interpretation of the reality.  If you cut the apple in halves, you might see it as 2 fruits or 3 pieces.  2 or 3 objects.  It depends how you see it.
If you see 2 objects it is because you choose so.
If these fruits lie in the forest and there is nobody around to see them, are they still 2 fruits?  Are they still fruits at all?  Or just part of the forest?
Title: Re: Platonism
Post by Sir Col on Sep 22nd, 2008, 1:30pm
Where do you draw the line on two objects belonging to the same class? Indeed two objects might possess everything we consider necessary to make them equivalent on a macro-level (like two apples), but if we examine them closely we will find differences, which, excluding sufficiently vague definitions of class, would disqualify them from belonging to the same class. Even two "identical" photons differ in the respect that the quintessential definition of any object must include its position in space and time. As no two bodies can occupy the same point in time and space simultaneously they must differ in at least one way and cannot be exactly the same.

Of course, if two objects are absolutely identical then they must be the same object and thus only one exists. If they differ in any respect then they belong to different classes and must be unique.

Hence no two objects of the same class exist.  ::)
Title: Re: Platonism
Post by towr on Sep 22nd, 2008, 1:45pm

on 09/22/08 at 13:17:21, Grimbal wrote:
But it is just your interpretation of the reality.  If you cut the apple in halves, you might see it as 2 fruits or 3 pieces.  2 or 3 objects.  It depends how you see it.
If an object is cut into two it's not one object any more but two. Interpretation and seeing has nothing to do with it.
You have one piece from one set (the first fruit), and two pieces from another set (the other fruit). It's all just patterns. The patterns are there whether someone is around to denote them or not.


Quote:
If these fruits lie in the forest and there is nobody around to see them, are they still 2 fruits?
Yes.

Quote:
Are they still fruits at all?
Yes.

Quote:
Or just part of the forest?
Also.
Title: Re: Platonism
Post by towr on Sep 22nd, 2008, 1:53pm

on 09/22/08 at 13:30:05, Sir Col wrote:
Where do you draw the line on two objects belonging to the same class? Indeed two objects might possess everything we consider necessary to make them equivalent on a macro-level (like two apples), but if we examine them closely we will find differences, which, excluding sufficiently vague definitions of class, would disqualify them from belonging to the same class.
What makes you think that? Of course there must be difference, otherwise there is no point to having classes at all. Throwing non-identical objects together is the entire point.
Different objects that can perform the same function fit in the same functional class. Nothing vague about that type of class.


Quote:
Even two "identical" photons differ in the respect that the quintessential definition of any object must include its position in space and time.
Not according to any dictionary I know of. In fact almost no object has its time and place in the definition.
Title: Re: Platonism
Post by SMQ on Sep 22nd, 2008, 2:19pm

on 09/22/08 at 13:30:05, Sir Col wrote:
Even two "identical" photons differ in the respect that the quintessential definition of any object must include its position in space and time. As no two bodies can occupy the same point in time and space simultaneously they must differ in at least one way and cannot be exactly the same.

I'm afraid you're mistaken with regard to photons (and other bosons (http://en.wikipedia.oeg/wiki/Boson)).  Because of their "wave nature" they can indeed occupy exactly the same position in time and space (and also have exactly the same energy, spin, phase, and direction -- the only other measurable qualities of a photon), but because of their inherent "quantumness" they are still discrete and countable.

You are correct in that coherent photons cannot be distinguished from one another -- they are in all respects identical -- but because the energy of a single photon is strictly related to its wavelength/frequency, by measuring the total energy of the group of coherent photons they can still be counted even without distinguishing them.  And if the group of coherent photons were to encounter an atom with an electron in an appropriate energy state, only a single photon from the group will be absorbed (though there's no way to know or distinguish which one): the rest will continue on unaffected.

--SMQ
Title: Re: Platonism
Post by Grimbal on Sep 22nd, 2008, 2:22pm

on 09/22/08 at 13:45:43, towr wrote:
If an object is cut into two it's not one object any more but two. Interpretation and seeing has nothing to do with it.


I meant "see" as "perceive by intellect".

I could argue that in an apple cut in halves there are at least 3 objects: the halves and the whole apple.  The apple doesn't cease to exist, it is just that you shift the focus to the parts, not the whole.
Title: Re: Platonism
Post by ThudanBlunder on Sep 22nd, 2008, 2:37pm

on 09/22/08 at 13:45:43, towr wrote:
The patterns are there whether someone is around to denote them or not.

Are you a closet Platonist? ;D
I would say that these 'patterns' are associations/attributes created by the mind.
With no mind the to perceive them, in what way can these objects even be said to exist?
Title: Re: Platonism
Post by Sir Col on Sep 22nd, 2008, 3:06pm

on 09/22/08 at 13:53:43, towr wrote:
Not according to any dictionary I know of. In fact almost no object has its time and place in the definition.

Try counting the number of blooming flowers on a rose tree. When you do it affects the number of flowers you would consider to be blooming. Time plays its part.

Try counting the number of ice cubes in a bucket in a freezer compared to a very hot oven. Position (environmental influence) plays a very important role.

In the class of colliding aircraft it is precisely time and place that causes the number to be equal to zero or two.

If you wish to use class to count objects then do you base this on the properties they have in common or their differences? For example, an apple is red or green and is approximately spherical. So there are sixteen apples on a snooker table. Redefine... an apple is red or green, it is approximately spherical, and tastes nice. If I don't like the taste of apples then how do I count them? Redefine... an apple is red or green, it is approximately spherical, and tastes nice or horrible depending on preference. So a red or green ball in snooker is an apple after all. Okay smart arse, add to the definition that you don't find them on a snooker table. So what about that bowl of fruit sitting on the snooker table?


rmsgrey, I know next to nothing about quantum mechanics but how can two different physical objects occupy the same point in time and space simultaneously?

If that were possible then their differences could not be determined by the very fact that they are coincidental and they must instantaneously be the same thing. Could it not be that they came so close to each other that we could no longer measure their proximity?
Title: Re: Platonism
Post by Grimbal on Sep 22nd, 2008, 3:38pm

on 09/22/08 at 15:06:21, Sir Col wrote:
rmsgrey, I know next to nothing about quantum mechanics but how can two different physical objects occupy the same point in time and space simultaneously?

In fact, at the quantum level, particles are indistinguishable.  If 2 electrons meet, they bump off each other, but you cannot tell which is which.  They even can mix up their quantum state.  Some other particles don't mind sharing the same state, i.e. same space, speed, spin.  You can "pile them up" so to say in one position.  
It is like a polynomial with a double root.  You can count the multiplicity of the root, even though you can not distinguish them.

And actually, quantum physics is one domain where I would tend to feel that integers do exist in real life after all.
Title: Re: Platonism
Post by Sir Col on Sep 23rd, 2008, 12:01am

on 09/22/08 at 15:38:09, Grimbal wrote:
In fact, at the quantum level, particles are indistinguishable.  If 2 electrons meet, they bump off each other, but you cannot tell which is which.

Forget the quantum level... this reminds me of twins I teach!
Title: Re: Platonism
Post by rmsgrey on Sep 23rd, 2008, 4:42am

on 09/22/08 at 15:06:21, Sir Col wrote:
rmsgrey, I know next to nothing about quantum mechanics but how can two different physical objects occupy the same point in time and space simultaneously?

If that were possible then their differences could not be determined by the very fact that they are coincidental and they must instantaneously be the same thing. Could it not be that they came so close to each other that we could no longer measure their proximity?

I think you meant SMQ - my sole "contribution" so far has been to point out that planetary orbits aren't perfect ellipses - still, since I've been invoked...

Bosons (particles with integer spin) generally act more like waves than particles - in particular, they can "stack" - multiple particles can share the exact same quantum state - at which point they are theoretically indistinguishable.

Fermions (particles with half-integer spin) generally act more like particles than waves - in particular, they can't stack - no two fermions can occupy the same quantum state - which is what keeps things like neutron stars from collapsing to a point.


At the fundamental level, it does seem that the universe does become very simple - very strange, but also very simple (it could be that the simple aspects are all we can comprehend of things at that level, but they do seem to provide an exceptionally accurate picture, so any complexities also lack any observable consequences). At that level, it seems that the objects are their ideal forms...
Title: Re: Platonism
Post by Sir Col on Sep 23rd, 2008, 11:55am

on 09/23/08 at 04:42:30, rmsgrey wrote:
I think you meant SMQ...

No, I definitely had you in mind when I asked the question.  ::)

Sorry for mixing you two up!

I won't hihack the thread, but quantum mechanics seems such twaddle to me. Whenever I've had serious conversations with physicists and asked them to explain it to me they seem to agree. Of course they thought they were articulating the validity of the theories perfectly well, but the more they spoke, the more they proved my point. Most attempts to persuade me of its validity usually end with the speaker calling me an ignorant fool with a brain too small to understand. I admit I am a simple man, but if it really were a simple theory and explains our reality so well then why hasn't it superseded the Newtonian deterministic system of reality? Why do we continue to waste the time of young people on an ineffective system that fails to describe our universe?

Feel free to "persuade" me, but in the meantime, back on topic...

I think the difficulty we have with understanding the thoughts of a Platonic reality is that our very thinking undermines proper objectivity. In other words, our learned (or assumed) experiences that have brought us to the point of critically considering the theory of forms predisposes our thinking to its validity. The only way to be entirely objective in these discussions is to approach it without any influence from reality, but this then disqualifies you from communicating with the rest of us. For example, if we could ever discern the thought patterns of infants we would be unable to make sense of their impressions because they would only be able to communicate in terms that are incompatible with our own reality. Equally anything they could communicate would only be by virtue of the limited external influences they have already experienced and would thus be tainted and worthless.
Title: Re: Platonism
Post by SMQ on Sep 23rd, 2008, 2:02pm

on 09/23/08 at 11:55:32, Sir Col wrote:
I won't hihack the thread, but quantum mechanics seems such twaddle to me.

Let's start a new one (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_general;action=display;num=1222203684) then. ;)

--SMQ


Powered by YaBB 1 Gold - SP 1.4!
Forum software copyright © 2000-2004 Yet another Bulletin Board