The Big Rock Paradox: Stephen Hawking's Thought-Experiment

[apeiron]

Well show where I misrepresented your arguments then. Do something apart from bubbling from a watery grave.

 

[Hippasos]

If we can imagine omnipotent, we can say it exists in our imagination just like numbers, but they are not reality?

For omnipotent every weight is the same.

So for omnipotent every rock is the same whatever it weights.

Therefore for omnipotent its simply a matter of decision (free will) whether lift the rock or not.

Careful political life of an omnipotent:

If omnipotent (or its omnipotent similar) once should decide it should not to be omnipotent any more, or to be non-existent, it wouldn't be omnipotent never again - unless of course he had a good omnipotent friend...

:)

 

[JoeDawg]

Well show where I misrepresented your arguments then. Do something apart from bubbling from a watery grave.

You championed observational evidence. There is none for omni - anything.

But feel free to continue the insults, it only makes you look like a rabid troll.

 

[apeiron]

Please get it right at some stage. What I championed was limits. Omni- was misleading I said. And modern physics is all about discovering limits too scale.

 

[JoeDawg]

Please get it right at some stage. What I championed was limits. Omni- was misleading I said. And modern physics is all about discovering limits too scale.

And I said Omni wasn't about limits, it was nonsense. Round we go.

 

[apeiron]

Fine. So you say omni is nonsense. I say its limits. And I challenged you to refute the observational evidence we have for limits.

Are you saying c is nonsense or something? You will do anything to avoid answering a direct question.

So the only one spinning aimlessly here is you. Gurgle, glug, glug.

 

[apeiron]

1) So for omnipotent every rock is the same whatever it weights.

2) If omnipotent (or its omnipotent similar) once should decide it should not to be omnipotent any more, or to be non-existent, it wouldn't be omnipotent never again -:)

Nice thought but "a rock that couldn't be lifted" would have to have a different effective weight from the set of all those ordinary rocks that could be lifted. You would have just sorted rocks into two classes, the infinitely heavy and the effectively weightless.


The question of whether an omnipotent being should have the power to make itself merely potent has more mileage though. I've seen it argued out before.

Myself, I would examine the assumption that this being exists in time and so could be something before, and then something else a little later. It would seem the being would have to be outside merely space and time (so as to control them rather than being subservient to the limits they exert). And a timeless being would be thus by nature unchanging.

It is not a question of could it, or even would it want to, but that change is just not a meaningful qualifier regarding its situation. We may as well ask whether an omnipotent being would jgd[kes[m? There is no answer because the question is contentless.

Of course, really the problem here lies in the positing of a "being" in the first place as it is a concept that brings with it linguistic baggage asserting autonomy, choice and other human associated qualities. The issue does not arise if we just stick to the more naked idea of omnipotence - as when we move the discussion to irrestible forces meeting immoveable objects. A force would have no reason to want to change. Now we can see why the question would be properly contentless.

 

[JoeDawg]

Fine. So you say omni is nonsense. I say its limits. And I challenged you to refute the observational evidence we have for limits.

Limits aren't relevant to the discussion, because omnipotence is not a limit issue. Its about being limitless. Omnipotence has no basis in observation, it is fantasy.

Are you saying c is nonsense or something?

C would be a limit, which omni is not.
You can't be this dense, so I'm going to guess, its just insufferable arrogance.
Or maybe you're drunk.

 

[apeiron]

Limits aren't relevant to the discussion, because omnipotence is not a limit issue. Its about being limitless. Omnipotence has no basis in observation, it is fantasy.

Again you have not followed the argument. It was an epistemological issue that was being discussed originally. Modelling. And I was saying that omnipotence is a limit concept that would have to be derived by taking the notion of potence to its extreme. It would be where you would get to if you went as far as you could go in that linguistic direction.

So ontologically, you might feel the urge to call omnipotence a limitless ability. But epistemologically, you would in fact be taking the limit of potency. It is just the same as we use other limit concepts such as infinity. You are imagining what it would be like to be able to count forever, when of course you could never in reality count forever. But you then just take the limit and start operating with that limit concept (encountering paradoxes as you go).

By tracking the derivation of concepts it becomes easier to see why paradoxes arise. In your mind you have created the unreal to bound the real. Then what most people don't get (unless this is an area they have studied) is that extremes like this always must come in complementary pairs. It is not just concepts like omnipotence. You always must get a clash between two mutually contradictory concepts - because it was in opposition that they were derived. Going in one direction to an extreme must leave behind everything that it is not.

A challenge: think of any useful metaphysical extreme that is not part of a familiar complementary pair. Scott Kelso recently wrote a whole book just listing them.

However I then made the further argument that reality itself is observed to be dichotomously bounded by limits. So - surprise - limits-based logic looks also to have ontic validity. It is the way reality operates out there too.

But sorry if this went right over your head and made you grumpy.

It is a good job I didn't correct you on the proper definition of limitless in this new context.

The limitless (indeed, the apeiron if you study your metaphysics :tongue:) would be the vague - the sea of pure potential from which crisp dichotomies arise.

It would be Peircean firstness, Mahayanan sunyata, the quantum foam, to invoke various metaphysical traditions. Or the limitless would be a state of maximal and unbroken symmetry I would say.

You can't be this dense, so I'm going to guess, its just insufferable arrogance. Or maybe you're drunk.

Pot kettle black I think.

 

[JoeDawg]

But sorry if this went right over your head and made you grumpy.

LOL

Reread your responses, you are the one who got rude and indignant.
Not me, I find your arrogance amusing.

I disagree with your assessment, if that hurts your ego or feelings, too bad.
I think you are wrong. Get over it.

Its a simple matter of vague and contradictory defintion.
This is what the rock analogy is designed to do.
Make people think about the definition of omni.

You've gone beyond that, trying to fix and redefine the word.
This doesn't address the issue, it ignores it.
Which seems a good enough thing to do now with regards to you.
Thanks for the laugh, though.

Omni is self-contradicting and vague, period.

 

[apeiron]

I disagree with your assessment, if that hurts your ego or feelings, too bad.
I think you are wrong. Get over it.

I merely ask that you supply reasoned arguments against what others might say, not fall back on contentless statements like "I disagree", "I don't like it", "My mummy told me".

So I repeat the challenge that stands at the core of my position here: can you think of any useful metaphysical extreme that is not also part of a complementary pair?

Thesis and antithesis. The dialectical method. Have you not actually studied real philosophy?

 

[WaveJumper]

Suppose an omnipotent being exists. If it does, it would be able to do anything (by definition!). Therefore, it would be able to produce a rock it couldn't lift. Therefore, it wouldn't be able to do anything it wants, therefore it wouldn't be omnipotent. What do you think?

I think you are pushing human logic where it clearly fails. How is your question different to:

"Can an electron be in 2 or more places at once?"

What would stop a deity from being able to lift the rock and not lift the rock at the same time?

Putting forward human logic as something all-powerful is typical of certain doctrines. Unfortunately they are wrong. Human logic is very likely nothing special and their "insights" into the nature of a hypothetical all-powerful God, is simply a reflection of their own delusion of understanding everything there is to understand about existence and reality.

 

[kote]

Putting forward human logic as something all-powerful is typical of certain doctrines. Unfortunately they are wrong. Human logic is very likely nothing special and their "insights" into the nature of a hypothetical all-powerful God, is simply a reflection of their own delusion of understanding everything there is to understand about existence and reality.

I think it's less than that. In this case we just have an inconsistent concept.

A rock is by definition finite. A rock not liftable by God would have to be infinite. You have proposed an object that is both finite and infinite - a logical contradiction. The question is as meaningless as "is the number 3 happy or sad."

I'm sorry guys, but this is logic 101 - simple absurdity. Asking the question doesn't break logic. It just makes you an idiot. It's impossible to disprove logic, because to do so would require logical argument. An assumption of logic is also required for any math or science to be intelligible. It's required for any knowledge or argument, period, to be intelligible.

But if you deny that 1+1=2 is a necessary truth... well then I guess I can't argue with you, can I?

 

[WaveJumper]

I think it's less than that. In this case we just have an inconsistent concept.

A rock is by definition finite. A rock not liftable by God would have to be infinite.

Assumptions are not facts. They are human 'baggage', you have to shake it off if are describing anything that's supposed to resemble an all powerful deity.

You have proposed an object that is both finite and infinite - a logical contradiction. The question is as meaningless as "is the number 3 happy or sad."

Allow me to disagree that your logic is the greatest thing that could ever exist. I don't share that sentiment, at all. I am sure a caveman would disagree that man could go to the Moon. Your current knowledge of the universe is definitely NOT all there is to know. Period.

I'm sorry guys, but this is logic 101 - simple absurdity. Asking the question doesn't break logic. It just makes you an idiot. It's impossible to disprove logic, because to do so would require logical argument.

Who said anything about disproving logic? It's your idea, certainly not mine. My idea was scepticism that human logic is all powerful. It is not, claims to the contrary are hilarious.

An assumption of logic is also required for any math or science to be intelligible. It's required for any knowledge or argument, period, to be intelligible.

Is that supposed to be a proof that human logic is all powerful?

But if you deny that 1+1=2 is a necessary truth... well then I guess I can't argue with you, can I?

How many electrons are there when a single electron is in a superposition of states?

 

[kote]

Allow me to disagree that your logic is the greatest thing that could ever exist. I don't share that sentiment, at all. I am sure a caveman would disagree that man could go to the Moon. Your current knowledge of the universe is definitely NOT all there is to know. Period.

No one ever said logic tells you anything about the universe. I don't see why you insist on bringing synthetic propositions into a discussion of analytic propositional logic.

How many electrons are there when a single electron...

Are you serious? Is this guy serious?

 

[WaveJumper]

How many electrons are there when a single electron...

Are you serious? Is this guy serious?

Where is the evidence that MWI is wrong?

Have you seen an interference pattern?

 

[kote]

To be fair, I'll answer your original question.

"Can an electron be in 2 or more places at once?"

No. An electron, as a specific type of object, must contain as essential the essential properties of the object class. An object is defined as a continuous region of extension. For something to be in more than one place at the same time, it cannot have continuous extension. It is therefore not the same object but two or more distinct objects. No single object can exist in two or more places at once. I could write this as a formal proof, but I am aware that such proofs hold no weight with you.

Of course, you can redefine electron or object as you wish, in which case you will either get a definite answer, or you will strip your question of meaning. "Yes," "no," or "you idiot, numbers don't have feelings." Those are your options. They all fit very nicely into our logical system and are in no way contradictory or paradoxical.

The fact that you can't come up with a self-consistent definition of an electron is not evidence that logic is impossible. It's evidence that you don't have a well defined idea of an electron.

 

[WaveJumper]

To be fair, I'll answer your original question.

No. An electron, as a specific type of object, must contain as essential the essential properties of the object class. An object is defined as a continuous region of extension. For something to be in more than one place at the same time, it cannot have continuous extension. It is therefore not the same object, but two or more distinct objects.

Double slit experiment with single electrons. / of argument.

 

[apeiron]

Of course, you can redefine electron or object as you wish, in which case you will either get a definite answer, or you will strip your question of meaning. "Yes," "no," or "you idiot, numbers don't have feelings." Those are your options. They all fit very nicely into our logical system and are in no way contradictory or paradoxical.

The fact that you can't come up with a self-consistent definition of an election is not evidence that logic is impossible. It's evidence that you don't have a well defined idea of an election.

This line of argument is based on many conventional assumptions. All models must be based on intuitive axioms - even models of logic (which are models of causality). And so you can only get so far if the output of your particular brand of logic seems in obvious conflict with some pretty solid observational evidence. As is the case with QM twin slit (and even more so with quantum eraser versions of twin slits).

In this case, the QM description of the electron - all the wavefunction machinery of QM - is spectacularly well defined. Tested to 18 decimal places, etc. And it is standard brand logic, the easy interpretation, that fails.

Which is why we need - as Peirce said even before QM came along - a logic of vagueness. It would be a way to get beyond the either/or excluded middle axiom that is the basis of conventional logic.

Vagueness is something to which the law of contradiction does not apply said Peirce.

So with an electron, is it a smear or is it a point object? Well its status is actually vague until it has been crisply shaped up by boundary constraints supplied by its total environment.

With QM, you do run slap into the fact that conventional logic 101 is broke. Or at least, it cannot apply in the widest description of reality. To fix things, this is why I think it useful to go back all the way to Aristotle and see how he was making sense of his own heritage - the systems approaches following from Anaximander and then the atomism of Democritus et al.

 

[kote]

And so you can only get so far if the output of your particular brand of logic seems in obvious conflict with some pretty solid observational evidence.

I'm still not sure why anyone thinks observations can have anything to do with analytic logic. Observations have to do with the truth values of propositions, not their validity.

The question was, "how many X are there when you have a single X." The answer is one, by definition. A definition cannot be false. Specific definitions might not be representative of reality, and they might be self-inconsistent (not valid), but definitions don't have such a property as truth.

Let "2" be defined as the addition of 1 and 1. 2=1+1. QED. The supposedly well-defined electron you just formalized in QM isn't defined at all without an assumption of the validity of math, which requires an assumption of the validity of logic.

Any argument from observation that makes a claim about logic is circular and necessarily assumes logic.

 

[apeiron]

The supposedly well-defined electron you just formalized in QM isn't defined at all without an assumption of the validity of math, which requires an assumption of the validity of logic.

Any argument from observation that makes a claim about logic is circular and necessarily assumes logic.

Yes this is a circular story. Or rather a cycle of interaction between modelling and measurements. The modelling relation story - Robert Rosen wrote a great recent book covering much of this ground, Essays on Life Itself.

Psychology 101 says you have to have some kind of ideas to make sense of the impressions. And then the impressions in turn build your ideas. Epistemology 101 should tell us that models of reality are just the same to-and-fro done more systematically and formally.

 

[jcearley]

I think that people get stuck on there narrow view of what something that exists has to be defined as. Where as omnipotence to a human seems to encompass everything you can "do" in the real known world rather then what you don't know that you can do outside of it. I hate to quote bible references however there is a big important message that I really on.
It says "Our knowledge is but a grain of sand on an endless sea shore compared to that of gods."
So in my mind to have that kind of knowledge, is to be all power and omnipotent, if everything is connected ie string theory then why couldn't everything that is and was be one huge consciousness. Then God wouldn't have to lift the rock because he or it would simultaneously be the rock and be the median that the rock exist on and everything else in the universe.
So yes I believe god could lift the rock Lol.
We don't know enough yet, keep gathering those grains of sand.

 

[disregardthat]

"Can an electron be in 2 or more places at once?"

This question assumes that "being at a place" is well-defined. However, observation shows that "being at a place", in the context of having of a unique position in a certain moment, does not apply to physical objects.

By the definition of "being at a place", i.e. having a unique position, we can answer the assumed well-defined question "Can anything be in 2 places at once?" and say no, nothing can be in 2 or more places at once because 2 different places is not a unique position.

Unfortunately, the electron apparently does not have property of "being at a place", so the question is meaningless. It is only natural at this point to redefine the phrase "being at a place" in terms of QM when talking about objects in this context.