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

[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.