Tarski's Indefinability Theorem. It is generalized to all formal systems, not just math.
For an example of how this is applied in philosophy, look at John Lucas' application of Godel (or perhaps more accurately, Tarski) to the question of determinism and free will. Of course, Lucas is also known for saying things like that his arguments only apply to consistent thinkers, and thus only to male non-politicians. Whatever, it was the 60s I guess.
But for those of you arguing that Godel only dealt with math, you should read on. Godel himself argued that his incompleteness theorems had broader philosophical implications about the mind and the universe. In some basic theorems on the foundations of mathematics and their implications, Godel argues the superiority of the human mind over finite machines based on his Incompleteness Theorems.
In a later revision by Hilary Putnam (2006), it is pointed out that the human mind is fallible, and thus Godel was wrong simply because humans are inconsistent (I agree). However, Putnam notes that the same argument does in fact apply to math and science. In other words, if we are to believe that the human faculty of science and/or math is consistent, then we cannot prove its consistency, or we cannot represent it with a Turing machine. Which is basically what I'm saying. Philosophy pwns math and science; they are its bitches.
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MrMisterJesus dying on the cross in pain? Morally better than us. One has to go "all in".Registered Userregular
I'm not sure if Maudlin is incorrect, out of date, or if my experience is just somehow weird. Both examples that he cited are things that were explicitly discussed both in and out of lectures in my physics department in grad school. And his second point, regarding virtual particles, strikes me as one of failing to understand the physics he's talking about. Yes, the state is static and 'unchanging' over time and yes, the vacuum is a seething mass of virtual particles. It's both, and they aren't mutually exclusive. Virtual particles only exist because their creation and annihilation is so rapid (except for one very special case) that their existence doesn't violate conservation of energy beyond the bounds established by the energy-time uncertainty relation. Over any discrete period of time, the vacuum is static - its energy is constant. It is only by examining to vacuum in a frozen infinitesimal slice of time that you can see the interplay of virtual particles. So while "static" is inaccurate when referring to these moment-to-moment states, it is perfectly accurate over any time of measure. Calling it non-static would be equally invalid for any period of time, despite being completely valid for infinitesimals.
Maudlin expressed his point rather vaguely--in terms of tendencies rather than absolute rules--so it's compatible with there being places and people in the physics community who are interested in those questions. Indeed, he thinks those questions are just questions about understanding the physics, so there's no reason a physicist couldn't be interested in them. It's interesting to hear from someone in the physics community that there is such interest (I am certainly not in a position to bring to bear first-person evidence in order to fact-check).
As per the vacuum--this is just a guess, and definitely above my pay grade--but it sounds to me like you might be using 'static' in different senses. It sounds to me like, for Maudlin, if something is static over time it doesn't change at all (it's not just that its energy remains constant). And if something is complete, there's no aspect of the physical system which it does not represent. So, if something is both static and complete over some period of time, then there must be no aspect of the physical system which is changing. But this contradicts the notion that there is something in the physical system which is changing over time--namely, virtual particles are generating and annihilating each other in a 'buzzing hive' of activity.
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MrMisterJesus dying on the cross in pain? Morally better than us. One has to go "all in".Registered Userregular
But for those of you arguing that Godel only dealt with math, you should read on. Godel himself argued that his incompleteness theorems had broader philosophical implications about the mind and the universe. In some basic theorems on the foundations of mathematics and their implications, Godel argues the superiority of the human mind over finite machines based on his Incompleteness Theorems.
It's also worth noting that Godel went insane and spent his latter years trying to mathematically demonstrate the existence of God. He might not be the most reliable interpreter of his own results.
Admittedly the notion of a "proof" is being stretched to mean the conscious process of determining truth, which isn't very precise.
Perhaps another way to say it is to say that any language that is expressive enough to form statements about its own foundations will necessarily fail to give us any ultimate answer to anything without some underlying acceptance of inconsistency or incompleteness. If the system isn't expressive enough to form statements about its own foundations, then it isn't expressive enough. But at least it escapes the dilemma.
So science probably can't explain science. Hawking's TOE seems to be a known impossibility.
I'm not sure if Maudlin is incorrect, out of date, or if my experience is just somehow weird. Both examples that he cited are things that were explicitly discussed both in and out of lectures in my physics department in grad school. And his second point, regarding virtual particles, strikes me as one of failing to understand the physics he's talking about. Yes, the state is static and 'unchanging' over time and yes, the vacuum is a seething mass of virtual particles. It's both, and they aren't mutually exclusive. Virtual particles only exist because their creation and annihilation is so rapid (except for one very special case) that their existence doesn't violate conservation of energy beyond the bounds established by the energy-time uncertainty relation. Over any discrete period of time, the vacuum is static - its energy is constant. It is only by examining to vacuum in a frozen infinitesimal slice of time that you can see the interplay of virtual particles. So while "static" is inaccurate when referring to these moment-to-moment states, it is perfectly accurate over any time of measure. Calling it non-static would be equally invalid for any period of time, despite being completely valid for infinitesimals.
Maudlin expressed his point rather vaguely--in terms of tendencies rather than absolute rules--so it's compatible with there being places and people in the physics community who are interested in those questions. Indeed, he thinks those questions are just questions about understanding the physics, so there's no reason a physicist couldn't be interested in them. It's interesting to hear from someone in the physics community that there is such interest (I am certainly not in a position to bring to bear first-person evidence in order to fact-check).
As per the vacuum--this is just a guess, and definitely above my pay grade--but it sounds to me like you might be using 'static' in different senses. For Maudlin, if something is static over time it doesn't change at all (it's not just that its energy remains constant). And if something is complete, there's no aspect of the physical system which it does not represent. So, if something is both static and complete over some period of time, then there must be no aspect of the physical system which is changing. But this contradicts the notion that there is something in the physical system which is changing over time--namely, virtual particles are generating and annihilating each other in a 'buzzing hive' of activity.
Well, nobody really claims that any physical model is complete in that sense. A description of a system can be 'complete' in the sense that it covers every degree of freedom of the system without actually describing every aspect of the system. The entirety of thermodynamics works this way. You can have an accurate statistic description of a system which is 'complete' in the sense that any system which meets your description will behave identically to another such system, but it ignores things like the indistinguishibility of particles.
If I had, for example, three elections in a line: O ---- O ---- O they are indistinguishable from one another. I can write a Hamiltonian that describes the system accurately and in a fashion that I would tend to consider 'complete', despite the fact that my Hamiltonian would describe a system wherein you permuted the locations of those particles amongst one-another. So it's not a 'logically complete' description, for lack of a better term, but it is 'physically complete'.
Our description of the vacuum appears to be at least basically physically complete in that it describes the behavior of the vacuum accurately. It can't be logically complete for the same reason that my Hamiltonian of the three-electron system above can't be complete: there is no way to probe the system and discover the properties which a logically complete description would describe. I can't paint one of the electrons blue and another one green to see which is which, and the combination of the uncertainty relation and the fact that a vacuum is necessarily empty prevent me from finding out anything about the actions of virtual particles in vacuum.
A good description of Feynman's diagrams actually addresses something like this very issue. Even a very simple Feynman diagram (which is a pictoral representation of a quantum field calculation) is actually a summation of every possible permutation and refinement of that diagram. The diagram of two electrons interacting via boson exchange is 3 lines, but is equivalent to any number of more complex-looking diagrams wherein virtual particles appear and annihilate, interacting with one another and the electron-boson-electron system in the mean-time. This knowledge of "glossing over the details" is inherent, and we just accept it because some things in the physical world are either strictly unknowable, or at least appear strictly unknownable to modern physics.
I guess that's a philosophical problem of the type he's describing?
I guess that's a philosophical problem of the type he's describing?
I think you're mostly describing a scientific problem. The philosophical problem is that you drew three electrons on a line. You drew a left one, a right one, and a center one. You distinguished them from one another before you even told me that you couldn't.
EDIT: This is the sort of thing I mentioned earlier. I don't assume that this means your 3-electron system is totally B.S. and that my philosophy about it is superior. And I'm sure that beneficial science can proceed from your statements. But at some point, philosophically, I have to believe that the way you drew three electrons on a line would itself be shown to be incorrect. At some point I suspect that physicists are making assumptions of knowledge about those things which were also assumed to be unknowable.
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MrMisterJesus dying on the cross in pain? Morally better than us. One has to go "all in".Registered Userregular
I guess that's a philosophical problem of the type he's describing?
Most likely.
Unfortunately, this is not really my bailiwick, so I can't say much intelligibly in response to your specific points (aside from that, apparently, my guess was wrong).
I guess that's a philosophical problem of the type he's describing?
I think you're mostly describing a scientific problem. The philosophical problem is that you drew three electrons on a line. You drew a left one, a right one, and a center one. You distinguished them from one another before you even told me that you couldn't.
EDIT: This is the sort of thing I mentioned earlier. I don't assume that this means your 3-electron system is totally B.S. and that my philosophy about it is superior. And I'm sure that beneficial science can proceed from your statements. But at some point, philosophically, I have to believe that the way you drew three electrons on a line would itself be shown to be incorrect.
Well, I mean, I can distinguish the left from the right from the center. They will feel different forces. But if I had electrons named Alice, Bob, and Charlie I couldn't tell whether they'd lined up in ABC, ACB, CAB, ... etc order. Similarly, I can't tell whether the force that Leftmost Electron feels is directly via interaction with Center and Rightmost Electrons, or if it's mediated by zero-net-change interaction with any number of virtual particles between them. That's why I called 'physically complete'.
A perfectly complete description of the system would know if those intermediary interactions occurred, and would have serial-number-stamped electrons in their appropriate places. But there are infinitely many such perfectly complete systems that are physically indistinguishable, so we call the description 'complete' provided that every system so-described behaves identically in every physically-distinguishable fashion. There's an awareness that this isn't actual completeness, but I'm not sure I see how that lack of completeness is a physics problem. If some new parameterization is discovered whereby previously indistinguishable systems become distinguishable then we need a new method of describing them, but there aren't any physicists who aren't aware of that fact.
Edit: Although yes, you can't literally have three electrons in a line. They aren't balls that you can line up. And if they were, they wouldn't stay in that configuration without help. But you can have an accurately-described system of three electrons.
Yeah ok so philosophical problem. You can't distinguish them. But you can.
How much does physics even know if they are in fact three particles that could line up, and not some sort of energy wave or something? I'm asking because I don't know, in case that wasn't obvious.
Yeah ok so philosophical problem. You can't distinguish them. But you can.
How much does physics even know if they are in fact three particles that could line up, and not some sort of energy wave or something? I'm asking because I don't know, in case that wasn't obvious.
Technically we know that they aren't three particles that you can line up. They're three localized excitations of a quantum field. We don't know that the field itself isn't actually just an observational artifact of some more fundamental operation. Some people believe fairly strongly that this is the case, and theories about what that more-fundamental thing is abound, but there isn't actually any evidence that this is the case.
In some situations, it just so happens that quantum field excitations behave exactly as if they were little billiard balls floating in space. In other situations they behave absolutely nothing whatsoever like little billiard balls, which is why quantum mechanics seems so weird when you try to think about billiard ball particles.
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GnomeTankWhat the what?Portland, OregonRegistered Userregular
edited May 2012
I was reading a theory recently, by uhh, I can't remember who (sorry, I am not a practicing physicist), that the reason we see so many strange quantum reactions with particles (sometimes they act like waves, other times like particles), is because they are a wave and a particle, at the same time, at all times.
There was some experiment a guy did with little balls suspended on liquid silicon, where it was shown how a particle could push a wave around in front of it, effectively creating some of the phenomenon we see in quantum mechanics (such as the double slit experiment). Was fascinating stuff. No idea how plausible it really is.
In some situations, it just so happens that quantum field excitations behave exactly as if they were little billiard balls floating in space. In other situations they behave absolutely nothing whatsoever like little billiard balls, which is why quantum mechanics seems so weird when you try to think about billiard ball particles.
As long as you don't try to tell me that they're really just "information" then we're cool.
I was reading a theory recently, by uhh, I can't remember who (sorry, I am not a practicing physicist), that the reason we see so many strange quantum reactions with particles (sometimes they act like waves, other times like particles), is because they are a wave and a particle, at the same time, at all times.
There was some experiment a guy did with little balls suspended on liquid silicon, where it was shown how a particle could push a wave around in front of it, effectively creating some of the phenomenon we see in quantum mechanics (such as the double slit experiment). Was fascinating stuff. No idea how plausible it really is.
That's basically accurate. Particles are waves...they're just a type of wave that behaves like what we would consider a particle in some instances.
The Nobel Prize in Physics a couple of years ago was awarded for the creation of a Bose-Einstein Condensate, which is a state of matter wherein you can directly observe wave-like interactions in what would normally be considered solid, macroscopic matter. They took a cloud of...I want to say Rubidium ions and took a picture of it interfering with itself like the traditional double-slit laser.
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GnomeTankWhat the what?Portland, OregonRegistered Userregular
Yeah, very cool stuff. Physics is just my hobby, I am a programmer by day...you understand this stuff at a level I never will....but damn if it's not fascinating.
Scientists are often very accepting of philosophically contradictory statements. It doesn't necessarily present an immediate problem to further scientific inquiry. But eventually the philosophical problem must be resolved, or it will cause problems in the science. And I think in many cases physicists chase problems for entire careers without acknowledging that a simple philosophical quandary makes their pursuit almost certainly pointless. I would not be surprised to find a physicist who mathematically formalized that "this statement is false" is a true statement, because it helped to answer some experimental or mathematical quandary, and then spent decades trying to experimentally or mathematically resolve all of the other problems this formalization created.
So can you actually give any examples? I'm not sure how a logically inconsistent statement (mathematically or otherwise) can yield an accurate result.
A logically inconsistent statement cannot yield a result at all. The concept of a result coming from an inconsistent statement doesn't make sense.
Scientists are often very accepting of philosophically contradictory statements. It doesn't necessarily present an immediate problem to further scientific inquiry. But eventually the philosophical problem must be resolved, or it will cause problems in the science. And I think in many cases physicists chase problems for entire careers without acknowledging that a simple philosophical quandary makes their pursuit almost certainly pointless. I would not be surprised to find a physicist who mathematically formalized that "this statement is false" is a true statement, because it helped to answer some experimental or mathematical quandary, and then spent decades trying to experimentally or mathematically resolve all of the other problems this formalization created.
So can you actually give any examples? I'm not sure how a logically inconsistent statement (mathematically or otherwise) can yield an accurate result.
A logically inconsistent statement cannot yield a result at all. The concept of a result coming from an inconsistent statement doesn't make sense.
That's incorrect. A logically inconsistent statement yields all possible results.
You are making the implication that logic and fact and thought didn't exist before philosophy said it existed. As if humans were just jelly masses that slithered around randomly hitting things with clubs using pure instinct before philosophy came a long and told us all how to be problem solvers.
Basically, yes. We tend to maintain that Thales of Miletus was the first philosopher of the Western tradition insofar as he articulated a non-religious explanation for the way things be. After Thales, we find the development of Western philosophy and the rise of all of the specialized fields of study that philosophy spawned.
Yet this does nothing to further your argument that logic and fact only exist because philosophy says they exist, and that without philosophy I could make no pronouncement of fact.
It's not that philosophy "says" that logic and facts exist. Rather, thinking logically is a manifestation of philosophy. Considering the universe in terms of facts is a manifestation of thinking philosophically.
completely ignoring things like the foundations of geometry and algebra being laid thousands of years before philosophy was a codified branch of study.
While it can't be argued that the study of philosophy has certainly enhanced our study of math and science, and has given us amazing academic logical frameworks and forced us to confront the ethics of our science, to imply that math and science wouldn't exist if philosophy had not "given us" fact, just isn't correct. The foundations of these things were being laid long before anyone decided to actually study how we made reasoned decisions.
Even if this is true on a philosophical level (and similarly, this applies to the claim that natural selection is a tautology), I don't see the point. Do you adjust the theory to fit the philosophy? or do you accept that there are times when an observation of the natural world doesn't adhere to strict epistimological logic?
What is the problem with doing both? Why not construct a wealth of theories to explain a particular phenomena, rather than dogmatically cling to only one story and chastise anyone who offers a contrary account?
It seems to me that if science took seriously its claims to fallibilism and open-minded research, it would embrace a wealth of theories to compliment different epistemological / metaphysical / ontological presuppositions.
What, precisely, was Krauss's claim in the book? From the articles I've read, it appears that Krauss asserted that quantum fields can create particles in a perfect vacuum, and thus that something can indeed come out of "nothing." Is that an accurate representation of Krauss' claim? Because if it is, I think the philosopher is probably right in that we'd have to first agree that a vacuum truly is "nothing," and that the presence of quantum fields doesn't invalidate that designation.
Quantum fields are not "nothing". To say that they are is to state that "something" is "nothing", which is a contradiction.
Perhaps it would be helpful to clarify something: There is a difference between "nothing" and "not-material".
I'm very interested in your assertion that "the universe doesn't do that," though.
Okie.
First, we could argue about whether or not the universe is a formal system that can be articulated in terms of logical statements converted into Godel numbers. Given Rorty's critique of the notion that our mental conceptualizations mirror nature, we at least have to offer an argument that acknowledges Rorty and so argues that our mathematical formalizations mirror the way things be. I can find a way around Rorty by appealing to Rationalism, but if we're going to be British Empiricists, I'm not sure how we get the "mental systemization = the universe" premise up and running.
Said another way, we have to prove that "if, then" and "and" and "or" mirror features of the universe. If we're going to express that tree over there, in terms of a formal system, then we need an argument that allows us to capture the entirety of that tree as a formal rationalistic system.
Spinoza can do that. Your average physicist can't.
Second, "the universe", by which I mean shit that bumps into other shit, does not produce situations of (X and ~X at the same time, in the same way), or self-negating facts.
If I had, for example, three elections in a line: O ---- O ---- O they are indistinguishable from one another.
I'm curious. Since they form a line, they would have to be in different locations. Couldn't they be distinguished in terms of their spatial location? To be truly indistinguishable, they would have EVERYTHING in common, and so fall subject to the "identity of indiscernibles". But since the electrons form a line, they would be distinguishable, insofar as they are in different locations.
(Yar dealt with this quite well, but he failed to get up off the mat and so left it as a "philosophical problem". I'm wanting to go a step further, and state that it's not just a philosophical problem: your statement was factually incorrect since they can be distinguished.)
Very good physicists tend to be very good at physics, and I, at least, am inclined to the view that if you want to know what really exists, it's better to ask a scientist than a philosopher. But it's not obvious that even talented physicsts are very smart about other matters, such as those that require conceptual clarity, subtle distinctions, reflectiveness about presuppositions, and the appreciation of logical and inferential entailments of particular propositions. More than anything, I hope Krauss's tantrum and its aftermath will help disabuse the culture of the myth that being good at physics means being good at thought.
Second, "the universe", by which I mean shit that bumps into other shit, does not produce situations of (X and ~X at the same time, in the same way), or self-negating facts.
Systems do not create self negating facts. They can be created within them/defined in them but do not actually create them. Why would the normal workings of a formal system produce a nonsensical situation?
The fact that I can state "the set of sets which do not contain themselves does/does not contain itself" does not mean that the set of sets which does not contain themselves exists. Suggesting that this is something that differentiates the systems implies that these nonsensical things exist. Its similar to suggesting that we can draw conclusions from the truth value of the statement "the set of sets which do not contain themselves does not contain itself". The truth value of that statement does not exist. There is nothing to draw conclusions from.
Systems do not create self negating facts. They can be created within them/defined in them. Why would the normal workings of a formal system produce a nonsensical situation.
Your first two statements are problematic.
1) Systems do not create self-negating facts.
2) Self-negating facts can be created /defined within a system.
These seem to be
1) System-X does not create X.
2) X is created within System-X.
My guess is that the distinction you would make is that "the system" does not create any of the statements that follow from the definitions / axioms of the system. Instead, a person uses the axioms / definitions of the system to create statement within the system.
If that is your understanding, then I would suggest that it is flawed. Any particular system, composed of definitions and axioms, already contains everything that follows from those definitions / axioms. Spinoza did not "create" the propositions of his system. Instead, he discerned what propositions existed within the system.
So, if X can be articulated within System-X, then System-X did create X, insofar as the system consists of the definitions and axioms that entail X. If X follows from the definitions and axioms of system-X, then X is included in that system.
"Creation" may be a problematic concept.
If P, then Q.
P.
Therefore: ___
Do you maintain that I "create" the Q in that conclusion? If so, that is a problematic notion. I would say that one discerns that Q is the conclusion. That's not an act of creation; it's an act of discerning what is already there.
The fact that I can state "the set of sets which do not contain themselves does/does not contain itself" does not mean that the set of sets which does not contain themselves exists.
This is an interesting thesis. Perhaps you would like to argue for it.
Suggesting that this is something that differentiates the systems implies that these nonsensical things exist. Its similar to suggesting that we can draw conclusions from the truth value of the statement "the set of sets which do not contain themselves does not contain itself". The truth value of that statement does not exist. There is nothing to draw conclusions from.
I'm not sure what work "existence" is doing in your post.
If the rules of set theory are such that the statement "The set of all sets that do not contain themselves" follows from the rules, then what would be your critique of this situation?
Perhaps absolute certainty isn't remotely as important as you make it out to be.
If by "certainty" you mean 'deduction", then I would respectfully disagree. For an explanation of why deduction is better than induction / abduction, let’s talk about The Raven Paradox
Induction works by evidencing universals by means of particulars. We find one black raven, then another black raven, then another black raven, and after some quantity of black ravens are found, we state that “All ravens are black.” The idea is that one black raven counts as “evidence” for statements regarding all ravens.
A problem occurs when we start to think about what “All R are B” means, and how inductive evidence supports “All R are B”.
Consider the following:
“All ravens are black” is logically equivalent “Everything that is not black is not a raven.”
Previously, the inductivist maintained that one black raven is evidence that all ravens are black. However, we have just discerned that “all ravens are black” is logically equivalent to “Everything that is not black is not a raven.”
This black raven is evidence for the claim “All ravens are black.”
In a similar fashion: This non-black non-raven is evidence for the claim “Everything that is not black is not a raven.”
So, this blue ball is inductive evidence for the claim that “All ravens are black.”
Suddenly, the science of ornithology is beholden to observations of balls and chairs. While a particular ornithologist may have 500 black ravens, to evidence her claim that all ravens are black, I have 500 non-pink non-ravens to offer in support of my claim that all ravens are pink.
This is a problem for science.
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FencingsaxIt is difficult to get a man to understand, when his salary depends upon his not understandingGNU Terry PratchettRegistered Userregular
Yeah ok so philosophical problem. You can't distinguish them. But you can.
How much does physics even know if they are in fact three particles that could line up, and not some sort of energy wave or something? I'm asking because I don't know, in case that wasn't obvious.
Technically we know that they aren't three particles that you can line up. They're three localized excitations of a quantum field. We don't know that the field itself isn't actually just an observational artifact of some more fundamental operation. Some people believe fairly strongly that this is the case, and theories about what that more-fundamental thing is abound, but there isn't actually any evidence that this is the case.
In some situations, it just so happens that quantum field excitations behave exactly as if they were little billiard balls floating in space. In other situations they behave absolutely nothing whatsoever like little billiard balls, which is why quantum mechanics seems so weird when you try to think about billiard ball particles.
I don't really know anything about science, but isn't this just one of those instances where scientists use abstractions of concepts to explain something because the concepts themselves are insanely complicated that are in fact very hard to explain?
If I had, for example, three elections in a line: O ---- O ---- O they are indistinguishable from one another.
I'm curious. Since they form a line, they would have to be in different locations. Couldn't they be distinguished in terms of their spatial location? To be truly indistinguishable, they would have EVERYTHING in common, and so fall subject to the "identity of indiscernibles". But since the electrons form a line, they would be distinguishable, insofar as they are in different locations.
(Yar dealt with this quite well, but he failed to get up off the mat and so left it as a "philosophical problem". I'm wanting to go a step further, and state that it's not just a philosophical problem: your statement was factually incorrect since they can be distinguished.)
(how did I miss this thread for five pages)
This is a bit tricky. It depends on how exactly you're confining the electrons.
Pretend you have electrons buckets (infinite square wells, to be precise).
If you put each electron in a different bucket, they can be distinguished by the fact they are in different buckets.
If you put all three electrons in the same bucket, they're indistinguishable with respect to each other. If you make a measurement and discern, "I have spotted an electron right here in the bucket!" there is no way to make a subsequent measurement and be sure you spotted the same electron, even in principle. This is because the electrons are governed by wavefunctions, so when you make a measurement at a point in space, there's a probability of measuring all three of the electrons, pretty much always. So, again, you can never be sure if you've measured the "same" electron.
When you have different buckets, the electronic wavefunctions are completely separated, so there's no (or vanishingly small) chance when you measure one electron in one bucket, that you're actually measuring the tail of one of the electronic wavefunctions from another bucket.
If you put all three electrons in the same bucket, they're indistinguishable with respect to each other. If you make a measurement and discern, "I have spotted an electron right here in the bucket!" there is no way to make a subsequent measurement and be sure you spotted the same electron, even in principle. This is because the electrons are governed by wavefunctions, so when you make a measurement at a point in space, there's a probability of measuring all three of the electrons, pretty much always. So, again, you can never be sure if you've measured the "same" electron.
But each electron would occupy a different location, correct?
0 = Electron
[ ] = Bucket
T1 : [000]
T2 : [000]
The leftmost 0 at T1 might be the rightmost 0 at T2, right?
I'm curious why it would matter if you are measuring the same electron. If we cannot distinguish the electrons based upon continuous properties, then why would it matter if you measure the same or a different electron at T1 and T2?
If you put all three electrons in the same bucket, they're indistinguishable with respect to each other. If you make a measurement and discern, "I have spotted an electron right here in the bucket!" there is no way to make a subsequent measurement and be sure you spotted the same electron, even in principle. This is because the electrons are governed by wavefunctions, so when you make a measurement at a point in space, there's a probability of measuring all three of the electrons, pretty much always. So, again, you can never be sure if you've measured the "same" electron.
But each electron would occupy a different location, correct?
0 = Electron
[ ] = Bucket
T1 : [000]
T2 : [000]
The leftmost 0 at T1 might be the rightmost 0 at T2, right?
I'm curious why it would matter if you are measuring the same electron. If we cannot distinguish the electrons based upon continuous properties, then why would it matter if you measure the same or a different electron at T1 and T2?
Electrons don't occupy a particular space in the way we perceive normal matter as occupying space. It's impossible to pin their location down--that is, they don't really have one. Electrons are capable of occupying multiple places at once (so is any particle--read about the double-slit experiment, which is surprisingly not a porn movie title). That is what is meant by "uncertainty" in this case--not just that we can't figure out where the electron is, but that it really isn't in any one place. It's a wave, after all, just as much as it is a particle.
I've even heard it suggested that there may only be one electron with a very complex and self-intersecting path through spacetime. There's nothing obvious to support that, but it's cute to imagine, and it would explain why all electrons seem to be identical.
If you put all three electrons in the same bucket, they're indistinguishable with respect to each other. If you make a measurement and discern, "I have spotted an electron right here in the bucket!" there is no way to make a subsequent measurement and be sure you spotted the same electron, even in principle. This is because the electrons are governed by wavefunctions, so when you make a measurement at a point in space, there's a probability of measuring all three of the electrons, pretty much always. So, again, you can never be sure if you've measured the "same" electron.
But each electron would occupy a different location, correct?
0 = Electron
[ ] = Bucket
T1 : [000]
T2 : [000]
The leftmost 0 at T1 might be the rightmost 0 at T2, right?
I'm curious why it would matter if you are measuring the same electron. If we cannot distinguish the electrons based upon continuous properties, then why would it matter if you measure the same or a different electron at T1 and T2?
My statement wasn't actually about distinguishing between the electrons in the example. There are actually some issues around that, as well, but what I was talking about was sufficiently describing a system.
Let's pretend for the moment that you can see the electrons in question and ignore issues of choice of coordinates and symmetry and shit. Obviously you could point to the left-hand electron (L), the right-hand one (R), or the middle one (M) and know which one you're pointing at. What I was saying is that you can, based on your understand that L, M, and R all exist and your knowledge of their properties (energy, momentum, spin, etc.) you can write a description of the system that perfectly (from a physicist's point of view) characterizes it. If we call the description S then any system which is described by S will behave in an identical fashion. Provided that the laws on which you based your description are accurate, S is sufficient to tell you everything you might want to know about the system's behavior.
Now, pretend that I have a system, described by S, and using some sort of magical tool I go in and pick up the L and R electrons and swap them without otherwise effecting the system. Because electrons are indistinguishable, the new system with L and R swapped is still characterized by S. These systems are trivially different: L and R swapped places. Yet, despite that, they are, as far as physics is concerned, identical systems.
There are other ways that you can create systems which are 'physically identical' despite actually being different. This is the philosophical problem I was talking about (well, one of them). Physics 'doesn't care' about the problem because in terms of doing physics (or, indeed, engineering or chemistry or anything else dependent upon the physical properties of systems) these systems are exactly the same. Yet they're also obviously different. The sticky point is that they're different in a way that physics says isn't real. Electrons aren't just similar, they are, as far as science is concerned, literally the same. Two electrons with the same spin, energy, momentum, etc. are the same thing. Their only differentiating factor is their location, which is why we can look at S and label the electrons L, R, and M.
I mentioned symmetry before. In mechanics (the branch of physics concerned with the behavior of physical systems; this can be stuff like pulleys and pendula (pendulums?) or it can be stuff like electrons when they're behaving 'classically') when we're talking about a system we tend to use a couple of equations to describe it, called the Hamiltonian and the Lagrangian. They actually do the same job but operate with different variables and in different mathematical spaces. The sweet thing about these equations is that they are functions of vectors. Vectors have the property that they are constant under change of coordinates, which means that the equation we use to describe the system is also constant under change of coordinates. In fact, the Hamiltonian is related to the Lagrangian in that it is a special type of coordinate transformation that goes from 'velocity coordinates' to 'momentum coordinates'.
So what's the point? The point is that our description, S, doesn't care about the coordinate system it's in. Which means that you can talk about a system using polar coordinates or Cartesian or whatever you want without having to start over from scratch. It also means that you can rotate the coordinate system without altering your description. This freedom of rotation means that any system involving a symmetric arrangement of components is indistinguishable from a system rotated about its axis of symmetry. So in the three-electrons-in-a-line example you can't *really* distinguish L and R.
I've even heard it suggested that there may only be one electron with a very complex and self-intersecting path through spacetime. There's nothing obvious to support that, but it's cute to imagine, and it would explain why all electrons seem to be identical.
Feynman's suggestion was actually that not only were all electrons the same particle, all electrons and positrons (anti-electrons) are the same particle. Positrons are just the electron travelling backward in time.
He was joking when he said it, though, and even at the time pointed out that it doesn't fit the observed universe...if it's all the same particle going back and forth in time there's no obvious way to explain the disparity of matter and anti-matter.
Instead, he discerned what propositions existed within the system.
But all propositions exist within all systems. It makes as much sense to say "the set which contains sets that do not contain themselves contains itself" as it does to say "Trees are true". Constructing statements which describe objects that do not exist is not difficult
For instance
Let P = (P and ~P)
If P then Q
P <- This is the point where we have a problem
Therefore ___
P is nonsensical, yet nothing prevents us from making the statement P=(P and ~P). But it becomes a problem when we then assert P. Physics cannot generate statements like P because the rules are unobservable and statements which do not violate the rules, but are not objects that exist cannot be observed. For all intents and purposes, P does not equal (P and ~P), P does not exist. It is as non nonsensical as saying 1=2 and believing it.
I'm not sure what work "existence" is doing in your post.
If the rules of set theory are such that the statement "The set of all sets that do not contain themselves" follows from the rules, then what would be your critique of this situation?
The statement may exist. But the set itself nonsensical. We were to use the set in a proof; should some other aspect require something of this set we would necessarily get a contradiction. We live in the world of the objects that exist, and not the statements which we can make about the world which are nonsensical.
Maybe this will make sense. Let us take Russel's paradox and rephrase the defined set to:
The object which contains all sets that do not contain themselves
And then complete the statement implicit in the paradox
The object which contains all sets that do not contain themselves is a set
The above statement is not true.
Physics can only deal with objects which meet an equivalent criteria. Since we cannot observe P [given that P =(P and ~P)] and cannot observe the rules we cannot generate statements like that.
Suddenly, the science of ornithology is beholden to observations of balls and chairs. While a particular ornithologist may have 500 black ravens, to evidence her claim that all ravens are black, I have 500 non-pink non-ravens to offer in support of my claim that all ravens are pink.
This is a problem for science.
If you want to be as literal as you are, then we can simply move to a Bayesian framework and those issues are entirely solved. [Or more correctly, we reject the proposition that (A and implies A->B. And we can see why this makes sense by using the same observation (A and to conclude that B->A or that all black things are Ravens]
Alternately, we could simply accept it as fundamentally not a paradox. Non-pink, non-ravens DO offer support of the claim that all ravens are pink. But we don't give a shit, because we have ravens that are black, such all ravens are pink is false. The paradox is only close to paradox if we must accept that all evidence of the truth value of a statement is equal because then we have blue hats as evidence that all ravens are pink is true and the existence of black ravens implying that all ravens are pink is false as placed on equal footing.
Once we abandon the idea that this must be the case, then we are right back to why we attempt to falsify in science, rather than collecting information to support the truth of a statement. Which makes a lot of sense. In science we keep searching for that pink raven, and failing to find it[and only finding black ones], we offer more and more support to the idea that all ravens are black. That is, as we find more and more pink chairs and not pink ravens, the truth value of our statement becomes more certain.
Instead, he discerned what propositions existed within the system.
But all propositions exist within all systems. It makes as much sense to say "the set which contains sets that do not contain themselves contains itself" as it does to say "Trees are true". Constructing statements which describe objects that do not exist is not difficult
For instance
Let P = (P and ~P)
If P then Q
P <- This is the point where we have a problem
Therefore ___
P is nonsensical, yet nothing prevents us from making the statement P=(P and ~P). But it becomes a problem when we then assert P. Physics cannot generate statements like P because the rules are unobservable and statements which do not violate the rules, but are not objects that exist cannot be observed. For all intents and purposes, P does not equal (P and ~P), P does not exist. It is as non nonsensical as saying 1=2 and believing it.
I can't exactly tell whether it's important or not, but making statements describing objects which do not exist and constructing propositions that cannot be true are two different things. Hell, even making statements about objects that do not exist and objects that cannot exist are two separate issues.
As for objects that do not exist, physics in particular does not have much to say on the issue. I can certainly give us great reason to think that particular objects are or are not possible (in a natural sense).
Also, while you can literally type the letters "P equals P and not P" that isn't saying a lot. You cannot meaningfully assert it, not because of any limitation of science, but because of limit of meaning.
I'm not entirely sure how this impacts your overall argument, largely because I'm not entirely sure what you're getting at here. But I feel like it might be important to the overall discourse.
"The only way to get rid of a temptation is to give into it." - Oscar Wilde
"We believe in the people and their 'wisdom' as if there was some special secret entrance to knowledge that barred to anyone who had ever learned anything." - Friedrich Nietzsche
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MrMisterJesus dying on the cross in pain? Morally better than us. One has to go "all in".Registered Userregular
edited May 2012
As far as I can see, the solution to the paradox of the raven is just to reject the notion that all instantiations of a universally generalized material conditional confirm it. And we should reject that claim exactly because of Hempel-like cases. If I see a book in my library, it does not disconfirm the existence of the Higgs Boson, despite it being an instantiation of a universal material conditional which is logically equivalent to the negation of the claim that there exists Higgs bosons. At one point people hoped that the universal-generalization story would be true, because they thought that would give them an account of scientific laws and how they were supported by the evidence. But now people tend to think that universally generalized material conditionals aren't even good candidates for explaining what counts as a scientific law, so that motivation is gone (for instance: unlike scientific laws, material conditionals only range over what is actual. Many things which physically could exist do not in fact exist, e.g. a diamond as big as a house. Material conditionals do not discriminate between a diamond as big as a house and a uranium sphere a mile wide--the former of which is physically possible but happens not to exist, the latter of which is physically impossible because not stable). The logic of confirmation isn't as simple or easily described as Hempel hoped: oh well.
Now, pretend that I have a system, described by S, and using some sort of magical tool I go in and pick up the L and R electrons and swap them without otherwise effecting the system. Because electrons are indistinguishable, the new system with L and R swapped is still characterized by S. These systems are trivially different: L and R swapped places. Yet, despite that, they are, as far as physics is concerned, identical systems.
What if we make this distinction:
1) Identical.
2) Functionally Identical.
It seems that physicists are talking about #2, rather than #1.
Now, pretend that I have a system, described by S, and using some sort of magical tool I go in and pick up the L and R electrons and swap them without otherwise effecting the system. Because electrons are indistinguishable, the new system with L and R swapped is still characterized by S. These systems are trivially different: L and R swapped places. Yet, despite that, they are, as far as physics is concerned, identical systems.
What if we make this distinction:
1) Identical.
2) Functionally Identical.
It seems that physicists are talking about #2, rather than #1.
Does that seem fair to you?
You're going to have to explain what you mean by this distinction. What's the difference between "identical" and "functionally identical"?
As far as I can see, the solution to the paradox of the raven is just to reject the notion that all instantiations of a universally generalized material conditional confirm it. And we should reject that claim exactly because of Hempel-like cases. If I see a book in my library, it does not disconfirm the existence of the Higgs Boson, despite it being an instantiation of a universal material conditional which is logically equivalent to the negation of the claim that there exists Higgs bosons. At one point people hoped that the universal-generalization story would be true, because they thought that would give them an account of scientific laws and how they were supported by the evidence. But now people tend to think that universally generalized material conditionals aren't even good candidates for explaining what counts as a scientific law, so that motivation is gone (for instance: unlike scientific laws, material conditionals only range over what is actual. Many things which physically could exist do not in fact exist, e.g. a diamond as big as a house. Material conditionals do not discriminate between a diamond as big as a house and a uranium sphere a mile wide--the former of which is physically possible but happens not to exist, the latter of which is physically impossible because not stable). The logic of confirmation isn't as simple or easily described as Hempel hoped: oh well.
/tangent
So, what would count as inductive confirmation / evidence of a universal that would not be subject to the raven paradox?
Instead, he discerned what propositions existed within the system.
But all propositions exist within all systems.
That's not true:
Rule 1: Add a U to the end of any string ending in I. For example: MI to MIU.
Rule 2: Double any string after the M (that is, change Mx, to Mxx). For example: MIU to MIUIU.
Rule 3: Replace any III with a U. For example: MUIIIU to MUUU.
Rule 4: Remove any UU. For example: MUUU to MU.
Rule 5: The first proposition is MI.
Physics cannot generate statements like P because the rules are unobservable and statements which do not violate the rules, but are not objects that exist cannot be observed. For all intents and purposes, P does not equal (P and ~P), P does not exist. It is as non nonsensical as saying 1=2 and believing it.
I'm not sure what this means.
What do you mean by "exist"? I thought I understood what you meant earlier...but I think that "exist" is doing a lot of work in your argument, and I'm not sure how its' doing that work.
The statement may exist. But the set itself nonsensical. We were to use the set in a proof; should some other aspect require something of this set we would necessarily get a contradiction. We live in the world of the objects that exist, and not the statements which we can make about the world which are nonsensical.
Yeah...that doesn't really clarify what you mean by "exist".
- Do trees exist?
- Do logical laws exist?
- Do physical laws exist?
- Do numbers exist?
- Do numerical signs exist?
- Do quantities exist?
- Do categories exist?
- Do processes exist?
Physics can only deal with objects which meet an equivalent criteria. Since we cannot observe P [given that P =(P and ~P)] and cannot observe the rules we cannot generate statements like that.
Ok, now I don't know what you mean by "observe". Because I read your statement P=(P and ~P). Reading is an observation. So...
Now, pretend that I have a system, described by S, and using some sort of magical tool I go in and pick up the L and R electrons and swap them without otherwise effecting the system. Because electrons are indistinguishable, the new system with L and R swapped is still characterized by S. These systems are trivially different: L and R swapped places. Yet, despite that, they are, as far as physics is concerned, identical systems.
What if we make this distinction:
1) Identical.
2) Functionally Identical.
It seems that physicists are talking about #2, rather than #1.
Does that seem fair to you?
You're going to have to explain what you mean by this distinction. What's the difference between "identical" and "functionally identical"?
Those 3Dss are not identical, since they are different colors, and in different locations. But they are functionally identical, with respect to their function of playing 3DS games.
My understanding is that, with the electron system, CpTHamilton claimed that after we moved the electrons around the systems were identical. But they weren't technically "identical" since the location-property was different.
To which he says that location isn't a relevant property.
That's fine. But it's still a property. It just isn't a property that is relevant to the FUNCTION of the system.
So, the systems are functionally identical, rather than identical.
The rules of a formal system an axiom of which is the law of non-contradiction prevents it.
If you want to articulate a system not beholden to that rule, then have fun.
And the rules of Set Theory have an Axiom which prevents Russel's Paradox. When we find paradoxs we tend to develop axioms to remove them. We don't do this for no reason.
How would one articulate the inequality without violating the logical rules?
Fucking really? You don't understand probability?
Well, I have this non-pink non-raven right here...
Which we don't give a shit about as expressed earlier, because we have black ravens. Therefore "All Ravens are Pink" is false. The proposition for which a non-x non-raven is evidence for IS NOT TRUE when x is not black. Because we have stronger evidence that requires its falseness.
The point is that we do not have to resolve the "paradox"
Now, pretend that I have a system, described by S, and using some sort of magical tool I go in and pick up the L and R electrons and swap them without otherwise effecting the system. Because electrons are indistinguishable, the new system with L and R swapped is still characterized by S. These systems are trivially different: L and R swapped places. Yet, despite that, they are, as far as physics is concerned, identical systems.
What if we make this distinction:
1) Identical.
2) Functionally Identical.
It seems that physicists are talking about #2, rather than #1.
Does that seem fair to you?
It may be. It's actually an open question whether there's a difference between 'identical' and 'functionally identical' when it comes to (what we think are) fundamental particles, which is where the philosophical issue comes in (I guess it's a philosophical issue, anyway).
If we could rely on position, at least, to keep things differentiated it wouldn't be an issue. Even taking into account swapping the positions of nominally identical particles we could, theoretically, consider their entire history. Outside of thought experiments it's not possible to move a charged particle without exerting a force on something, so with sufficient information it would theoretically be possible to always distinguish between two electrons by tracing their positions back through time to their individual moments of creation.
Problematically, though, we can't rely on position for three reasons:
1) the position of an electron is not fixed; it's a probabilistic property, so at best we can give a confinement radius of highest probability where the electron probably is. But! This radius can be made (almost) arbitrarily small. Down to a Plank length, anyway, which is significantly smaller than the nominal radius of an electron and since Pauli's Exclusion Principle says that identical electrons can't occupy the same space simultaneously, that's good enough.
2) Pauli's Exclusion can be violated. It takes absolutely absurd amounts of energy, but it can (and does) happen. Dwarf stars hold their shape on exclusion pressure (the restoring force exerted by fermions' desire not to occupy the same space in opposition to the gravitational force pressing the star inward towards its core), but a sufficiently large mass can generate sufficient gravitational force to overcome exclusion pressure. If the force is big enough to completely overcome exclusion pressure the result is a black hole and all of the particles inside it occupy the same space simultaneously. But nothing comes out of a black hole besides Hawking radiation, so we can pretty much ignore that case.
3) Pauli's Exclusion only applies to fermions -- that is, particles with non-integer spin values. Leptons (electrons, muons, taus, etc) and quarks are fermions, and anything composed of an odd number of fermions is also a fermion (so protons, neutrons, etc.). But anything composed of an even number of fermions is, itself, a boson. Bosons don't follow Pauli, so are not constrained to not occupy the same state simultaneously. Normally this means things like photons; a bunch of photons sharing the same quantum state (identical photons all in the same place simultaneously) is a laser. However, 'composite bosons' behave the same way. So a massive particle composed of an even number of fermions, like the ion Sodium-23 for example, is also a boson and isn't bound by Pauli.
So it's possible (and, in fact, experimentally verified) to take two fermions, turn them into bosons, and then put them in the same place at the same time. If you then split them off into different locations and restore their fermionic status, there is no way to determine which was which. So even if we had the capability to trace the path of a particle exactly back through time any arbitrary distance, it would be possible to construct our little three-particle setup using fermions that had, at some point, existed simultaneously in the same place at the same time. Meaning that they are, in every sense, indistinguishable.
Edit:
To put the quandary another way:
Consider a bag of marbles. If there are 10 marbles in 10 colors, it's easy to talk about the odds of drawing Marble 9 out of the sack blind. If all of the marbles are the same color then we could, perhaps, talk about drawing a specific marble on the basis of their position in the bag, say "the bottom-most marble". The situation with indistinguishable particles is akin to saying, "What are the odds that I will draw this marble (while holding up one of the ten) from the bag?" then dropping it in and mixing them up. You can't tell them apart, so is that question about probability even a meaningful question?
Krauss just reminds me of people who believe that science can explain everything, and is the most perfect field in all academia. I've met people like this, who believe that nothing accept science matters. The Liberal Arts are just worthless according to them. Its always sad when someone believes their field to be above all other, or that their field makes another field obsolete.
It may be. It's actually an open question whether there's a difference between 'identical' and 'functionally identical' when it comes to (what we think are) fundamental particles, which is where the philosophical issue comes in (I guess it's a philosophical issue, anyway).
Well, given that physicists are concerned with how the universe functions, why wouldn't they just admit that they are only talking about functional identity?
Going beyond that seems to just be saying, "Your stupid philosophical distinction is stupid and philosophical." I'm not sure what physics loses by saying, "Yeah, it's a functional distinction. Now let me explain to you how it works, and what data I have to verify the story I'm telling you."
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For an example of how this is applied in philosophy, look at John Lucas' application of Godel (or perhaps more accurately, Tarski) to the question of determinism and free will.
But for those of you arguing that Godel only dealt with math, you should read on. Godel himself argued that his incompleteness theorems had broader philosophical implications about the mind and the universe. In some basic theorems on the foundations of mathematics and their implications, Godel argues the superiority of the human mind over finite machines based on his Incompleteness Theorems.
In a later revision by Hilary Putnam (2006), it is pointed out that the human mind is fallible, and thus Godel was wrong simply because humans are inconsistent (I agree). However, Putnam notes that the same argument does in fact apply to math and science. In other words, if we are to believe that the human faculty of science and/or math is consistent, then we cannot prove its consistency, or we cannot represent it with a Turing machine. Which is basically what I'm saying. Philosophy pwns math and science; they are its bitches.
Maudlin expressed his point rather vaguely--in terms of tendencies rather than absolute rules--so it's compatible with there being places and people in the physics community who are interested in those questions. Indeed, he thinks those questions are just questions about understanding the physics, so there's no reason a physicist couldn't be interested in them. It's interesting to hear from someone in the physics community that there is such interest (I am certainly not in a position to bring to bear first-person evidence in order to fact-check).
As per the vacuum--this is just a guess, and definitely above my pay grade--but it sounds to me like you might be using 'static' in different senses. It sounds to me like, for Maudlin, if something is static over time it doesn't change at all (it's not just that its energy remains constant). And if something is complete, there's no aspect of the physical system which it does not represent. So, if something is both static and complete over some period of time, then there must be no aspect of the physical system which is changing. But this contradicts the notion that there is something in the physical system which is changing over time--namely, virtual particles are generating and annihilating each other in a 'buzzing hive' of activity.
It's also worth noting that Godel went insane and spent his latter years trying to mathematically demonstrate the existence of God. He might not be the most reliable interpreter of his own results.
edit:
I was about to jump in and correct you on that =P
Yeah, the proof of an axiom only takes one line.
Perhaps another way to say it is to say that any language that is expressive enough to form statements about its own foundations will necessarily fail to give us any ultimate answer to anything without some underlying acceptance of inconsistency or incompleteness. If the system isn't expressive enough to form statements about its own foundations, then it isn't expressive enough. But at least it escapes the dilemma.
So science probably can't explain science. Hawking's TOE seems to be a known impossibility.
Well, nobody really claims that any physical model is complete in that sense. A description of a system can be 'complete' in the sense that it covers every degree of freedom of the system without actually describing every aspect of the system. The entirety of thermodynamics works this way. You can have an accurate statistic description of a system which is 'complete' in the sense that any system which meets your description will behave identically to another such system, but it ignores things like the indistinguishibility of particles.
If I had, for example, three elections in a line: O ---- O ---- O they are indistinguishable from one another. I can write a Hamiltonian that describes the system accurately and in a fashion that I would tend to consider 'complete', despite the fact that my Hamiltonian would describe a system wherein you permuted the locations of those particles amongst one-another. So it's not a 'logically complete' description, for lack of a better term, but it is 'physically complete'.
Our description of the vacuum appears to be at least basically physically complete in that it describes the behavior of the vacuum accurately. It can't be logically complete for the same reason that my Hamiltonian of the three-electron system above can't be complete: there is no way to probe the system and discover the properties which a logically complete description would describe. I can't paint one of the electrons blue and another one green to see which is which, and the combination of the uncertainty relation and the fact that a vacuum is necessarily empty prevent me from finding out anything about the actions of virtual particles in vacuum.
A good description of Feynman's diagrams actually addresses something like this very issue. Even a very simple Feynman diagram (which is a pictoral representation of a quantum field calculation) is actually a summation of every possible permutation and refinement of that diagram. The diagram of two electrons interacting via boson exchange is 3 lines, but is equivalent to any number of more complex-looking diagrams wherein virtual particles appear and annihilate, interacting with one another and the electron-boson-electron system in the mean-time. This knowledge of "glossing over the details" is inherent, and we just accept it because some things in the physical world are either strictly unknowable, or at least appear strictly unknownable to modern physics.
I guess that's a philosophical problem of the type he's describing?
I think you're mostly describing a scientific problem. The philosophical problem is that you drew three electrons on a line. You drew a left one, a right one, and a center one. You distinguished them from one another before you even told me that you couldn't.
EDIT: This is the sort of thing I mentioned earlier. I don't assume that this means your 3-electron system is totally B.S. and that my philosophy about it is superior. And I'm sure that beneficial science can proceed from your statements. But at some point, philosophically, I have to believe that the way you drew three electrons on a line would itself be shown to be incorrect. At some point I suspect that physicists are making assumptions of knowledge about those things which were also assumed to be unknowable.
Most likely.
Unfortunately, this is not really my bailiwick, so I can't say much intelligibly in response to your specific points (aside from that, apparently, my guess was wrong).
Well, I mean, I can distinguish the left from the right from the center. They will feel different forces. But if I had electrons named Alice, Bob, and Charlie I couldn't tell whether they'd lined up in ABC, ACB, CAB, ... etc order. Similarly, I can't tell whether the force that Leftmost Electron feels is directly via interaction with Center and Rightmost Electrons, or if it's mediated by zero-net-change interaction with any number of virtual particles between them. That's why I called 'physically complete'.
A perfectly complete description of the system would know if those intermediary interactions occurred, and would have serial-number-stamped electrons in their appropriate places. But there are infinitely many such perfectly complete systems that are physically indistinguishable, so we call the description 'complete' provided that every system so-described behaves identically in every physically-distinguishable fashion. There's an awareness that this isn't actual completeness, but I'm not sure I see how that lack of completeness is a physics problem. If some new parameterization is discovered whereby previously indistinguishable systems become distinguishable then we need a new method of describing them, but there aren't any physicists who aren't aware of that fact.
Edit: Although yes, you can't literally have three electrons in a line. They aren't balls that you can line up. And if they were, they wouldn't stay in that configuration without help. But you can have an accurately-described system of three electrons.
How much does physics even know if they are in fact three particles that could line up, and not some sort of energy wave or something? I'm asking because I don't know, in case that wasn't obvious.
Technically we know that they aren't three particles that you can line up. They're three localized excitations of a quantum field. We don't know that the field itself isn't actually just an observational artifact of some more fundamental operation. Some people believe fairly strongly that this is the case, and theories about what that more-fundamental thing is abound, but there isn't actually any evidence that this is the case.
In some situations, it just so happens that quantum field excitations behave exactly as if they were little billiard balls floating in space. In other situations they behave absolutely nothing whatsoever like little billiard balls, which is why quantum mechanics seems so weird when you try to think about billiard ball particles.
There was some experiment a guy did with little balls suspended on liquid silicon, where it was shown how a particle could push a wave around in front of it, effectively creating some of the phenomenon we see in quantum mechanics (such as the double slit experiment). Was fascinating stuff. No idea how plausible it really is.
As long as you don't try to tell me that they're really just "information" then we're cool.
That's basically accurate. Particles are waves...they're just a type of wave that behaves like what we would consider a particle in some instances.
The Nobel Prize in Physics a couple of years ago was awarded for the creation of a Bose-Einstein Condensate, which is a state of matter wherein you can directly observe wave-like interactions in what would normally be considered solid, macroscopic matter. They took a cloud of...I want to say Rubidium ions and took a picture of it interfering with itself like the traditional double-slit laser.
A logically inconsistent statement cannot yield a result at all. The concept of a result coming from an inconsistent statement doesn't make sense.
That's incorrect. A logically inconsistent statement yields all possible results.
Basically, yes. We tend to maintain that Thales of Miletus was the first philosopher of the Western tradition insofar as he articulated a non-religious explanation for the way things be. After Thales, we find the development of Western philosophy and the rise of all of the specialized fields of study that philosophy spawned.
It's not that philosophy "says" that logic and facts exist. Rather, thinking logically is a manifestation of philosophy. Considering the universe in terms of facts is a manifestation of thinking philosophically.
What on earth are you talking about?
Why must there be a gap between these two things?
This is historically incorrect.
What is the problem with doing both? Why not construct a wealth of theories to explain a particular phenomena, rather than dogmatically cling to only one story and chastise anyone who offers a contrary account?
It seems to me that if science took seriously its claims to fallibilism and open-minded research, it would embrace a wealth of theories to compliment different epistemological / metaphysical / ontological presuppositions.
Quantum fields are not "nothing". To say that they are is to state that "something" is "nothing", which is a contradiction.
Perhaps it would be helpful to clarify something: There is a difference between "nothing" and "not-material".
Okie.
First, we could argue about whether or not the universe is a formal system that can be articulated in terms of logical statements converted into Godel numbers. Given Rorty's critique of the notion that our mental conceptualizations mirror nature, we at least have to offer an argument that acknowledges Rorty and so argues that our mathematical formalizations mirror the way things be. I can find a way around Rorty by appealing to Rationalism, but if we're going to be British Empiricists, I'm not sure how we get the "mental systemization = the universe" premise up and running.
Said another way, we have to prove that "if, then" and "and" and "or" mirror features of the universe. If we're going to express that tree over there, in terms of a formal system, then we need an argument that allows us to capture the entirety of that tree as a formal rationalistic system.
Spinoza can do that. Your average physicist can't.
Second, "the universe", by which I mean shit that bumps into other shit, does not produce situations of (X and ~X at the same time, in the same way), or self-negating facts.
I'm curious. Since they form a line, they would have to be in different locations. Couldn't they be distinguished in terms of their spatial location? To be truly indistinguishable, they would have EVERYTHING in common, and so fall subject to the "identity of indiscernibles". But since the electrons form a line, they would be distinguishable, insofar as they are in different locations.
(Yar dealt with this quite well, but he failed to get up off the mat and so left it as a "philosophical problem". I'm wanting to go a step further, and state that it's not just a philosophical problem: your statement was factually incorrect since they can be distinguished.)
^ This
Systems do not create self negating facts. They can be created within them/defined in them but do not actually create them. Why would the normal workings of a formal system produce a nonsensical situation?
The fact that I can state "the set of sets which do not contain themselves does/does not contain itself" does not mean that the set of sets which does not contain themselves exists. Suggesting that this is something that differentiates the systems implies that these nonsensical things exist. Its similar to suggesting that we can draw conclusions from the truth value of the statement "the set of sets which do not contain themselves does not contain itself". The truth value of that statement does not exist. There is nothing to draw conclusions from.
Your first two statements are problematic.
1) Systems do not create self-negating facts.
2) Self-negating facts can be created /defined within a system.
These seem to be
1) System-X does not create X.
2) X is created within System-X.
My guess is that the distinction you would make is that "the system" does not create any of the statements that follow from the definitions / axioms of the system. Instead, a person uses the axioms / definitions of the system to create statement within the system.
If that is your understanding, then I would suggest that it is flawed. Any particular system, composed of definitions and axioms, already contains everything that follows from those definitions / axioms. Spinoza did not "create" the propositions of his system. Instead, he discerned what propositions existed within the system.
So, if X can be articulated within System-X, then System-X did create X, insofar as the system consists of the definitions and axioms that entail X. If X follows from the definitions and axioms of system-X, then X is included in that system.
"Creation" may be a problematic concept.
If P, then Q.
P.
Therefore: ___
Do you maintain that I "create" the Q in that conclusion? If so, that is a problematic notion. I would say that one discerns that Q is the conclusion. That's not an act of creation; it's an act of discerning what is already there.
This is an interesting thesis. Perhaps you would like to argue for it.
I'm not sure what work "existence" is doing in your post.
If the rules of set theory are such that the statement "The set of all sets that do not contain themselves" follows from the rules, then what would be your critique of this situation?
If by "certainty" you mean 'deduction", then I would respectfully disagree. For an explanation of why deduction is better than induction / abduction, let’s talk about The Raven Paradox
Induction works by evidencing universals by means of particulars. We find one black raven, then another black raven, then another black raven, and after some quantity of black ravens are found, we state that “All ravens are black.” The idea is that one black raven counts as “evidence” for statements regarding all ravens.
A problem occurs when we start to think about what “All R are B” means, and how inductive evidence supports “All R are B”.
Consider the following:
“All ravens are black” is logically equivalent “Everything that is not black is not a raven.”
Previously, the inductivist maintained that one black raven is evidence that all ravens are black. However, we have just discerned that “all ravens are black” is logically equivalent to “Everything that is not black is not a raven.”
This black raven is evidence for the claim “All ravens are black.”
In a similar fashion: This non-black non-raven is evidence for the claim “Everything that is not black is not a raven.”
So, this blue ball is inductive evidence for the claim that “All ravens are black.”
Suddenly, the science of ornithology is beholden to observations of balls and chairs. While a particular ornithologist may have 500 black ravens, to evidence her claim that all ravens are black, I have 500 non-pink non-ravens to offer in support of my claim that all ravens are pink.
This is a problem for science.
I don't really know anything about science, but isn't this just one of those instances where scientists use abstractions of concepts to explain something because the concepts themselves are insanely complicated that are in fact very hard to explain?
(how did I miss this thread for five pages)
This is a bit tricky. It depends on how exactly you're confining the electrons.
Pretend you have electrons buckets (infinite square wells, to be precise).
If you put each electron in a different bucket, they can be distinguished by the fact they are in different buckets.
If you put all three electrons in the same bucket, they're indistinguishable with respect to each other. If you make a measurement and discern, "I have spotted an electron right here in the bucket!" there is no way to make a subsequent measurement and be sure you spotted the same electron, even in principle. This is because the electrons are governed by wavefunctions, so when you make a measurement at a point in space, there's a probability of measuring all three of the electrons, pretty much always. So, again, you can never be sure if you've measured the "same" electron.
When you have different buckets, the electronic wavefunctions are completely separated, so there's no (or vanishingly small) chance when you measure one electron in one bucket, that you're actually measuring the tail of one of the electronic wavefunctions from another bucket.
But each electron would occupy a different location, correct?
0 = Electron
[ ] = Bucket
T1 : [000]
T2 : [000]
The leftmost 0 at T1 might be the rightmost 0 at T2, right?
I'm curious why it would matter if you are measuring the same electron. If we cannot distinguish the electrons based upon continuous properties, then why would it matter if you measure the same or a different electron at T1 and T2?
I've even heard it suggested that there may only be one electron with a very complex and self-intersecting path through spacetime. There's nothing obvious to support that, but it's cute to imagine, and it would explain why all electrons seem to be identical.
My statement wasn't actually about distinguishing between the electrons in the example. There are actually some issues around that, as well, but what I was talking about was sufficiently describing a system.
Let's pretend for the moment that you can see the electrons in question and ignore issues of choice of coordinates and symmetry and shit. Obviously you could point to the left-hand electron (L), the right-hand one (R), or the middle one (M) and know which one you're pointing at. What I was saying is that you can, based on your understand that L, M, and R all exist and your knowledge of their properties (energy, momentum, spin, etc.) you can write a description of the system that perfectly (from a physicist's point of view) characterizes it. If we call the description S then any system which is described by S will behave in an identical fashion. Provided that the laws on which you based your description are accurate, S is sufficient to tell you everything you might want to know about the system's behavior.
Now, pretend that I have a system, described by S, and using some sort of magical tool I go in and pick up the L and R electrons and swap them without otherwise effecting the system. Because electrons are indistinguishable, the new system with L and R swapped is still characterized by S. These systems are trivially different: L and R swapped places. Yet, despite that, they are, as far as physics is concerned, identical systems.
There are other ways that you can create systems which are 'physically identical' despite actually being different. This is the philosophical problem I was talking about (well, one of them). Physics 'doesn't care' about the problem because in terms of doing physics (or, indeed, engineering or chemistry or anything else dependent upon the physical properties of systems) these systems are exactly the same. Yet they're also obviously different. The sticky point is that they're different in a way that physics says isn't real. Electrons aren't just similar, they are, as far as science is concerned, literally the same. Two electrons with the same spin, energy, momentum, etc. are the same thing. Their only differentiating factor is their location, which is why we can look at S and label the electrons L, R, and M.
I mentioned symmetry before. In mechanics (the branch of physics concerned with the behavior of physical systems; this can be stuff like pulleys and pendula (pendulums?) or it can be stuff like electrons when they're behaving 'classically') when we're talking about a system we tend to use a couple of equations to describe it, called the Hamiltonian and the Lagrangian. They actually do the same job but operate with different variables and in different mathematical spaces. The sweet thing about these equations is that they are functions of vectors. Vectors have the property that they are constant under change of coordinates, which means that the equation we use to describe the system is also constant under change of coordinates. In fact, the Hamiltonian is related to the Lagrangian in that it is a special type of coordinate transformation that goes from 'velocity coordinates' to 'momentum coordinates'.
So what's the point? The point is that our description, S, doesn't care about the coordinate system it's in. Which means that you can talk about a system using polar coordinates or Cartesian or whatever you want without having to start over from scratch. It also means that you can rotate the coordinate system without altering your description. This freedom of rotation means that any system involving a symmetric arrangement of components is indistinguishable from a system rotated about its axis of symmetry. So in the three-electrons-in-a-line example you can't *really* distinguish L and R.
Feynman's suggestion was actually that not only were all electrons the same particle, all electrons and positrons (anti-electrons) are the same particle. Positrons are just the electron travelling backward in time.
He was joking when he said it, though, and even at the time pointed out that it doesn't fit the observed universe...if it's all the same particle going back and forth in time there's no obvious way to explain the disparity of matter and anti-matter.
But all propositions exist within all systems. It makes as much sense to say "the set which contains sets that do not contain themselves contains itself" as it does to say "Trees are true". Constructing statements which describe objects that do not exist is not difficult
For instance
Let P = (P and ~P)
If P then Q
P <- This is the point where we have a problem
Therefore ___
P is nonsensical, yet nothing prevents us from making the statement P=(P and ~P). But it becomes a problem when we then assert P. Physics cannot generate statements like P because the rules are unobservable and statements which do not violate the rules, but are not objects that exist cannot be observed. For all intents and purposes, P does not equal (P and ~P), P does not exist. It is as non nonsensical as saying 1=2 and believing it.
The statement may exist. But the set itself nonsensical. We were to use the set in a proof; should some other aspect require something of this set we would necessarily get a contradiction. We live in the world of the objects that exist, and not the statements which we can make about the world which are nonsensical.
Maybe this will make sense. Let us take Russel's paradox and rephrase the defined set to:
The object which contains all sets that do not contain themselves
And then complete the statement implicit in the paradox
The object which contains all sets that do not contain themselves is a set
The above statement is not true.
Physics can only deal with objects which meet an equivalent criteria. Since we cannot observe P [given that P =(P and ~P)] and cannot observe the rules we cannot generate statements like that.
If you want to be as literal as you are, then we can simply move to a Bayesian framework and those issues are entirely solved. [Or more correctly, we reject the proposition that (A and
Alternately, we could simply accept it as fundamentally not a paradox. Non-pink, non-ravens DO offer support of the claim that all ravens are pink. But we don't give a shit, because we have ravens that are black, such all ravens are pink is false. The paradox is only close to paradox if we must accept that all evidence of the truth value of a statement is equal because then we have blue hats as evidence that all ravens are pink is true and the existence of black ravens implying that all ravens are pink is false as placed on equal footing.
Once we abandon the idea that this must be the case, then we are right back to why we attempt to falsify in science, rather than collecting information to support the truth of a statement. Which makes a lot of sense. In science we keep searching for that pink raven, and failing to find it[and only finding black ones], we offer more and more support to the idea that all ravens are black. That is, as we find more and more pink chairs and not pink ravens, the truth value of our statement becomes more certain.
I can't exactly tell whether it's important or not, but making statements describing objects which do not exist and constructing propositions that cannot be true are two different things. Hell, even making statements about objects that do not exist and objects that cannot exist are two separate issues.
As for objects that do not exist, physics in particular does not have much to say on the issue. I can certainly give us great reason to think that particular objects are or are not possible (in a natural sense).
Also, while you can literally type the letters "P equals P and not P" that isn't saying a lot. You cannot meaningfully assert it, not because of any limitation of science, but because of limit of meaning.
I'm not entirely sure how this impacts your overall argument, largely because I'm not entirely sure what you're getting at here. But I feel like it might be important to the overall discourse.
"We believe in the people and their 'wisdom' as if there was some special secret entrance to knowledge that barred to anyone who had ever learned anything." - Friedrich Nietzsche
/tangent
What if we make this distinction:
1) Identical.
2) Functionally Identical.
It seems that physicists are talking about #2, rather than #1.
Does that seem fair to you?
So, what would count as inductive confirmation / evidence of a universal that would not be subject to the raven paradox?
That's not true:
Rule 1: Add a U to the end of any string ending in I. For example: MI to MIU.
Rule 2: Double any string after the M (that is, change Mx, to Mxx). For example: MIU to MIUIU.
Rule 3: Replace any III with a U. For example: MUIIIU to MUUU.
Rule 4: Remove any UU. For example: MUUU to MU.
Rule 5: The first proposition is MI.
The proposition MU does not exist in this system.
The rules of a formal system an axiom of which is the law of non-contradiction prevents it.
If you want to articulate a system not beholden to that rule, then have fun.
I'm not sure what this means.
What do you mean by "exist"? I thought I understood what you meant earlier...but I think that "exist" is doing a lot of work in your argument, and I'm not sure how its' doing that work.
Yeah...that doesn't really clarify what you mean by "exist".
- Do trees exist?
- Do logical laws exist?
- Do physical laws exist?
- Do numbers exist?
- Do numerical signs exist?
- Do quantities exist?
- Do categories exist?
- Do processes exist?
Ok, now I don't know what you mean by "observe". Because I read your statement P=(P and ~P). Reading is an observation. So...
How would one articulate the inequality without violating the logical rules?
Undergrads love to respond to me by saying, "But Ravens tell us more about ravens than balls tell us about ravens!"
And then I reply, "Alright. But non-black non-raven things tell us about the statement 'All non-black things are non-ravens', right?"
Then they get sad.
Well, I have this non-pink non-raven right here...
Those 3Dss are not identical, since they are different colors, and in different locations. But they are functionally identical, with respect to their function of playing 3DS games.
My understanding is that, with the electron system, CpTHamilton claimed that after we moved the electrons around the systems were identical. But they weren't technically "identical" since the location-property was different.
To which he says that location isn't a relevant property.
That's fine. But it's still a property. It just isn't a property that is relevant to the FUNCTION of the system.
So, the systems are functionally identical, rather than identical.
MU
And the rules of Set Theory have an Axiom which prevents Russel's Paradox. When we find paradoxs we tend to develop axioms to remove them. We don't do this for no reason.
Fucking really? You don't understand probability?
Which we don't give a shit about as expressed earlier, because we have black ravens. Therefore "All Ravens are Pink" is false. The proposition for which a non-x non-raven is evidence for IS NOT TRUE when x is not black. Because we have stronger evidence that requires its falseness.
The point is that we do not have to resolve the "paradox"
You aren't saying that within the system. You're making that declaration external to the system.
Edit: That's how we can ask the question.
It may be. It's actually an open question whether there's a difference between 'identical' and 'functionally identical' when it comes to (what we think are) fundamental particles, which is where the philosophical issue comes in (I guess it's a philosophical issue, anyway).
If we could rely on position, at least, to keep things differentiated it wouldn't be an issue. Even taking into account swapping the positions of nominally identical particles we could, theoretically, consider their entire history. Outside of thought experiments it's not possible to move a charged particle without exerting a force on something, so with sufficient information it would theoretically be possible to always distinguish between two electrons by tracing their positions back through time to their individual moments of creation.
Problematically, though, we can't rely on position for three reasons:
1) the position of an electron is not fixed; it's a probabilistic property, so at best we can give a confinement radius of highest probability where the electron probably is. But! This radius can be made (almost) arbitrarily small. Down to a Plank length, anyway, which is significantly smaller than the nominal radius of an electron and since Pauli's Exclusion Principle says that identical electrons can't occupy the same space simultaneously, that's good enough.
2) Pauli's Exclusion can be violated. It takes absolutely absurd amounts of energy, but it can (and does) happen. Dwarf stars hold their shape on exclusion pressure (the restoring force exerted by fermions' desire not to occupy the same space in opposition to the gravitational force pressing the star inward towards its core), but a sufficiently large mass can generate sufficient gravitational force to overcome exclusion pressure. If the force is big enough to completely overcome exclusion pressure the result is a black hole and all of the particles inside it occupy the same space simultaneously. But nothing comes out of a black hole besides Hawking radiation, so we can pretty much ignore that case.
3) Pauli's Exclusion only applies to fermions -- that is, particles with non-integer spin values. Leptons (electrons, muons, taus, etc) and quarks are fermions, and anything composed of an odd number of fermions is also a fermion (so protons, neutrons, etc.). But anything composed of an even number of fermions is, itself, a boson. Bosons don't follow Pauli, so are not constrained to not occupy the same state simultaneously. Normally this means things like photons; a bunch of photons sharing the same quantum state (identical photons all in the same place simultaneously) is a laser. However, 'composite bosons' behave the same way. So a massive particle composed of an even number of fermions, like the ion Sodium-23 for example, is also a boson and isn't bound by Pauli.
So it's possible (and, in fact, experimentally verified) to take two fermions, turn them into bosons, and then put them in the same place at the same time. If you then split them off into different locations and restore their fermionic status, there is no way to determine which was which. So even if we had the capability to trace the path of a particle exactly back through time any arbitrary distance, it would be possible to construct our little three-particle setup using fermions that had, at some point, existed simultaneously in the same place at the same time. Meaning that they are, in every sense, indistinguishable.
Edit:
To put the quandary another way:
Consider a bag of marbles. If there are 10 marbles in 10 colors, it's easy to talk about the odds of drawing Marble 9 out of the sack blind. If all of the marbles are the same color then we could, perhaps, talk about drawing a specific marble on the basis of their position in the bag, say "the bottom-most marble". The situation with indistinguishable particles is akin to saying, "What are the odds that I will draw this marble (while holding up one of the ten) from the bag?" then dropping it in and mixing them up. You can't tell them apart, so is that question about probability even a meaningful question?
Well, given that physicists are concerned with how the universe functions, why wouldn't they just admit that they are only talking about functional identity?
Going beyond that seems to just be saying, "Your stupid philosophical distinction is stupid and philosophical." I'm not sure what physics loses by saying, "Yeah, it's a functional distinction. Now let me explain to you how it works, and what data I have to verify the story I'm telling you."