(although there's a problem which is that the 'nothing' which Krauss is talking about is still affected by stuff like space and time, whereas the 'nothing' most philosophers are thinking about is outside of the universe)
Yes, exactly. Since 'nothing' is basically in infinitely flexible term (as is 'something'), it's an impossible task to ever demonstrate that one can come from the other because a determined & dishonest interlocutor can always just adjust what they mean by 'nothing' or 'something' (or both).
In the book, Krauss makes it pretty clear that what he means is that particles - particularly hydrogen atoms - can seem to spontaneously just pop into existence under very specific conditions, and this may explain what happened to form our universe. But people don't want to hear that, so they break out the semantics & apologetics.
You may be misrepresenting Krauss. You're saying he's just doing science and philosophers are perceiving this as an attack. However, looking at some of the other shit the guy says in his responses, I think it is very likely that he meant it as an attack. Insofar as he was trying to discredit any philosophical/religious concepts, he failed without a doubt.
Why would the book, on its own make you a scientists. Possessing science does not make you a scientist in the same way possessing a chair does not make you a carpenter.
Because science is a process, not a communicable substance. I don't have science and a thing isn't made of science. You can practice science by only taking part in a subset of the overall process, but mathematics and philosophy do not, as fields of inquiry, instantiate the entire process at all. There are no experimental mathematicians (well, there probably are, but it doesn't mean the same thing if someone's using that title). Metaphysicists don't invalidate hypotheses on the subject of being.
I am not sure what you're getting at. We agree that having the book does not make you a scientist. But what about that matters for our discussing.
Mathematics and philosophy do, as fields of inquiry, apply the same process as the physical sciences. They simply have a better way of invalidating hypothesis.[and sometimes don't even need to propose them in the first place, because they know their dealing with an invertible function]
Edit: To claim that math and philosophy are not science is to fundamentally misunderstand the scientific process.
Why would the book, on its own make you a scientists. Possessing science does not make you a scientist in the same way possessing a chair does not make you a carpenter.
Because science is a process, not a communicable substance. I don't have science and a thing isn't made of science. You can practice science by only taking part in a subset of the overall process, but mathematics and philosophy do not, as fields of inquiry, instantiate the entire process at all. There are no experimental mathematicians (well, there probably are, but it doesn't mean the same thing if someone's using that title). Metaphysicists don't invalidate hypotheses on the subject of being.
Scientists fail to do these things all the time. There are scientists who don't do experiments, and also scientists that fail to invalidate any hypotheses.
"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
I'm sorry to say this, and I don't want to insult you or anything, but you're a bigot if you really believe that.
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GnomeTankWhat the what?Portland, OregonRegistered Userregular
Not to disagree, but how does MLK being religious have anything to do with science really not requiring religion? I agree he was religious, and I certainly agree his faith shaped his politics...but what is the correlation with the current topic?
AManFromEarthLet's get to twerk!The King in the SwampRegistered Userregular
Science really has no need for religion in its processes.
That does not mean religion is useless for society.
Lolken took exception to the idea that it was.
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GnomeTankWhat the what?Portland, OregonRegistered Userregular
Yeah, I'm not postulating that religion is useless to society, though I do think free-reign of religion can cause serious societal issues...but I think the issues whether science needs religion, which as you said, I think it's pretty clear that it doesn't.
Yeah, I'm not postulating that religion is useless to society, though I do think free-reign of religion can cause serious societal issues...but I think the issues whether science needs religion, which as you said, I think it's pretty clear that it doesn't.
I'm not entirely sure that we have a better notion of what constitutes a religion any more than we have one of what constitutes science.
Neither one of them are very clear or distinct terms.
"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
The 'usefulness' regarding areas of study like philosophy or science(intertwined as they are) strikes me as somewhat irrelevant. It's not like humanity has been determined to conform to some efficiency model. I'm not sure why a utilitarian tier involving different areas of study or practice is necessary. It seems that any reasonable individual can recognize some degree of value in most study, and for any particular practitioner to denounce whichever area seems more like psychological insecurity or ignorance.
Why would the book, on its own make you a scientists. Possessing science does not make you a scientist in the same way possessing a chair does not make you a carpenter.
Because science is a process, not a communicable substance. I don't have science and a thing isn't made of science. You can practice science by only taking part in a subset of the overall process, but mathematics and philosophy do not, as fields of inquiry, instantiate the entire process at all. There are no experimental mathematicians (well, there probably are, but it doesn't mean the same thing if someone's using that title). Metaphysicists don't invalidate hypotheses on the subject of being.
Scientists fail to do these things all the time. There are scientists who don't do experiments, and also scientists that fail to invalidate any hypotheses.
Scientists who don't do experiments still do work based on data from someone else's experiments.
Why would the book, on its own make you a scientists. Possessing science does not make you a scientist in the same way possessing a chair does not make you a carpenter.
Because science is a process, not a communicable substance. I don't have science and a thing isn't made of science. You can practice science by only taking part in a subset of the overall process, but mathematics and philosophy do not, as fields of inquiry, instantiate the entire process at all. There are no experimental mathematicians (well, there probably are, but it doesn't mean the same thing if someone's using that title). Metaphysicists don't invalidate hypotheses on the subject of being.
I am not sure what you're getting at. We agree that having the book does not make you a scientist. But what about that matters for our discussing.
Mathematics and philosophy do, as fields of inquiry, apply the same process as the physical sciences. They simply have a better way of invalidating hypothesis.[and sometimes don't even need to propose them in the first place, because they know their dealing with an invertible function]
Edit: To claim that math and philosophy are not science is to fundamentally misunderstand the scientific process.
Really? What experimental data does mathematics produce again?
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MrMisterJesus dying on the cross in pain? Morally better than us. One has to go "all in".Registered Userregular
At the risk of sounding like a dick myself, I kind of wish MrMister had started this thread
I actually was planning on doing it later today! But I have been beaten to the punch. So instead of authoring a thread, without further comment I present some things that are interesting.
First, David Albert, the philosopher who reviewed Kraus's book in the New York Times, also actually holds a Ph.D. in physics and has co-authored a number of seminal physics papers with Yakir Aharonov. This makes it all the more ridiculous that Kraus has repeatedly referred to him as a 'moron philosopher' who 'probably didn't even read the book.' Here is Albert's response to the charge that his review was inappropriate because it failed to engage with the larger portion of the contents of the book (spoiler alert, he also has a problem with the physics):
I did, for the record, read all of Professor Krauss’ book. And I would have very much liked to say more about the specifically scientific issues he discusses in my review. But the space allotted me by the Times was very limited – and I figured (given the title and sub-title of the book) that the issue that was first and foremost in Professor Kraus’ mind was the question of creation from nothing – and so I thought it best to use what space I had to write as clearly and simply and directly as I could about that.
But maybe it’s worth saying, now that the question has been raised, that the discussions of quantum mechanics in A Universe From Nothing are – from a purely scientific point of view – very badly confused. Let me mention just one example. Professor Kraus’ argument for the ‘reality’ of virtual particles, and for the instability of the quantum-mechanical vacuum, and for the larger and more imposing proposition that ‘nothing is something’, hinges on the claim that “the uncertainty in the measured energy of a system is inversely proportional to the length of time over which you observe it”. And it happens that we have known, for more than half a century now, from a beautiful and seminal and widely cited and justly famous paper by Yakir Aharonov and David Bohm, that this claim is false.
Of course, the physical literature is full of sloppy and misleading talk about the ‘energy-time uncertainty relation’, and about the effects of ‘virtual particles’, and so on – and none of that does much harm in the context of calculations of scattering cross-sections or atomic energy levels or radioactive decay rates. But the business of pontificating about why there is something rather than nothing without bothering to get crucial pieces of the physics right, or to think about them carefully, or to present them honestly, strikes me as something of a scandal.
Second, Kraus consistently conflates philosophers and theologians. He is one of those physicists, like Hawking, who likes to speak disparagingly of the former by lumping them in with the latter. The irony here is that many philosophers--if not the majority--think that the question of why there is anything at all, and why it is this, is either: 1) unanswerable (and hence uninteresting), or 2) nonsense, because concepts of explanation and justification cannot sensibly be applied to the universe as a whole. They accept the answer: 'it just does, and it just is.' In pointing out that Kraus has failed to answer this question by reference to quantum fields, they are not trying to score points for theology, or to claim that the real answer has to do with God. Their view is that the question is either unanswerable or nonsense, so of course, they hold, Kraus has not answered it with physics. That just follows a fortiori.
Imagine someone claimed that new advances in physics have answered the question: "is the sentence 'this sentence is false' true or false?' The philosopher objects not because they think it is a good question which goes unanswered by physics (which somehow proves that god exists?), but precisely because it is a bad one which cannot be answered at all. 'This sentence is false' is not well-formed. There is no answer to what it's truth value is, because it doesn't have one. Hence, it is certainly not the case that new advances in physics can tell us what its truth value is.
I find that this unreflective anti-philosophical sentiment is a common strain in the new atheist community. They lash out at philosophers because they associate them with mysticism. They forget that philosophers were the pioneer atheists, ever since Hume killed God in 1776.
Third and finally, Tim Maudlin, a prominent philosopher of physics, has some interesting things to say about the relationship between physics--especially fundamental physics--and philosophy. The upshot is that many of the questions philosophers are interested in now are, in a straightforward way, just about understanding the physics. But these questions nonetheless get shunned in physics departments for reasons of institutional culture. He hopes for a blending in the addressing of foundational topics--that practitioners are able to apply both the impressive formal mathematical competence of the physicist and the neatness and conceptual clarity of the philosopher.
It is true that there are some particular questions that fall more into the domain of philosophy (e.g. accounts of the nature of scientific practice) and others that are firmly in the domain of physics (e.g. methods of calculating scattering cross-sections), but for the particular sorts of questions we are largely interested in here, I can see no way to assign the topic to “physics” or “philosophy”. Take the case of the “nature of the wavefunction”, for example. In one sense a “wavefunction” (as its name implies) is a mathematical object—e.g. a complex function on another mathematical object called “configuration space”—that is employed in physics as a representation of a physical system. That immediately raises many questions. One, which Einstein, Podolosky and Rosen famously raised, is whether that particular mathematical representation is complete. That is, does it explicitly or implicitly represent all of the physical features, the values of all of the physical degrees of freedom, of the system. Can two systems represented by the same wavefunction nonetheless be physically different in some respect? Can the same system be properly represented by two different wavefunctions? Are there mathematical degrees of freedom in the representation that do not correspond to physical degrees of freedom in the system itself? (As an example of the latter, should the physical state of the system correspond to vector or a ray in a Hilbert space? If a ray, then it is misleading to say that the physical state is represented by a vector in the space: the vector has mathematical properties that do not correspond to physical properties of the system.) If one asks whether this sort of question is one of philosophy or of physics, I (and Einstein) would say it is a matter of physics. Indeed, it seems to be an absolutely essential question if one is to understand the physical account of the world being provided by the mathematics. But it is a sociological fact that while it is perfectly acceptable and even expected to discuss questions like this in a philosophy department, or a philosophy course, it can be rare, or even frowned upon, to discuss them in a physics department or physics course. We all know the phrase “shut up and calculate”. This phrase was not invented by philosophers, and in my experience physics students immediately recognize what it describes in their physics courses. Steven Weinberg tells the cautionary tale of the promising physics student whose career was ruined because “He tried to understand quantum mechanics”.
The point of the story is that the physicist, as physicist, should not try to have a clear, exact understanding of the physical meaning of the mathematical formalism. But certainly this ought to be a question in the domain of physics! It is just a weird sociological fact that, since the advent of quantum theory and the objections to that theory brought most forcefully by Einstein, Schrödinger, and later Bell, a standard physics education does not address these fundamental questions and many physics students are actively dissuaded from asking them. But anyone with a philosophical temperament cannot resist asking them. So, for better or worse, discussing these questions is more universally recognized as an important and legitimate task in philosophy departments than in physics departments (even Bell characterized his seminal work in foundations as secondary to his “real” physics work at CERN). And the habits of mind—a certain sort of precision about concepts and arguments—that are needed to pursue these questions happen to be exactly those habits instilled by a good education in philosophy. So while Krauss and Hawking lament that many philosophers don’t know enough physics (which is true), it is equally the case that many physicists are sloppy thinkers when it comes to foundational matters. I’m not sure that collaboration is the proper model here—as the “example” of Einstein collaborating with himself suggests!—but rather an appreciation of both which details of the physics are important and where the physics is simply not clear and precise as physics. Learning sophisticated mathematics, which a a large part of a physics education, does nothing to instill appreciation of the sort of conceptual and argumentative clarity needed to tackle these foundational issues.
Let me give a quick example. Take the “vacuum state” in quantum field theory. (No, I’m not raising the question of whether it is “nothing”!) It is commonly said that the vacuum state is positively a buzzing hive of activity: pairs of “virtual particles” being created an annihilated all the time. But it is also commonly said that the quantum state of system is complete: to deny this is to posit “hidden variables”, and those are not regarded by most physicists with favor. But it is clear that these two claims contradict each other. Consider a system in the vacuum state over some period of time. Over that period of time, the quantum state is static: it is always the same. So if the quantum state is complete, nothing physical in the system can be changing. But the “buzzing hive” of virtual particles is presented as constantly changing: particle pairs are being created and destroyed all the time. So which is it? This strikes me as a straightforward question of physics. But it is more likely to be asked, I think, by a philosopher. And insofar as the observable predictions of the theory do not depend directly on the answer, it is even likely to be dismissed by the physicist as “merely philosophical”. But without an answer, we really have no understanding of the vacuum state, or the status of “virtual particles”.
Why would the book, on its own make you a scientists. Possessing science does not make you a scientist in the same way possessing a chair does not make you a carpenter.
Because science is a process, not a communicable substance. I don't have science and a thing isn't made of science. You can practice science by only taking part in a subset of the overall process, but mathematics and philosophy do not, as fields of inquiry, instantiate the entire process at all. There are no experimental mathematicians (well, there probably are, but it doesn't mean the same thing if someone's using that title). Metaphysicists don't invalidate hypotheses on the subject of being.
Scientists fail to do these things all the time. There are scientists who don't do experiments, and also scientists that fail to invalidate any hypotheses.
Scientists who don't do experiments still do work based on data from someone else's experiments.
That is not true. There are a number of areas of science where experimentation is not possible. Now, scientists do attempt to use some facts that may have been proven by people who themselves used fact, so on and so forth back to some experiment. But it is not the case that the totality of all scientific endeavor relies entirely on experimental data. Simply because there are experiments that cannot be run.
"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
Why would the book, on its own make you a scientists. Possessing science does not make you a scientist in the same way possessing a chair does not make you a carpenter.
Because science is a process, not a communicable substance. I don't have science and a thing isn't made of science. You can practice science by only taking part in a subset of the overall process, but mathematics and philosophy do not, as fields of inquiry, instantiate the entire process at all. There are no experimental mathematicians (well, there probably are, but it doesn't mean the same thing if someone's using that title). Metaphysicists don't invalidate hypotheses on the subject of being.
Scientists fail to do these things all the time. There are scientists who don't do experiments, and also scientists that fail to invalidate any hypotheses.
Scientists who don't do experiments still do work based on data from someone else's experiments.
That is not true. There are a number of areas of science where experimentation is not possible. Now, scientists do attempt to use some facts that may have been proven by people who themselves used fact, so on and so forth back to some experiment. But it is not the case that the totality of all scientific endeavor relies entirely on experimental data. Simply because there are experiments that cannot be run.
Why would the book, on its own make you a scientists. Possessing science does not make you a scientist in the same way possessing a chair does not make you a carpenter.
Because science is a process, not a communicable substance. I don't have science and a thing isn't made of science. You can practice science by only taking part in a subset of the overall process, but mathematics and philosophy do not, as fields of inquiry, instantiate the entire process at all. There are no experimental mathematicians (well, there probably are, but it doesn't mean the same thing if someone's using that title). Metaphysicists don't invalidate hypotheses on the subject of being.
Scientists fail to do these things all the time. There are scientists who don't do experiments, and also scientists that fail to invalidate any hypotheses.
Scientists who don't do experiments still do work based on data from someone else's experiments.
That is not true. There are a number of areas of science where experimentation is not possible. Now, scientists do attempt to use some facts that may have been proven by people who themselves used fact, so on and so forth back to some experiment. But it is not the case that the totality of all scientific endeavor relies entirely on experimental data. Simply because there are experiments that cannot be run.
Like what?
Establishing the block universe. Multiple things in evolution and paleontology. Of course scientists try to make good explanations for these things. But as no one can actually experiment on dinosaurs, our resources are limited. Lots of geology is like this, such as certain things with respect to weather or plate tectonics. Lots of sociology can't be done with experiments, also anthropology. Also not a science where everything is subject to experimentation.
LoserForHireX on
"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
Why would the book, on its own make you a scientists. Possessing science does not make you a scientist in the same way possessing a chair does not make you a carpenter.
Because science is a process, not a communicable substance. I don't have science and a thing isn't made of science. You can practice science by only taking part in a subset of the overall process, but mathematics and philosophy do not, as fields of inquiry, instantiate the entire process at all. There are no experimental mathematicians (well, there probably are, but it doesn't mean the same thing if someone's using that title). Metaphysicists don't invalidate hypotheses on the subject of being.
Scientists fail to do these things all the time. There are scientists who don't do experiments, and also scientists that fail to invalidate any hypotheses.
Scientists who don't do experiments still do work based on data from someone else's experiments.
That is not true. There are a number of areas of science where experimentation is not possible. Now, scientists do attempt to use some facts that may have been proven by people who themselves used fact, so on and so forth back to some experiment. But it is not the case that the totality of all scientific endeavor relies entirely on experimental data. Simply because there are experiments that cannot be run.
Like what?
Establishing the block universe. Multiple things in evolution and paleontology. Of course scientists try to make good explanations for these things. But as no one can actually experiment on dinosaurs, our resources are limited. Lots of geology is like this, such as certain things with respect to weather or plate tectonics. Lots of sociology can't be done with experiments, also anthropology. Also not a science where everything is subject to experimentation.
Evolution, meteorology, geology and such are all done with experimental data. Paleontology is still done with data, although often more discovered data then data gleamed from experimentation.
The examples you used are really really very wrong.
Sorry for not reading the entire thread, but I do agree with what Mr^2 has said on this page.
I've long personally believed that the division between science and philosophy should be completely abolished, and I feel like this is an inevitable conclusion for a neuroscientist. The a priori/a posteriori dichotomy used to distinguish philosophy from science is complete and utter nonsense; there is no philosophy without empirical observations and there is no science without logical deduction. Every philosopher should be a scientist, and every scientist a philosopher.
Why would the book, on its own make you a scientists. Possessing science does not make you a scientist in the same way possessing a chair does not make you a carpenter.
Because science is a process, not a communicable substance. I don't have science and a thing isn't made of science. You can practice science by only taking part in a subset of the overall process, but mathematics and philosophy do not, as fields of inquiry, instantiate the entire process at all. There are no experimental mathematicians (well, there probably are, but it doesn't mean the same thing if someone's using that title). Metaphysicists don't invalidate hypotheses on the subject of being.
Scientists fail to do these things all the time. There are scientists who don't do experiments, and also scientists that fail to invalidate any hypotheses.
Scientists who don't do experiments still do work based on data from someone else's experiments.
That is not true. There are a number of areas of science where experimentation is not possible. Now, scientists do attempt to use some facts that may have been proven by people who themselves used fact, so on and so forth back to some experiment. But it is not the case that the totality of all scientific endeavor relies entirely on experimental data. Simply because there are experiments that cannot be run.
Like what?
Establishing the block universe. Multiple things in evolution and paleontology. Of course scientists try to make good explanations for these things. But as no one can actually experiment on dinosaurs, our resources are limited. Lots of geology is like this, such as certain things with respect to weather or plate tectonics. Lots of sociology can't be done with experiments, also anthropology. Also not a science where everything is subject to experimentation.
Evolution, meteorology, geology and such are all done with experimental data. Paleontology is still done with data, although often more discovered data then data gleamed from experimentation.
The examples you used are really really very wrong.
Excuse me. "Discovered" data is not experimental in nature. You asked for things that aren't done in experimentation. Certainly some parts of evolution, meterology, and geology are all done in experiments. However, what experiment was run to establish the system of plate tectonics that we use today? Please, point me to the experiment that was run.
You can't. Many, if not all, of those things are based on empirical observation sure, but mere empirical observation and experimentation are two different things. I don't think that you want to equate those things. Maybe you do, but I don't. I think that there is a valuable difference between empirical observation and experimentation.
Also, I love how you overlooked sociology and anthropology. Other areas where observation is used, and experimentation is limited or non-existence.
"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
Someone who doesn't MrMr isn't a human being. I'll say it.
"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
Why would the book, on its own make you a scientists. Possessing science does not make you a scientist in the same way possessing a chair does not make you a carpenter.
Because science is a process, not a communicable substance. I don't have science and a thing isn't made of science. You can practice science by only taking part in a subset of the overall process, but mathematics and philosophy do not, as fields of inquiry, instantiate the entire process at all. There are no experimental mathematicians (well, there probably are, but it doesn't mean the same thing if someone's using that title). Metaphysicists don't invalidate hypotheses on the subject of being.
Scientists fail to do these things all the time. There are scientists who don't do experiments, and also scientists that fail to invalidate any hypotheses.
Scientists who don't do experiments still do work based on data from someone else's experiments.
That is not true. There are a number of areas of science where experimentation is not possible. Now, scientists do attempt to use some facts that may have been proven by people who themselves used fact, so on and so forth back to some experiment. But it is not the case that the totality of all scientific endeavor relies entirely on experimental data. Simply because there are experiments that cannot be run.
Like what?
Establishing the block universe. Multiple things in evolution and paleontology. Of course scientists try to make good explanations for these things. But as no one can actually experiment on dinosaurs, our resources are limited. Lots of geology is like this, such as certain things with respect to weather or plate tectonics. Lots of sociology can't be done with experiments, also anthropology. Also not a science where everything is subject to experimentation.
Evolution, meteorology, geology and such are all done with experimental data. Paleontology is still done with data, although often more discovered data then data gleamed from experimentation.
The examples you used are really really very wrong.
I'm not sure how Krause was incorrect. Doesn't quantum uncertainty mean that it is impossible for there to be less than a quantum field? I mean, our understanding of how certain chemical reactions work relies on quantum uncertainty allowing particles to move through other particles.
Isn't the answer just "in the beginning there was nothing, but, because you can never be sure there actually is nothing, eventually that nothing happened to be something, and that something propagated?"
It's like Storrow Drive: it's two lanes, then three lanes, then two lanes. Can't explain that.
At the risk of sounding like a dick myself, I kind of wish MrMister had started this thread
I actually was planning on doing it later today! But I have been beaten to the punch. So instead of authoring a thread, without further comment I present some things that are interesting.
First, David Albert, the philosopher who reviewed Kraus's book in the New York Times, also actually holds a Ph.D. in physics and has co-authored a number of seminal physics papers with Yakir Aharonov. This makes it all the more ridiculous that Kraus has repeatedly referred to him as a 'moron philosopher' who 'probably didn't even read the book.' Here is Albert's response to the charge that his review was inappropriate because it failed to engage with the larger portion of the contents of the book (spoiler alert, he also has a problem with the physics):
I did, for the record, read all of Professor Krauss’ book. And I would have very much liked to say more about the specifically scientific issues he discusses in my review. But the space allotted me by the Times was very limited – and I figured (given the title and sub-title of the book) that the issue that was first and foremost in Professor Kraus’ mind was the question of creation from nothing – and so I thought it best to use what space I had to write as clearly and simply and directly as I could about that.
But maybe it’s worth saying, now that the question has been raised, that the discussions of quantum mechanics in A Universe From Nothing are – from a purely scientific point of view – very badly confused. Let me mention just one example. Professor Kraus’ argument for the ‘reality’ of virtual particles, and for the instability of the quantum-mechanical vacuum, and for the larger and more imposing proposition that ‘nothing is something’, hinges on the claim that “the uncertainty in the measured energy of a system is inversely proportional to the length of time over which you observe it”. And it happens that we have known, for more than half a century now, from a beautiful and seminal and widely cited and justly famous paper by Yakir Aharonov and David Bohm, that this claim is false.
Of course, the physical literature is full of sloppy and misleading talk about the ‘energy-time uncertainty relation’, and about the effects of ‘virtual particles’, and so on – and none of that does much harm in the context of calculations of scattering cross-sections or atomic energy levels or radioactive decay rates. But the business of pontificating about why there is something rather than nothing without bothering to get crucial pieces of the physics right, or to think about them carefully, or to present them honestly, strikes me as something of a scandal.
Second, Kraus consistently conflates philosophers and theologians. He is one of those physicists, like Hawking, who likes to speak disparagingly of the former by lumping them in with the latter. The irony here is that many philosophers--if not the majority--think that the question of why there is anything at all, and why it is this, is either: 1) unanswerable (and hence uninteresting), or 2) nonsense, because concepts of explanation and justification cannot sensibly be applied to the universe as a whole. They accept the answer: 'it just does, and it just is.' In pointing out that Kraus has failed to answer this question by reference to quantum fields, they are not trying to score points for theology, or to claim that the real answer has to do with God. Their view is that the question is either unanswerable or nonsense, so of course, they hold, Kraus has not answered it with physics. That just follows a fortiori.
Imagine someone claimed that new advances in physics have answered the question: "is the sentence 'this sentence is false' true or false?' The philosopher objects not because they think it is a good question which goes unanswered by physics (which somehow proves that god exists?), but precisely because it is a bad one which cannot be answered at all. 'This sentence is false' is not well-formed. There is no answer to what it's truth value is, because it doesn't have one. Hence, it is certainly not the case that new advances in physics can tell us what its truth value is.
I find that this unreflective anti-philosophical sentiment is a common strain in the new atheist community. They lash out at philosophers because they associate them with mysticism. They forget that philosophers were the pioneer atheists, ever since Hume killed God in 1776.
Third and finally, Tim Maudlin, a prominent philosopher of physics, has some interesting things to say about the relationship between physics--especially fundamental physics--and philosophy. The upshot is that many of the questions philosophers are interested in now are, in a straightforward way, just about understanding the physics. But these questions nonetheless get shunned in physics departments for reasons of institutional culture. He hopes for a blending in the addressing of foundational topics--that practitioners are able to apply both the impressive formal mathematical competence of the physicist and the neatness and conceptual clarity of the philosopher.
It is true that there are some particular questions that fall more into the domain of philosophy (e.g. accounts of the nature of scientific practice) and others that are firmly in the domain of physics (e.g. methods of calculating scattering cross-sections), but for the particular sorts of questions we are largely interested in here, I can see no way to assign the topic to “physics” or “philosophy”. Take the case of the “nature of the wavefunction”, for example. In one sense a “wavefunction” (as its name implies) is a mathematical object—e.g. a complex function on another mathematical object called “configuration space”—that is employed in physics as a representation of a physical system. That immediately raises many questions. One, which Einstein, Podolosky and Rosen famously raised, is whether that particular mathematical representation is complete. That is, does it explicitly or implicitly represent all of the physical features, the values of all of the physical degrees of freedom, of the system. Can two systems represented by the same wavefunction nonetheless be physically different in some respect? Can the same system be properly represented by two different wavefunctions? Are there mathematical degrees of freedom in the representation that do not correspond to physical degrees of freedom in the system itself? (As an example of the latter, should the physical state of the system correspond to vector or a ray in a Hilbert space? If a ray, then it is misleading to say that the physical state is represented by a vector in the space: the vector has mathematical properties that do not correspond to physical properties of the system.) If one asks whether this sort of question is one of philosophy or of physics, I (and Einstein) would say it is a matter of physics. Indeed, it seems to be an absolutely essential question if one is to understand the physical account of the world being provided by the mathematics. But it is a sociological fact that while it is perfectly acceptable and even expected to discuss questions like this in a philosophy department, or a philosophy course, it can be rare, or even frowned upon, to discuss them in a physics department or physics course. We all know the phrase “shut up and calculate”. This phrase was not invented by philosophers, and in my experience physics students immediately recognize what it describes in their physics courses. Steven Weinberg tells the cautionary tale of the promising physics student whose career was ruined because “He tried to understand quantum mechanics”.
The point of the story is that the physicist, as physicist, should not try to have a clear, exact understanding of the physical meaning of the mathematical formalism. But certainly this ought to be a question in the domain of physics! It is just a weird sociological fact that, since the advent of quantum theory and the objections to that theory brought most forcefully by Einstein, Schrödinger, and later Bell, a standard physics education does not address these fundamental questions and many physics students are actively dissuaded from asking them. But anyone with a philosophical temperament cannot resist asking them. So, for better or worse, discussing these questions is more universally recognized as an important and legitimate task in philosophy departments than in physics departments (even Bell characterized his seminal work in foundations as secondary to his “real” physics work at CERN). And the habits of mind—a certain sort of precision about concepts and arguments—that are needed to pursue these questions happen to be exactly those habits instilled by a good education in philosophy. So while Krauss and Hawking lament that many philosophers don’t know enough physics (which is true), it is equally the case that many physicists are sloppy thinkers when it comes to foundational matters. I’m not sure that collaboration is the proper model here—as the “example” of Einstein collaborating with himself suggests!—but rather an appreciation of both which details of the physics are important and where the physics is simply not clear and precise as physics. Learning sophisticated mathematics, which a a large part of a physics education, does nothing to instill appreciation of the sort of conceptual and argumentative clarity needed to tackle these foundational issues.
Let me give a quick example. Take the “vacuum state” in quantum field theory. (No, I’m not raising the question of whether it is “nothing”!) It is commonly said that the vacuum state is positively a buzzing hive of activity: pairs of “virtual particles” being created an annihilated all the time. But it is also commonly said that the quantum state of system is complete: to deny this is to posit “hidden variables”, and those are not regarded by most physicists with favor. But it is clear that these two claims contradict each other. Consider a system in the vacuum state over some period of time. Over that period of time, the quantum state is static: it is always the same. So if the quantum state is complete, nothing physical in the system can be changing. But the “buzzing hive” of virtual particles is presented as constantly changing: particle pairs are being created and destroyed all the time. So which is it? This strikes me as a straightforward question of physics. But it is more likely to be asked, I think, by a philosopher. And insofar as the observable predictions of the theory do not depend directly on the answer, it is even likely to be dismissed by the physicist as “merely philosophical”. But without an answer, we really have no understanding of the vacuum state, or the status of “virtual particles”.
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.
I've never been told to "shut up and calculate", nor have I ever heard anyone else told to do so or heard from a peer that they were told to do it. Perhaps his experience comes from a prior generation of physicists? Or maybe the southeast is just a more progressive physics community than I'd expect?
At the risk of sounding like a dick myself, I kind of wish MrMister had started this thread
I actually was planning on doing it later today! But I have been beaten to the punch. So instead of authoring a thread, without further comment I present some things that are interesting.
First, David Albert, the philosopher who reviewed Kraus's book in the New York Times, also actually holds a Ph.D. in physics and has co-authored a number of seminal physics papers with Yakir Aharonov. This makes it all the more ridiculous that Kraus has repeatedly referred to him as a 'moron philosopher' who 'probably didn't even read the book.' Here is Albert's response to the charge that his review was inappropriate because it failed to engage with the larger portion of the contents of the book (spoiler alert, he also has a problem with the physics):
I did, for the record, read all of Professor Krauss’ book. And I would have very much liked to say more about the specifically scientific issues he discusses in my review. But the space allotted me by the Times was very limited – and I figured (given the title and sub-title of the book) that the issue that was first and foremost in Professor Kraus’ mind was the question of creation from nothing – and so I thought it best to use what space I had to write as clearly and simply and directly as I could about that.
But maybe it’s worth saying, now that the question has been raised, that the discussions of quantum mechanics in A Universe From Nothing are – from a purely scientific point of view – very badly confused. Let me mention just one example. Professor Kraus’ argument for the ‘reality’ of virtual particles, and for the instability of the quantum-mechanical vacuum, and for the larger and more imposing proposition that ‘nothing is something’, hinges on the claim that “the uncertainty in the measured energy of a system is inversely proportional to the length of time over which you observe it”. And it happens that we have known, for more than half a century now, from a beautiful and seminal and widely cited and justly famous paper by Yakir Aharonov and David Bohm, that this claim is false.
Of course, the physical literature is full of sloppy and misleading talk about the ‘energy-time uncertainty relation’, and about the effects of ‘virtual particles’, and so on – and none of that does much harm in the context of calculations of scattering cross-sections or atomic energy levels or radioactive decay rates. But the business of pontificating about why there is something rather than nothing without bothering to get crucial pieces of the physics right, or to think about them carefully, or to present them honestly, strikes me as something of a scandal.
Second, Kraus consistently conflates philosophers and theologians. He is one of those physicists, like Hawking, who likes to speak disparagingly of the former by lumping them in with the latter. The irony here is that many philosophers--if not the majority--think that the question of why there is anything at all, and why it is this, is either: 1) unanswerable (and hence uninteresting), or 2) nonsense, because concepts of explanation and justification cannot sensibly be applied to the universe as a whole. They accept the answer: 'it just does, and it just is.' In pointing out that Kraus has failed to answer this question by reference to quantum fields, they are not trying to score points for theology, or to claim that the real answer has to do with God. Their view is that the question is either unanswerable or nonsense, so of course, they hold, Kraus has not answered it with physics. That just follows a fortiori.
Imagine someone claimed that new advances in physics have answered the question: "is the sentence 'this sentence is false' true or false?' The philosopher objects not because they think it is a good question which goes unanswered by physics (which somehow proves that god exists?), but precisely because it is a bad one which cannot be answered at all. 'This sentence is false' is not well-formed. There is no answer to what it's truth value is, because it doesn't have one. Hence, it is certainly not the case that new advances in physics can tell us what its truth value is.
I find that this unreflective anti-philosophical sentiment is a common strain in the new atheist community. They lash out at philosophers because they associate them with mysticism. They forget that philosophers were the pioneer atheists, ever since Hume killed God in 1776.
Third and finally, Tim Maudlin, a prominent philosopher of physics, has some interesting things to say about the relationship between physics--especially fundamental physics--and philosophy. The upshot is that many of the questions philosophers are interested in now are, in a straightforward way, just about understanding the physics. But these questions nonetheless get shunned in physics departments for reasons of institutional culture. He hopes for a blending in the addressing of foundational topics--that practitioners are able to apply both the impressive formal mathematical competence of the physicist and the neatness and conceptual clarity of the philosopher.
It is true that there are some particular questions that fall more into the domain of philosophy (e.g. accounts of the nature of scientific practice) and others that are firmly in the domain of physics (e.g. methods of calculating scattering cross-sections), but for the particular sorts of questions we are largely interested in here, I can see no way to assign the topic to “physics” or “philosophy”. Take the case of the “nature of the wavefunction”, for example. In one sense a “wavefunction” (as its name implies) is a mathematical object—e.g. a complex function on another mathematical object called “configuration space”—that is employed in physics as a representation of a physical system. That immediately raises many questions. One, which Einstein, Podolosky and Rosen famously raised, is whether that particular mathematical representation is complete. That is, does it explicitly or implicitly represent all of the physical features, the values of all of the physical degrees of freedom, of the system. Can two systems represented by the same wavefunction nonetheless be physically different in some respect? Can the same system be properly represented by two different wavefunctions? Are there mathematical degrees of freedom in the representation that do not correspond to physical degrees of freedom in the system itself? (As an example of the latter, should the physical state of the system correspond to vector or a ray in a Hilbert space? If a ray, then it is misleading to say that the physical state is represented by a vector in the space: the vector has mathematical properties that do not correspond to physical properties of the system.) If one asks whether this sort of question is one of philosophy or of physics, I (and Einstein) would say it is a matter of physics. Indeed, it seems to be an absolutely essential question if one is to understand the physical account of the world being provided by the mathematics. But it is a sociological fact that while it is perfectly acceptable and even expected to discuss questions like this in a philosophy department, or a philosophy course, it can be rare, or even frowned upon, to discuss them in a physics department or physics course. We all know the phrase “shut up and calculate”. This phrase was not invented by philosophers, and in my experience physics students immediately recognize what it describes in their physics courses. Steven Weinberg tells the cautionary tale of the promising physics student whose career was ruined because “He tried to understand quantum mechanics”.
The point of the story is that the physicist, as physicist, should not try to have a clear, exact understanding of the physical meaning of the mathematical formalism. But certainly this ought to be a question in the domain of physics! It is just a weird sociological fact that, since the advent of quantum theory and the objections to that theory brought most forcefully by Einstein, Schrödinger, and later Bell, a standard physics education does not address these fundamental questions and many physics students are actively dissuaded from asking them. But anyone with a philosophical temperament cannot resist asking them. So, for better or worse, discussing these questions is more universally recognized as an important and legitimate task in philosophy departments than in physics departments (even Bell characterized his seminal work in foundations as secondary to his “real” physics work at CERN). And the habits of mind—a certain sort of precision about concepts and arguments—that are needed to pursue these questions happen to be exactly those habits instilled by a good education in philosophy. So while Krauss and Hawking lament that many philosophers don’t know enough physics (which is true), it is equally the case that many physicists are sloppy thinkers when it comes to foundational matters. I’m not sure that collaboration is the proper model here—as the “example” of Einstein collaborating with himself suggests!—but rather an appreciation of both which details of the physics are important and where the physics is simply not clear and precise as physics. Learning sophisticated mathematics, which a a large part of a physics education, does nothing to instill appreciation of the sort of conceptual and argumentative clarity needed to tackle these foundational issues.
Let me give a quick example. Take the “vacuum state” in quantum field theory. (No, I’m not raising the question of whether it is “nothing”!) It is commonly said that the vacuum state is positively a buzzing hive of activity: pairs of “virtual particles” being created an annihilated all the time. But it is also commonly said that the quantum state of system is complete: to deny this is to posit “hidden variables”, and those are not regarded by most physicists with favor. But it is clear that these two claims contradict each other. Consider a system in the vacuum state over some period of time. Over that period of time, the quantum state is static: it is always the same. So if the quantum state is complete, nothing physical in the system can be changing. But the “buzzing hive” of virtual particles is presented as constantly changing: particle pairs are being created and destroyed all the time. So which is it? This strikes me as a straightforward question of physics. But it is more likely to be asked, I think, by a philosopher. And insofar as the observable predictions of the theory do not depend directly on the answer, it is even likely to be dismissed by the physicist as “merely philosophical”. But without an answer, we really have no understanding of the vacuum state, or the status of “virtual particles”.
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.
I've never been told to "shut up and calculate", nor have I ever heard anyone else told to do so or heard from a peer that they were told to do it. Perhaps his experience comes from a prior generation of physicists? Or maybe the southeast is just a more progressive physics community than I'd expect?
In my experience with, admittedly only second and third year physics courses, "shut up and calculate" was always used in a jovial sense - kind of a handwave to the fact that, whatever you may think it means, the mathematics do appear to describe the physical systems under interrogation (i.e. the transition from the weird quantum to more "normal" realm is accurately described by the equations, even if the implications of that seem - to our normal experience of the world - absurd).
But yeah, I never encountered a physicist who didn't think this was an important distinction - nor one who wasn't interested in it. "Shut up and calculate", as I understand it, is more of a refrain you resort to for the one dickhead who only wants to prove he's smarter then the lecturer when discovering the subatomic universe acts completely counter-intuitively on the attoscopic level.
The incompletness theorum is basically predicated upon the notion that any completely self-contained system will either produce a statement of the form "This statement is false" or it will produce both the statement "X is true / the case" and "~X is true / the case".
The universe doesn't do that. Which, perhaps, says something about Gödel's proof.
I'm still note entirely clear on whether physicists maintain that their conceptual systems mirror the way things be (it seems like many of them do) but that presupposition can be problematic in a number of ways, and at least needs to be argued for.
Gödel is neat and all, but applying it to physics is problematic insofar as that application relies upon a number of assumptions regarding both the universe and its knowability.
I'm so glad to have another in here who agrees with my understanding of the philosophical implications of Godel to science.
ELM, that is. J, you seem to have "disagreed" with him by acknowledging exactly what I think he was saying. In other words, if you aren't making certain assumptions about the universe and its knowability, well then you've perhaps correctly ascertained the significance of Godel to physics.
I'm very interested in your assertion that "the universe doesn't do that," though.
I really can't see how you can group mathematics and any of the sciences together. Their methods and outputs are quite fundamentially different.
Mathematics: Starting from initial axioms / postulates which are simply accepted as true, creates theorems which are also true. Mathematics is not a priori. It is a completely artificial construct. All of it, even simple things like how to count or add two integers together are based on postulates which are not proven, simply accepted. But, once those postulates are accepted the rest of it follows with absolute certainty (that being the advantage of working with an artifical construct instead of from empirical observation).
Science: Uses induction based on iterative experiments to create theories which are plausible within the margin of error of the data available.
The methods of science can never produce theories which are "true" in the sense of a mathematical theorem or whatever gibberish a philospher might prattle on about. Induction from data can never provide a theory which we can be 100% sure to be true. It can provide a theory which is plausible and consistant with all known data within the margin of error for the measurements of that data.
Mathematics: starting from initial axioms / postulates which are simply accepted as true, create theorems which are also true.
Science: starting with the scientific method, which is simply accepted as a procedural means to truth, create theorems which are thus accepted as truth.
In other words, they are both in the form of: starting with a philosophical basis that we accept as a useful means of describing and resolving truth, go formalize some truths.
Math and science are both off-shoots of philosophy. Referring back to the xkcd comic, math is only "pure" until you start looking at the philosophical basis of mathematics, and the various philosophical arguments for and against it. Suddenly we have a guy to the right of math, stoicly unconcerned with whether or not math realizes his true rank in relative purity.
The main difference between math and science are how much our observations of the physical world play any critical role in the philosophical basis for resolving truth. In science, our senses and observations are fairly important aspects to the truth process. In math, much less so (though still to some degree).
This is why modern science gets so tripped up on the effects of observation when bridging the gap between physics and math.
It's also why Green Dream and saggio aren't arriving at the same notion of "truth" due to a conflict over whether or not it requires some connection to our observations of the physical world.
But Goum is just wrong. Math is not science. I think what's he's getting at is that math is philosophy, as is science.
Second, Kraus consistently conflates philosophers and theologians. He is one of those physicists, like Hawking, who likes to speak disparagingly of the former by lumping them in with the latter. The irony here is that many philosophers--if not the majority--think that the question of why there is anything at all, and why it is this, is either: 1) unanswerable (and hence uninteresting), or 2) nonsense, because concepts of explanation and justification cannot sensibly be applied to the universe as a whole. They accept the answer: 'it just does, and it just is.' In pointing out that Kraus has failed to answer this question by reference to quantum fields, they are not trying to score points for theology, or to claim that the real answer has to do with God. Their view is that the question is either unanswerable or nonsense, so of course, they hold, Kraus has not answered it with physics. That just follows a fortiori.
Exactly. Krauss seems to think that the challenge is along the lines of, "ha, God wins, science is false!" When instead it is simply a philosophical debate that Krauss isn't capable of handling. This is a problem I totally believe exists among a lot of physicists. They aren't of a mindset to grasp the very significant philosophical failings of the scientific work they've done. Not in some spiritual "you know not what you do" manner, but in a very real, "you are logically incorrect and don't realize it" manner.
Take the “vacuum state” in quantum field theory. (No, I’m not raising the question of whether it is “nothing”!) It is commonly said that the vacuum state is positively a buzzing hive of activity: pairs of “virtual particles” being created an annihilated all the time. But it is also commonly said that the quantum state of system is complete: to deny this is to posit “hidden variables”, and those are not regarded by most physicists with favor. But it is clear that these two claims contradict each other. Consider a system in the vacuum state over some period of time. Over that period of time, the quantum state is static: it is always the same. So if the quantum state is complete, nothing physical in the system can be changing. But the “buzzing hive” of virtual particles is presented as constantly changing: particle pairs are being created and destroyed all the time. So which is it? This strikes me as a straightforward question of physics. But it is more likely to be asked, I think, by a philosopher. And insofar as the observable predictions of the theory do not depend directly on the answer, it is even likely to be dismissed by the physicist as “merely philosophical”. But without an answer, we really have no understanding of the vacuum state, or the status of “virtual particles”.
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.
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.
The incompletness theorum is basically predicated upon the notion that any completely self-contained system will either produce a statement of the form "This statement is false" or it will produce both the statement "X is true / the case" and "~X is true / the case".
The universe doesn't do that. Which, perhaps, says something about Gödel's proof.
I'm still note entirely clear on whether physicists maintain that their conceptual systems mirror the way things be (it seems like many of them do) but that presupposition can be problematic in a number of ways, and at least needs to be argued for.
Gödel is neat and all, but applying it to physics is problematic insofar as that application relies upon a number of assumptions regarding both the universe and its knowability.
I'm so glad to have another in here who agrees with my understanding of the philosophical implications of Godel to science.
ELM, that is. J, you seem to have "disagreed" with him by acknowledging exactly what I think he was saying. In other words, if you aren't making certain assumptions about the universe and its knowability, well then you've perhaps correctly ascertained the significance of Godel to physics.
I'm very interested in your assertion that "the universe doesn't do that," though.
This really bugs me. To my understanding, Godel merely proved that in classical arithmetic that one could generate a number (representing a theorem) that could neither be proven true or false in classical arithmetic (what I learned as Robinson's Arithmetic). I think that you make a lot more out of what Godel did than is warranted. He didn't show that incompleteness is just a part of any and all systems ever. Just one particular system, and even then completeness isn't really that big of a deal. It's still sound, so we can be accurate with the things that we can prove one way or another, but it's simply limited that it can't prove every theorem positively or negatively.
Now, I'm not an expert in either logic or mathematics, so I have a bit of trouble understanding everything that's going on there.
For reference, I've used the Stanford Encyclopedia entry in composing this. Godel
"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
The incompletness theorum is basically predicated upon the notion that any completely self-contained system will either produce a statement of the form "This statement is false" or it will produce both the statement "X is true / the case" and "~X is true / the case".
The universe doesn't do that. Which, perhaps, says something about Gödel's proof.
I'm still note entirely clear on whether physicists maintain that their conceptual systems mirror the way things be (it seems like many of them do) but that presupposition can be problematic in a number of ways, and at least needs to be argued for.
Gödel is neat and all, but applying it to physics is problematic insofar as that application relies upon a number of assumptions regarding both the universe and its knowability.
I'm so glad to have another in here who agrees with my understanding of the philosophical implications of Godel to science.
ELM, that is. J, you seem to have "disagreed" with him by acknowledging exactly what I think he was saying. In other words, if you aren't making certain assumptions about the universe and its knowability, well then you've perhaps correctly ascertained the significance of Godel to physics.
I'm very interested in your assertion that "the universe doesn't do that," though.
This really bugs me. To my understanding, Godel merely proved that in classical arithmetic that one could generate a number (representing a theorem) that could neither be proven true or false in classical arithmetic (what I learned as Robinson's Arithmetic). I think that you make a lot more out of what Godel did than is warranted. He didn't show that incompleteness is just a part of any and all systems ever. Just one particular system, and even then completeness isn't really that big of a deal. It's still sound, so we can be accurate with the things that we can prove one way or another, but it's simply limited that it can't prove every theorem positively or negatively.
Now, I'm not an expert in either logic or mathematics, so I have a bit of trouble understanding everything that's going on there.
For reference, I've used the Stanford Encyclopedia entry in composing this. Godel
His theorem was applied to more than one particular system, but it is limited to certain classes of systems. It definitely doesn't just apply to all logical systems ever, and, as you said, it doesn't actually say anything about the capabilities of a system to which it does apply as regards statements within the scope of provability.
The significance of Godel is better explained in Tarski perhaps. But even if you want to restrict it merely to the arithmetic bit, then it still applies to any axiomatic system capable of explaining natural numbers.
The generalized philosophical implications are merely that a system which can be expressed therefore can't possibly generate an expression that explains the system itself. If you limit yourself to a single system of defining truth, all truths in that system will ultimately rely on some assumed axiom that cannot be proven within the system.
A lot of people try to take that in the wrong direction. I'm not saying, "haha, axioms can't be proven, therefore give into solipsism!!!" It's meant primarily as an answer to anyone who believes in a single system (be it scientific method or arithmetic or whatever) as capable of expressing "absolute" truths that do not rely on any assumptions or rely on verification from other independent systems of truth.
We verify our reasoning with our observations and our observations with reason. Neither one alone gives us meaningful defensible truth. We verify math with logic and logic with math. And so on. If you believe that there is some underlying single arbiter that can verify any of them as true or false, you're equivalently believing in God and you are denying what is at least strongly suggested by Godel, Tarski, Heisenberg, Hume, et. al.
It's not necessarily to say that an objective physical reality doesn't exist, but rather that a formal language to describe anything absolute about it can't possibly exist, because of the necessary nature of formal languages themselves. No matter what system we come up with for expressing truth, that system must necessarily always rely on some convenient assumptions that we can't know to be true or false. That doesn't mean there is no truth, it's just a facet of what truth is.
The significance of Godel is better explained in Tarski perhaps. But even if you want to restrict it merely to the arithmetic bit, then it still applies to any axiomatic system capable of explaining natural numbers.
The generalized philosophical implications are merely that a system which can be expressed therefore can't possibly generate an expression that explains the system itself. If you limit yourself to a single system of defining truth, all truths in that system will ultimately rely on some assumed axiom that cannot be proven within the system.
A lot of people try to take that in the wrong direction. I'm not saying, "haha, axioms can't be proven, therefore give into solipsism!!!" It's meant primarily as an answer to anyone who believes in a single system (be it scientific method or arithmetic or whatever) as capable of expressing "absolute" truths that do not rely on any assumptions or rely on verification from other independent systems of truth.
We verify our reasoning with our observations and our observations with reason. Neither one alone gives us meaningful defensible truth. We verify math with logic and logic with math. And so on. If you believe that there is some underlying single arbiter that can verify any of them as true or false, you're equivalently believing in God and you are denying what is at least strongly suggested by Godel, Tarski, Heisenberg, Hume, et. al.
It's not necessarily to say that an objective physical reality doesn't exist, but rather that a formal language to describe anything absolute about it can't possibly exist, because of the necessary nature of formal languages themselves. No matter what system we come up with for expressing truth, that system must necessarily always rely on some convenient assumptions that we can't know to be true or false. That doesn't mean there is no truth, it's just a facet of what truth is.
It may be the painkillers, but I think that made more sense to me than anything of yours I've read on this board, Yar.
I'm not sure why it's an important revelation, but I'll give you a high-five of agreement on this chunk at least.
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Tiger BurningDig if you will, the pictureRegistered User, SolidSaints Tuberegular
The generalized philosophical implications are merely that a system which can be expressed therefore can't possibly generate an expression that explains the system itself. If you limit yourself to a single system of defining truth, all truths in that system will ultimately rely on some assumed axiom that cannot be proven within the system.
This is flatly incorrect. The role of axioms in formal systems does not rely on the completeness of the system. A system is not incomplete because it cannot derive its axioms. Godel's result is that in a sufficiently recursive system there will be theorems that are true but non-derivable. But that formal systems rely on axioms that are not provable within the system was understood before Godel and is sort of a trivial observation anyway
Excuse me. "Discovered" data is not experimental in nature. You asked for things that aren't done in experimentation. Certainly some parts of evolution, meterology, and geology are all done in experiments. However, what experiment was run to establish the system of plate tectonics that we use today? Please, point me to the experiment that was run.
You can't. Many, if not all, of those things are based on empirical observation sure, but mere empirical observation and experimentation are two different things. I don't think that you want to equate those things. Maybe you do, but I don't. I think that there is a valuable difference between empirical observation and experimentation.
Also, I love how you overlooked sociology and anthropology. Other areas where observation is used, and experimentation is limited or non-existence.
I agree with you that there are scientific fields where experiments are not feasible. I'm not sure why this is even a concern, however, as science is interested in testable (and thus falsifiable) conclusions, not experiments. An example of a test is whether or not said theory has any predictive capability. It doesn't have to be future predictive (though that is typically assumed, sometimes we can't wait that long), it can be predictive of other data. For instance, evolutionary theory predicted that a transitional form between fish and amphibians probably happened around 375 million years ago. So paleontologists dug around in strata dated to about that time period, and lo and behold, Tiktaalik was found.
I'm going to disagree with Shryke, here, lots of scientists don't do experiments. But as I stated above, experiments aren't the point of science, testable conclusions typically are.
Edit: In short, experiments are one way to test conclusions. They are by no means the only way.
This is flatly incorrect. The role of axioms in formal systems does not rely on the completeness of the system. A system is not incomplete because it cannot derive its axioms. Godel's result is that in a sufficiently recursive system there will be theorems that are true but non-derivable. But that formal systems rely on axioms that are not provable within the system was understood before Godel and is sort of a trivial observation anyway
It isn't just that axiomatic systems are axiomatic, but rather that such systems can't possibly prove their own axioms, without running into inconsistency.
To say that there will be statements that are true but not derivable is the flipside of the same coin. Because the truth of the axioms relies on something other than the system those axioms define, there will statements that can exploit this, which are expressed in the language of the system, but because of the nature of what is assumed in the axioms and how it is understood, cannot be resolved by the system.
The nature of the assumptions in ZFC, for example, such as the assumptions on infinite sets, or on the constructibility of sets from smaller subsets, are what eventually lead to certain impossibilities regarding infinite subsets of infinite sets. This is a logical cousin to the fact that the system cannot derive its own axioms.
The simpler example is in naive set theory and Russel's paradox. "The set of all sets not members of themselves." The philosophical problem is elegantly stated within. When you try to use the system to make an original statement about the system (i.e., sets of sets defined recursively by set membership) you can easily constuct nonsense. Even simpler: "this statment is false."
The significance of Godel is better explained in Tarski perhaps. But even if you want to restrict it merely to the arithmetic bit, then it still applies to any axiomatic system capable of explaining natural numbers.
The generalized philosophical implications are merely that a system which can be expressed therefore can't possibly generate an expression that explains the system itself. If you limit yourself to a single system of defining truth, all truths in that system will ultimately rely on some assumed axiom that cannot be proven within the system.
A lot of people try to take that in the wrong direction. I'm not saying, "haha, axioms can't be proven, therefore give into solipsism!!!" It's meant primarily as an answer to anyone who believes in a single system (be it scientific method or arithmetic or whatever) as capable of expressing "absolute" truths that do not rely on any assumptions or rely on verification from other independent systems of truth.
We verify our reasoning with our observations and our observations with reason. Neither one alone gives us meaningful defensible truth. We verify math with logic and logic with math. And so on. If you believe that there is some underlying single arbiter that can verify any of them as true or false, you're equivalently believing in God and you are denying what is at least strongly suggested by Godel, Tarski, Heisenberg, Hume, et. al.
It's not necessarily to say that an objective physical reality doesn't exist, but rather that a formal language to describe anything absolute about it can't possibly exist, because of the necessary nature of formal languages themselves. No matter what system we come up with for expressing truth, that system must necessarily always rely on some convenient assumptions that we can't know to be true or false. That doesn't mean there is no truth, it's just a facet of what truth is.
You do realize that he proved the completeness of logic right? All the stuff about the axioms of a system not being able to prove the system don't apply to logic.
How does Tarski fit into this? Everything that I can read on him (again SEP), suggests that he was also focused on mathematics, and didn't show a similar problem with logic. Again, he showed that mathematics has issues of completeness, but not logic. He also had some issues telling the difference between logic and math at some levels, but it seems like he largely cleared that up.
I don't know nearly enough about Heisenberg to comment on anything concerning him with this. I only know pop science stuff about uncertainty.
As for Hume, he believed that there were things that we could know for certain. So I have no idea what you're going on about with him. One of those things we can know for certain is mathematics. So how does Hume fit in with anything you've said?
"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
This is flatly incorrect. The role of axioms in formal systems does not rely on the completeness of the system. A system is not incomplete because it cannot derive its axioms. Godel's result is that in a sufficiently recursive system there will be theorems that are true but non-derivable. But that formal systems rely on axioms that are not provable within the system was understood before Godel and is sort of a trivial observation anyway
It isn't just that axiomatic systems are axiomatic, but rather that such systems can't possibly prove their own axioms, without running into inconsistency.
To say that there will be statements that are true but not derivable is the flipside of the same coin. Because the truth of the axioms relies on something other than the system those axioms define, there will statements that can exploit this, which are expressed in the language of the system, but because of the nature of what is assumed in the axioms and how it is understood, cannot be resolved by the system.
The nature of the assumptions in ZFC, for example, such as the assumptions on infinite sets, or on the constructibility of sets from smaller subsets, are what eventually lead to certain impossibilities regarding infinite subsets of infinite sets. This is a logical cousin to the fact that the system cannot derive its own axioms.
The simpler example is in naive set theory and Russel's paradox. "The set of all sets not members of themselves." The philosophical problem is elegantly stated within. When you try to use the system to make an original statement about the system (i.e., sets of sets defined recursively by set membership) you can easily constuct nonsense. Even simpler: "this statment is false."
I don't think that axioms actually play directly into Godel. I mean the axioms of a system are inherently improvable using that system, but that's just the nature of axioms.
Godel's thing was that there are true but non-axiomatic statements in any consistent system which the system cannot prove.
Edit: the example from Wikipedia illustrates it pretty well.
"The truth value of this statement cannot be proven using the theory T" (paraphrased from wikipedia)
It's different from "This statement is false" in that the statement is true, whereas "this is false" has an undefined truth value.
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Tiger BurningDig if you will, the pictureRegistered User, SolidSaints Tuberegular
edited May 2012
And to say that axioms are unprovable (which I did too) in the system is inaccurate. The proof of an axiom is just a statement of the axiom.
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I'm sure his science is fine.
I am not sure what you're getting at. We agree that having the book does not make you a scientist. But what about that matters for our discussing.
Mathematics and philosophy do, as fields of inquiry, apply the same process as the physical sciences. They simply have a better way of invalidating hypothesis.[and sometimes don't even need to propose them in the first place, because they know their dealing with an invertible function]
Edit: To claim that math and philosophy are not science is to fundamentally misunderstand the scientific process.
Scientists fail to do these things all the time. There are scientists who don't do experiments, and also scientists that fail to invalidate any hypotheses.
"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
http://www.genconnect.com/wp-content/uploads/2012/01/mlk.jpg
I'm sorry to say this, and I don't want to insult you or anything, but you're a bigot if you really believe that.
I'm not certain I understand your point, can you elaborate?
That does not mean religion is useless for society.
Lolken took exception to the idea that it was.
I'm not entirely sure that we have a better notion of what constitutes a religion any more than we have one of what constitutes science.
Neither one of them are very clear or distinct terms.
"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
Scientists who don't do experiments still do work based on data from someone else's experiments.
Really? What experimental data does mathematics produce again?
I actually was planning on doing it later today! But I have been beaten to the punch. So instead of authoring a thread, without further comment I present some things that are interesting.
First, David Albert, the philosopher who reviewed Kraus's book in the New York Times, also actually holds a Ph.D. in physics and has co-authored a number of seminal physics papers with Yakir Aharonov. This makes it all the more ridiculous that Kraus has repeatedly referred to him as a 'moron philosopher' who 'probably didn't even read the book.' Here is Albert's response to the charge that his review was inappropriate because it failed to engage with the larger portion of the contents of the book (spoiler alert, he also has a problem with the physics):
Second, Kraus consistently conflates philosophers and theologians. He is one of those physicists, like Hawking, who likes to speak disparagingly of the former by lumping them in with the latter. The irony here is that many philosophers--if not the majority--think that the question of why there is anything at all, and why it is this, is either: 1) unanswerable (and hence uninteresting), or 2) nonsense, because concepts of explanation and justification cannot sensibly be applied to the universe as a whole. They accept the answer: 'it just does, and it just is.' In pointing out that Kraus has failed to answer this question by reference to quantum fields, they are not trying to score points for theology, or to claim that the real answer has to do with God. Their view is that the question is either unanswerable or nonsense, so of course, they hold, Kraus has not answered it with physics. That just follows a fortiori.
Imagine someone claimed that new advances in physics have answered the question: "is the sentence 'this sentence is false' true or false?' The philosopher objects not because they think it is a good question which goes unanswered by physics (which somehow proves that god exists?), but precisely because it is a bad one which cannot be answered at all. 'This sentence is false' is not well-formed. There is no answer to what it's truth value is, because it doesn't have one. Hence, it is certainly not the case that new advances in physics can tell us what its truth value is.
I find that this unreflective anti-philosophical sentiment is a common strain in the new atheist community. They lash out at philosophers because they associate them with mysticism. They forget that philosophers were the pioneer atheists, ever since Hume killed God in 1776.
Third and finally, Tim Maudlin, a prominent philosopher of physics, has some interesting things to say about the relationship between physics--especially fundamental physics--and philosophy. The upshot is that many of the questions philosophers are interested in now are, in a straightforward way, just about understanding the physics. But these questions nonetheless get shunned in physics departments for reasons of institutional culture. He hopes for a blending in the addressing of foundational topics--that practitioners are able to apply both the impressive formal mathematical competence of the physicist and the neatness and conceptual clarity of the philosopher.
That is not true. There are a number of areas of science where experimentation is not possible. Now, scientists do attempt to use some facts that may have been proven by people who themselves used fact, so on and so forth back to some experiment. But it is not the case that the totality of all scientific endeavor relies entirely on experimental data. Simply because there are experiments that cannot be run.
"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
Kierkegaard didn't get the memo :O(
Like what?
Establishing the block universe. Multiple things in evolution and paleontology. Of course scientists try to make good explanations for these things. But as no one can actually experiment on dinosaurs, our resources are limited. Lots of geology is like this, such as certain things with respect to weather or plate tectonics. Lots of sociology can't be done with experiments, also anthropology. Also not a science where everything is subject to experimentation.
"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
The only K-gaard I'm up to speed on is Korsgaard, unfortunately.
Evolution, meteorology, geology and such are all done with experimental data. Paleontology is still done with data, although often more discovered data then data gleamed from experimentation.
The examples you used are really really very wrong.
the "no true scotch man" fallacy.
I do it all for the
For those whose interests are piqued by this particularly kerfuffle, here are some links to further reading:
Brian Leiter summarizes the affair (in a manner highly critical of Kraus--BL can be a bit nasty) while linking to a bunch of other stuff--like Kraus' interview in The Atlantic, Kraus' half-apology he later issued at behest of Daniel Dennett, and some relatively high-level discussion on a cosmology blog
Adam Frank argues that highly theoretical science is so untethered from direct experiment that it blends with philosophy
Again on the Leiter blog, a philosopher defends Kraus at some length; other philosophers comment in the comments.
I've long personally believed that the division between science and philosophy should be completely abolished, and I feel like this is an inevitable conclusion for a neuroscientist. The a priori/a posteriori dichotomy used to distinguish philosophy from science is complete and utter nonsense; there is no philosophy without empirical observations and there is no science without logical deduction. Every philosopher should be a scientist, and every scientist a philosopher.
Excuse me. "Discovered" data is not experimental in nature. You asked for things that aren't done in experimentation. Certainly some parts of evolution, meterology, and geology are all done in experiments. However, what experiment was run to establish the system of plate tectonics that we use today? Please, point me to the experiment that was run.
You can't. Many, if not all, of those things are based on empirical observation sure, but mere empirical observation and experimentation are two different things. I don't think that you want to equate those things. Maybe you do, but I don't. I think that there is a valuable difference between empirical observation and experimentation.
Also, I love how you overlooked sociology and anthropology. Other areas where observation is used, and experimentation is limited or non-existence.
"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
Someone who doesn't
"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
Observed data, but not experimental data.
Isn't the answer just "in the beginning there was nothing, but, because you can never be sure there actually is nothing, eventually that nothing happened to be something, and that something propagated?"
It's like Storrow Drive: it's two lanes, then three lanes, then two lanes. Can't explain that.
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.
I've never been told to "shut up and calculate", nor have I ever heard anyone else told to do so or heard from a peer that they were told to do it. Perhaps his experience comes from a prior generation of physicists? Or maybe the southeast is just a more progressive physics community than I'd expect?
In my experience with, admittedly only second and third year physics courses, "shut up and calculate" was always used in a jovial sense - kind of a handwave to the fact that, whatever you may think it means, the mathematics do appear to describe the physical systems under interrogation (i.e. the transition from the weird quantum to more "normal" realm is accurately described by the equations, even if the implications of that seem - to our normal experience of the world - absurd).
But yeah, I never encountered a physicist who didn't think this was an important distinction - nor one who wasn't interested in it. "Shut up and calculate", as I understand it, is more of a refrain you resort to for the one dickhead who only wants to prove he's smarter then the lecturer when discovering the subatomic universe acts completely counter-intuitively on the attoscopic level.
I'm so glad to have another in here who agrees with my understanding of the philosophical implications of Godel to science.
ELM, that is. J, you seem to have "disagreed" with him by acknowledging exactly what I think he was saying. In other words, if you aren't making certain assumptions about the universe and its knowability, well then you've perhaps correctly ascertained the significance of Godel to physics.
I'm very interested in your assertion that "the universe doesn't do that," though.
Mathematics: starting from initial axioms / postulates which are simply accepted as true, create theorems which are also true.
Science: starting with the scientific method, which is simply accepted as a procedural means to truth, create theorems which are thus accepted as truth.
In other words, they are both in the form of: starting with a philosophical basis that we accept as a useful means of describing and resolving truth, go formalize some truths.
Math and science are both off-shoots of philosophy. Referring back to the xkcd comic, math is only "pure" until you start looking at the philosophical basis of mathematics, and the various philosophical arguments for and against it. Suddenly we have a guy to the right of math, stoicly unconcerned with whether or not math realizes his true rank in relative purity.
The main difference between math and science are how much our observations of the physical world play any critical role in the philosophical basis for resolving truth. In science, our senses and observations are fairly important aspects to the truth process. In math, much less so (though still to some degree).
This is why modern science gets so tripped up on the effects of observation when bridging the gap between physics and math.
It's also why Green Dream and saggio aren't arriving at the same notion of "truth" due to a conflict over whether or not it requires some connection to our observations of the physical world.
But Goum is just wrong. Math is not science. I think what's he's getting at is that math is philosophy, as is science.
Lol oh noes. I'll leave off this for now.
Exactly. Krauss seems to think that the challenge is along the lines of, "ha, God wins, science is false!" When instead it is simply a philosophical debate that Krauss isn't capable of handling. This is a problem I totally believe exists among a lot of physicists. They aren't of a mindset to grasp the very significant philosophical failings of the scientific work they've done. Not in some spiritual "you know not what you do" manner, but in a very real, "you are logically incorrect and don't realize it" manner.
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.
This really bugs me. To my understanding, Godel merely proved that in classical arithmetic that one could generate a number (representing a theorem) that could neither be proven true or false in classical arithmetic (what I learned as Robinson's Arithmetic). I think that you make a lot more out of what Godel did than is warranted. He didn't show that incompleteness is just a part of any and all systems ever. Just one particular system, and even then completeness isn't really that big of a deal. It's still sound, so we can be accurate with the things that we can prove one way or another, but it's simply limited that it can't prove every theorem positively or negatively.
Now, I'm not an expert in either logic or mathematics, so I have a bit of trouble understanding everything that's going on there.
For reference, I've used the Stanford Encyclopedia entry in composing this. Godel
"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
His theorem was applied to more than one particular system, but it is limited to certain classes of systems. It definitely doesn't just apply to all logical systems ever, and, as you said, it doesn't actually say anything about the capabilities of a system to which it does apply as regards statements within the scope of provability.
The generalized philosophical implications are merely that a system which can be expressed therefore can't possibly generate an expression that explains the system itself. If you limit yourself to a single system of defining truth, all truths in that system will ultimately rely on some assumed axiom that cannot be proven within the system.
A lot of people try to take that in the wrong direction. I'm not saying, "haha, axioms can't be proven, therefore give into solipsism!!!" It's meant primarily as an answer to anyone who believes in a single system (be it scientific method or arithmetic or whatever) as capable of expressing "absolute" truths that do not rely on any assumptions or rely on verification from other independent systems of truth.
We verify our reasoning with our observations and our observations with reason. Neither one alone gives us meaningful defensible truth. We verify math with logic and logic with math. And so on. If you believe that there is some underlying single arbiter that can verify any of them as true or false, you're equivalently believing in God and you are denying what is at least strongly suggested by Godel, Tarski, Heisenberg, Hume, et. al.
It's not necessarily to say that an objective physical reality doesn't exist, but rather that a formal language to describe anything absolute about it can't possibly exist, because of the necessary nature of formal languages themselves. No matter what system we come up with for expressing truth, that system must necessarily always rely on some convenient assumptions that we can't know to be true or false. That doesn't mean there is no truth, it's just a facet of what truth is.
It may be the painkillers, but I think that made more sense to me than anything of yours I've read on this board, Yar.
I'm not sure why it's an important revelation, but I'll give you a high-five of agreement on this chunk at least.
This is flatly incorrect. The role of axioms in formal systems does not rely on the completeness of the system. A system is not incomplete because it cannot derive its axioms. Godel's result is that in a sufficiently recursive system there will be theorems that are true but non-derivable. But that formal systems rely on axioms that are not provable within the system was understood before Godel and is sort of a trivial observation anyway
I'm going to disagree with Shryke, here, lots of scientists don't do experiments. But as I stated above, experiments aren't the point of science, testable conclusions typically are.
Edit: In short, experiments are one way to test conclusions. They are by no means the only way.
It isn't just that axiomatic systems are axiomatic, but rather that such systems can't possibly prove their own axioms, without running into inconsistency.
To say that there will be statements that are true but not derivable is the flipside of the same coin. Because the truth of the axioms relies on something other than the system those axioms define, there will statements that can exploit this, which are expressed in the language of the system, but because of the nature of what is assumed in the axioms and how it is understood, cannot be resolved by the system.
The nature of the assumptions in ZFC, for example, such as the assumptions on infinite sets, or on the constructibility of sets from smaller subsets, are what eventually lead to certain impossibilities regarding infinite subsets of infinite sets. This is a logical cousin to the fact that the system cannot derive its own axioms.
The simpler example is in naive set theory and Russel's paradox. "The set of all sets not members of themselves." The philosophical problem is elegantly stated within. When you try to use the system to make an original statement about the system (i.e., sets of sets defined recursively by set membership) you can easily constuct nonsense. Even simpler: "this statment is false."
You do realize that he proved the completeness of logic right? All the stuff about the axioms of a system not being able to prove the system don't apply to logic.
How does Tarski fit into this? Everything that I can read on him (again SEP), suggests that he was also focused on mathematics, and didn't show a similar problem with logic. Again, he showed that mathematics has issues of completeness, but not logic. He also had some issues telling the difference between logic and math at some levels, but it seems like he largely cleared that up.
I don't know nearly enough about Heisenberg to comment on anything concerning him with this. I only know pop science stuff about uncertainty.
As for Hume, he believed that there were things that we could know for certain. So I have no idea what you're going on about with him. One of those things we can know for certain is mathematics. So how does Hume fit in with anything you've said?
"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
I don't think that axioms actually play directly into Godel. I mean the axioms of a system are inherently improvable using that system, but that's just the nature of axioms.
Godel's thing was that there are true but non-axiomatic statements in any consistent system which the system cannot prove.
Edit: the example from Wikipedia illustrates it pretty well.
"The truth value of this statement cannot be proven using the theory T" (paraphrased from wikipedia)
It's different from "This statement is false" in that the statement is true, whereas "this is false" has an undefined truth value.