Academics of all stripes enjoy conducting informal polls of their peers to gauge the popularity of different stances on controversial issues. But the philosophers — and in particular, David Bourget & David Chalmers — have decided to be more systematic about it. (Maybe they have more controversial issues to discuss?)
They targeted 1,972 philosophy faculty members at 99 different institutions, and received results from 931 of them. Most of the universities were in English-speaking countries, and the others were chosen for strength in analytic philosophy, so the survey has an acknowledged bias toward analytic/Anglocentric philosophy. They asked for simple forced-response answers (no essay questions!) concerning 30 different topics, from belief in God to normative ethics to the nature of time. The answers are pretty intriguing.
Results below the fold. Note that atheism easily trumps theism, and compatibilism is the leading approach to free will (although not by a huge amount). Only about half of the recipients identify as naturalists, which is smaller than I would have thought (and smaller than the percentage of “physicalists” when it comes to the mind, which is surprising to me). When they dig into details, there is a strong correlation between theism and whether a person specializes in philosophy of religion, predictably enough. Among philosophers who don’t specifically specialize in religion, the percentage of atheists is pretty overwhelming.
1. A priori knowledge: yes 71.1%; no 18.4%; other 10.5%.
2. Abstract objects: Platonism 39.3%; nominalism 37.7%; other 23.0%.
3. Aesthetic value: objective 41.0%; subjective 34.5%; other 24.5%.
4. Analytic-synthetic distinction: yes 64.9%; no 27.1%; other 8.1%.
5. Epistemic justification: externalism 42.7%; internalism 26.4%; other 30.8%.
6. External world: non-skeptical realism 81.6%; skepticism 4.8%; idealism 4.3%; other 9.2%.
7. Free will: compatibilism 59.1%; libertarianism 13.7%; no free will 12.2%; other 14.9%.
8. God: atheism 72.8%; theism 14.6%; other 12.6%.
9. Knowledge claims: contextualism 40.1%; invariantism 31.1%; relativism 2.9%; other 25.9%.
10. Knowledge: empiricism 35.0%; rationalism 27.8%; other 37.2%.
11. Laws of nature: non-Humean 57.1%; Humean 24.7%; other 18.2%.
12. Logic: classical 51.6%; non-classical 15.4%; other 33.1%.
13. Mental content: externalism 51.1%; internalism 20.0%; other 28.9%.
14. Meta-ethics: moral realism 56.4%; moral anti-realism 27.7%; other 15.9%.
15. Metaphilosophy: naturalism 49.8%; non-naturalism 25.9%; other 24.3%.
16. Mind: physicalism 56.5%; non-physicalism 27.1%; other 16.4%.
17. Moral judgment: cognitivism 65.7%; non-cognitivism 17.0%; other 17.3%.
18. Moral motivation: internalism 34.9%; externalism 29.8%; other 35.3%.
19. Newcomb’s problem: two boxes 31.4%; one box 21.3%; other 47.4%.
20. Normative ethics: deontology 25.9%; consequentialism 23.6%; virtue ethics 18.2%; other 32.3%.
21. Perceptual experience: representationalism 31.5%; qualia theory 12.2%; disjunctivism 11.0%; sense-datum theory 3.1%; other 42.2%.
22. Personal identity: psychological view 33.6%; biological view 16.9%; further-fact view 12.2%; other 37.3%.
23. Politics: egalitarianism 34.8%; communitarianism 14.3%; libertarianism 9.9%; other 41.0%.
24. Proper names: Millian 34.5%; Fregean 28.7%; other 36.8%.
25. Science: scientific realism 75.1%; scientific anti-realism 11.6%; other 13.3%.
26. Teletransporter: survival 36.2%; death 31.1%; other 32.7%.
27. Time: B-theory 26.3%; A-theory 15.5%; other 58.2%.
28. Trolley problem: switch 68.2%; don’t switch 7.6%; other 24.2%.
29. Truth: correspondence 50.8%; deflationary 24.8%; epistemic 6.9%; other 17.5%.
30. Zombies: conceivable but not metaphysically possible 35.6%; metaphysically possible 23.3%; inconceivable 16.0%; other 25.1%.
Yes, some of the descriptions might not mean that much at first glance. Google is your friend!
Tony Rz:
I want you to understand that I feel no need to convert you, and am fine with whatever choice you make (until it begins to harm others.) But just the fact that you’re posting here implies that you might have some questions about it yourself. On top of that, there are different perspectives that can apply, so the assertion aspect of your comments deserves a response.
No future, no hope, no joy? How do you arrive at that? My future may stop at death, unless I’ve made some kind of lasting impression – so that’s something to try and achieve. Hope and joy occur as long as anyone’s alive, regardless of their perspective on life.
“So whatever your knowledge of Physics or Philosophy, where is your meaning, for you are at the very most an asterisk in some book you will never know.”
Life goes on. Humans can learn, and change what they do based on it, so if I manage to produce some of that change, that’s meaning enough for me. That and positive interactions with others, as simple as those are. Most of our desires are pretty easy to meet when you think about it.
“Does the black void of nothingness care?”
Probably not – caring is a living trait. How much do the other people around you care? That hasn’t changed regardless of your perspective on metaphysics and creation. Is it important to make an impression on the entire universe, and isn’t that hubris/egotism on a stunning scale?
Here’s an interesting aspect of naturalism. We stop thinking of ourselves as transcendent, and start thinking of ourselves as one organism among millions, carving out a niche. We’re not expected to do anything, but have the ability to do a lot – this means everything we do is an achievement of one kind of another, especially in comparison to many other life forms. Our desires being shaped by evolution does not change our ability to meet them, and in fact it is easier than impressing the universe or whatever. And the limited time we have to do all this is the prime motivator – eternity means there’s always time to do it later, and would probably make accomplishments completely pointless.
To me, there’s nothing nihilistic, depressing, or meaningless about all this – it’s actually fascinating. Part of this is, I have a deep desire to make sense of things, and naturalism was the thing that accomplished it better than anything else. Your mileage may vary.
Cheers!
With God you’re more than one among a million, each person is a special creation known personally, each is His favorite, the trouble is that few know Him, little if at all.
@Al Denelsbeck
I apologize, but I am not going to reply to you: there are so many absurdities, silly prejudices, and instances of sheer ignorance in what you write, that it would take me a day to sort them out properly. I don’t have neither the time nor the will to do that, so I will follow vmarko’s example and let you simmer in your ignorance – which you have given ample demonstration of. Your remarks on modal logic and classical logic vs. probability theory are simply delirious. You don’t even know what “triviality of the logical system” means (“ex falso quodlibet”: google it), and yet think you can evaluate modal logic and give your opinion on its “intuitiveness””. You go on a super silly rant about probability theory vs. classical logic, and you don’t understand that the two are intimately connected, and that the former actually relies on the latter (see, e.g., here ). In short, I repeat, you don’t know what you are talking about, so I am not going to waste my time 🙂
Ah, I forgot: I should have also added that the idea that science does not use logic, but exclusively probability theory, also comes from ignorance: the theory of relativity is founded on classical logic (so much so that there are first-order formalizations of special relativity), while quantum mechanics is founded on von Neumann’s quantum logic. You are confusing two different things here; one thing is to say that scientific theories are “provisional”, which is of course true, and another thing to say that scientific theories themselves (i.e., the propositions and laws constituting the theory) must be probabilistic, which is false (classical mechanics being the plainest and most obvious example).
Ah, the bliss of ignorance 🙂
I’m amused to see that the rules for a discussion of free will on comment threads remain eternal:
(i) assert that free will either (a) obviously exists, so philosophers are wasting their time supposing otherwise; or (b) obviously does not exist given modern science, so that philosophers are just displaying a tired obeisance to outdated religion; or ( c), most commonly, both.
(ii) Have an incoherent philosophical discussion of free will which displays most of the mistakes that first year philosophy undergraduates learn about when they study free will, and which have been very well understood in the free will literature for decades if not centuries.
(iii) continue to maintain in the process that philosophy can’t contribute anything.
Riccardo said:
“Ah, I forgot: I should have also added that the idea that science does not use logic, but exclusively probability theory, also comes from ignorance: the theory of relativity is founded on classical logic (so much so that there are first-order formalizations of special relativity), while quantum mechanics is founded on von Neumann’s quantum logic.”
Never said science doesn’t use logic, nor did I say that about philosophy either. It simply doesn’t rely on either. From the logical conclusion comes the test, and when the test fails, the conclusion, however strong logically, gets thrown out. That’s why so many philosophers hate empiricism so much.
“I apologize, but I am not going to reply to you: there are so many absurdities, silly prejudices, and instances of sheer ignorance in what you write, that it would take me a day to sort them out properly.”
That’s quite all right. I actually waited to see if either you or vmarko could address the salient points, such as why so many of those basic philosophical concepts remained ambiguous and without agreement, even among philosophy faculty, and of course what they provided that was distinct from the empirical understandings. What I got instead was a lot of twaddle and assertions, which I’m used to seeing from theology and pseudoscience.
I can see three reasons why neither of you answered the important questions, even though I brought them up in each comment:
a) You actually never recognized them as salient;
b) You had no answer for them;
c) You had an answer that you didn’t want to give.
All of the three provide the same score anyway. I’ll let you guess what that is.
But since I’ve long held the opinion that people who think philosophy is hot shit are self-absorbed and impressed with their own brilliance, I thank you for not just reinforcing it, but displaying it prominently on yet another forum.
Enjoy contemplating the gestalt of ‘seven!’
@David Wallace
Have an incoherent philosophical discussion of free will which displays most of the mistakes that first year philosophy undergraduates learn about when they study free will, and which have been very well understood in the free will literature for decades if not centuries.
That’s exactly the point: one should understand that if you want to talk about x, then you need to know something about x. Otherwise you are only going to embarrass yourself, has we have seen prominently above, and as we see even more clearly by… :
@Al Denelsbeck
Never said science doesn’t use logic, nor did I say that about philosophy either. It simply doesn’t rely on either. From the logical conclusion comes the test, and when the test fails, the conclusion, however strong logically, gets thrown out. That’s why so many philosophers hate empiricism so much.
Many philosophers have been empiricist, only they developed versions of empiricism which are slightly more refined and convincing than your first-year-not-too-bright-undergraduate empiricism. It is of course true (albeit in a first approximation, Kuhn would have something to say about this) that if given data falsifies a theory T, formulated by means of a given mathematical framework relying on, e.g., classical logic, you must revise or abandon the theory. It is of course also true, however, that data themselves do not provide you with a logically consistent theory to explain those data in the first place. The process is much more complex than what you make it seem; it is not the case that one stares at the data and then comes up with the appropriate theory or conceptual framework to explain those data. Very often the contrary happens: one develops a theory or conceptual framework, from philosophical and mathematical arguments (involving the analysis of previous theories or conceptual frameworks for the phaenomenon at hand), and only then this theory is checked against the data. More: you can have two conceptual frameworks or theories which explain or predict the *same data*, but one is philosophically much better than the other (example: Minkowski’s space-time versus the Lorentzian formulation of special relativity theory). To make a long story short, logico-mathematical theories can exist without reference to data: that’s exactly why they can go wrong, or study wildly remote possibilities. But that is exactly why it is interesting to study them per se , since each wrong or unlikely theory is a description of a way the world is not like; and from wrong theories, or conceptual frameworks which are unlikely to be correct, one can learn a lot about how the right theory should look like. If you had bothered to study philosophy or the history of science seriously, you would have understood that science crucially relies on logic and mathematics as much as it relies on data, since with the latter alone you don’t go anywhere near real science, but you remain in that limbo represented by natural history in the past ages: just a collection of facts about the world, without understanding of what those facts mean, nor the capability of forming any prediction.
I can see three reasons why neither of you answered the important questions, even though I brought them up in each comment:
a) You actually never recognized them as salient;
b) You had no answer for them;
c) You had an answer that you didn’t want to give.
The correct answer is d): we gave you all the answers you need (see above), but you are too arrogant in your ignorance to admit that perhaps you should revise your position 🙂
@Al Deneslbeck
Enjoy contemplating the gestalt of ‘seven!’
Again, google is your friend : Peano arithmetic . Investigations into the “gestalt of seven” are the reason why you are enabled to write these moronic comments all over the place…
Cheers
Philosophy has been going on for over 2,500 years. The Philosophers of the Past were not stupid people, probably some of the brightest in the history of the species. But can we point to one “philosophical problem” philosophy has solved in its history? Doesn’t that tell us something “essential” about the nature of “philosophical problems” and their “philosophical answers”? E.g. philosophical problems are not “really hard problems” but that the methodological assumptions of philosophy are fundamentally suspect?
I am delighted to have discovered Professor Carroll’s blog via Slate.com, as I am now discussing these fundamental questions with my very bright and inquisitive teenage sons and we all have different views about them. But, professor, with all due respect, by what alchemy do you transform 931 “philosophy faculty members” into “scholars who are experts in the fundamental nature of reality” and take the fact that 72.8% of them don’t believe in God as conclusive proof that God doesn’t exist? What would Socrates have made of the notion that Truth could be determined by a popularity poll? The head spins.
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Riccardo said, even after vowing not to pursue this:
“Many philosophers have been empiricist,…”
Funny, this actually doesn’t contradict my statement in any way, even though you ostensibly said it in rebuttal. There yet remains a lot of people with degrees in philosophy that openly (as in, articles in major publications) denigrate empiricism.
Now, you would probably try to claim that my noticing this is evidence of the value of modal logic or whatever (which, you may note if you actually read close, I never dismissed – I gave you credit for that one,) but frankly, I never bothered with all the horseshit of trying to classify arguments in some diagrammatic fashion. Quite long ago, I just learned how to pay attention, and how to avoid assuming an argument was something else.
So, the philosophical question: Did you realize that you hadn’t actually contradicted me, and wanted to see if I’d catch it? Did you miss applying the logic entirely, showing you really haven’t learned from philosophy despite championing it? Is there some other motivation we can assign to this action?
The pragmatic, stop-contemplating-your-navel-and-aim-for-real-accomplishments answer: Who cares? The results remain the same.
“…only they developed versions of empiricism which are slightly more refined and convincing than your first-year-not-too-bright-undergraduate empiricism.”
Or, did you really just want to continue to sound like a self-important twit? It would appear to be the last one.
I’m really not concerned with what philosophers believe they have accomplished, especially after it’s been in use for centuries by other disciplines (way to lead the charge, guys.) Nor do I give the tiniest bit of excrement for their refinements, since they haven’t changed any of the uses it’s been put to. They can delve into auto mechanics and label the troubleshooting process with new words too, but this doesn’t mean they’ve added a damn thing.
But, you’re right. I didn’t give a complicated treatise on empiricism while commenting on a blog post, and that is indeed truly my failing. I simply spoke about the key point of failure that philosophy still cannot grasp. I kept my point simple and direct; woe!
“It is of course true (albeit in a first approximation, Kuhn would have something to say about this) that if given data falsifies a theory T, formulated by means of a given mathematical framework relying on, e.g., classical logic, you must revise or abandon the theory… [yadda yadda blather blather, look how much I can expound and never get the point.]”
Congratulations, you actually came in and explained exactly why philosophy fails so badly and tried to make it look like you were informing me about something.
I’m going to once again do my first-year inept childlike grasp thing and condense it down to the point of failure. The logic is only as good as the data. This is what you learn when you study the long history of science and philosophy and, really, our entire learning process. Everything from planetary orbits to the five fundamental geometric shapes to the four humours to ohmygod Freud demonstrates this repeatedly. Now, I will admit that this is noticed only by those who can look at all of the results objectively, and not just the ones that support their standpoint.
So (and I do beg your pardon for speaking so far below your exalted level,) when the results of logic have been so varied, what exactly is the value of logic? Does this possibly mean, and I’m going out on a limb here, that logic really isn’t very strong at all, or perhaps even that humankind really doesn’t know what the hell it is – maybe even that there really isn’t any such thing as logic in the first place, only pattern recognition and the reapplication of past experience?
I’ll let you ponder all that. The people responsible for actually getting results just discard the idea that logic is solid and rely on the tests instead. It’s the difference between creating working vaccines and sitting in a dark corner wondering if the concept of “vaccine” is nuanced enough.
I should also thank you once again for demonstrating that every last person who wants to glorify philosophy always falls back on claiming it means abstract thought, and thus that everyone who formulates any idea of cause-and-effect owes their very thinking processes to philosophers. Which is one hell of an accomplishment when you come to think about it, since capuchin monkeys have even grasped this concept! Must have gotten it through osmosis – no, that can’t be it, that’s a hard science. Let’s just call it one of those “other ways of knowing” and then philosophers can still take credit.
“The correct answer is d): we gave you all the answers you need (see above), but you are too arrogant in your ignorance to admit that perhaps you should revise your position”
Um, no, there’s actually not a damn thing to be found that addressed those points. Merely asserting it doesn’t work. But keep being condescending, because at least you’re providing some entertainment with your misdirection.
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vmarko:
“The interpretations are irrelevant. Heisenberg’s inequalities are a hard-proven theorem within quantum mechanics, which has to hold in all interpretations, including many-worlds and Bohm.”
Agreed, but what’s your point? “Heisenberg’s inequalities” have nothing to do with determinism vs. indeterminism, they are just predictions about the relations between measurements of non-commuting variables like position and momentum (or the relation between the spread of the wavefunction when projected onto a position basis vs. a momentum basis, if you prefer). Bohm and MWI don’t predict anything different about these relations.
“Ordinary nonrelativistic Schrodinger’s equation (for a free particle) is linear. The Standard Model is not. Care to guess which is an approximation of which?”
What aspect of the Standard Model are you saying is non-linear? I haven’t studied quantum field theory yet, but according to this paper, although equations of quantum field theory can be non-linear, “the field operators remain linear, as does the whole quantum mechanical setup for these quantum field theories.”
‘Sure, “just” specify initial conditions to infinite precision. The Heisenberg’s inequalities give you a theoretical boundary on the precision of initial conditions’
When I made the comment about infinite precision I was talking about classical physics, where it’s assumed that position and velocity do have precise values even if we don’t know them, and that the dynamics are determined by these precise values. In QM, it is a mistake to think of Heisenberg’s uncertainty principle in such terms–unless you believe in some form of hidden-variables theory, it’s not true that the particle has an exact position and momentum at all times but you just can’t know them, the quantum state vector is supposed to represent the full physical state of the system. Of course, you can choose to believe in a hidden-variables theory where the particle has extra well-defined properties beyond those in the quantum state, but note that in Bohmian mechanics the only hidden variable is position, Bohm does not assume that measurements of momentum are simply measuring a preexisting hidden “velocity” variable. I don’t think anyone has actually come up with a hidden-variables interpretation which assigns the particle both an exact position and an exact momentum, such that the exact values match what you get if you try to actually measure either property.
Torbjörn Larsson said
‘“qualia” is obviously a damned stupidity’
So if I shoot off your kneecap, it won’t actually hurt you?
@Al Denelsbeck
Funny, this actually doesn’t contradict my statement in any way[…]So, the philosophical question: Did you realize that you hadn’t actually contradicted me, and wanted to see if I’d catch it? Did you miss applying the logic entirely, showing you really haven’t learned from philosophy despite championing it? Is there some other motivation we can assign to this action?
1) You started by claiming that classical logic is worthless for science, and that probability theory is the real deal. Your claim went as follows: Classical logic actually has “true” as a value – fine for math, fine for statements, worthless for any hard science. Again, what we deal with routinely is probability – B has happened every time we’ve observed it, especially after we did A, so provisionally we’re going to go with A causing B”.
2) I made the point that (a) probability theory is essentially an extension of classical logic, (b) you are confusing uncertainty regarding the truth of scientific theories with uncertainty in the claims or laws of the scientific theories, and I pointed out examples of scientific theories which rely on classical logic (classical mechanics, relativity theory). Morevoer, I pointed at the fact that even quantum mechanics relies on a particular system of (non classical) logic.
3) You decided to revise your position, and said that: Never said science doesn’t use logic, nor did I say that about philosophy either. It simply doesn’t rely on either. From the logical conclusion comes the test, and when the test fails, the conclusion, however strong logically, gets thrown out. That’s why so many philosophers hate empiricism so much. . Notice that just a post above you made the claim that logic is “worthless” for science. I will let posterity to decide whether this is a contradiction… 😉
4) I then went on to consider this aforementioned revision of your claim, and pointed out that conceptual and mathematical frameworks are as important to scientific endeavour as data. We all agree that you don’t have science if you have a heap of data; you only have science if you have a theory explaining those data; and formulation of a theory does not simply arise from the data themselves by staring long enough at them. I substantiated these claims by pointing at various examples in the history of science. Let me line up some of them for you: a) the formulation of the Copernican heliocentric model of the solar system relied crucially on new philosophical considerations, which led to the rejection of the Tolemaic system, even though the latter was in terms of explanatory power even superior to the Copernican model; b) the development of classical mechanics relied crucially on the Leibnitzian-Cartesian meccanicist philosophy, of course on top of the tools of real analysis; c) the development of special relativity theory relied crucially on a philosophical operationalist analysis of the notion of simultaneity (one could even say phenomenological, as Gian-Carlo Rota correctly pointed out), as well as on a background deterministic philosophy.
d) The discovery of Higg’s boson relied crucially on the theoretical work done by Higgs 50 years before the boson was actually observed, theoretical work which of course drove the empirical investigations
e) Peano Arithmetic -> intuitionism -> intuitionistic logic -> Heyting arithmetic -> Shannon MSc thesis -> all sorts of cool computer sciency stuff that you use every day. Actually the birth of logical computing by means of calculators is another instance of the fact that often theories and ideas precede and are needed to understand and interpret data, but I won’t go into it now.
5) All of the above goes to support the conclusion that philosophical frameworks, often in the background, and mathematical tools are as important as the data for scientific investigation. Your response to the above was: [yadda yadda blather blather, look how much I can expound and never get the point.]
6) You then went on to ignore all my yadda yadda 🙂 and restated you point: The logic is only as good as the data. […] Now, I will admit that this is noticed only by those who can look at all of the results objectively, and not just the ones that support their standpoint. To which I say that you are again missing the point, namely, that theories which can explain and predict data do not arise simply by staring at the data themselves, but are a product of a much more complicated interaction between experimental and conceptual investigations, as the examples above show.
7) Then you went on to say that So […] when the results of logic have been so varied, what exactly is the value of logic? Does this possibly mean, and I’m going out on a limb here, that logic really isn’t very strong at all, or perhaps even that humankind really doesn’t know what the hell it is – maybe even that there really isn’t any such thing as logic in the first place, only pattern recognition and the reapplication of past experience? This would need a longer reply, but I am just going to point out that without abstract logic and mathematics science would not have arisen in the first place, since science, as I expounded above, requires not only data (which are certainly necessary) but also a language and fundamental concepts and philosophical commitments to work with to construct theories. Of course you could always try to do science without logic or mathematics, without abstract concepts nor philosophical frameworks, but only using pattern recognition. Let us know how that goes 🙂
8) It’s the difference between creating working vaccines and sitting in a dark corner wondering if the concept of “vaccine” is nuanced enough. That this is what you believe logic and philosophy are about explains what the problem is, i.e., that you don’t know much about logic, mathematics or philosophy.
9) [skipping some nonsense] everyone who formulates any idea of cause-and-effect owes their very thinking processes to philosophers. Which is one hell of an accomplishment when you come to think about it, since capuchin monkeys have even grasped this concept!
See, see is another instance in which you show that you are ignorant of what philosophy (and maths, and physics… how long is this list? 🙂 ) is about. Consider the problem of causality. The question is: when can it be considered true that event A causes event B ? Now you would probably say that this is a trivial question, since capuchin monkeys already “know” the answer: it is when P(B|A)>T where T is some kind of probability threshold (although I am not sure capuchin monkeys know the notion of conditional probability..). Now, let me notice that (i) this definition makes sense only if you have an appropriate definition of what P(B|A) means in the first place, i.e., what kind of conceptual framework for probability and randomness you consider, whether Kolmogorov’s axiomatization or something else (reference) (ii) that P(B|A) is high does not necessarily mean that A causes B: for instance P(“the stock market crashes”|”I blow my nose”) might be very high, but that does not mean that my blowing my nose causes the stock market to crash. (iii) how should we consider cases of preemption? (reference) (iv) would it not be better to define instead “A causes B” as P(B|A)>P(B)? But then how do we deal with spurious regularities? Take A=”drop in barometric pressure”, B=”drop in column of mercury”, C=”A strom happens”. Then certainly P(A|B)>P(A|not B), thus the drop in the column of mercury would be the cause of the storm, which is certainly not the case, as the cause of the storm is the drop in barometric pressure. So it seems that to find a good model for the concept of causality is not that straightforward after all, and that is something for which you need philosophy.
10) Um, no, there’s actually not a damn thing to be found that addressed those points. Merely asserting it doesn’t work. But keep being condescending, because at least you’re providing some entertainment with your misdirection. I think there is a rationality failure here. You have been asserting stuff without providing any argument worth noting, and dismissed entire fields which you are not familiar about, only because you have prejudices. That’s all it is: it is like the old lady who decided the world stands on a turtle, and would never hear anything to the contrary. I instead explained to you where I think you go wrong, I gave you numerous examples and references supporting what I say, I pointed you to various instances showing that you approach is naive and based on a superficial knowledge of the matter. Superficiality is a human trait: I myself have also often dismissed biology and life sciences as crap, on the basis of the superficial impression that even an half-wit can carry out research in biology. However, I have most certainly changed my opinion on the matter, because I am not like you 🙂
Cheers,
R.
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@ Jesse:
“Agreed, but what’s your point? “Heisenberg’s inequalities” have nothing to do with determinism vs. indeterminism, they are just predictions about the relations between measurements of non-commuting variables like position and momentum […]. Bohm and MWI don’t predict anything different about these relations.”
Ok, my point is that (a) Heisenberg’s inequalities hold in all QM interpretations (it seems you agree with this), and (b) Heisenberg’s inequalities actually *do* have something to do with the question of determinsm vs. indeterminism (it seems you do not agree with this). Therefore, if you want to discuss (b), it is not important to invoke any particularities of various interpretations of QM, since they all agree on the status of Heisenberg’s inequalities (statement (a)), and are thus not going to contribute anything useful to the discussion of (b). So let’s not complicate the discussion by getting into QM interpretations. 🙂
“What aspect of the Standard Model are you saying is non-linear? I haven’t studied quantum field theory yet, but according to this paper, although equations of quantum field theory can be non-linear, “the field operators remain linear, as does the whole quantum mechanical setup for these quantum field theories.”.”
The Lagrangian of the SM is nonlinear in field variables. If you haven’t studied QFT, it might appear a bit confusing — the “wavefunction” in QM represents the state of the system, while in QFT it represents a “field operator” acting on a state (which is a different object). This conceptual jump is necessary in order to deal with the nonconservation of the number of particles, and is usually dubbed “second quantization”, although the latter terminology is somewhat misleading.
The paper that you have quoted is correct, but you need to be aware (as was also emphasized in the introduction of the paper) that there are many types of nonlinearities. You need to be careful about saying with respect to “which object” are equations linear or not. Hence the confusion — in QFT, states are linear, but wavefunction-fields are not (for brevity I’m heavily oversimplifying the exact statement).
However, none of this actually impacts the (in)determinism argument, which is about the *classical* equations of motion, which are nonlinear in classical observables (like position and momentum). See below.
“When I made the comment about infinite precision I was talking about classical physics, where it’s assumed that position and velocity do have precise values even if we don’t know them, and that the dynamics are determined by these precise values. In QM, it is a mistake to think of Heisenberg’s uncertainty principle in such terms […].”
Ok, there are two ways one can think of Heisenberg’s inequalities. For example, if we discuss position and momentum of a single particle, one can say that (a) Heisenberg’s inequalities imply that the particle intrinsically *does not have* values of position and momentum beyond a certain precision, or (b) that the particle still *does* have a value of both position and momentum, but we just can’t measure them beyond the precision dictated by Heisenberg’s inequalities. The (a) route is the standard QM, while the (b) route is the hidden-variable scenario. I have never seen a convincing hidden-variable theory (and don’t believe any such exists), and until someone constructs such a model, I will go with the standard QM and assume (a) is valid.
Now, I’ll try to give you a sketch of a proof that Heisenberg’s inequalities destroy predictability in classical nonlinear deterministic systems. Let’s start by what we want to describe — whatever everyday-world classical physical system you wish (my pet-peeve is the double pendulum, but anything better than a free particle will do). Your system is macroscopic, with a lot of particles, etc. It is perfectly ok to start (in principle) from the Standard Model, and approximate it by (a) taking a classical limit (i.e. removing everything “quantum”) and (b) discard all unnecessary degrees of freedom, while keeping only the relevant part of the system in question. After doing this, one typically ends up with a set of partial (or ordinary) differential equations, which are nonlinear in positions, momenta, etc., and look like Netwon’s laws of motion (there are many examples of this). The classical limit is the “hbar-goes-to-zero” rule, which should be good enough for most macroscopic systems.
Now you say “those equations are deterministic” (due to a well-defined Cauchy problem, etc.). I respond “yes, but only if you know initial conditions with infinite precision, which you don’t, unfortunately”. Then you say “But regardless of me knowing them or not, they do exist with infinite precision”, to which I say “no, they do not, due to Heisenberg’s inequalities”. To see why, consider taking a slightly more precise approximation from the Standard Model down to our classical equations of motion — add a first-order quantum correction, i.e. re-derive the equations while keeping the terms linear in hbar. The equations will become more complicated (due to the presence of hbar terms), but they are in general still deterministic, still have a well-defined Cauchy problem (hopefully), and the hbar-corrections are too small do make any serious difference to the gross behaviour of the system (and we can safely ignore them).
But, lo and behold, what happened to initial conditions! Since we are not neglecting the hbar-linear terms, the Heisenberg’s inequalities appear, claiming that initial conditions must have finite certainty. According to QM, this is fundamental (as opposed to hidden-variable theories), and it renders the Cauchy problem for our approximate equations inapplicable, since the Cauchy problem assumes initial conditions with infinite precision. Furthermore, given that equations are nonlinear in positions and momenta (even the leading-order terms, not just the hbar-corrections), the small uncertainties of initial conditions eventually lead to bifurcations in the solutions, chaos theory kicks in and blows up the uncertainties to macroscopic levels — after a finite time. At this point, your simple-real-world-classical-mechanics system becomes completely unpredictable, and determinism dies a bitter death. 🙂
As a nail in the coffin, going beyond these approximations (i.e. including hbar^2 terms and higher) is certainly not going to restore determinism back, because Heisenberg’s inequalities do not have these additional terms, and will remain unchanged to arbitrary level of approximation.
I hope this clears things up. 🙂
HTH, 🙂
Marko
The paper that you have quoted is correct, but you need to be aware (as was also emphasized in the introduction of the paper) that there are many types of nonlinearities. You need to be careful about saying with respect to “which object” are equations linear or not. Hence the confusion — in QFT, states are linear, but wavefunction-fields are not (for brevity I’m heavily oversimplifying the exact statement).
Well, as I said I haven’t studied QFT, so I can’t comment directly on whether the nonlinearities in it are sufficient to allow the theory to be chaotic. Does QFT still involve something akin to the “quantum state” of a region of space and everything in it, as in non-relativistic QM? If so it should be possible to look at the dynamics of a single point or vector in Hilbert space or something like it, and say whether these dynamics exhibit sensitive dependence on initial conditions. But I vaguely remember reading that there are foundational questions about whether QFT even makes sense as anything more than an approximate perturbation-series treatment of some more fundamental theory, so I don’t know if this notion of precise “states” with well-defined dynamics even applies. Also, is it a mainstream view among physicists that QFT allows for true chaos in a way that non-relativistic QM does not, or is this your own original argument? If it’s a mainstream view, could you refer me to a link or book that says this?
Your system is macroscopic, with a lot of particles, etc. It is perfectly ok to start (in principle) from the Standard Model, and approximate it by (a) taking a classical limit (i.e. removing everything “quantum”) and (b) discard all unnecessary degrees of freedom, while keeping only the relevant part of the system in question. After doing this, one typically ends up with a set of partial (or ordinary) differential equations, which are nonlinear in positions, momenta, etc., and look like Netwon’s laws of motion (there are many examples of this). The classical limit is the “hbar-goes-to-zero” rule, which should be good enough for most macroscopic systems.
Now you say “those equations are deterministic” (due to a well-defined Cauchy problem, etc.). I respond “yes, but only if you know initial conditions with infinite precision, which you don’t, unfortunately”. Then you say “But regardless of me knowing them or not, they do exist with infinite precision”, to which I say “no, they do not, due to Heisenberg’s inequalities”.
I don’t think this argument can be sound, because it makes no special reference to the nonlinearity of quantum field theory. Suppose we lived in a universe where non-relativistic QM was exactly correct and the “Standard Model” referred to the fundamental dynamics of that universe, couldn’t the version of you in that universe make precisely the same argument as above, word-for-word? But in that universe it’s easy to see that the argument cannot be correct, because the underlying dynamics are totally linear and deterministic. It may be that one can approximate the dynamics with a classical theory, but the fact that the classical theory is non-linear must just be an area where the approximation is incorrect, not a demonstration that the HUP implies predictions are impossible. And if that would be a flaw in the argument in the non-relativistic QM universe, it could just as easily be a flaw in the same argument when it’s made in a QFT universe.
Dr. Carrol,
I am curious where you stand on the theories of time? I suspect that you are a “B-Theorist”. My own position is that past and present are real, but not future.
I enjoy your work very much.
TD
Tommy D, does that mean you reject the relativity of simultaneity? (I suppose an A-theorist could accept relativity of simultaneity in the physical sense that no physical experiment or observation can ever pick out a preferred definition of simultaneity, yet still believe that there is an undetectable “metaphysically preferred” definition of simultaneity…this seems inelegant to me though)
@ Jesse:
“Well, as I said I haven’t studied QFT, so I can’t comment directly on whether the nonlinearities in it are sufficient to allow the theory to be chaotic.”
Oh, now I think I finally understand what is confusing you. 🙂 I never said that QFT or QM should be chaotic themselves. There is an important detail to understand here about chaos theory.
Chaos may (and does) appear when the equations of motion that one uses are nonlinear in terms of variables which describe the state of the system. But note that you can also have *additional* variables in the equations, which *do not* describe the state of the system. Nonlinearity in terms of those variables does *not* produce chaos. This is the case in both QFT and QM, but not in classical theory.
In QFT, the state of the system is described by a vector from the so-called “Fock space”, which is a (big and complicated) vector space. The equations of QFT are *linear* in the state vectors, superposition principle holds, and consequently there is no chaos in QFT. However, the equations of QFT are very nonlinear in field variables and observables like positions and momenta — but these do not represent states of the system, so it doesn’t matter for linearity and chaos.
QM is an approximation of QFT where you linearize the QFT equations of motion in one field (of your choice), and make all other fields classical. Then you *redefine the state* of your system to be described by the (expectation-)value of that field, call the resulting space “the Hilbert space”, and call the value of the field “the wavefunction”. Note the change of the object used to describe the state of the system. Given that the equations of motion are now linearized in the wavefunction, the superposition principle again holds, and there is no chaos. Like in QFT, the QM equations of motion are still very nonlinear in terms of the other fields (which are now approximated as classical) and observables like position and momenta. But these are not used to describe the state of the system, so it still does not matter for linearity and chaos.
The classical theory is an approximation of QM (and therefore also of QFT), where you make all the fields classical, and you redefine (again) the state of the system to be described by the (expectation-)values of positions and momenta. Note another change of the object used to describe the state of the system. The space of states is now called “the phase space”. But the equations of motion are nonlinear in terms of these variables (as they have been from the very beginning back in QFT and QM), so the superposition principle does not hold for these states (the phase space is not a vector space!), and the theory becomes intrinsically nonlinear. At this point chaos appears. Note that we have avoided chaos in QM by linearizing the QFT equations in the wavefunction. If you try to do the same here — linearize classical equations in positions and momenta — you will get a trivial theory which can describe only free particles. This is an over-approximated theory, not very useful for anything. You need to keep interaction terms in equations in order to have a realistic theory, and these will induce chaos because the state of the system is being described by the same variables in which the theory is nonlinear. As explained above, this is not the case in QM and QFT, so here you have chaos, and there you don’t.
As a side remark, there are models (like in the paper you quoted) where people are studying nonlinear QM (for various reasons), where they give up the superposition principle for the states (wavefunctions), and consequently chaos can appear. This is called “quantum chaos”. But this is not the usual QM, and I am not sure if such a model can be obtained as an approximation of the Standard Model. I am also not sure about the usefulness of those models (I can only guess that people who study quantum chaos do have some motivation for doing it… 🙂 …).
“Also, is it a mainstream view among physicists that QFT allows for true chaos in a way that non-relativistic QM does not, or is this your own original argument?”
That is *not* the argument, as I explained above. As far as chaos is concerned, QFT and QM are both non-chaotic, and they can both be approximated down to a classical theory which *is* chaotic. That would be a correct statement, and it is of course the mainstream view, I didn’t make all this up! 🙂 That said, I would have a hard time finding a typical QFT textbook where the word “chaos” appears explicitly — it is usually enough to say that the Lagrangian is nonlinear in fields (every textbook says that), while the conclusions about chaos are understood to follow. Maybe better look at some textbook which deals with chaos as a subject.
“I don’t think this argument can be sound, because it makes no special reference to the nonlinearity of quantum field theory.”
Yes, I missed to spell out that part in the previous post, but have discussed it above. 🙂 The nonlinearity of QFT equations (in terms of fields) and the nonlinearity of QM equations (in terms of “approximated-to-classical” fields) will eventually turn into a nonlinearity of equations in the classical theory (in terms of positions and momenta). Note that in the QFT and QM those fields, positions and momenta are *not* used to describe the state of the system (hence no chaos!), while in the classical theory they *are* used to describe the state (hence chaos!).
“It may be that one can approximate the dynamics with a classical theory, but the fact that the classical theory is non-linear must just be an area where the approximation is incorrect, not a demonstration that the HUP implies predictions are impossible.”
As I mentioned above, you can approximate QFT and QM down to a classical theory, and you can either keep it nonlinear or linearize it. The linearized classical theory is a worse approximation, since it ignores interactions between particles. There is no chaos in linearized theory, but on the other hand it is completely trivial, and contradicts basically all experiments — there are interactions (forces) in nature that we see even at the most classical everyday level, which cannot be ignored. So the only classical approximation of QFT/QM that is useful (for making predictions) is the nonlinear one, which has chaos built-in.
HTH, 🙂
Marko
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Jesse.
Thanks for the question on simultineity and relativity. Very good point. I guess if I can accept superposition and “many worlds” at an instant in my vicinity, which I do accept, then “many histories” and “many futures” could be just as real.
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