Stephen Hawking’s Defense of Positivism

By: Bruce
March 3, 2011

In my last post I finished comparing Popper and Kuhn and again concluded that there really isn’t much difference between the two other than on the issue of Scientific Realism vs. Positivism. That is to say, Popper believes that science actually discovers theories close and closer to the truth whereas Kuhn believes it becomes more useful over time in ways that we humans wish it to be and that there is not necessarily some underlying truth to be discovered.

In a previous post I previously considered the advantages of Scientific Realism vs. Positivism. (See also here) Both have pros and cons, but Scientific Realism is the clear winner when it comes to generating new conjectures and theories. If one were to solely believe in Positivism one would never actually believe in their own theories enough to think up new questions/problems to solve and test. The end result would be the stagnation of science.

However, this fact aside, does this mean Scientific Realism is actually true and Positivism false?

Hawking’s Defense of a Positivist View of Reality

Recently Hawking wrote a book called The Grand Design. In that book, Hawking makes a number of controversial assertions. The one that got the most press time – don’t you just love the media? – was the claim that the laws of physics are sufficient to create the universe and that God has no role to play. This is, actually, a very interesting point and one that deserves rigorous criticism – which I’ll gladly give it in the future.

But in reality, this wasn’t the most important challenge that Hawking makes. The really big challenge Hawking makes in his book is that Positivism is actually the nature of reality, not Scientific Realism. We saw in this past post that Hawking is a Positivist.

I perceive much in common between Hawking’s and Kuhn’s views. But whereas Kuhn’s concern was from the point of view of a historian – he merely wanted to know how we progress in science – Hawking is an eminent scientist and actually argues that there is no underlying reality for science to find.

In a recent article in Scientific American (October 2010) he summarizes the arguments he makes in his book. If Hawking is correct, it will have serious consequences for Scientific Realism and for our desires to find a “Theory of Everything.”

Most people believe that there is an objective reality out there and that our senses and our science directly convey information about the material world. Classical science is based on the belief that an external world exists whose properties are definitive and independent of the observer who perceives them. In philosophy, that belief is called realism.

Those who remember Timothy Leary and the 1960s, however, know of another possibility: one’s concept of reality can depend on the mind of the perceiver. That viewpoint, with various subtle differences, goes by names such as antirealism, instrumentalism or idealism. According to those doctrines, the world we know is constructed by the human mind employing sensory data as its raw material and is shaped by the interpretive structure of our brains. …

The way physics has been going, realism is becoming difficult to defend. (p. 70)

And what does Hawking suggest instead?

Instead we adopt a view that we call model-dependent realism: the idea that a physical theory or world picture is a model (generally of a mathematical nature) and a set of rules that connect the elements of the model to observations. According to model-dependent realism, it is pointless to ask whether a model is real, only where it agrees with observation. (p. 70)

Possible Ramifications To Positivist Universe

If there is only a model-dependent realism to be found, what does that mean for science? For one thing, Hawking argues, we should not expect to find a single “theory of everything.” “It now appears that this quest may yield [in string theory] not a single theory but a family of interconnected theories, each describing its own version of reality…” (p. 70)

Would this really be so bad to find that Kuhn was right after all and that scientific progress does not grow closer to some all encompassing view of reality? [1]

Notes

[1] I confess, I don’t even come close to understanding string theory and it’s ‘family of theories’ well enough to comment on this much. From what I understand, this is a matter of ‘string math’. There were five different mathematical ways to express strings that each turned out to be equivalent to each other. However, each way had certain advantages and disadvantages. The best part about this is that one can flip to the version that is easiest at the moment. Plus, each one eliminates certain kinds of error factors. I can see why this would appeal to a positivist like Hawking. But I’m not sure this really undermines the scientific realist world view either, again showing that both view can be useful, but not necessarily at the same time.

For example, a more recent proposal is that quantum field theory and string theory are one and the same, except that string theory is the 11 dimensional holographic projection of 4 dimensional quantum field theory. (See Brian Greene’s The Hidden Reality). In this view, there is still an underlying reality, it’s just that it can be mathematically viewed from more than one point of view.

To a lesser degree, I’ve noticed this in many aspects of life. We often express the same thing in different ways, often in seemingly opposite ways. For example, I’m convinced that the ‘orthodox’ Christian concept of creation ex nihilo and the Mormon concept of creation from ‘pre-existing matter’ will eventually be forced by the laws of physics into being one and the same concept with each being merely different ways of wording the same thing. But this only turns out to be true if we accept the lawful nature of reality. In other words, both points of view can only both turn out to be true if both accept that they were only approximate concepts of a very more specific set of laws and therefore they weren’t actually mutually exclusive to begin with.

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18 Responses to Stephen Hawking’s Defense of Positivism

  1. Stan on March 3, 2011 at 5:46 PM

    I love these posts! Philosophy is so tantalizing and frustrating in that after a great deal of work and study we find we can’t really know anything anyway. Very humbling. I think all of philosophy is summed up nicely in the “I can clearly not choose the wine in front of me…” scene in the princess bride.

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  2. FireTag on March 3, 2011 at 7:25 PM

    What seems to be “model dependent reality” seems to be simple duality: one reality can be described in multiple, mathematically equivalent ways.

    The 60′s Leary was more the idea that the brain is capable of perceiving differently the same reality. Now it would have been interesting if the brain itself hadn’t been anchored in one reality.

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  3. Andrew S on March 3, 2011 at 11:19 PM

    I haven’t been completely on-the-ball with this series, but there is something that is bothering me.

    How can we not have scientific realism???

    Like, how can there *not* be an explanation with algorithms (to use the terms from previous articles)? Even if we don’t currently understand those algorithms, how can they just…not exist?

    Even if we have model-dependent realism, I don’t see why it would be the case that we can’t reconcile multiple models. As you say for both the religious models or for the string theory/quantum theory, reconciliation points to an underlying reality…

    So, with model-dependent realism, we should still be able to ask the questions, “Where doesn’t this model agree with observation?” The answer to this question will tell us where our model only *approximates* more specific sets of laws, and where it is, therefore, incomplete or “wrong.”

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  4. Thomas Parkin on March 4, 2011 at 2:53 AM

    Hawking’s pissed because God squoze him down into that little chair. I’d be pissed, too, probably.

    Bruce, ever read _Wittgenstein’s Poker_? Kind of a little biography of Wittgenstein, Popper and a nearly violent encounter they had at Cambridge. Fun read.

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  5. Clark on March 4, 2011 at 12:19 PM

    I’ve not read much of Hawking as such. But is he pushing positivism proper or merely a deflationary account of truth? From what little of Hawking’s more philosophical writings I’ve read he tends to be pretty philosophically naive. It might be he is adopting instrumentalism proper (in which case he’s neither a positivist nor a deflationist) But he sure sounds like a deflationist, perhaps under the influence of Fine’s NOA.

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  6. Clark on March 4, 2011 at 12:22 PM

    Andrew, one can be a realist without being a scientific realist. There are many problems with scientific realism but the most obvious one of traditional scientific realism is the convergence problem. That is a scientific realist tends to think our descriptions are getting more accurate with time in a triangle like convergence. One thing Kuhn got right was that big upheavals in “paradigms” make this convergence model problematic. While one needn’t adopt Kuhn’s own problematic notion of the incommensurate nature of theories I think the scientific realist really is in a problematic position.

    Of course I’m a Peircean and think there are ways to maintain realism without adopting some of the problematic claims of scientific realism.

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  7. Bruce on March 4, 2011 at 4:05 PM

    Andrew S,

    Actually, I’m curious what a non-algorithmic but also non-random phenomenon looks like too.

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  8. Blake on March 5, 2011 at 11:46 AM

    “For example, I’m convinced that the ‘orthodox’ Christian concept of creation ex nihilo and the Mormon concept of creation from ‘pre-existing matter’ will eventually be forced by the laws of physics into being one and the same concept with each being merely different ways of wording the same thing. But this only turns out to be true if we accept the lawful nature of reality. In other words, both points of view can only both turn out to be true if both accept that they were only approximate concepts of a very more specific set of laws and therefore they weren’t actually mutually exclusive to begin with.”

    I don’t believe that you understand the point of the tradition’s commitment to creatio ex ninilo — or what it claims regarding the relation between God and the rest of created reality that derives its being and existence in its totality from God — including laws of nature.

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  9. Bruce on March 5, 2011 at 1:26 PM

    “I don’t believe that you understand the point of the tradition’s commitment to creatio ex ninilo — or what it claims regarding the relation between God and the rest of created reality that derives its being and existence in its totality from God — including laws of nature”

    I don’t believe you understood what I said. :P

    Each time the Catholic Church or Protestant Churches tries to fit creatio ex nihilo into existing physics (which they often do), they step further away from their original commitment to the original doctrine.

    They just don’t realize that is what they are doing. (They think they are defending ex nihilo through science of course.) Just one little step at a time, of course, so they don’t realize it’s happening.

    Of course the reverse also seems true to me. The Mormon concept of creation from pre-existin matter has eroded in the same way. We no longer think of it the way our 19th century brother and sisters did.

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  10. FireTag on March 5, 2011 at 2:00 PM

    Blake:

    I think the POINT to note about the tradition’s commitment to creatio ex ninilo is that it was a doctrine created to justify a pre-existing authoritative position for a clerical and theological order as gatekeepers between Christ and humanity.

    The Mormon and Western Christian traditions agree that Christ is at the center of everything, but may not be able to overcome the authority issues ABOUT THEIR OWN ROLES well enough to develop a mutually acceptable description of HOW Christ is at the center of everything.

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  11. Badger on March 6, 2011 at 3:13 PM

    I don’t have much to say about the physics, but for a fairly accessible mathematical example of a non-random, non-algorithmic phenomenon, we can look at Conway’s game of Life (http://www.math.com/students/wonders/life/life.html; also on Wikipedia). Briefly, this is a kind of solitaire played on a checkerboard. You start by putting down a pattern of checkers (British: draughts), representing something like trees. At each turn, trees with too few neighboring trees die of “isolation”, and their checkers are removed. The same happens to trees with too many neighbors (“overcrowding”). On the other hand, new trees can appear in currently empty locations that have the right number of neighboring trees (“reproduction”). Check the web sites for specifics.

    There are no decisions to make. The point of the game (as a game) is just to see what happens, and to try to come up with initial patterns that produce interesting results. If you want to try it, there are free computer programs to make the moves for you, so you don’t have to perform tedious and error-prone manipulations of real checkers.

    On a more theoretical level, some questions about what can or cannot happen in the game are mathematically interesting. Here’s one example. You play on an unlimited board, (and with an unlimited supply of checkers). This avoids special cases arising when the checkers reaching the edge of the board. However, your initial pattern can only use a finite number of checkers. Question: from a given initial position, will all the trees eventually die out? (disclaimer: I’m pretty sure this works, but it might be necessary to use a slightly more complicated question of this type. I’m not a “Life” expert.) Let’s call an initial position “mortal” if the answer is yes, and immortal otherwise. Rephrasing, which initial positions are immortal?

    Life is completely deterministic, so there is no sense in which the answer to “mortal or immortal?” can be said to be random. Often the question is very easy to answer; for example, a single checker dies on the first move, so is mortal. Three checkers in an “L” configuration is obviously immortal if you play a couple moves. However, in general if someone gives you a complicated pattern with many checkers, it may not be at all obvious. You can play for a while and see what happens. If it dies out, you know it was mortal, but if not, you don’t know anything–it may be immortal, or maybe you just didn’t play long enough.

    Is there a more clever approach that can answer the mortality question in all cases? Perhaps surprisingly, the answer is no (subject to my disclaimer above). This is not a statement about the present state of human knowledge. Rather, it can be proved mathematically that no algorithm exists that is capable of answering the question correctly, in all cases.

    Taking a second look at “play until it dies out”, there are two variations: (a) play until mortality, up to some time limit; or (b) play until mortality, with no time limit. Algorithm (a) gives incorrect answers for mortal patterns that are sufficiently long-lived. Algorithm (b) never answers incorrectly, but it also never answers at all for immortal patterns! So (a) fails on “correctly” and (b) on “in all cases”.

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  12. Bruce on March 7, 2011 at 8:18 PM

    Badger,

    Do I understand you correctly that you are not claiming the game of life is non-algorithmic (obviously it is) but determining immortal vs. moral is non-algorithmic, right?

    Yes, there are whole classes of problems that can’t be solved by general algorithms. This would seem to be one of them. It sounds a lot like the halting problem, actually.

    However, I would point out that this problem isn’t so much “non-algorithmic” as literally unsolvable by any current understanding we have. If we are going to count ‘unsolvable’ as non-algorithmic then there are a whole lot of them.

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  13. Bruce on March 7, 2011 at 10:45 PM

    Oh, a couple of other things.

    The game of life scenerio was probably proven to not be solvable via a general algorithm via reduction to the halting problem. That means we can translate one problem to be the other problem.

    If that is true (and I’m pretty sure it is) then the following would be true:
    1. We can often prove cases are immortal, but not every case.
    2. We can always do so if the board is finite
    3. The only case we know for sure we can’t prove to be immortal is the set of rules that map directly to the game of life itself. (That would take a bit more explanation, but it’s central to the halting problem — i.e. it’s built on self reference.)

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  14. Badger on March 9, 2011 at 1:16 AM

    Bruce, thanks for the continuation of the discussion.

    …you are not claiming the game of life is non-algorithmic (obviously it is) but determining immortal vs. mor[t]al is non-algorithmic, right?

    Yes, exactly.

    It sounds a lot like the halting problem, actually.

    Yes, and as you suspected, there is a reduction of Life to the halting problem. I thought Life might be more accessible to a wider audience, but it’s just a variation on the theme.

    …this problem isn’t so much “non-algorithmic” as literally unsolvable by any current understanding we have.

    I don’t understand the distinction you are making between non-algorithmic and unsolvable. In this case the mortal configurations are recursively enumerable, so in terms of the arithmetical hierarchy there is nothing intermediate in difficulty between Life/Halting and decidable problems. So that can’t be what you have in mind, but I’m drawing a blank thinking of an alternative.

    You’re certainly right in saying there are many examples of equivalent difficulty.

    For your numbered questions,

    1. Yes
    2. True, for the same reason that the halting problem is solvable for a computer with bounded memory.
    3. I think I know what you’re thinking of here: the standard proof of the undecidability of Halting produces a single example of this nature via a diagonal argument. However, that’s not the end of the story, and many–infinitely many, in fact–other specific instances are known to be undecidable.

    Rice’s theorem comes to mind as a relatively accessible example. It states, very imprecisely, that any nontrivial question about the “meaning” of a computer program is undecidable. A couple examples, both undecidable by Rice’s theorem: (1) given a program, does it compute a constant, i.e, does it produce the same output for every input? (2) given two programs, are they equivalent, i.e., do they always produce the same output when given the same input?

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  15. Bruce on March 9, 2011 at 8:43 PM

    Badger,

    Interesting about Rice’s theorem. I’ll have to add to my reading list.

    What I actually had in mind was the fact that just because you can’t come up with a general algorithm for the halting problem doesn’t mean you can’t decide if a program does or doesn’t halt in a lot of specific cases.

    I’m reading Penrose right now, so (without getting into it in a comment) Penrose would agree with you that Godel’s theorem (another reduction of the halting problem, or rather the halting problem is a reduction of it) is ‘non-algorithmic’. But I think he’s got this one wrong for many reasons I can’t explain in a simple comment. I guess the main thing I disagree with Penrose on is that he seems to be trying to compare mathematicians to a general algorithm. I actually have no reason at all to believe mathematicians can generally solve any of the problems you list either. So it seem like an unfair comparison to me. My guess is that the right algorithm could solve all sorts of halting problems, just like a mathematician can. It just can’t solve all of them, just like I believe mathematicians can’t.

    As for ‘unsolvable’ vs. ‘non-algorithmic’ I suppose the way you are talking they are one and the same.

    But you have to understand the original context of my statements. I was looking at it from the thread of the conversation only. Andrew S asked what a non-scientific realism would look like. I then extended that to say that I wanted to know what a non-algorithmic phenomenon would look like.

    I had in mind the realm of the physical world when I said that. AndrewS and I have already batted back and forth all the unsolvable problems within mathematics.

    But if you came across a non-algorithmic piece of the physical world, what would it look like? I can’t wrap my mind around the concept as of yet. So far, all of the physical world has been algorithmic (if perhaps intractable.)

    I guess it might look a lot like how the ancients saw the world where anything that moved on it’s own was believed to have mind of it’s own and be alive. Thus the wind, the tides, and even the quaking earth are all mischievous gods.

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  16. Why Scientific Realism Wins | Wheat and Tares on March 10, 2011 at 3:31 PM

    [...] In my last post I quoted Stephen Hawking’s defense of Positivism. He even goes so far as to suggest that there is no all encompassing view of reality but instead only “a family of interconnected theories, each describing its own version of reality…” (p. 70) [...]

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  17. Badger on March 14, 2011 at 10:41 PM

    Bruce, apologies for disappearing in the midst of the conversation. I’m with you on Penrose, although I admit it’s based on just one book that I read some time ago. However, his grasp of mathematical logic was clearly imperfect on a few points. Like you, I never could go along with the argument you mentioned. In the book I read seemed to be that quantum indeterminacy could (must?) somehow filter up through layers of macromolecules, subcellular structures, neurons, vaguely specified internal brain structures, and finally the brain and human mind, with the end result of giving human intellect access to, apparently, something like an oracle for membership in the set of true (provable? it’s been a while) mathematical statements.

    I’m not convinced that his argument is even meaningful, let alone correct, but I’d still recommend the book (Emperor’s New Mind?) if anyone asked me about it. He’s a good writer, and the occasional frustration I felt with him is part of the reason I remember the book as well as I do.

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  18. Steve Johnston on February 3, 2012 at 6:10 AM

    For a discussion of the historical clash between positivism and realism in physics, please take a look at:

    Model-Dependent Realism – A Positivistic Approach to Realism
    http://softwarephysics.blogspot.com/2011/01/new-introduction-to-softwarephysics.html

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