Sharp Blue: Science and truth


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<< Previous in Series: “Maps of Physics”

This forms an extended aside.

A little while ago, Alan Forrester (who has clearly taken to heart David Deutsch’s The Fabric of Reality) posted a reply to my article “Maps of Physics” at Elegance Against Ignorance. I think that he’s misunderstood me on a few points, and I’d like to clarify my position. I’ll first outline my view of science and truth and then comment on his critiques.

Alan rightly thinks I’m an instrumentalist, by which he means that I think that scientific theories are “instruments” that are useful in modelling nature as opposed to embodiments of truth. However, I’m not an instrumentalist in the wider philosophical sense of thinking that ideas are only true if they’re useful (a position held, so far as I can discern, by my friend Cerstin Henning). I think that ideas are true if they’re true and false if they’re false, and that the axes of truth and utility are not coincident. There are plenty of things that are true but of very little use, and there are also plenty of things (such as Newtonian mechanics) that we know to be false and yet are extremely handy in practice. The great value of scientific theories is not their supposed truth, but rather their extreme usefulness. Indeed, scientific explanations of the world are among the most useful (and beautiful) structures ever devised by human intellect.

The idea that science is the search for truth is an old one, but it’s not true (at least in any useful way!). Instead of considering all of science, I’ll restrict my attention to physics, because that’s the field in which the ideas of “theory”, “truth” and so on are easiest to describe. Let’s consider what it would mean for a physical theory to be true. A theory in physics is a mathematical structure of some kind together with a mapping from that structure (or perhaps some subset thereof) to entities that are postulated to exist in reality and their behaviours. The mapping is often called an “interpretation” of the theory. A theory might then be considered to be true if those postulated entities are things that really exist and the behaviours inherent in the theory are the ways those entities really behave. In other words, a true theory is an exact representation of some aspect of reality. If science were a search for truth, then the structures and relationships in successive scientific theories in a given field would presumably have to be successively more like the structures and relationships that exist out there in the world. But this isn’t the case!

The problem with the idea of science as the search for truth is that successive theories often contain structures that are utterly unlike each other. Even if we are destined to finally arrive at a theory of everything, we must surely doubt that the entities in our current theories bear even the slightest resemblance to the deep structures of the world. For example, the central mathematical structures in classical mechanics are the tangent or cotangent bundles over the configuration manifold, neither of which is in anything other than the vaguest sense like the Hilbert spaces of quantum mechanics. In classical mechanics, observables are functions on the aforementioned bundles, whereas in quantum mechanics they’re Hermitian operators. In whatever finally replaces quantum mechanics, they’ll most likely be something just as different. In our theories of spacetime, the changes between successive theories have not yet been so great, but if a theory of spin foams becomes our best theory of gravity, we’d face an even more extremely change than that seen in the transition to quantum mechanics: from a picture of space as a continuous manifold to a picture of space as a graph of spins. Even if we limit ourselves to a single theory, the idea that its structures map onto structures in the world is problematic, because the same theory can be formulated in lots of different ways. Are the things really out in the world the matrices of Heisenberg’s mechanics or the wave-functions of Schrödinger’s wave mechanics? There’s also the problem that even if we restrict our attention to just one formulation of one theory, there are multiple possible interpretations (only one of which, presumably, even has a chance of being true). The obvious example here is once again quantum mechanics, which is surrounded by a cloud of interpretations of varying levels of acceptability.

If physics isn’t a search for truth, then what is it? That’s simple: as I’ve said before, it’s the search for useful theories! In other words, physics is the search for theories about the universe that are ever more comprehensive and which ever more closely match experimental data. It is not cumulative: we don’t learn one “law of nature” and then another. Nor is is always gradual: later theories are often radically unlike earlier ones. It is not the bolting on of ever more elaborate epicycles. So why do people persist in seeing physics (and the rest of science) as the search for truth? Partly, I think, as an attempt to draw a line in the sand in the the argument against the social constructionists and cultural relativists. Some people seem to worry that if science is anything less than the search for Truth then the whole edifice will be swept away by the deluge of postmodernist philosophy that claims that no way of viewing the world is better than any other. But the whole world is so full of evidence for the efficacy of science and the pathetic inadequacy of supposed “alternative ways of knowing” that this seems unlikely, at least outside the involuted world of “critical theory”. A second source of confusion is the lingering presence of the discredited idea of inductionism.

Inductionism is the idea that science works by performing lots of experimental measurements and then “inducing” laws of nature from them. For example, we might measure the strength of electrical forces at difference distances from charges and induce the inverse square law of electrostatics. From this vantage point, science might indeed look like a search for truth, because at any stage we could increase the accuracy of our experiments and hence the fit of our induced law with reality: we might go from an inverse 2±0.2 power law to an inverse 2±0.1 power law to an inverse 2±0.01 power law… And, because induction would work “backwards” from the data to theory, whatever theory is induced must be “true”. Surpisingly many people think science works like this, but it doesn’t. There are many problems with inductionism that has caused it to be generally discarded, most of which I’ll not discuss here. One of them is that given a certain quantity of experimental data there are an infinity of theories that “pass through” the data points, and nothing to choose between them. Naive inductionists don’t realise this, and think that a given heap of experimental results allows the induction of a unique theory. Instead, scientists propose new theories that solve problems with existing theories (where a “problem” might be a misfit between two or more theories, a lack of elegance or computational power in a single theory, or a misfit between predictions and data), and then discard the ones that are disproven by experimental tests (in particular, by carefully selecting experimental tests that rule out all but one of the “in play” theories).

I think that Alan considers me not just an instrumentalist but a logical positivist (someone who thinks that theories must contain nothing that cannot in principal be measured). He implies this when he says of my view that physics is not true but rather useful:

The problem with this is that physical theories always refer to things beyond what we measure.

Of course, on the view that I’ve expounded here (and, for that matter, in “Maps of Physics” itself), I have no difficulty with this idea! Indeed, the presence of things beyond what we measure is the very basis of my assertion that physics is not primarily about truth, for there are an infinity of possible structures in our theories that go beyond what we measure, there’s no way to reduce this infinity to just one, and only one could be true. Equally, though, when he goes on to say

Physicists look at problems with current physical theories, the clash between quantum theory and relativity, or the problem of how to actually build a quantum computer or whatever and they try to solve these problems. They propose solutions to these problems and then criticise them according to whether or not they provide good explanations.

he’s not supporting his own position that “physics is the search for truth” so much as my position that the useful theories survive.

Alan also says some interesting things about the links between phenomena, but I’ll have to criticise those ideas some other day.

Update (30/4): Hunt Stilwell has posted a response to this: “Science as Story-Telling

Next in Series: “Spacetime and Coordinates” >>

In what sense is Newtonian mechanics false?

Newtonian mechanics would incorrectly predict electron movements and interactions, for example. In that sense it is "false". It is a great approximation for large, slow-moving objects, though.

In the sense that it makes predictions that prove to be wildly incorrect. Here are some examples:

  • The combination of Newtonian mechanics and electromagnetism predicts that electrons in atoms will radiate away all their kinetic energy and fall into the nucleus in about 0.01ns. Quantum mechanics predicts that electrons will never fall into the nucleus. I don't know the observation lower bound on the lifetime of hydrogen atoms against collapse, but it must be at least trillions of years. Thus classical mechanics makes a prediction that is incorrect by a factor of at least 10^30! In other words, post-classical mechanics isn't even a small correction.
  • The theory of Newtonian gravitation incorrectly predicts the rate of precession of the perihelion of Mercury as 5557 seconds of arc per century. The observed value is 5600 arcseconds per century. This value is predicted correctly by general relativity.
  • Newtonian dynamics predicts that the relationship between kinetic energy and momentum will be E = p^2 / 2m. Special relativity predicts E = [ p^2 + (mc)^2 ]^(1/2). Experiments with particle accelerators strongly support the prediction of relativistic dynamics.

There are lots of other examples too!

Personally, I'd be more inclined to say that Newtonian mechanics is "limited" than false. Within its proper boundaries, the difference between Newton & relativity has no functional consequence.

I am inclined to agree with Harvey. It seems to do perfectly fine under certain conditions. It looks like a special case of General Relativity, rather than a false (or falsified) physical theory. I was under the impression that this was the way physicists themselves viewed it.

I'm not sure why you can't just say that scientific theorizing is about getting closer approximations to the truth. If so, then it is about truth after all but doesn't undermine any of your main points.

This discussion is in want of a definition of truth. It seems like the burden for truth being used would require omniscience.

If truth is corespondence to reality, then newtonian mechanics can be regarded as mostly true. Not perfectly, it has well known limitations, but it does have broad areas of corespondence. Indeed it is only useful because of this corespondence.

If science is not engaged in the pursuit of that which it true, what is its point? For that matter, what is the point of our own existence? Indeed, as a scientist, I believe my goal to be the pursuit of the understanding of those fundamental truths (absolutes) that govern the physical world around us. In short, anything less than an honest desire to understand the true nature of the universe is falsehood itself. Science should never be content to settle simply for "utility."

Then what is your criterion for the truth of a statement about the world? It's one thing to believe that you're searching for fundamental truths or to desire to do so, but what does this actually mean? These are not rhetorical questions: I would honestly like to know how a physical theory can be "true" rather than merely "useful", and nobody has yet given me a reasonable answer.

this is all bullshit...

There can logically be no absolutes (such absolutes would constitute the seldom-defined "Truth"). Therefore, Truth is essentially invalid. An ontology, of any type, is an absurdity. Therfore, science is movement towards validity, not Truth.

Truth could be defined as absolute accuracy. For example, 1+2=3 is true (I hope!). Yet as long as there are 'unknowns' no scientific theory or law can lay claim to being the truth. To reiterate an earlier comment, science is the movement towards validity (or accuracy). To attain truth in all fields of study would in essence mean the end of science. I'm relatively certain the end of science will not come about in our lifetimes. On a more personal note, I don't believe 'understanding' is all it is cracked up to be. Appreciation seems much more important. If you are blessed with a mind that can appreciate the subtlety and absoluteness of mathematics, then more power to you! But for the rest of us mere mortals, reductio ad absurdum doesn't hold much meaning or appeal. Guess I'm just pragmatic, empirically challenged, and simple-minded!

I am really kind of new to this stuff although I have been studying electronics for the last 6 years. I have to say that science seems to be letting me down a little with the electron theory. I stumbled across this article while trying to find a hole in the electron theory and it interested me to see that I am not the only one that just can't settle for the status quo about how things work. If anyone has more information for me or would like to e-mail me if they are bored and have nothing to do, I would like to explain my point a little better. I just want to know how a theory of moving holes, and extra electrons floating around silicon a boron doped wafers explain in the slightest way how electricy flows? through a transistor. My e-mail is if anyone is interested to talk about it.

I can't be bothered with anything these days, but shrug. I just don't have anything to say recently. I haven't gotten much done recently. Nothing seems worth thinking about.

To me this article suggests that we as a race try to stay away from the truth because it seems that if something is true then it is undiniable and there wouldn't be any, for lack of a better term, wiggle room. We search for something that works for us wether it is true or not. If something works for even one subject no matter how insugnificent then we will use it until something better shows up.

All this Aristotle's-categories centric tripe isn't philosophy. It's only an apologia for the overwhelming insufficiencies of science.

First of all, what the author is talking about is empiricism, trial and error, and postulates made of inference called syllogisms. Philosophers, not academics forced to study logic like the atomitons they've been trained to be, know there are no universal forms that fit into neat little categories for the use of science. Science is but a sophisticated witchcraft that yields only slightly more spectacular results.

It's been known for a very long time, 1+1 does not equal 2, except in the abstract reasoning that goes on in our minds. In the real world, the thing in itself, there are no two things that are alike enough that we can add them, 1+1, and describe what we then have as 2, and have it mean anything more than what our minds perceive and wrongly accept as sameness BEFORE we inspected these two distinct things we added to come up with the abstract sum of 2.

Furthermore, even when we accept that these empirical ideas are useful, we must also recognize the real world, the thing in itself, is so utterly complex that our grasp of these experimental hints (as is science) is so insignificant, as to be utterly and completely overwhelmed by a reality we cannot grasp.

We are not blind me touching an elephant. We are amoebas floating in an ocean trying to ponder a whale.

Universals do not exist except by the affinity of our minds to create them. They DO NOT EXIST, none of them!

Now, science, that which has created so many shiny objects, these objects of human fascination and a wonderlust of admiration; science bases its truth claim upon this admiration humans have for the results possible by applying the rules of empirical reason to our environment. This admiration is the sole support for any argument that science provides truth.

Science is very dangerous, VERY DANGEROUS. It is dangerous because humans do not understand what truth is.

Truth is not ephemeral, transitory or approximate. Truth is static. Truth is either true ALL THE TIME - EVERY TIME, or it is not truth.

Empirical truths are all ephemeral, transitory and approximate. Empirical truths are also only true some of the time, and turn out to be wholly false at other times. Any scientist will tell you that if you press them hard enough about their scientific postulates.

When real philosophers, again, not academic dunderheads, speak of truth, they speak of categorical truth, true every time in every instance.

So, if you want to write and apologia for science, say so... But don't call it philosophy. You'd do as well or better to call it, religion.

Categorical truths, the goal of philosophy, are very difficult to discern. And plying Aristotle's categories is an immediate surrender to never gaining any ground.

I am a real philosopher. Perhaps the first since Descartes, and certainly the most important philosopher ever.

In 2006 I filled in Kant's conjectured categorical (moral) imperative he left blank and a conjecture as well as a query when he died in 1804.

The moral imperative of life is to live a life that detracts not at all from the lives available to those who will follow us into this world.

That is categorical knowledge. You can bank on it being true in every instance.

The moral imperative of life is no mere 1+1=2 statement.

And, philosophy is no mere science, hackneyed as here, or otherwise.

So, go fuk yourself.

Don Robertson, The American Philosopher

Um, wow...

I wonder if Descartes would be posting to Sharp Blue if he were still alive.

You, Don, are deceived. The moral imperative of life is not a negative. And by choosing to violate it by insulting as many as you can, you mark yourself as an amoral, or worse immoral deceiver. The moral imperative of life, by the way, is to improve yourself to the best of your ability, and to nurture others to do the same for themselves.

Your hubris in making such remarks is reminiscent of a squalling infant who objects to the disinterested glance of strangers.

Grow up, and learn manners.

Every functional person relies on truth in the sense that "truth" means a correspondence of a represenation to something in the real world, not just in our heads. If I say "hand me that glass of water," I'm assuming there is a glass of water. If you hand it to me and I drink it, I believe I have pretty good evidence that I made a valid ("true") assumption, as long as we agree we are not considering how my glass or the water are explainable at the subatomic level, how it would look in a black hole, or or how far after the big bang I drank the water. From a Newtonian physics of "middle-sized" things, it seems to me we can make perfectly sound true claims.

I think the kind of truth that many scientists strive for, has become ambiguous due to the complexity of instruments and calculations. It's hard to tell sometimes whether or not a theory is "just" functional or if it is saying something about the real world. But I agree with the opinion that science should strive for truth and not just functional statements. I don't agree that if we don't have all of it, we don't have any of it. I believe that "My cup is cracked" and "My door is open" are valid claims, as long as you interpret the terms in the usual way. Do the qualifiers mean I really don't have truth? I'd suggest it simply means I don't have all knowledge of this situation, just knowledge of certain features in a certain context. But it's still knowledge, not opinion or just funcational claims. I'm comfortable calling them true.

I am student of class XII, I could not understnd 'Eindtein Theory of relativity'. Any body can explain me clearly. Merchant

that's weird about the theory of truth. my whole life thinking things were true come to find out that much of it are just theory of another pesrson opinions and we dont know wat the truth is.

Isn't it possible that both theories are true but third variables, "not yet known to exist" are at play in the small and large scales, that are not at play in the medium scales?

To the point that 1+1 does or doesn't equal 2 or the question of absolute or relative; isn't it more a matter of imperfect definition? That the two theories are contradictory but are both correct does not, for me, prove the relativity of truth or that one is wrong but rather the limitations of our current knowledge. That our immediate assumption is that one must be right and one must be wrong or that truth is absolute or truth is relative seems a bit to hasty.

I have a theory of my own: That truth can be both absolute and relative simultaneously. It is simply a matter of variables, definitions and perspectives. That is my truth.

Don Robertson, The American Philosopher... what a powerful title. It is unfortunate it reflects poorly on Americans as well as philosophers. You seem to have overlooked, and I am sure you have for quite some time, the "truth" that philosophy all by itself will get you nowhere. You need certain tangible items regardless of their "categorical" value arbitrarily declared by you. You personally could spend all the time you want in your head discovering moral imperatives yet you wouldn't be able to convey this philosophical BS you've been spewing for who knows how many years without applying tools such as 1 + 1 = 2. We are tiny, our knowledge is tinier still. We are, however, learning as a civilization. We are learning even more so as we find what we don't know. But however the truth is defined, it must include the observable world as well as our thoughts. For if it is only in our minds with no footing in the world as it presents itself to us, real or not, there is no differentiation between a madman raving about any idea and the world's greatest philosopher raving about categorical imperatives. Which brings me to the following painfully obvious yet unavoidable questions:

1) Why is the moral imperative merely not to detract from the lives of those that will follow, instead of to improve them? 2) Is your closing statement not a blatant example of hypocrisy?

Just a thought reading through all this (though perhaps years late):

Can something be true and simply inaccurate? Newtonian physics (along with 1+1=2) was true, and accurate, enough to get us to the moon.

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