Wednesday, November 18, 2020

The incompleteness of current physics

  1. There is causation in the physical world.

  2. Causation is irreducible.

  3. Our fundamental physics does not use the concept of causation.

  4. So, our fundamental physics is incomplete as a description of the physical world.


Blair said...

Cartwright has argued for this. :)

But I think 2 doesn't hold. There are many concepts which we have not yet analyzed sufficiently. But that a good analysis is difficult business is not surprising. So a lacking analytical definition is not good evidence for irreducibility. That would only be the case if we hadn't made any progress at all in beginning to define causation. But there are several such imperfect approaches. Counterfactual and probabilistic ones for example.

In contrast to this, we haven't made any progress at all in defining qualia concepts such as colors or emotions. This is much better evidence for them being not analyzable.

Alexander R Pruss said...

Counterfactual and probabilistic approaches, I think, make use of things that themselves depend on causal concepts. The right kind of probability for this is objective propensity, and that's a causal concept. And the main counterfactual account of causation depends on alethic modality, and the best accounts of alethic modality involve causal powers. :-)

Blair said...

Oh, that's of course a large topic... Popper's theory of propensities was (not an analysis of the concept of probability but) a specific hypothesis about objective chance under the assumption of an indeterministic interpretation of quantum mechanics. It concerned with things like the probability of the decay of a radium atom. It, in an indeterministic setting, cannot simply be an expression of our ignorance of the exact physical parameters. Even Laplace's Demon couldn't predict the time of the decay better than us. I think Popper didn't discuss dependency explicitly, but a case where two radium atoms are in superposition seems to be a perfect example of probabilistic dependence under his propensity theory. But it is also a case where there is, according to physics consensus, absolutely no causal dependence (otherwise superposition could be exploited to transmit information faster than light).

Now there are also completely different propensity theories according to which propensity has nothing to do with indeterministic interpretations of quantum mechanics but rather with causation. When A has causal influence on B then, allegedly, P(B|A)>P(B) but not P(A|B)>P(A). But this would not be consistent with probability theory. Such a propensity theory seems to confuse causation with correlation. To say that P(B|A)>P(B) is to say that A and B are correlated ("positively probabilistically dependent"), and because our concept of correlation is symmetric, it implies P(A|B)>P(A). Probability theory confirms this intuition; the causal interpretation of P(B|A) does not. We may be inclined to say: too bad for such a causally loaded propensity theory.

But I wouldn't use Popper's propensity theory either for a probabilistic theory of causation, because causation isn't plausibly dependent on the existence of quantum indeterminism. The probability interpretation for a probabilistic analysis of causation just has to be objective, since causation is objective. (Something like "objective Bayesian" or "logical" probability perhaps.)

The reason I'm so optimistic about probabilistic theories is that relatively new approaches in causal modelling (using Bayesian networks) have identified certain relations of probabilistic dependency which are characteristic for causal networks. The idea isn't so new, it goes back to Reichenbach's theories on the common cause principle. People like Wolfgang Spohn and Hartry Field have suggested defining causation with statistical properties of such causal nets.

Admittedly, there is an open problem: Causal modelling requires picking so called exogenous and endogenous variables for causal arrows to be defined. I think Spohn mandates simply picking those variables as exogenous which are earlier in time. This stipulates that causes come before their effects, which might be problematic. I guess we want to explain why causes come before their effects, and we don't want to a priori exclude causation from future to past. But I'm optimistic a better criterion for distinguishing exogenous from endogenous variables can be found: The most popular approach to explain the direction of time is to argue that the entropy gradient of the universe somehow accounts for it. I think to explain the time-directednes of causation with statistical features of entropy is similarly promising.

That's of course all not a rigorous argument, just some reasons for optimism, in my view at least. Perhaps I'm totally wrong. :)

But regarding your remark on counterfactuals and alethic modality: Could you say more about that? How would counterfactuals depend on alethic modality? Both could (if one likes) be analyzed with the help of possible world semantics. But then counterfactuals depend on some notion of closeness between possible worlds, while alethic modality (possibility, necessity, contingency etc) does arguably neither depend on nor provide such a notion. So how could counterfactuals depend on alethic modality?

Alexander R Pruss said...

I certainly think quantum indeterminism is a causal dependence: the superposed state has a causal power to collapse into a pure state. Adding that statement by itself to the physics cannot allow for faster than light information transfer, since it doesn't change any of the empirical consequences of the physics.

It is pretty clear to me that one can have instances of causation without much of a causal network: a one-time choice by an immaterial and atemporal agent, say.

I agree that one shouldn't say that a value for P(A|B) in general implies a propensity for B to produce A. That would be silly for the reason you mention. Rather, I would have assumed that the right propensity theory says something like this: fundamental conditional objective probabilities are the transition chances--i.e., propensities--of the causal stochastic processes that underlie reality, and non-fundamental objective probabilities are derived from these via the axioms of probability. More precisely: for a fixed field (or maybe sigma-field, if we want countable additivity) of events, we objectively have P(A|B)=q iff every function Q on the space of events such that
(i) Q satisfies the axioms of probability, and
(ii) for all C, D and r, if D has propensity of degree r of producing event C, then we have Q(C|D)=r
also satisfies Q(A|B)=q. On this interpretation, the values are grounded in the propensities, but only some of them are equal to propensities.

I've just made that up, but I would assume it's somewhere in the literature. :-)

The use of the increase of entropy to fix the direction of time and causation is really dubious. For instance, it seems clear that one can have unidirectional causation and time in systems that satisfy the assumptions of the Poincare recurrence theorem, even though one does not have constant increase of entropy.

The distinction between possible and impossible worlds depends on alethic modality, unless one has something like Lewis's theory. And Lewis's theory is false for a multiplicity of reasons (e.g., the ones here: :-) )

Of course, all this is highly controversial. And in particular those with Humean intuitions, of which I have only a few, will find it deeply implausible.

Blair said...

Interesting. Maybe a different argument against fundamental causation: Assume causation was indeed irreducibly fundamental. Then how would a world look like were this fundamental causation didn't exist while everything else was the same? Would we notice any difference? If not, that missing irreducible thing plausibly wasn't what we meant with the term "causation".

Another point is that causation seems to be a redundant concept. If English had no term for causation (or indeed if no language had it) would we miss it? It doesn't seem so. Every statement "a causes b" (where a and b are noun phrases) can apparently be converted into an equivalent statement of the form "B because A" (where A and B are clauses). "The heavy rain on Monday caused the collapse of the dam" becomes "The dam collapsed because it rained heavily on Monday". Alternatively one could use the schema "b occurred because a occurred". Or simply "a explains b". It seems plausible that nobody would miss the concept of causation because it can be fully replaced by explanation. The reverse of course doesn't hold since there are explanations which are non-causal. To assign causation any special role apart from explanation seems to depend on the historical accident that English contained a word for causation... Indeed, the main difference between statements of the form "a causes b" and "B because A" (or "a explains b") seems to be merely that the first implies that a and b are distinctly located in space-time while the latter doesn't require that.

But apart from that, you wrote "the best accounts of alethic modality involve causal powers". What are those accounts? I never heard of that. Sorry, I didn't check your book. :)

Alexander R Pruss said...

If you took causation out, you'd have a world where it looks like you have plenty of explanations of events but they're mere coincidences and not real explanations. The oomph would have gone out of the explanations. In other words, you'd have one of those massive sceptical hypotheses.

I am open to the idea that explanation and not causation is fundamental. But fundamental physics doesn't talk about explanation either.

That said, it's false that causation is just explanation between distinct events in spacetime, since it's possible to have a nonspatial atemporal being causing something.

Casual power accounts of modality are put forth by Jon Jacobs and me (in different ways), and perhaps earlier by Aquinas. :-)

Michael Gonzalez said...

Blair: I highly recommend Pruss' book, not just to better understand why a causal account of alethic modality is best; but also to get a very good overview of other accounts, and their strengths and weaknesses. I found it extremely instructive.

Pruss: I find myself very skeptical of your third premise here.

For one thing, there is no single account of fundamental physics; merely a mathematical formalism. There are many different accounts that make use of that formalism, and many of them do indeed rely on the concept of causation (some are even fully deterministic).

Moreover, as soon as one transitions from the uncertainties of subatomic physics to the level of chemistry and so on, we use the concept of causation all the time. Given that there needs to eventually be a clear bridge from the one level to the other, it could be that clearer and more explicit mention of causation will be recognized at that point.

And thirdly, could it be that Physicists don't explicitly talk about causation because they have been brought up and educated in the shadow of Hume? This could lead them to talk about laws of nature and regularities without realizing that these are not explanatory at all without a deeper, causation-based analysis (as Swinburne has been at pains to point out for the past half-century). Physicists often run into this problem, and engage in a bit of double-talk by both acknowledging that laws of nature are mere generalized statements but also speaking of how they "forbid" and "prevent" things and would be "violated" by certain events.

So, it could just be that they are not philosophically/conceptually aware enough to realize the role causation must play in any real explanations of physical phenomena.

Blair said...

The problem with taking out fundamental causation and then this making no empirical difference whatsoever is that it would cast serious doubt on the assumption that this is what we mean with causation. Imagine going to some scientists and saying: "You claim smoking causes cancer? How could you have evidence for this claim? Causation is some fundamental undefinable unobservable relation, we couldn't distinguish a world without it from a world with it, and hence there can be no evidence for or against smoking causing cancer. The later Hume was right after all, if there is causation we couldn't know anything about it!" I think the scientists would reply: "When you talk about 'causation' you seem to talk about something else than we do. Causation is all but unobservable, indeed we have quite a lot of evidence that smoking causes cancer. A world where smoking didn't cause cancer would look very different from ours."

Fundamental causation without an observable difference would also seem like an ad-hoc hypothesis, like assuming for no reason at all the existence of certain ghosts which are unobservable in principle.

Regarding fundamental physics -- explanation is no part of fundamental physics, but fundamental physics employs explanation, like all sciences: They try to explain their evidence. And what is it that they do when they explain? In fundamental physics the case seems quite clear: They unify. They compress. They try to reduce the greatest amount of phenomena to the smallest amount of hypotheses. They try to minimize the ratio between the complexity of their hypothesis and the complexity of the empirical facts it entails. This ratio is minimal when the hypothesis is maximally simple and the entailed phenomena are maximally complex.

One could perhaps equate simplicity with low information content and complexity with high information content. The best compression, the ultimate explanation, would be a maximally simple Theory of Everything which entails every observable fact. It would mean our universe has low information content. Now the information content I in bits is related to probability by P(x) = 2^I(x), i.e. each bit, each atomic fact, is statistically independent from the others and equiprobable for being 0 or 1, false or true. This would mean a theory which compresses the phenomena better is literally more likely.

It is not yet quite clear how this picture of explanation as compression would relate to causation. But there is at least some analogy in terms of entropy. It seems rather uncontroversial to say the state of the universe at its beginning caused the state of the universe today, but awkward to say the the state of the universe today caused the state of the universe at the beginning. Where does this asymmetry come from when the physical laws are plausibly time symmetric?

One intuitive difference between the early state and the current state seems obvious: The early state of the universe was, in some unspecified sense, much simpler than the current state. This would fit the compression picture of explanation.

And a quite objective difference between the early state and the current state is that the early state has low entropy and the current state has high entropy.

There thus seems to be some connection between low entropy and simplicity, and between high entropy and complexity. Between information content and physical entropy. If causation is related to entropy, and entropy is related to complexity, and complexity to information content, and information content to compression, and compression to explanation -- then we have uncovered the link between causation and explanation. And we already know that some such link must exist, since causation implies explanation. Additionally we'd have a link between fundamental physics and explanation. I'd be very surprised if this sketch of a theory turned out to be completely false, the details fit each other too well.

Blair said...

I wouldn't share the intuition that an "nonspatial atemporal" thing can be a cause of something. Do you perhaps mean with "nonspatial atemporal" it exists like a physical law? We would say that a law explains its instances but hardly that it causes them. They are not both spatio-temporal and distinct. If the law exists everywhere and always, it overlaps its instances. If laws don't exist in space-time at all, they aren't spatio-temporally located. It is appropriate to say that Newton's theory explains Kepler's laws, but it is awkward to say it causes them. Similarly, it sounds strange to say that the expansion of the universe "causes" red shift, since redshift and expansion seem to overlap. Or that the metallicity of some rod "causes" its conductivity, or that the speed of the particles of a gas "causes" its temperature. The case is even clearer for things like "The irrationality of pi 'causes' the impossibility of squaring the circle." The failures of people (if not the impossibility of what they attempted) who tried to square the circle could perhaps be located in space-time, albeit in a gerrymandered fashion. But the irrationality of pi hardly can.

Mathematical objects could be perhaps least controversially be said to be nonspatial and atemporal, or "outside" space-time. But something static like a number could hardly count as an agent, a "being".

"Casual power accounts of modality are put forth by Jon Jacobs and me (in different ways), and perhaps earlier by Aquinas. :-)"

I may look at it -- it sounds unusual enough to be interesting. My own view is that the analycity/syntheticity explanation was right all along, but that's a wide field.

Michael Gonzalez said...


1) I don't believe Pruss meant that abstract objects (like laws or properties or mathematical objects) have causal power. He meant a non-abstract yet non-spatiotemporal being like God.

2) I think you're transgressing the bounds of sense to even ask about why the earlier states of the Universe cause the later ones but not the other way around. And everything extrapolated or built onto that is just farther into the territory of nonsense (I don't mean that as an insult, like saying "rubbish" or "silliness"; I mean "non-sense", as in failing to make sense).

If entropy on the whole had a tendency to decrease, rather than increase, that wouldn't say anything about causation, and it certainly wouldn't justify asking why later states don't cause previous ones. The only appropriate answer to that question is "huh??". Prior states existed and the relevant entities exercised their causal capacities, leading to the production of the present state. Future states haven't done anything yet, so how could they be causes of anything?

You talk about the time reversibility of physical laws, but I don't see how this relates to the direction of causation or of time. Imagine a machine which, when I put X's into this side, it goes through some process and spits out Y's at the other end. If it turned out that you can also put Y's in at the other end and it will do the exact reverse of those processes and spit out X's at this end, would that say anything about future, past, causation, or time?? Of course not. Indeed, the cases are different precisely because in one case we started with (earlier) some X's and (later) got Y's, and in the other case we started with (earlier) some Y's and (later) got X's. It is a simple mistake to think that time or causation have been reversed, when what's been reversed is what the machine did. Likewise, if you reverse a physical law you are just describing a different state of affairs which started with Y's and eventually yielded X's.

You pointed out a string of relations, but the link between causation and explanation has nothing to do with those relations. It would hold even if those relations did not. Perhaps the biggest confusion is when you talk about "information content". Information is only such to informable creatures. I mean, we can talk about the information content of a system in a sort of potential or counter-factual sense (how much could be extracted or processed by informable beings). But the state of the world doesn't count as information unless someone is informed.

Finally, the desire to "compress" things in our theorizing is because simplicity is considered an explanatory virtue. That the world has gone from being "simpler" to more "complex" in a physical, entropy-related sense is an entirely different matter from out desire to give the simplest explanation that will account for the most complex data set. If the world were going from complex to simple, we would still have the exact same desire because it is an explanatory and epistemological virtue. These concepts are unrelated.

Explanation in terms of causation makes sense because we know causation to be real from our direct experience of being causes ourselves. It forms some of the most fundamental aspects of our cognitive and conceptual apparatus for skillfully coping in the world. We have certain powers and can exercise them at will. There are other things which have powers to effect each other, but only do so when acted upon (they have no will). With these two categories in place, we proceed to study the world and discover the general natures of things (specifying them to the greatest precision we can, so that we can predict and account for them) which presupposes the idea of causal powers.

Michael Gonzalez said...

Anyway, as you say, these are all "wide fields", and a justification of each point would be far beyond what I'm willing to type (and probably beyond the character limit of this blog). I recommend a healthy dose of Wittgenstein and Merleau-Ponty (the latter even more so than Heidegger, though Heidegger is quite useful too). A distillation that is very clear would be Peter Hacker; but his writing can be quite dense... and perhaps some Hubert Dreyfus. For the arrow of time, Tim Maudlin is helpful but William Lane Craig is better.

Best wishes. Sorry for the long post.

Alexander R Pruss said...


God is the main example of an atemporal nonspatial being.

Compression is not itself explanatory, as it doesn't distinguish coincidental compression from the true reasons for something. If I drop a big bag of coins, they might all land heads. In that case, I can compress the data about how they land, but the compressed data does not express their arrangement. Now, if a supernatural agent exists and intentionally arranges the world in such a way that its data can be compressed, then the compression is explanatory. Similarly, if there is a "pushy law". But the mere fact of compression, without anything further behind it, is a mere coincidence.

Note that in a Poincare recurrent universe, the future low entropy state is just as simple as the past low entropy state. But presumably only the past one explains.

We directly observe our causing things. When I feel myself pushing a button, "pushing" is essentially causal.

Blair said...

I don't think an atemporal nonspatial agent makes sense, godly or not. For an agent to be an agent it arguably needs, among other things, the ability to be in different states, but that's not possible without time. That's why mathematical objects can't be in different states. Also the idea would have the same problem as non-abstract (platonic) numbers: It's completely unclear how they could be in any causal/explanatory relationship with the spatio-temporal world.

Coincidences: A supposed explanation gets less explanatory the weaker it (probabilistically) entails the explananda. It has higher information content because it compresses the facts less efficiently. A Theory of Everything would have to logically entail all the facts. But if it e.g. was an indeterministic theory and didn't entail quantum mechanical collapses then it would compress the universe not very strongly compared to a deterministic theory. It wouldn't explain why a particle p collapses at time t rather than at another time.

For given I(H) and I(E), I(H & E) is lower when I(E|H) is lower. (For given P(H) and P(E), P(H & E) is higher when P(E|H) is higher.) Imagine the universe as a block universe. We want to compress it. The more compressible it is, the lower its information content. The less atomic facts are there about it.

Possible future low entropy: Arguably people living in that "future" would say they are earlier and we are later. We would say we are earlier and they are later. From our perspective they would move backwards in time, and from their perspective we would move backwards in time. They would explain their circumstances with events which lay, from their perspective, in their past, and from our perspective in their future. And the other way round. I think the directions of the time dimension in that universe is best described as two inwards pointing arrows like this: --><--

Pushing: We explain our pushing with our intention to push, just like we explain our perception of a chair with the existence of a chair. But those explanations may be wrong. We may be dreaming. Then there was no chair and we didn't push anything. We just believed so. We don't directly experience these explanatory ("causal") relations. If we did, we couldn't be mistaken about them. We just perform inference to the best explanation, and the best explanation could be wrong.

Michael Gonzalez said...

My earlier tome notwithstanding, if nothing else, it should be clear that "moving backward in time" makes no sense (especially in a block Universe in which nothing moves at all, but is just extended). We can play the game of talking as though entropy increase and decrease just is what is meant by temporal order, but the statements "entropy stayed the same for five months" or "we were surprised to discover that entropy decreased for about a million years before beginning to increase again" are clearly meaningful (which they would not be if temporal order and entropy were identical).

Captain Hindsight said...

Where is causation supposed to be in the physical world?

Besides that, of course our discription of the physical world will be incomplete as long as we are discribing it with a consitent formal language such as mathematics given Gödel's incompleteness theorems for any consitent formal languages.
Really any rational person has an incomplete discription as long as that person relies so heavily on logic, which is another part of that incomplete consistent formal language of mathematics.

So yeah "causal finitims" will never preveal in this regard. How about "Causal Infinitism" then?
That might solve this issue quite easily here.

Alexander R Pruss said...

I don't know that the Goedel theorems necessarily limit the completeness of physics. The first-order theory of real numbers (unlike that of the integers) is decidable, and while *current* physics uses calculus, which goes beyond the first-order theory of real numbers, it's not completely obvious that a future physics could not be embedded in a decidable mathematical theory (though it would be surprising if it were).

In any case, even if we need an incomplete mathematical theory for physics, we might say that a description of the physical world is complete if it *entails* all the facts. And that's compatible with the Goedel theorems, as long as entailment is a weaker relation than provability.