I am confused by these posts. On one hand, Eliezer argues for an account of causality in terms of probability, which as we know are subjective degrees of belief. So we should be able to read off whether X thinks A causes B from looking at conditional probabilities in X's map.
But on the other hand, he suggests (not completely sure this is his view from the article) that the universe is actually made of cause and effect. I would think that the former argument instead suggests causality is "subjectively objective". Just as with probability, causality is fundamentally an epistemic relation between me and the universe, despite the fact that there can be widespread agreement on whether A causes B. Of course, I can't avoid cancer by deciding "smoking doesn't cause cancer", just as I can't win the lottery by deciding that my probability of winning it is .9.
For instance, how would an omniscient agent decide if A causes B according Eliezer's account of Pearl? I don't think they would be able to, except maybe in cases where they could count frequencies as a substitute for using probabilities.
OK, let's say you're looking down at a full printout of a block universe. Every physical fact for all times specified. Then let's say you do Solomonoff induction on that printout -- find the shortest program that will print it out. Then for every physical fact in your printout, you can find the nearest register in your program it was printed out of. And then you can imagine causal surgery -- what happens to your program if cosmic rays change that register at that moment in the run. That gives you a way to construe counterfactuals, from which you can get causality.
ETA: There's still some degrees of freedom in how this gets construed though. Like, what if the printout I'm compressing has all its info time-reversed -- it starts out with details about what we'd call the future, then the present, then the past. Then I'd imagine that the shortest program that'd print that out would process everything forward, store it in an accumulator, then run a reversal on that accumulator to print it out, the problem being that the registers printed out from might be downstream from where the value was. It seems like you need some extra magic to be sure of what you mean by "pretend this fact here had gone the other way"
For instance, how would an omniscient agent decide if A causes B according Eliezer's account of Pearl?
An omniscient agent would have no reason to decide if A causes B, since causality is a tool for predicting the outcomes of interventions, and the omniscient agent already knows what's going to happen. The concept of "causality" is only useful from a perspective of limited knowledge, much like probability. And the concept of an "intervention" only makes sense in a level of abstraction where free will is apparent.
Pearl addresses this in slide 47 of this lecture. Causality disappears if you consider the entire universe as your object of investigation.
The introduction to causality is intended to be bog-standard. All departures from mainstream academia are errors and should be flagged accordingly.
I can't particularly recall hearing anyone suggest that a universe is a connected fabric of causes and effects in the Pearlian sense of causality. Since Special Relativity there have been many suggestions that a universe is a connected fabric of 'events', or points in spacetime.
I can't particularly recall reading that you can only meaningfully talk about things you can find by tracing causal links (this theory will be developed further in upcoming posts).
Wolfram 2002 argues that spacetime may actually be a discrete causal network and writes:
The idea that space might be defined by some sort of causal network of discrete elementary quantum events arose in various forms in work by Carl von Weizsäcker (ur-theory), John Wheeler (pregeometry), David Finkelstein (spacetime code), David Bohm (topochronology) and Roger Penrose (spin networks; see page 1055).
Later, in 10.9, he discusses using graphical causal models to fit observed data using Bayes' rule. I don't know if he ever connects the two points, though.
What would it even mean to say that the universe is a fabric of cause and effect "in the Pearlian sense of causality"? Pearl originated a new method of causal analysis, not a new concept of causation.
Physicists tell us that reality is, at the lower levels, described by differential equations. Those describing the temporal evolution of systems are generally hyperbolic differential equations. That is, they have microscopic causal structure: the properties at a point (x,t+dt) depend on the properties only in a small, finite neighbourhood of x at time t. This is what allows larger scale events to be described more abstractly in terms of causal graphs. (A known problem here is the time-symmetry of all these equations. I don't have a solution to that either.)
Some have speculated about the very finest scale being discrete, with fundamental laws of temporal evolution such as those of cellular automata or graph rewriting. That would also provide the fundamental causal structure from which causal structure on the macroscopic level emerges.
A universe whose fundamental laws were all elliptic differential equations -- those in which a change in boundary conditions in one place changes the solution everywhere at once -- would not support causal reasoning. Everything depends on everything else and none of its emergent phenomena would be describable by sparse causal graphs. I'm not sure you could have agents within such a universe, for it to look like anything to them, or any notion of time, but we can imagine such universes from outside.
"A universe is a connected fabric of causes and effects."
But if you're talking about the entire universe, then there aren't any causes and effects, just as there isn't any time. Causality only shows up when you look at a slice of the system, and whether A causes B or B causes A or they are actually independent can vary based on which slice you choose.
You've shown no great understanding of philosophy--or even a slight understanding.
To you. I for one have been sufficiently impressed that I'm willing to pay 5 karma to tell you.
For instance, Lukeprog is the only person I know who rejected religion for the right reasons: asking the questions in good faith, then looking up and thinking about the answers. Have you noticed the number of citations at the bottom of many of his main posts? It could have been only to show off, but I bet it would have been noticed here.
The evidence I have say Luke knows more abo...
I have a plausibly equivalent (or at least implies Ey's) candidate for the fabric of real things, i.e., the space of hypotheses which could in principle be true, i.e., the space of beliefs which have sense:
A Hypothesis has nonzero probability, iff it's computable or semi computable.
It's rather obviously inspired by Solomonoff abduction, and is a sound principle for any being attempting to approximate the universal prior.
Koan 4: How well do mathematical truths fit into this rule of defining what sort of things can be meaningful?
"Does your rule there forbid epiphenomenalist theories of consciousness - that consciousness is caused by neurons, but doesn't affect those neurons in turn? The classic argument for epiphenomenal consciousness has always been that we can imagine a universe in which all the atoms are in the same place and people behave exactly the same way, but there's nobody home - no awareness, no consciousness, inside the brain. The usual effect of the brain generating consciousness is missing, but consciousness doesn't cause anything else in turn - it's just...
Does your rule there forbid epiphenomenalist theories of consciousness - that consciousness is caused by neurons, but doesn't affect those neurons in turn?
A forest does not cause trees, and trees do not cause a forest; they are related, but their relation is of a different kind.
However, if you're willing to abuse definitions a little bit, you can pretend that relation is causal; if you define a forest in terms of things like tree-density, then the forest is "caused by" trees, but it's a causal dead-end which affects nothing in turn. The same holds for neurons and consciousness. However, it would be silly to talk about a bunch of trees in the same place which were not a forest, and similarly silly to talk about a working, talking brain without consciousness.
But while deep philosophical dilemmas such as these are never settled by philosophers, they are sometimes settled by people working on a related practical problem which happens to intersect the dilemma. There are a lot of people who think I'm being too harsh on philosophers when I express skepticism about mainstream philosophy; but in this case, at least, history clearly bears out the point.
It's worth mentioning that the first people to rigorously apply Bayes net methods to causal discovery (as far as I know; correct me if I'm wrong) were philosophers. ...
On the other hand, while "post-utopian" is linked to "colonial alienation" and vice versa, these two elements don't connect to the rest of the causal fabric - so that must not be a universe.
If I really want to, there's an easy way for me to sidestep this. I just postulate something called "post-consciousness" which is caused both by colonial alienation and by particular arrangements of neurons in the brains of particular people (in a similar way to that in which epiphenomenalists would say consciousness is caused). Presto! ...
..."You say that a universe is a connected fabric of causes and effects. Well, that's a very Western viewpoint - that it's all about mechanistic, deterministic stuff. I agree that anything else is outside the realm of science, but it can still be real, you know. My cousin is psychic - if you draw a card from his deck of cards, he can tell you the name of your card before he looks at it. There's no mechanism for it - it's not a causal thing that scientists could study - he just does it. Same thing when I commune on a deep level with the entire un
My reply, before reading other replies, is that the question is wrongly posed. The described phenomena can be part of a causal universe, because they are causal processes.
Consider the psychic cousin. I draw a card from his deck - it is (say) the three of clubs. Let us further assume that he correctly guesses the card that I have drawn, and does so in 99% of trials. In such circumstances, his statement of the card that I have drawn ('you have drawn the three of clubs!') is caused by my drawing the three of clubs. The mechanism of that causality may not be known, but it is there.
Similarly for the example of "communing on a deep level with the entire universe in order to realize that your partner truly loves you" - there's a causal link, there, and the cause is "your partner truly loves you". (Personally, I'd prefer to check the conclusion by some other means in order to prevent observer bias effects, but this becomes tricky for this example).
Purely spiritual phenomena, therefore, are firmly inside the realm of causal processes, even if they are not yet fully understood.
"Your partner truly loves you" could also be a purely spiritual phenomenon outside the realm of science. This implies that it has no observable consequences; a partner who truly loves you is no less and no more likely to dump you than one who doesn't. This is an unusual idea of true love.
Causal diagrams don't require understanding of the links- if the content of the card influences your cousin's claim, then we would draw an arc from the card to the claim in our causal diagram, even if we don't know how he's influenced by the card.
(Privately, I would suspect the speaker's belief is not rigorous, and would not put much weight by it, but why challenge them on a factual matter when we're discussing causal networks?)
It's not clear to me that you've sufficiently expanded your belief that your partner truly loves you, or what it means to commune with the universe, or what separates physical and non-physical processes. If we define as real things which are part of reality, and acknowledge that your belief in your partner's true love exists in reality, why are we not content to find real causes for that belief?
(Of course, there are many status reasons to turn to spiritual causes. But the instrumental benefits are probably outweighed by the epistemic detriments- or, at least, I should not privately believe their claim, even if I consider it worthy of public endorsement.)
"Magic" just means "I don't know how it works." (Pratchett, somewhere in the Tiffany Aching novels.)
If the world is exhibiting some regularity, you can always ask how that happens. "No mechanism" is itself a prediction: that none will be found. Where did that prediction come from?
I like this post a lot, even though it's short (or, er, bipartite). It covers the stuff it needs to.
Followup to: The Useful Concept of Truth
We previously asked:
What rule would restrict our beliefs to just statements that can be meaningful, without excluding a priori anything that could in principle be true?
It doesn't work to require that the belief's truth or falsity make a sensory difference. It's true, but not testable, to say that a spaceship going over the cosmological horizon of an expanding universe does not suddenly blink out of existence. It's meaningful and false, rather than meaningless, to say that on March 22nd, 2003, the particles in the center of the Sun spontaneously arranged themselves into a short-lived chocolate cake. This statement's truth or falsity has no consequences we'll ever be able to test experientally. Nonetheless, it legitimately describes a way reality could be, but isn't; the atoms in our universe could've been arranged like that on March 22nd 2003, but they weren't.
You can't say that there has to be some way to arrange the atoms in the universe so as to make the claim true or alternatively false. Then the theory of quantum mechanics is a priori meaningless, because there's no way to arrange atoms to make it true. And if you try to substitute quantum fields instead, well, what if they discover something else tomorrow? And is it meaningless -rather than meaningful and false - to imagine that physicists are lying about quantum mechanics in a grand organized conspiracy?
Since claims are rendered true or false by how-the-universe-is, the question "What claims can be meaningful?" implies the question "What sort of reality can exist for our statements to correspond to?"
If you rephrase it this way, the question probably sounds completely fruitless and pointless, the sort of thing that a philosopher would ponder for years before producing a long, incomprehensible book that would be studied by future generations of unhappy students while being of no conceivable interest to anyone with a real job.
But while deep philosophical dilemmas such as these are never settled by philosophers, they are sometimes settled by people working on a related practical problem which happens to intersect the dilemma. There are a lot of people who think I'm being too harsh on philosophers when I express skepticism about mainstream philosophy; but in this case, at least, history clearly bears out the point. Philosophers have been discussing the nature of reality for literal millennia... and yet the people who first delineated and formalized a critical hint about the nature of reality, the people who first discovered what sort of things seem to be real,were trying to solve a completely different-sounding question.
They were trying to figure out whether you can tell the direction of cause and effect from survey data.
Please now read Causal Diagrams and Causal Models, which was modularized out so that it could act as a standalone introduction. This post involves some simple math, but causality is so basic to key future posts that it's pretty important to get at least some grasp on the math involved. Once you are finished reading, continue with the rest of this post.
Okay, now suppose someone were to claim the following:
"A universe is a connected fabric of causes and effects."
vs.
(In the right-hand image we see a connected causal fabric; the sun raises the temperature, makes plants grow, and sends light into the eyes of the person eating from the plant. On the other hand, while "post-utopian" is linked to "colonial alienation" and vice versa, these two elements don't connect to the rest of the causal fabric - so that must not be a universe.)
This same someone might further claim:
"For a statement to be comparable to your universe, so that it can be true or alternatively false, it must talk about stuff you can find in relation to yourself by tracing out causal links."
To clarify the second claim, the idea here is that reference can trace causal links forwards or backwards. If a spaceship goes over the cosmological horizon, it may not cause anything else to happen to you after that. But you could still say, 'I saw the space shipyard - it affected my eyes - and the shipyard building was the cause of that ship existing and going over the horizon.' You know the second causal link exists, because you've previously observed the general law implementing links of that type - previously observed that objects continue to exist and do not violate Conservation of Energy by spontaneously vanishing.
And now I present three meditations, whose answers (or at least, what I think are the answers) will appear at later points in Highly Advanced Epistemology 101 For Beginners. Please take a shot at whispering the answers to yourself; or if you're bold enough to go on record, comments for collecting posted answers are linked.
Meditation 1:
"You say that a universe is a connected fabric of causes and effects. Well, that's a very Western viewpoint - that it's all about mechanistic, deterministic stuff. I agree that anything else is outside the realm of science, but it can still be real, you know. My cousin is psychic - if you draw a card from his deck of cards, he can tell you the name of your card before he looks at it. There's no mechanism for it - it's not a causal thing that scientists could study - he just does it. Same thing when I commune on a deep level with the entire universe in order to realize that my partner truly loves me. I agree that purely spiritual phenomena are outside the realm of causal processes, which can be scientifically understood, but I don't agree that they can't be real."
How would you reply?
Meditation 2:
"Does your rule there forbid epiphenomenalist theories of consciousness - that consciousness is caused by neurons, but doesn't affect those neurons in turn? The classic argument for epiphenomenal consciousness has always been that we can imagine a universe in which all the atoms are in the same place and people behave exactly the same way, but there's nobody home - no awareness, no consciousness, inside the brain. The usual effect of the brain generating consciousness is missing, but consciousness doesn't cause anything else in turn - it's just a passive awareness - and so from the outside the universe looks the same. Now, I'm not so much interested in whether you think epiphenomenal theories of consciousness are true or false - rather, I want to know if you think they're impossible or meaningless a priori based on your rules."
How would you reply?
Meditation 3:
Does the idea that everything is made of causes and effects meaningfully constrain experience? Can you coherently say how reality might look, if our universe did not have the kind of structure that appears in a causal model?
Mainstream status.
Part of the sequence Highly Advanced Epistemology 101 for Beginners
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