On dualism

My approach to interpretation of QM assumes that the mathematically describable aspects of the world are ultimately responsible for why some conscious observations are more commonly experienced than others. I'll call that "reductionism". Many philosophers don't share that view, and here, I will consider the alternative viewpoint, which is generally known as "dualism" as it usually posits that "mind" (consciousness, qualia) and "body" (the aspects of the physical world which can be described mathematically) are two very different things with no logically necessary connection between them.

Both views have counter-intuitive implications, which is one reason that no consensus has been reached on the issue in philosophical circles. The other reason is that no consensus is ever reached on any philosophical question :)

The counter-intuitive implication of reductionism is that qualia - the way the colors appear to us, for example - either 1) are caused by mathematical properties, or 2) don't actually exist (known as eliminativism).

The problem with 1) is that our perceptions of color, for example, seem to have a "qualitative" aspect (e.g. red, green, blue) that doesn't seem like the sort of thing that mathematics could explain. There is an "explanatory gap" between them. The philosopher David Chalmers famously called the problem of understanding how math could explain things like qualia the "hard problem" of consciousness.

The idea 2) that qualia don't actually exist may seem absurd on the face of it, but upon closer inspection, it's a viable possibility. We think that qualia exist because our brains tell us that they do, but our brains are often wrong about what they are experiencing. This could make sense if the brain is composed of several parts or modules. The part of the brain that decides what it's experiencing need not be the same part that is undergoing the experience in question, if any. Thus, it could decide wrongly. This argument is related to my partial brain thought experiment.

Given these issues, it's not surprising that people find reductionism implausible. The alternative hypothesis is dualism: that qualia really do exist, but not due to mathematically describable properties. This avoids the problem of how math could cause the way that colors look, as well as the difficulty of believing that our brains are wrong about what they experience.

It's hard to understand what minds could be if they are not mathematically describable. Dualism introduces the question "What is mind?" which seems to me is as hard a problem as "How could qualia be mathematically caused?"

The other problem with dualism is that it doesn't explain why our brains tell us we have qualia. Telling us is a physical action, mathematically describable as processes in the brain, and it has ordinary physical consequences such as me typing this sentence. The brain's actions are determined by mathematically describable physics: electrical signals, chemicals, etc. So dualist qualia are epiphenomenal; they can't be what causes our brains to tell us we have qualia.

So if dualism is true, then there are two things going on at the same time: We have qualia, and unrelated to that, for some other reason our brains tell us that we have qualia. A dualist could argue that while that seems counter-intuitive, there is at least no problem in principle as there would be in trying to connect qualia to a mathematical explanation. However, the same is true for eliminativism, and that has the advantage of being less complicated.

If dualism were true, we might expect that some explanation of the "coincidence" between our qualia and the brain's belief in its own qualia must be rooted in anthropic selection; e.g. that there are many sets of laws linking minds to physics and that cases in which the "coincidence" doesn't hold see usually see just a random jumble. It seems unlikely to me that such an explanation would work, but I won't say that for sure. Partially it makes sense: By hitching its wagon to the mathematically describable functions of a brain, a dualist law connecting minds to physics would be more likely to produce a complex but coherent set of qualia. However, there is leeway. For example, if what the brain thinks it enjoys gave rise to pain qualia, and what the brain thinks it dislikes gave rise to pleasure qualia, would that not be anthropically valid? Another problem is that all of those laws (some of which wouldn't respect the Born Rule) could give rise to partially coherent "Boltzman brains" that outnumber normal observers.

Intuitively, we would want an explanation in which we do have qualia and they are responsible for why our brains think we have them. There is a version of dualism, called interactionism, in which that would happen - but it requires that our brains' thoughts and behavior are not based on the mathematically describable physical world, and that is highly implausible given what we know about both brains and physics. There is another major problem with it: Even a mental world could be divided up into pure experience qualia versus mathematically describable interactions; thus, interactionism reduces to epiphenomenal dualism, just with some of the mathematically describable action hidden away from the world described by known physics.

This should not be confused with 'quantum approaches to consciousness', which while also implausible, assume that the brains' behavior is due to their ability to collapse the wavefunction - which, even if it could occur, would just be another mathematically describable physical process. Likewise, even if psychic abilities existed, they would have mathematically describable causes and effects.

In general, ANY type of physical behavior can be described mathematically.

"Mental monism" aka "idealism" is the view that only minds exist; i.e. the physical world is sort of like a shared dream. This avoids the problem of linking minds to physics, but still would need to explain physics, with all of its mathematical behavior. It's hard to see how it could avoid introducing some mathematically describable things to help it along, and thus just become dualism.

In any case, supposing that dualism is true, what would it imply for interpretation of QM?

First, there would have to be a new law of nature linking the mathematically describable physics to mental properties. This would revive the possibility of single-world hidden variables, because unlike reductive computationalism, there is no logical reason that the new law couldn't just take the hidden variables into account. However, while that would be logically possible, it wouldn't be the simplest possibility, which is that the wavefunction (which must exist anyway) is what is taken into account. So based on Occam's Razor, we'd still have reason to believe in some kind of many-worlds interpretation. This kind of argument has been made by David Chalmers, who also argues that computationalism would still hold, and Don Page has made a proposal for this kind of dualist MWI.

The explanation for Born's Rule would probably be different with dualism that with reductionism, though. While it's possible that (as Chalmers argues) computationalism would still hold, and that Born's rule would follow from counting implementations, a more direct explanation becomes available: The dualist law could simply mandate that measure is proportional to the squared amplitude of the wavefunction, just as it does in Page's model.

There are few limits that we can place on what such a law of nature could be like - if it does exist, that is. It's not something we could investigate or deduce by logic. That is one reason that my investigations focus on the more restricted possibilities given by reductionism/eliminativism; the other is that I find it more plausible.

1-page Bell's theorem

One particle is sent to Alice; the other to Bob; they may be very far apart.

Alice <----------------------------- source --------------------------------> Bob

Each can measure the ‘spin’ of their particle along some direction; each result is + or –. The probability that Alice and Bob get the same (+ or -) result as each other depends on the directions they measure along. For a certain type of source, if they both measure in the same direction, they always get opposite results.

Each of the Observers will ‘choose’ one of three directions: A, B, or C. This ‘choice’ can be made using any procedure or device, however complicated; therefore, it should be considered unpredictable, even though it may be made using deterministic physics.

Distant-Measurement-Independent Result (DMIR): The assumption that THE (single) result of each measurement can’t depend on which direction the other Observer ‘chose’.

Note: If DMIR is false there are 3 possibilities, of which the first two are taken seriously:
1) Nonlocality: An instant (faster-than-light) hidden signal which conveys the information about the measurement angle (which can be ‘chosen’ right before measurement) to the other particle, no matter where it is or how far away.
2) Multiple outcomes of each measurement actually do occur (as in the MWI).
3) “Conspiracy theories” in which the other particle somehow can predict the angle.

Assume DMIR. Then each particle needs to know in advance what result to give for any angle so that they will always give opposite results when both Observers choose the same angle. Hypothetical properties that’d determine the results are called hidden variables.

Notation: Let P(A+ & B-) mean the probability that the hidden variables are such that result + would be found by Alice if she measures along A, and result – if along B.

Since more-general cases are at least as probable as less-general ones:

P(A+ & B-) = P(A+ & B- & C-) + P(A+ & B- & C+) ≤ P(A+ & C-) + P(B- & C+)

It is not possible to measure Alice's particle along more than one direction, but measuring Bob’s particle should reveal the opposite of the result Alice's particle would have given. Let P(A+ // B+) be the probability that result + would be found by Alice in direction A, and result + would be found by Bob in direction B.

P(A+ // B+) ≤ P(A+ // C+) + P(B- // C-)

Quantum mechanically, if A and B are at a 90 degree angle, with the C direction halfway in between them, then P(A+ // B+) = .25,
and P(A+ // C+) = P(B- // C-) = .073

Since .25 > .146, the inequality is violated; DMIR is not consistent with QM.
Violations of such inequalities have been confirmed experimentally; DMIR is false!

Why do Anthropic arguments work?

See "Meaning of Probability in an MWI"

Anthropic arguments set the subjective probability of a type of observation equal to the fraction of such observations within a reference class. This is what I use for "effective probabilities" in the MWI after a split has occurred (the 'Reflection Argument' in the previous post).

There is sometimes some confusion and controversy about such arguments, so I will go into more detail here about how and why the argument works.

The anthropic 'probability' of an observation is equal to what the probability would be of obtaining that observation if an observation is randomly chosen.

Does this imply that a random selection is being assumed? Is it implied that there some non-deterministic process in which observers are randomly placed among the possible observations?

No! I am not assuming any kind of randomness at all. All that I am doing is using a general procedure – known as anthropic reasoning - to maximize the amount* of consciousness that guesses correctly the overall situation.

Suppose that, prior to making any observations, X is thought 50% likely to be true. If X is true then one person sees red and nine people see blue. If X is false, then nine people see red and one person sees blue. If you see red, you should think that X is probably false, with 90% confidence.

If people always follow this advice, then in cases like this, 90% of the people will be right. True, 10% will be wrong, but it’s the best we can do. The given confidence level should be used for betting and/or used as a prior probability for taking into account additional evidence using Bayes' theorem.

That is why the “effective probability” is proportional to the number of people or amount of consciousness; it is not because of some kind of ‘random’ selection process.

The next point is that "number of people" is not always the right thing to use for the anthropic effective probabilities. In fact, it only works as an approximation, and only in classical mechanics even then. The reason is that the amount of consciousness is not always the same for each "person". This is especially true if we consider effective probabilities in quantum mechanics, which are proportional to squared amplitude of the branch of the wavefunction. In such a case, we must set effective probabilities proportional to "amount of consciousness" which is a generalization of the idea of "number of people". I call this amount "measure of consciousness" (MOC) or "measure".

Note: In my interpretation of QM - the many computations interpretation - I do assume that the measure is proportional to the number of implementations of the computation, which can be thought of as the number of observers. However, many of the points I make in posts here do not rely on that interpretation, so the more general concept of measure is generally used.

There is no reason not to apply the same kind of reasoning to cases in which time is involved: In such cases, this maximizes the fraction* of consciousness which is associated with correct guesses. In a large enough population (which is certainly the case with the MWI), this is the same as maximizing the amount of consciousness associated with correct guesses at a given global time.

With all of this talk about consciousness, am I assuming any particular hypothesis about what consciousness is? No, I am not.

What about eliminativism - the idea that consciousness as it is commonly understood does not really exist? That's no problem either! I am just using consciousness as a way to talk about the thing that observers do when they observe. Even the most radical eliminativist does not deny that there is something about the brain that is related to observational processes; whatever that is, more people would have more of it.

Rather than "consciousness", perhaps it would be more precise to talk about "observations" or "queries". Remember, effective probability maximizes the fraction of correct answers; this implies that queries are being made. What about the quantum case, in which the "amount of queries" is proportional to squared amplitude? To make sense of this in an eliminativist view, it may be necessary to take a computationalist view, and let the "amount of queries" be the number of implementations of an appropriate computation. On the other hand, for a dualist, the effective probability should be set proportional to the amount of consciousness that sees a given "query".

Given these different philosophies, without implying any position on whether "consciousness" really exists or not, I will continue to use the term "amount of consciousness" to stand for whatever the quantity of interest is that generalizes the notion of "number of people" to give anthropic effective probabilities.

* When considering the consequences of a fixed model of reality, there is no difference between maximizing the amount of people who guess correctly as opposed to maximizing the fraction of people who guess correctly. However, if different hypotheses which predict different amounts of people are compared, there is a difference. This is closely tied to the philosophical arguments known as the Sleeping Beauty Problem and the Doomsday Argument. I discuss this important topic in the following post.