Free will theorem and human exceptionalism


Kallikanzarid

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How does Objectivism address the following issues with the free will hypothesis:

  1. The free will theorem states under very mild conditions that if humans are indeterministic, then so are elementary particles.
  2. Humans have evolved biologically from more primitive species. Also, studies of animal intelligence show that other mammals have (limited) capacity for abstract thought.

Both facts highly suggest that if free will is there, it's not limited to humans. In particular, if one wants to maintain "human exceptionalism", the following questions need to be answered:

  1. What is the difference between simple indeterminism and free will?
  2. What human ancestors had free will? By which process had free will evolved?
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Alexei, thanks for bringing the theorem of Conway and Kochen to our attention. The link refers to three serious criticisms that have been made of the argument. My own reservation would be along the lines of the first two.

To be not uniquely determined by antecedent conditions is a larger class than making a choice that is not determined by antecedent conditions. Choice requires consciousness, a type of control system in higher animals, and consciousness is a culmination of certain brain activities. I think it is correct to infer that if some of our choices are not determined by antecedent conditions, then some of our brain processes are not determined by antecedent conditions. Real physiological processes of the brain as control system cannot violate any physical laws. I have argued that that condition is satisfied for indeterministic brain processes even within classical physics in Volitional Synapses. That is, the required indeterminism is the case at the level of classical physical system behaviors in which quantum indeterminacy has already vanished.

Beyond the part on biological indeterminism in that essay, there is an essay pondering volitional consciousness in man and other animals. That is Ascent to Volitional Consciousness by John Enright, another Rand scholar and a friend of mine.

I should ask if you have read the part of Rand’s Atlas Shrugged known as Galt’s Speech. Is that much part of what you know about Rand’s philosophy?

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Alexei, thanks for bringing the theorem of Conway and Kochen to our attention. The link refers to three serious criticisms that have been made of the argument.

If you're referring to the Limitations section:

  • Conflation of indeterminism and free will: I'm well aware of that, that's why I restated the theorem in weaker terms above.
  • The criticism of Goldstein et al: I haven't noticed it before :sad: I'll read up on it, it seems like an interesting topic.
  • The pressuposition of indeterminism: I don't think that it applies to the most famous formulation, because it merely constrains indeterminism and does not attempt to "prove" it.

To be not uniquely determined by antecedent conditions is a larger class than making a choice that is not determined by antecedent conditions.

It could be, it depends on the precise distinction.

I have argued that that condition is satisfied for indeterministic brain processes even within classical physics in Volitional Synapses. That is, the required indeterminism is the case at the level of classical physical system behaviors in which quantum indeterminacy has already vanished.

I don't understand what you mean by indeterministic processes within classical physics. Fundamentally, classical mechanics is deterministic, and stochastic systems are characterized by randomness, and they are not fundamental. But assuming you're talking about some kind of stochastic system, how can you base volition on randomness yet still maintain that it's qualitatively different from simple indeterminism?

Beyond the part on biological indeterminism in that essay, there is an essay pondering volitional consciousness in man and other animals. That is Ascent to Volitional Consciousness by John Enright, another Rand scholar and a friend of mine.

I can't say much about it just by reading the abstract, except that I'm skeptical that there is "a choice to think".

I should ask if you have read the part of Rand’s Atlas Shrugged known as Galt’s Speech. Is that much part of what you know about Rand’s philosophy?

Yes, I've read the whole novel. Back in my Objectivist days I was mostly getting my Rand's non-fiction fix at ARI and various links at OO. And then there was a small compilation translated to Russian that I found in a library.

Edit: I was considering myself an Objectivist for roughly 3 years: from 2006 to late 2008. I read Atlas Shrugged in 2007 (before that I was reading stuff freely available on the Internet).

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In the Abstracts, there are links to the essays "Volitional Synapses" and "Ascent to Volitional Consciousness." Click on the Parts of the former and on the title of the latter.

"I don't understand what you mean by indeterministic processes within classical physics."

I'll wait until you have found time to read my specification of that idea in §VI, which is at the beginning of Part 3. Then we can pick up with any reservations you have about that specific picture of the physical world above the quantum regime. (It takes a few minutes to load, working through the preceding 182 pages, but it will load.)

-S

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I have read the section 6. You claim that in classical mechanics, sufficiently chaotic systems are not deterministic in the long run. It is not true, they are merely unstable. There's a difference.

Generally, the laws of classical mechanics are formulated as ordinary differential equations. Under mild restrictions, they have unique solutions given any initial conditions. For classical physical systems (for which the forces in the appropriate coordinate systems have potentials proportional to 1/|x|^(-n), n >= 1) Lipschitz continuity always holds in a system constrained by the following assumptions:

  1. That the energy is conserved (or, equivalently, that laws of physics don't change with time in the sense that a time translation of a valid solution is a valid solution), and in fundamental systems this always holds.
  2. That the initial total energy of the system is finite (which is equivalent to saying that no two particles have coinciding coordinates).

Since the Lipschitz condition holds everywhere for a system constrained by energy conservation, it has a unique global solution for any initial conditions. That's really it, that's determinism in classical physics in a nutshell. It's math, you can't disprove it by marveling a waterfall and appealing to intuition.

Off topic: real numbers (which can be defined as equivalence classes of sequences of rational numbers) are in general not computable. So your claim that all "non-random" sequences can be computed by algorithms is false.

Edit: I've just realized that I've made a stupid assumption that all forces in the system are repellent. In fact, there are cases when particles could bump into each other: for example, consider two uncharged particles of positive mass initially at rest. I'm not sure if the energy is defined when they have the same coordinates, and on such distances quantum effects become noticeable, anyway, so classical mechanics breaks down.

It's not relevant to most systems of classical mechanics, though:

  1. Matter in most everyday scenarios is composed of atoms, and atomic cores are positively charged (and electron shells are negatively charged, I'm not sure what matters more), so atoms can't collide in the above sense classically (instead they smoothly repel each other in a way that merely looks like rigid collision on large scales).
  2. Such collision solutions are not likely, in the sense that even the slightest perturbation ensures that they don't happen, and given random initial conditions with a continuous probability distribution, they have zero probability of happening, assuming that the number of particles is not 2.

So, here's a limitation to the existence of global solutions in classical systems. It still can't "conceal" free will, though, because the system is still well-behaved enough so that solutions, where they exist, are unique. Thus, if you want free will you'll have to ponder quantum mechanics, which is deterministic in the above sense in between measurements. And in cases of measurements the hypothesized indeterminism is constrained by the free will theorem, assuming that it is indeed correct.

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Off topic: real numbers (which can be defined as equivalence classes of sequences of rational numbers) are in general not computable. So your claim that all "non-random" sequences can be computed by algorithms is false.

Equivalence classes of Cauchy sequences. The real numbers are the topological metric closure of the rationals.

You correctly point out that "most" real numbers are not computable. By the Church-Turing thesis anything computable is computable with a Turing machine. The set of Turing machines is countably infinite. The real numbers are a non-countable infinite set so most of the reals do not have computable rational Cauchy sequences to approximate them.

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We mathematicians have to stick together. Who else will bring Light to the Darkness of the Heathen?

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Stephen, I've read the second essay, but I'm afraid it didn't do much for me. True, we have more intellectual capacity than (most) other animals, it's hard to dispute that. But while the author pats himself on the back by discussing "a choice to think" etc., he neglects to actually address the title of his work: ascent to volitional consciousness. His conclusion seems to be that "our volition is more informed than the one of animals", and I agree. But where is a qualitative difference, where is the ascent here?

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Alexei, partial differential equations for big physics, not ordinary. I have a degree in physics and some graduate study in it, as well as a degree in engineering.

Since when do all partial differential equations of physics have only unique solutions, as opposed to unique sets of solutions? Since when do outcomes of the evolution of a system under such an equation not depend on initial conditions and on boundary conditions? Since when are values of initial conditions and of boundary conditions determined by physical law across independent causal streams? Since when do boundary conditions always change in ways covered not only by identity, but by natural law? Since when is a control system only a system of physics, without engineering-like organization? Since when have control systems been made impossible by classical physics?

Since when is what we know about neurophysiology irrelevant to whether brain process is in the classical regime?

~~~~~

Chaos

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partial differential equations for big physics, not ordinary

In physics of continuous media, yes. In physics of systems of finite number of point particles, no. In classical physics, the former are the approximation to the latter, which are considered fundamental.

I have a degree in physics and some graduate study in it, as well as a degree in engineering.

I'll keep that in mind.

Since when do all partial differential equations of physics have only unique solutions, as opposed to unique sets of solutions? Since when do outcomes of the evolution of a system under such an equation not depend on initial conditions and on boundary conditions?

It's irrelevant to the question, especially the bit about boundary conditions. That is, unless you've managed to find a boundary in the classical description of the Universe.

Since when are values of initial conditions and of boundary conditions determined by physical law across independent causal streams?

I've addressed the boundary conditions above. And we can take the state of the Universe in an arbitrary moment of time as the initial conditions. Do I really have to explain all this to you?

Since when is a control system only a system of physics, without engineering-like organization?

And who's tinkering with the control parameters, God?

Since when have control systems been made impossible by classical physics?

Since they are not part of fundamental interactions. Yes, exactly since then. Control theory deals with control mechanisms which are *external* to the system in question. It's merely a useful simplification.

Since when is what we know about neurophysiology irrelevant to whether brain process is in the classical regime?

It's not irrelevant, but unless neurons somehow break laws of physics...

I hope you're done insulting my intelligence. Would you please continue in a less combative tone?

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How do we count intangibles?

How do you count love or justice or good?

I await the wise mathematicians to lead this heathen from my lonely darkness to glorious light.

:smile:

Michael

Pythagorus started it. He identified the reality behind the observable reality as mathematical principles. The way physics has evolved has been very much along that lines that Pythagorus envisioned. The facts observed in nature lead us step by step to the underlying abstract structure of Nature.

Ba'al Chatzaf

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If one is a determinist I assume you are not taking part in this discussion for what would be the point for you are at least implicitly sanctioning, respecting humans, some form of non-determinism. The universe is what it is, but what are we? In dealing with this question we will inevitably leave physics behind which physicists would be loath to do, it seems.

--Brant

champions of free will?

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If one is a determinist I assume you are not taking part in this discussion for what would be the point for you are at least implicitly sanctioning, respecting humans, some form of non-determinism. The universe is what it is, but what are we? In dealing with this question we will inevitably leave physics behind which physicists would be loath to do, it seems.

--Brant

champions of free will?

Brant, you're just <ahem> determined to argue about this aren't you. :-)

Cut Bob some slack. Like all of us, he's doing what he has to do, which is what he most wants to do (i.e., most values) at a given point in time -- in this case, to discuss determinism vs. free will.

BTW, my perspective, which I have long been convinced is compatible with the deeper principles of Objectivism (causality and identity per se), is "value determinism" coupled with "conditional free will."

Absent coercion or disability, we are free to do that which we most value--and we have to do that which we most value (otherwise, it wouldn't be what we most value then)--and we could have done other than we did in a particular situation, but only if we had instead valued that alternative more than what we chose to do.

This view is a form of Compatibilism, and it seems to make more sense to me than Hard Determinism, Indeterminism, or Libertarian Free Will (of which orthodox Objectivism's view is a variant). You can put these four views in a nice, tight little four-way grid that shows the logical relation between them. I'm working on this for a forthcoming JARS essay. Stay tuned.

REB

REB

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Would it be too off the mark to say , if science were personified , it seems to be really good at answering perhaps all the how questions, but at times hubrisly forgets the why's aren't even on the table?

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How does Objectivism address the following issues...

K,

There's a presumption here that should be cleared up.

Objectivism doesn't "address" anything on OL. Nor does anyone speak in the name of "Objectivism" whatever the hell that entity that's supposed to address stuff is.

This is a discussion site, not a preaching one.

There is no approved doctrine here, no dogma, no accepted and revered creation story (not even the big bang).

OL started precisely to get away from that mentality.

Here people get together because they found value in Rand's ideas, but it is merely a bonding point. Each one is responsible for his own thinking and conclusions. There is no party line.

The way I usually put it is that, here, Objectivism is a starting point to work through ideas and develop from, not an end point where you are finally revealed the ultimate mysteries of the universe.

From what I can tell, you seem to have already found the second and wish to spread the good news, but trounce some enemies first.

OL isn't that kind of site.

You may end up calling this relativism, but it isn't. If I see some real interest out of you instead of aggressive attitude, I might explain further. If not, well... not.

Michael

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Roger, I'm not sure I follow. If at any given point we *have* to pursue that which we value most, then it looks like our actions are completely determined by our values, where is non-determinism in that? Also, how do you answers the questions I posed in the OP?

Michael, I don't mind replacing "Objectivism" with "Objectivists". And I assure you, I'm not aggressive except when I'm responding to aggressive rhetoric which includes degree-waving and lots of emotional rhetorical questions.

Brant, are you claiming that humans are somehow non-physical? Also, I can't see how participating in a discussion implies acceptance of non-determinism.

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Michael, I don't mind replacing "Objectivism" with "Objectivists". And I assure you, I'm not aggressive except when I'm responding to aggressive rhetoric which includes degree-waving and lots of emotional rhetorical questions.

K.,

Let's put it this way.

The kind of formal Objectivist who would answer your question in the manner you seem to seek does not approve of OL all that much. Maybe I'm mistaken about what you seek. That's why I prefer openness.

Most regulars on OL don't even call themselves Objectivists, and when they do, they mean something entirely different than a member of an organized movement or philosophy. Not all are that way, but the vast majority of regulars are.

That's not even by design. That's just who shows up when you have a non-preaching approach, open the floor for discussion, and foster goodwill as one of the normal expectations.

As far as your assurances go, I appreciate them, but I look at what people do and what they say, then I tend to favor what they do as a better indication of their intentions.

Michael

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