
The Strong Free Will Theorem (2009) [pdf] - lainon
http://www.ams.org/notices/200902/rtx090200226p.pdf
======
simonh
I really think this, along with much philosophical musing about free will, is
entirely missing the point. Pre-determination is essential to free will. You
literally cannot have free will without it. Random choice, or even non-
predetermined correlated outcomes of entangled objects don't lead to free
will, they lead to uncertain decisions and those are not the same thing.

If my decisions are not a product of my prior state, then they are not my
decisions. The definition of 'me' is my prior state. If my decisions are
unpredictable given complete knowledge of my prior state, and the ability to
extrapolate it forward, then the decisions do not come from me. If they're not
mine, then I have no responsibility for them. Any discussion of my
responsibility for my actions must take into account my personal contribution
to the decision as a being.

Dualism does not solve this problem. It simply foists a chunk of a person's
state into some non-material constituent, but if that constituent does not
have a persistent (though presumably malleable) state or does not
deterministically contribute to the process, again whence comes
responsibility?

~~~
whack
> _If my decisions are not a product of my prior state, then they are not my
> decisions. The definition of 'me' is my prior state._

There are two problems with this definition of free will.

First, it implies that your present self (and future selves) are all entirely
subservient to your prior state, and surrounding environment. Ie, the present
you has no way of overcoming your past self or your environment. This means
that you're essentially sitting in a roller-coaster ride, with no levers to
pull or opportunity for change. Sure, your past self made the decision to get
on the ride. But your present and future self are all helpless from that point
on.

Second, did even your past have any free will? The chain of causation extends
all the way back. Your past self at time T-X is itself entirely subservient to
your past self at time T-X-1. Extend this all the way back, and you realize
that you're subservient to your "self" at the moment of conception. At no
point did your consciousness have any ability to change the course of the life
that was already plotted for it. If I predict at the moment of your birth,
every single thing that will happen in your life and every decision you will
make, can you really claim to possess free will?

Hence why people try to cling on to randomness and uncertainty. _" If the
future can be perfectly predicted, people definitely do not have free will =>
ergo, if the future cannot be perfectly predicted, then maybe we have free
will?"_ I agree with you though that this is shoddy reasoning. Just because
there exists randomness at the quantum level, just means that we're passengers
in a driverless car that's rolling dice. Randomness that we have no control
over, does not grant us free will in any way.

~~~
mreome
I think simonh was not arguing against the chain of causation, but rather
agreeing with it, and arguing against _" If the future can be perfectly
predicted => people definitely do not have free will"_ and in favor of _" If
the future can not be perfectly predicted => people definitely do not have
free will"_

If an entity's decision process is is not not dependent and _repeatable_ based
entirely on it's internal state and perceptions of it's environment, then it
must be dependent on some external random element, and that element not being
part of that entity, means it's choice is not entirely of it's own free will.

This argument rejects duality of course, as one's "will" itself could be the
external element.

~~~
whack
> _I think simonh was ... arguing against "If the future can be perfectly
> predicted => people definitely do not have free will"_

Just so I'm understanding you correctly: Are you claiming that even if the
future can be perfectly predicted, people can still have free will?

At the moment of your conception, if I were to predict with 100% accuracy and
confidence, every decision you will ever make in your life, would you still
claim to possess free will?

~~~
rocqua
> even if the future can be perfectly predicted, people can still have free
> will?

Not OP, but essentially yes.

Things get weird if you use your predictions to influence what I do. But I'd
say that takes away my agency, whilst keeping my free-will intact.

In general, those who claim determinism and free-will do not clash are called
'compatibilists'. Often, the argument is kind-of semantic. It starts with the
idea that what most people consider 'free-will' is so ill defined we ought to
work on the definition. It then follows that most definitions are very clear
on whether we have free-will. Then, since most people feel like we have free-
will, the definition that fits with that is chosen.

At least, that is the case for me. Personally, I think the real difficult
discussion lies with the concept of 'x is possible' in a deterministic world.
Here, I grasp for bayesian statistics.

~~~
whack
That's an interesting perspective. I don't agree with it myself, but I agree
that it's impossible to resolve this discussion without a clear definition.

Personally, I define free will as having the ability to _" change"_. To
overcome your both your past self, and your environment. Ie, a billiards ball
has no free will, because its motion is compelled by its past state, and by
the environment around it. Similarly for cars, computers and every other
inanimate object. Whereas a human can be said to have free will, because
regardless of his past nature, and regardless of the environment around him,
he still has the free will to transcend all that and do something wholly
"unexpected". To me, that's what separates free will from an automaton. Hence
why my definition of free will isn't compatible with determinism.

I appreciate your point though that others might define free will in a wholly
different manner.

~~~
simonh
When we take this argument out of imagined philosophical universes with
perfectly deterministic Newtonian-like rules, we find that in fact randomness
is everywhere. Quantum mechanics tells us that the behaviour of every particle
and photon in our bodies behaves under some level of random influence. Perfect
predictability is a fantasy. However conceptually we can simplify this and
just imagine that my sate, the definition of how I am as a being, includes a
source of randomness.

My argument then is that sure some of my choices are random, mainly because I
choose to not use my memories and skills I have learned and hand over the
choice to the RNG. That's also often a choice though. See my comment elsewhere
on this page on No Country for Old Men.

You talk about unexpectedness. How do you define unexpected in such a way that
it is distinguished from random? That's crucial. Truly random behaviour is not
intentional and not 'ours'.

One way in which people change their minds is though the assimilation of new
information. That's fully compatible with my take on free will. Our prior
state includes the decision making apparatus that evaluates and incorporates
the new information. Our consistency as a persistent self has not been
compromised, it's just been transformed by new information or a new way of
thinking about things. We have changed, but in a way that we are 'built' to
do. Given omniscience (which is impossible, but for the sake of argument),
that transformation would have been predictable in principle and again for me
that's not a problem. Someone who knew me well might have predicted that I
would change my mind.

That is not a problem. There's a quote in a comment nearby from Godel that
addresses this very well.

I suppose I am a compatibilist, but I object to the use of the term
'compatible'. I think some degree of determinism is _required_ in order to
have free will. It's essential. Without it, 'I' am taken out of the chain of
responsibility for my actions. If they do not flow from me, from my state, my
memories, my decision making processes and if those things are not to some
extent consistent, then those actions are not mine.

------
esotericn
Free will is not well defined.

What does it mean for "will" to be "free"? If you could rewind time around one
of your decisions, and replay it, you'd make the same decision every time,
unless there was a random element involved, because the state would be the
same every time.

And if there's a random element involved, it's not really your will, is it?

~~~
ifdefdebug
Your decision is between black and red while looking at the spinning roulette
wheel. The random element is the outcome of your bet, which can not possibly
be inferred from the current state at the time of making the decision. So if I
could rewind and replay, and actually make a different decision each time, it
would really be my will, I think.

Most, if not all, real-world decisions take a non-zero uncertainty about the
outcome into account.

~~~
esotericn
In that case, you didn't "will" the different decision, it was a result of
your internal RNG.

~~~
tylerjwilk00
It's not random though - it is probabilistic. And even if it was an internal
'RNG' it is is still _their's_ not someone else's.

~~~
esotericn
If you take an action based on determining the probabilities of an event, you
would take that action every single time because the state would be identical
every time.

You look at the roulette board. You bet on red.

We rewind time.

You still bet on red. The state is identical.

Did _you_ come up with that decision? Of course you did, who else could have?

My claim is not that there's no "you".

It's that "free will" is meaningless unless we use a weird interpretation of
terminology.

If you'd do the same thing every time, there's no 'freedom'.

If you do different things, but it's based on some sort of tiebreaker RNG,
there's no 'will'.

~~~
simonh
That is true, but only for some definitions of free and will. I don't accept
definitions of 'free' that exclude inputs from my personal mental state. If my
mental state doesn't determine the choice, then the choice isn't mine.

Note that there could be random elements in my mental makeup. i.e. my mental
state might include input from an RNG, but it's still part of me and as long
as it's not the only input into any of my choices, we can still talk about
responsibility.

See my comment about No Country for old Men on choosing to use randomness.

------
waynecochran

       Although, as we show in [1], determinism may
       formally be shown to be consistent, there is no
       longer any evidence that supports it, in view of the
       fact that classical physics has been superseded by
       quantum mechanics, a non-deterministic theory.
    

I am surprised at the number of folks who still try to argue that science
(particularly physics) has "proved" that these is no free will. This may in
fact be true, but you can't argue that it follows from Physics in a post-
Quantum world.

~~~
lastofus
The followup argument is usually something along the lines of quantum
mechanics is just probabilistic as far as we know.

Quantum physics doesn't allow for free will in an otherwise deterministic
universe, any more than hooking up a RNG to a computer allows for the computer
to have free will.

~~~
waynecochran
Not in my understanding. The probabilities are only involved when a quantum
superposition collapses to a classic state. Note that the paper makes it clear
that probabilities are _not_ used anywhere in their argument.

------
starbeast
I been juggling the following three papers for a bit and trying to brush my
maths up. I don't know why I feel a hunch between them, but I do know that the
hunch is to do with this problem.

[https://arxiv.org/pdf/1803.06824.pdf](https://arxiv.org/pdf/1803.06824.pdf)

[https://arxiv.org/pdf/1306.0533.pdf](https://arxiv.org/pdf/1306.0533.pdf)

[https://arxiv.org/pdf/1204.2779.pdf](https://arxiv.org/pdf/1204.2779.pdf)

I will almost certainly be wrong about whatever it is. However I may have more
updates on how wrong and what it is I am wrong about, in maybe a decade or so
;)

------
dooglius
> Another customarily tacit assumption is that experimenters are free to
> choose between possible experiments. To be precise, we mean that the choice
> an experimenter makes is not a function of the past

Garbage in, garbage out. It isn't clarified whether an experimenter in a
nondegenerate superposition of states (will choose x, will choose y, will
choose z) is considered to have "free will". If you call that free will, then
the result that result that the particle can end up in a superposition of
states is not novel. If you don't call that free will, then the assumption is
false and the theorem vacuous.

~~~
n4r9
You need this sort of axiom to eliminate superdeterminism. If an
experimenter's choice of direction is fully determined by their past light-
cone then a shared physical state in the overlapping past light-cones of A and
B could conceivably drum up any correlations it wants.

It's a conspiratorial line of thought on a par with Descartes' evil demon, but
in a rigorous proof you have to rule these sorts of things out.

The axiom comes into play at the top-right of p.229:

> ...since by MIN the response of b cannot vary with x, y, z, θ^G_0 is a
> function just of w

~~~
dooglius
Right, I see how it's being used in the proof, my point is that what the
theorem proves, regardless of how the notion of "is determined by" is
clarified, is not at all interesting or surprising.

~~~
n4r9
It's essentially a recasting of Bell's Theorem; in that sense it's both
interesting and surprising if you thought that local hidden variables might
still explain quantum theory. All you need - for both this and Bell's proof -
is that directions are chosen with sufficient "randomness" or "freedom" so as
to be considered independent of their past light cones. At least, independent
enough so that the previously quoted step is possible.

------
EamonnMR
I've honestly had trouble understanding how one would go about defining free
will in a way that it could be observed. I can explain how I made my decisions
and non-decisions, I know the difference between freedom and duress, but I
have yet to see a definition of what free will is meant to mean, and why I am
supposed to have it, while dice, my phone, and a plant growing towards the sun
are not. It probably also requires a strong definition of consciousness,
right?

------
TheOtherHobbes
This is a subtle version of the Post Hoc Ergo Propter Hoc fallacy.

Assumption: free will is defined by unpredictability and indeterminacy.
(Actually not a given. This is hotly debated, to put it mildly.)

Therefore if a physical system behaves in an intrinsically unpredictable way
(quantum systems do...) it is showing evidence of free will.

If you start from the premise that the universe and everything in it is
sentient (etc, etc) this makes perfect sense. Of a sort.

But it's not in any way a proof of that premise.

In fact it doesn't even come close to being a proof. All it does is take the
long way around proving that constrained unpredictable systems are in fact
unpredictable but constrained - something that's proven by Kochen-Sprecker
anyway.

Then it pulls the free will rabbit out of the hat and says "Of course! This is
just like human free will!"

I'm going to go with "no" on this one.

The irony is that KS is usually taken as a proof that quantum systems aren't
just indeterminate, they're essentially partially unknowable. There is no
possible one-to-one mapping between states and observables.

If particle free will existed there would either be a tighter constraint on
the possible mappings, which would disprove KS, or the free will would be
indistinguishable from quantum randomness, which makes it an untestable
metaphysical epiphenomenon.

Either way it doesn't add anything to our understanding.

Of course if someone designs an experiment where particles use observables to
signal their consciousness to human experimenters, I'll change my mind about
that.

------
ganzuul
If life has meaning, will is not free. - This is the strongest statement that
I think can be said about the subject.

There is a great conceptual distance between the self-assertion popuparized by
Descartes and the theories and observations of physics. Science, even
cosmology, has a very long way to go before its methods begin to answer the
questions of philosophy.

------
lainon
I am myself skeptic of this. First of all - How does on control indeterminism?

And does QM indeterminism really play a role on a neuronal level? This paper
by Tegmark argues it doesn't - [https://arxiv.org/abs/quant-
ph/9907009](https://arxiv.org/abs/quant-ph/9907009)

~~~
mannykannot
This seems to be a weak free will theorem: "Our provocative ascription of free
will to elementary particles is deliberate, since our theorem asserts that if
experimenters have a certain freedom, then particles have exactly the same
kind of freedom." To me, they seem to be saying that the freedom of free will
is a limited freedom from determinism, not the freedom of being able to choose
a future.

The theory seems to be developed within the Copenhagen Interpretation
framework of metaphysics, and I wonder if it is compatible with Many Worlds.

------
michael2l
Quite apart from the math and science of deterministic physics and
probabilistic quantum physics, there's a broader evolutionary question.

Why would we evolve this hallucination that we have free will, if in fact we
fundamentally don't? It seems like a lot of effort and metabolic energy on a
moment-by-moment basis to maintain the illusion. I guess you could make an
argument we're in some sort of simulation the maker of which required this
illusion to be present for reasons of their own.

But the conscious awareness of our moment-by-moment availability of choice is
one of the most difficult things to deny even if you're incredibly skeptical
about everything else you can observe through the senses (a la descartes).

~~~
tasty_freeze
Why do you think maintaining the sense of free will is evolutionarily costly?
If anything, to me, it seems like a heuristic shortcut that is imperfect but
is useful most of the time, and saves resources overall.

As a close analogy, we've all said something like, "My car wants to pull to
the right." Nobody claims the car has free will, but "wanting to pull to the
right" is a useful way to both communicate and to think about it. What is is
in the car's makeup that causes it to want to pull to the right?

There are plenty other examples where people have false beliefs yet still
cling to them. If you ask drivers if they are better or worse than average,
about 10% will say worse. My point is, having false beliefs doesn't always
exert a strong evolutionary pressure.

------
pcpcpc
Derk Pereboom posits that there is no free will but that fact is not
inconsistent with moral responsibility.

[http://derk-pereboom.net/views/](http://derk-pereboom.net/views/)

------
ThomPete
Most people miss the point when they discuss free will because they focus on
the idea of whether we are free to make decisions in real time.

Free will is something that happens OVER TIME.

In other words you have free will to the extent that your previous decisions
allowed you to survive which was again based on other previous decisions and
so you are constantly accumulating and changing "code to your program" so to
speak because you can reflect on the results of your pre-defined behavior.

------
ttflee
Is this another counter-Sokalian paper for fun?

------
jatsign
Can anyone dumb this down for me?

~~~
all2
> _It asserts, roughly, that if indeed we humans have free will, then
> elementary particles already have their own small share of this valuable
> commodity. More precisely, if the experimenter can freely choose the
> directions in which to orient his apparatus in a certain measurement, then
> the particle’s response (to be pedantic—the universe’s response near the
> particle) is not determined by the entire previous history of the universe._

That about sums it up. I think (and I could be very wrong) that the last
sentence refers to a particle's lack of dependence on previous state; that for
a measurement, only the present state will inform the measure.

That seems to infer something about the idea of 'free will', that is, 'free
will' in this context seems to refer to an independence from prior states.
Loosely, we can choose to step out of the path of our past's falling dominoes
and change the course of our lives. Or something like that.

~~~
criddell
Is that basically saying that at some level, we should be able to see effects
that have no cause? Is that what freewill boils down to?

~~~
cryptonector
More like effects whose cause we can't ascribe... would have a free will
component to their cause. It seems a bit silly because wherever you can
ascribe a cause, there's no free will, so when is there free will?

~~~
criddell
> so when is there free will?

I open to the possibility that the answer is _never_.

