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When we speak of "free will" we often imply it to be "a particular sort of capacity of rational agents to choose a course of action from among various alternatives". This capacity is contained by our body, since we want to exclude any influence from outside this system.

On a macroscopic level this manifests in a "I decide x out of the set X"-statement. All the elements of X are an option, thus we map a discrete action A to a discrete outcome x. Let us call this mapping i for idea.

i : A --> x

On a microscopic level this may manifest as "measure a random variable Y and return a result R". The result R has a particular probability of occurrence after the measurement m, given the probability distribution of Y

m : Y --> R

At this point we could presume that an idea i is simply a function of finite measurements R_n. This would suggest that the ideas we have, which are manifested as our free will are nothing but random events, whose only additional dependency is the prior set-up of the universe.

My question is: could we resolve this issue by saying that; the domain where free will exists, is underlying this and in some magical way(more precise theory of the workings) gives our macroscopic silhouette the direct connection to this underlying, in-control system which has the ability to shift the probability distribution so that the results R_n are highly affected and thus the actions we take?

Does this also imply that the set of alternatives X maybe stretched?

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    If our actions were controlled by random events beyond our control, it would be obvious to us that our actions were involuntary. Therefore, there's no doubt in my mind that free willrandomness. – user3017 Jan 21 '18 at 15:48
  • Could you elaborate why it would be obvious to us? – Michael Paris Jan 21 '18 at 15:59
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    Voluntary actions are those determined by the will, and the very idea of them being voluntary involves the idea that we are aware of determining them, so any involuntary action (such as a tick or a seizure) would lack that awareness. Now, if our actions were determined by some sort of random principle, that would preclude them from being willfully determined, so they would be involuntary, and the awareness of determining them would be lacking. Therefore, if you did something without wanting to do it, how could it not be obvious that your willingness was missing? – user3017 Jan 21 '18 at 16:47
  • Ok, so going to the question at hand. Can we resolve this issue by suggesting that there is a theory underlying the KNOWN random nature, which governs our reality. Leading us to believe that if free will exist it must be in a fabric much finer than we currently can observe? – Michael Paris Jan 21 '18 at 16:57
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    Free will determines our actions by means of a noumenal principle which is independent of natural determinations, as Kant held: "By freedom in the cosmological sense, [...] I understand the faculty of beginning a state from itself, the causality of which does not in turn stand under another cause determining it in time in accordance with the law of nature." (A533/B561) In other words, God created the human soul to handle this sort of thing. – user3017 Jan 21 '18 at 17:17
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This capacity is contained by our body, since we want to exclude any influence from outside this system.

This isn't entirely correct. For free will as we think of it to be viable, we must allow for external influences. If the guy at the counter offers me vanilla or chocolate, I must appeal to my mastery of the English language to comprehend his offerings; my learning of English is in large part an external influence. It's also very likely that I'll be strongly affected by my preference of taste; this requires at some point in time access to gustatory memories of tasting each, which is an external influence. Pretty much all experiences I refer to and skillsets I invoke are set at least in part by external influences.

What you're referring to here is only a specific class of external influences; those that compel actions. What exactly constitutes a compelled action is an unresolved issue. Here are three perspectives:

  • a choice is compelled unless there's some ontic way in which a choice not made nevertheless exists; this is popular with libertarians (e.g., this is descriptive of the "Principle of Alternate Possibilities")
  • a choice is compelled if an external agency asserts an intentional undue influence upon a given agent; this is popular with compatibilists (e.g., this is suggested relevant by Frankfurt cases)
  • all alleged choices are compelled; this is a hard determinist view
All the elements of X are an option, thus we map a discrete action A to a discrete outcome x.

I don't think the outcome really matters much with respect to free will per se. Choice per se extends to the point that we as agents initiate an action with a desired goal. A father might jump into a freezing lake to try and save his daughter; this doesn't mean he forsees a future of him saving his daughter, or saving his daughter is actually possible. Since there's not really any difference with respect to the agent per se, it would seem like if actually saving his daughter's life counts as a choice then merely attempting to should as well.

Now the outcome does indeed matter to us, but all we can do is try. Being a potent agent requires such things as attempting to model external reality as best we can, attempting to train our own capabilities to acquire skillsets we can use, and learning our own capabilities and limitations.

We could, however, model this as an idea leading to an action, where action is a goal based behavior. We could also model the action leading to an outcome; it just doesn't seem relevant to free will mechanics per se.

On a microscopic level this may manifest as "measure a random variable Y and return a result R". ... Could we resolve this issue by saying that; the domain where free will exists...gives our macroscopic silhouette the direct connection to this ... system which has the ability to shift the probability distribution so that the results R_n are highly affected and thus the actions we take?

Pé de Leão addressed these comments from a spiritualist perspective. The same view extends to a materialist perspective, which it appears you're taking. An easy way to think of this is to simply start with Pé de Leão's view that the soul is responsible for the will; then simply view the soul as made of flesh. With this view of mechanics, there's no longer need to figure out whether the micro level controls it or the macro level does, as the macro is implemented by the micro.

The weighting of probabilities argument doesn't really help you. It's fundamentally incoherent to claim both than an event is caused by an agency and that the event is random. Weighting doesn't solve this; if I am able to weight probabilities such that there's a 99% chance I get chocolate, then the weighting you can pin to me. But this implies that 1 out of 100 times I do this, "vanilla" will come up. In those 1 out of 100 cases, there's no good way to pin the decision of vanilla as opposed to chocolate to my agency.

If we want a libertarian model of free will, we still need the agent to be the cause of the outcome. Random mechanics, even weighted, do no good; what's required for libertarian mechanics is that the agent is an "original cause", not random. It must be possible in principle for the agent, just because he's so inclined to, to always pick chocolate; or to always alternate; not merely because it so happens that the random die rolls that way, but because the agent wishes it.

The same principle applies to a compatiblist model of free will. Compatibilist free will actually allows random events to happen; they just can't be part of the mechanics of free will. Under a typical compatiblist view, causal actions are the only kinds of actions that can be attributed to will.

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If free will is understood as the ability to choose, then free will is perfectly compatible with physics.

Quantum mechanics tells us that you should imagine the interplay between you and an external system as a tree of possibilities: the branches are representing the measure-free evolution of this external system (which is deterministic), while the nodes are representing the interactions between you and this system. At each nodes, that is every time you interact with this external system (there are different ways to interact with, but let's forget that), you're forcing the system to decide its next branch (which is going to evolve freely until the next interaction). This decision can be interpreted as free.

That is, (the laws of) physics is constraining the trees, and free will is determing which branch is "realized" explicitly, allowing you to discriminate a very specific path on this tree.

  • Exactly! Now imagine this tree at each node, the sum of the probabilities is 1. This means a branch is chosen according to the probability of this state. But if this "choice" IS the free will, it would imply that our free will can increase the probability of one branch to be very close to 1 or even equal to 1. And now we come back to my point, this implies that we "humans" are a system which can control the weights of those states. But a state can not change it's weights just by wanting. So it can neither be in the quantum realm nor the classical one. Right? – Michael Paris Mar 24 '18 at 0:15
  • That depends how you interpret the square norm of the wave function. You can always interpret QM as a "sociology" of particles if you want to: the weight can be changed individually, but you cannot act on them globally. – sure Mar 24 '18 at 8:20
  • I want to interpret it in the standard way. Square of coefficient is probability of occurrence. That implies that I can choose a very unlikely event, make it's probability high and "make it" happen. – Michael Paris Mar 24 '18 at 8:25
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    The thing is, as an individual, you're not indistinguishable from others, while particles are. That is, if you believe in the indistinguishability of electrons, and in an "identity" of electrons in some precise cases, you will have hard time to make the exact same experiment 10 000 times in a row with the very same electron in order to prove that they can indeed change the probability distribution at will. Moreover, if you believe in this kind of fundamental free will, it most likely is independ of the existence of feelings, memory, or will to achieve something consistent. – sure Mar 24 '18 at 8:30
  • So, while your electron might indeed have this ability to choose every time you interact with it (that is at each node), his choices are not necessarily consistent, which would explain why they appear random (yet the probability distribution is not necessarily uniform, especially when you have infinite many choices) – sure Mar 24 '18 at 8:47
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Respectfully, I think this question has some issues with the understanding of the physical world; either that or I'm misunderstanding what you've written. To clarify, I'm going to assume that by macroscopic you're referring to the Newtonian scale (Atoms and bigger) and that by microscopic you're referring to the quantum scale (Protons, electrons and smaller).

This idea that what happens at the quantum scale is inherently random represents a misunderstanding of how we use mathematics to resolve from quantum to Newtonian scales. The Schrodinger's Cat thought experiment is supposed to teach us exactly that. OF COURSE the cat's life is not dependent on a single decaying particle; the whole point of the experiment is to show that such thinking is a nonsense. In reality, the random component is there to provide a statistical way of measuring what an individual particle's path may have been when measuring them by the billions.

A-Ha! (I hear you say...) But what about Heisenberg? His uncertainty principle PROVES that quantum movements are uncertain, meaning that magic and God and ghosts and clairvoyants are all real because the very intent of my observation changes the outcome, right?

Well, no. What Heisenberg's Uncertainty Principle is really trying to teach us is that the smaller things are, the harder they are to observe. To prove this, let's try a thought experiment of our own.

You're playing billiards in a brightly lit room. Where are the balls on the table? Well, you can see them pretty clearly. Why? Because photons are bouncing off them and into your eyes. Do those photons impact the trajectory of the balls? Well, actually yes. But, the impact is so infinitesimally small that we can safely discount it.

But then we turn off the light. No problems I hear you say; I have some very small ball bearings that we can flick along the table and listen for their contact with the billiard balls. Does this impact the trajectory of the billiard balls? Yes, but not too badly.

What about marbles? What about other billiard balls? Worse yet, what about bowling balls?

In quantum physics, instead of the particle we use to do the measuring increasing in size, the size of the particle we wish to observe is actually decreasing. That means that Heisenberg's principle can be summed up in two statements:

1) All observation is essentially the collision of particles
2) The closer in size the particle under observation and the particle used to conduct the observation are, the more of an impact the observation will have on the original outcome.

This means that intent to observe does not directly impact the outcome; it's the act of observation, for the reasons described above.

The purpose of this context is to get to a very simple point. When physicists say that the universe contains deterministic laws, they're serious. We can launch interplanetary probes, listen to news broadcast all over the world simultaneously and even cook our toast for breakfast all thanks to the reliability of those laws to operate in a consistent manner over time. The real question is whether that's all the universe can contain. Quantum physics does not prove that the universe also contains random laws, it proves that some of the deterministic laws we've discovered are not complete enough to explain things on a very small scale, largely because our attempt to make the observation gets in the way.

So; IF the universe can only operate in a deterministic way, then it would mean that free will has to be an illusion. I've written much on this topic on this forum so for brevity I'd suggest going back to previous answers for a more complete answer as to why.

But, your question is free will in our physical system. Assuming that free will is real, then what it means for our physical system is that our understanding of it is by definition incomplete because free will implies that you can choose to do something outside the algorithm. In other words, the universe has to be non-deterministic in nature, even if you can describe it as mostly deterministic.

In that sense, the answer to your final question is YES. the set of alternatives X can be stretched, because a set of alternatives implies determinism. Free will on the other hand is the ability to choose between those alternatives in front of you but also to create your own and choose one of them. You may (for instance) choose to walk away from the choice completely and start walking a new path. Was that originally in the set of X?

I don't know.

The truth is that the math seems pretty clear. So does our experience, and the observations we make on that experience. The trouble is, they're both telling us different things. It's up to the individual to decide which is true for them until we get better information.

  • What about the double slit experiment or Bell's Inequalities? Your presentation of QM is so simplistic that it doesn't even contain QM in it; if QM were simply built off of uncertainty of particles due to HUP, it would simply be classical physics with uncertainty in it... that would not only look entirely different from QM, but it would predict entirely different kinds of results. In fact, the results it would predict don't match up with experiment, which is why we have QM in the first place. – H Walters Jan 21 '18 at 23:38
  • Hi H. Good to see you again. :) The simplistic presentation is there for brevity only. I'm not suggesting that QM is the same as classical physics with randomness built in, I'm just suggesting that the resolution between QM and Newtonian scales contains probabilistic elements that are often misunderstood. Quantum Mechanics does operate in a very different manner to Newtonian physics but our ability to directly observe phenomena at that scale is limited, especially by comparison to the precision of our mathematical models. – Tim B II Jan 21 '18 at 23:51
  • The simplistic presentation is too simplistic to be apt. There cannot be two separate scales, one for which QM holds and another for which classical physics (CP) holds, unless there's some real dividing line between the two. The most straightforward dividing line is "measurement", which applies the Born Rule to quantum states to convert them to classical states. BR application is indeed probabilistically random (but not quite classically so; oddly enough there's a difference). The reality of measurement is an unresolved problem, but if it does occur things are random. – H Walters Jan 22 '18 at 0:12
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    Random or probabilistic? Isn't the problem here that we're applying a statistical measure to an individually extrapolated particle or waveform? My understanding of BR is that it's essentially saying that results like that from the double slit experiment demonstrate statistical probability and that the folly is to think that it can tell you where a specific particle will go, other than to say it falls within a specific probability distribution. Remember, statistics are only for cases where specificity isn't possible; like this one. – Tim B II Jan 22 '18 at 0:29
  • These are two different topics. Regarding the randomness, let's start with terms. Probability describes something akin to a distribution; random we could write whole papers on, but in brief it describes the nature behind the outcome. Most charitably with respect to BR, random describes the degree to which information you can have tells you what the outcome would be... and that degree is 0%. But even this itself isn't quite enough to describe BR randomness; there's one more important quality; see at least from here to 13:38. – H Walters Jan 22 '18 at 1:10

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