Is Free-Will Coherent With Physics?

The model I roughly accept is one I first learned from Presbyterian theologian R.C. Sproul. Namely that your will is in fact determined by your desires. At least to first order you always choose exactly what you want most at that instant. Even the most sacrificial, selfless act imaginable was in fact what that person desired most to do at that instant in that context. It’s as C.S. Lewis once wrote, paraphrasing: “I’ve never committed a selfless act in my life.” So your will is determined, but not externally determined by physics and not directly determined by a puppet master God. It is self-determined. We are slaves to our desires.

However, one pathway for the supernatural would be when God supernaturally intervenes to change your desires, and so you make different choices. This view of free will is, I readily admit, heavily influence by my Calvinistic leanings.

I am using the standard idea of libertarian free will. If your equations describe something else, and I’m not sure they actually describe anything, then they aren’t applicable to the discussion. Nor do I think that mathematical formalism is necessary or, in some cases, even helpful. You will note that the arguments we have here generally manage without mathematical definitions.

Is there a third supernatural option? If so, what could it be, separate both from causation and chance? “Supernatural” is not an alternative to these, just another realm in which either might operate. It may be that the third thing only happens in a supernatural context, but what is that third thing? As @Rumraket said.

Yes. And the alternative version of free will you want reduces the explanations for your choice to what?

When you choose to do some option X instead of some other option Y, what explains why you chose X instead of Y? You might say your your desire for X over Y, but then that just pushes the question back to what explains why you desired X over Y? Are you in control of what you desire? If so, then what explains why you control your desires? Etc. etc.

You can’t escape it. There must either be in infinite regression of explanations (of which you have no control, and are merely subject to), or a brute fact (which, again, you also have no control over), or a vicious circle of explanations (which still isn’t something you control or can change).

Libertarial free will, the free will you seem to care about and want, appears to me logically incoherent.

There are other ideas of free will besides the libertarian one. This seems to be a late addition to the conversation, I did not operate under the assumption that we are talking on how just libertarian free will is coherent with physics. Nevertheless, I do think that when talking about free will, libertarian or otherwise, the usage of precise terms and formulations are important.

Yes, I do note that, but I do not think that is the correct way to do arguments. I believe that throwing around nebulous, imprecise arguments without the railings provided by solid formulation is not something good. This feels like Carnap v Heidegger…

@Rumraket, @John_Harshman, here’s how I (speculatively) think of libertarian free will. I don’t believe it is incoherent, but feel free to take a shot at it.

The basic idea is that an agent has libertarian free will when it is able to act in some way without being caused to act in that way by something other than the agent. Correct me if I’m wrong, but your argument that this is incoherent seems to be that either:

  1. Something explains why the agent acted in that way, in which case the agent was (ultimately) caused to act in that way by something other than the agent.
  2. Nothing explains why the agent acted in that way, in which case the agent’s action is a brute fact that the agent has no control over.

Here is the problem with this argument, from my perspective: neither of the implications in the second halves of those two options actually follow. Something can explain why the agent acted in some way without implying that the agent was caused to act by something else. For example, in my view a free agent might have made a choice A “because” of some reasons R. But the reasons R are not the cause of the agent acting that way. They are the reasons on which the agent acted, but the agent also had reasons S for making a different choice B instead of A, and could have chosen to act on those reasons instead. The agent itself is the cause of the action, and isn’t determined to act in one way or the other by something else.

It might be said, then, that it is a brute fact that the agent chose to act on reasons R (and so do A) rather than on reasons S (and so do B). But it would be begging the question against the concept of libertarian free will to claim that this renders LFW incoherent - this “brute fact” (that the agent acted on reasons R instead of S) is within the agent’s control. And, in fact, the agent’s choice to act on R rather than S isn’t entirely brute or inexplicable: it is explicable through the intelligibility of the reasons R. So the choice is neither caused by something other than the agent, nor it is inexplicable random chance outside the agent’s control.

Thus libertarian free will seems to me to be entirely coherent.


I choose not to participate in this discussion.

Oh darnit!



The others, however, do not allow for C not to equal N, as I understand it. Unless you are now defining C as anything humans do.

Sure. But why does that have to be mathematical? So far, free will can be defined only by what it isn’t. It isn’t caused, and it isn’t chance.

You assume that precision is only possible within mathematics, which I reject.

It doesn’t seem so to me. It seems mere equivocation between cause and caprice. It seems like a version of the homunculus idea of the mind. The homunculus works the brain’s levers, but who works the levers inside the homunculus? It seems another infinite regress. In other words, choice must involve some causal process, and something must begin that process. But something must begin the beginning. The agent you propose may be a black box, but how can what goes on inside that box be explained other than by some combination of chance and necessity? Is there an agent inside the agent?

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Don’t feel bad. You made the only choice you could.

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Not true. For example, one can have a completely deterministic “free will” similar to compatibilism, but that takes as input both X(t) and the “non-physical” state Y(t).

Correct, I think any precision requires mathematics. Logic, for example, is mathematics. You are free to reject this, though I find it ridiculous.

Some things cannot be quantified, Love, Peace, Joy, Thoughts, Feelings, Emotions (Free will)…We know what they are and can say we have more or less, but they are not subject to the laws of physics and math.

I think it was the last avengers movie when Iron Man’s daughter says, “I love you three thousand.” BOOM, love quantified, you may now do the math.

It seems that all you have done there is to split N into X and Y. I also think that the general consensus is that compatibilist free will is not free will.

Logic can be expressed in ordinary language and in fact always was until fairly recently. Formal mathematics can be expressed in ordinary language too. And language can indeed have as much clarity and rigor as you like. The mathemetical symbology is shorthand.

I’ve been trending towards this.

I do not think that free will exists in the degree that some people take it, that we can make a choice completely unfettered by all prior states, physical, social, rational and psychological. Why would one make a choice that disregards the impulses and deliberation leading up to it? To me, that would rule out free will more or less by definition.

I see free will as inherent in the creative human capacities of consciousness, imagination, problem solving, and rationality. These exist upon and emerge from the substrate of physics and chemistry, but add something peculiar, not just new rules but the ability to invent new rules.

It can be objected, that is not really free will, and the above can be framed in a deterministic, and even materialistic universe, and I would acknowledge that is a reasonable position. Please do not get me wrong, I do not suggest that the human mind has to be conferred from an outside source that in some way that transcends physics. But I do think that the advent of human rationality may have somehow escaped from physics, or perhaps introduced new rules into physics it would not have had otherwise.

Whatever could that possibly mean? Whatever could “top-down causation” possibly mean? It would appear to involve lifting yourself by your bootstraps.

Choice cannot be predicted by physical law.

It’s not about quantification. Math is more than quantification or symbology. It’s about precision.

N_T is not split into X and Y.

First off, I never claim that formal mathematics cannot be expressed in ordinary language. Mathematics is not mathematical symbology. A formalism can be written using English words, the point is that the core mathematics is preserved. Calling a map by \mapsto or writing it in words as “an object that takes an input and generates an output” does not change this. Such “ordinary language” is called the meta-language in mathematics. Mathematical formalism is not turning English words into symbols.

The point is that this act of using what you call “ordinary language” (or what I would call the meta-language) in arguments in a precise fashion (despite that you have correctly identified that it is indeed possible), has not been done by many people in this thread. If this was done, I would still call this mathematics, just written in the meta-language.

Second, a semi-related point: humans, through evolution, is endowed with a certain level of intuitive understanding of logic. However, much like how humans intuitively understand how to catch a ball, but have no intuitive understanding of the physics of gravity, one can not rely on this intuition to investigate complex problems. This is where mathematical formalism has to take over from intuition and nebulous phrases.

I understand, but the problem is I can give this exact description for a computer.

Why does the computer act the way it does instead of some other way? Well you see it’s the computers own nature to choose to do that, given those inputs. It is not the inputs that cause the computer to choose A over B, it is the nature of it’s hardware, how it is wired, that makes it have that reaction to that input. In this sense, it is the computer itself that is the cause of the choice of action, it was not determined to act in this way by something else.

How so? If the agent acts as the initiator of a causal chain, and does so for certain reasons (but could have done otherwise, for other reasons)… its not caused by something else, and its not capricious.

I’m not sure that I agree with you that “choice must involve some causal process” - when a free agent makes a choice, the agent itself is that cause of that event, initiating a new causal chain. (It might help to point out explicitly that I hold to a substance view of causation: substances are the causes of events. You might be thinking of events being the cause of other events.) So, the agent is the cause of the choice. The agent also is the cause of “the agent’s causing the choice”, but there’s no regress - “the agent’s causing the choice” isn’t really a distinct event from the choice itself. And there’s no circularity either - the agent (a substance) is obviously distinct from the choice (an event).

You ask what is going on “inside” the agent to causally explain why this choice is made, but in my view this is a category error. The agent is an irreducible entity and its free will actions are the exercises of irreducible causal powers - i.e. for human free will my view entails either some kind of hylemorphism or substance dualism, where the human person is a single, unified entity with causal powers that cannot be attributed merely to the molecules that make up the neurons that make up the brain.

Then I will say it another way, the statement, “I choose to love you enough to agree with you.” can never be precise. Feelings/choices/beliefs are relative and change constantly, ambiguously, without precision or reason. I understand that the discussions here tend to sway to the scientific side, and I applaud taking a scientific approach to theological questions, but it feels at times that you’re using a thermometer to measure the color of a rainbow.

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