Actually free from what? What is it you think “free will” is free from?
Sure it does. What is different about the computer-controlled car? How is it not choosing to go left or right, to get around some obstacle in it’s path?
Does it? What would guide your choice? Presumably it’s divorced from causation, because if it has a cause, only one option would be available. Presumably it isn’t chance, like nuclear decay, because chance isn’t choice. But what’s the third option?
But what is the meaning of “actually and truly available”?
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I walk into an ice cream shop, look at the sign, and think to myself, whoa, that is a lot of flavors. My brain is scanned by an advanced alien research craft and a snapshot taken of the exact electrical and chemical state. How do they predict my choice?
Now a electrical state could be in principle be classically predicted from capacitance, resistance, and inductance of my brain circuits, but I doubt anyone would make the case that is sufficient to predict my future reasoning. “Something different or play it safe… Wow, this is expensive, what would a bucket cost? Check out that tattoo. Getting to the front of the line…pressure’s on…”
The state of the universe must then include non-physical entities.
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In this formulation, the definition of free will does not require one to know what the nature of C is. The point is that if there is anything, anything at all, that humans can do that affects the time evolution of the universe, we label that as “free will”. This is a formulation that just shows that we are open to the existence of this “third source”, whatever it is. Again, I do not believe that there is such a “third source”, but if there is, then C_T[X(t)] \neq N_T[X(t)]. A study of the nature of this “third source” can wait after its detection.
Yes, and personally I would think that this is the case.
As @swamidass said, this is a completely different issue than the idea that “free will” cannot be formulated in a coherent way that respects what we know about the physics of the universe.
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I don’t think that’s formulated in a coherent way. “C” is just an undefined term, and it’s in the definition of the term that any real definition of free will would be located. Could there logically be a thing C that’s separate from N? How could it conceivably work? If by prior causation, that’s not free will. If by spontaneous effect, that’s not free will either, just caprice. If there’s another possibility, that would be a coherent definition of free will, but absent such a possibility, there is none.
C_T is properly formulated mathematically; it’s defined mathematically as an evolution operator that might or might nor be distinct from N_T.
The point of such mathematical formulation is that yes, there could logically be a thing C_T that might be separate from N_T. Whether it actually exists or not is what’s questioned.
Again, the existence of C_T can be detected through whether C_T[X(t)] \neq N_T[X(t)]. The detection of such existence does not preclude that we know how it actually works, the same way that we can detect the effects of gravity before knowing how it works. This is a formulation for the existence of a “third source”, not the formulation for the mechanical workings of such a source.
C_T is not necessarily “free will”. It is only “free will” if C_T[X(t)] \neq N_T[X(t)]; otherwise, it is exactly as you said, generated by prior causation.
Again, this is a formulation for the ability of physics to be coherent with the existence of this possibility, not for the workings of such a possibility itself.
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I think we have different definitions of “coherent”, and possibly different understandings of what “free will” would entail. I’d say the choice must be both uncaused and non-random, regardless of whether the choice occurs within or outside the universe.
I think we understand “logically” differently too. Is e^x=0 logically valid?
That would seem to me to be necessary but not sufficient. This mathematical definition of free will seems not to fit the concept of free will.
Yes, it could be.
I am working under the assumption that there is nothing outside the universe, i.e., everything is purely physical, or if there is something that is outside the universe, it does not affect the evolution of the physical universe. In this sense, all time evolution uncaused by humans are subsumed under N_T, which is contrasted with C_T, which has the human component.
This mathematical formulation is logically valid in the usual way: it does not run afoul of any of my assumptions, which in this case is the existence of the usual time-evolution operator in physics.
Again, as I mentioned in my caveats, this is just one definition of free will, and not one that I even hold. You can of course add your own modifications to it depending on what you understand “free will” to be, as long as it is mathematically formalized properly - otherwise I don’t think it would be rigorous enough to be meaningful. One might, for example, say that this is just an operational definition of free will the same way as how one have an operational definition of life.
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I want to point out @John_Harshman, that @PdotdQ’s exposition is consistent with my less detailed understanding of @david.heddle’s appeal to “time evolution” of the universe.
That’s physics talk. I think @PdotdQ immediately understood him. You and @david.heddle were speaking different languages.
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Great. But what was he saying? Can you translate? For that matter, what is @PdotdQ saying? How would you define free will?
I think everyone can agree that free will cannot exist in a materialistic perspective.
Assuming materialism as an axiom need not give you an answer about what is really happening when we make a choice.
The basic idea behind freewill is that a person cannot be reduced to just physical interactions between whatever atoms he/she is made of.
@RonSewell was also pointing to this.
Give the above, holding or not holding to freewill seems axiomatic to me. IMO there are only two answers peopel can come to based on the evidence -
a) The experience of being persons in a body, that all humanity shares is true and hence we human beings cannot be reduced to the result of material interactions alone. ergo, free will is real.
b) There is no way to tell whether we have free will or not.
Here is my translation.
Consistent with known physical laws, even in universe that is deterministic, there can be “black box” entities that are either not reducible or not governed by physical laws, but nonetheless interact with the universe in ways that affect it. The mind might be one of those things, perhaps by one of these three ways:
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Perhaps the mind is properly supernatural, not governed by physical laws but influencing how the brain works.
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Perhaps substance dualism of the soul is true, with the soul being that black-box entity.
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Perhaps the mind is emergent in a way that enables true top down causation, and therefore is not reducible physics.
Any one of those options, and probably others, would be examples of entities that could given account of free will without violating the laws of physics. We can debate if these things are real or true, but it seems at least some of these options are logically possible. If that is the case, we have an account of free will that is coherent, even if we haven’t proven it to be true.
It should be obvious that not everyone agrees, since @PdotdQ has just defined free will in a mateialistic perspective.
Sorry, but that isn’t the basic idea at all. One doesn’t follow from the other.
c) free will is self-contradictory and can’t even be defined, whether or not one adopts a materialist perspective.
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That’s right, sort off. @PdotdQ did not say that the black bax C is materialistic, rather that it influences the material world. However, if the black box is an emergent mind with true top down causation, this is essentially materialism, but non-reductive materialism.
I believe he did say that. He said that he assumed it was materialistic.
I disagree (whether with you or @PdotdQ or both is unclear). None of your possibilities entails or allows free will.
I agree that they’re all logically possible; what I deny is that they could logically result in free will. And thus they are accounts of something and are coherent, but they aren’t accounts of free will.
Not true. There are multiple theories of free will that can happen in a deterministic universe, such as compatibilism. It is not even true that materialism = determinism.
However, if you rather have a formulated framework that is non-physicalist, or something that is explicitly supernatural, the framework I wrote still works. To wit, you can easily generalize the framework by the map
Z(Y) \colon S(t) \mapsto S(t) \times I(t),\quad X(t)\mapsto \{X(t),Y(t)\} \; ,
where Y(t) is the state of whatever supernatural/non-physicalist universe you want, and I(t) the space of any possible such states. All this does is to now allow for the non-physical to be explicitly represented in the framework.
The “natural” or “physical” time evolution, N(t), will only take as input the X(t) part and not the Y(t) part. If the true time evolution turns out to take as input both X(t) and Y(t), then there is a non-physical component to the time evolution.
This will allow for things like
You are free to come up with your own definition. As I mentioned over and over, this is just one definition of free will that I do not even hold myself. It seems that you have some idea for the requirement of “free will” that I do not share. But it is difficult for me to understand what these extra requirements are unless if you formulate it in a mathematically precise manner. You can do this and show that it is indeed incoherent through logical contradiction.
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It seems to me that CT[X(t)]≠NT[X(t) wouldn’t be possible in a materialist perspective.
As to compatibilism, it reduces freewill based choices to something similar to what a self driving vehicle would make.