Is Determinism A Special Case Of Randomness?

by [anonymous]1 min read4th May 201588 comments

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I was trying to reconcile the fact that in a deterministic universe there could be life with free will, but I am going full circle now and am starting to think that everything is really random, if not I don't see how there could be free will in a deterministic universe.

If mathematicians measure randomness with probability, then there must be some things that have a 100% occurrence probability (in the current universe above atomic levels I presume), which now I see as special cases of randomness rather than opposites to randomness, and these lead us to think that there is determinism.

I think we may have this cognitive bias (deterministic views of reality) because it is extremely helpful to use these 100% probability occurrence things to model the universe rationally, learn, and to predict the future, but it is not the whole story or at least a complete description of reality.

What do you think?

EDIT 1: Thank you all for the comments below. I recognize I am naive in this topic.

Although I am not convinced yet, I think my possible argumentative error is:

P1: I observe free will in the behavior of living things.

P2: Deterministic physical mechanical processes don't permit free will.

C: Therefore physics must include random processes.

I think I only see a solution of free will in randomness, but maybe there are other solutions ( I will read the Free Will Sequence here on LW!)

EDIT 2: After reading some articles of the Free Will Sequence I realize the problem of investing energy around free will questions if free will is just a mistake in our thinking process.

It is something like why ask about time travel if time doesn't exist? or, why explore the mechanics of randomness vs determinism if randomness doesn't exist and thus the dichotomy "randomness vs determinism" doesn't exist in the first place? 

 

 

 

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Alternatively randomness could be a special case of determinism. Imagine a deterministic universe that branches into two different universes each time someone in the universe flips a coin. In one branch the coin lands head and the other it lands tails. To the people living inside the universe it would appear like a fundamentally random process, but in fact the universe is entirely deterministic.

In any case this doesn't have anything to do with free will. If you let a random number generator make your decisions for you, that's not free will.

3estimator6yAny "fundamentally" random process can be seen as a deterministic process. Since it will have a single outcome, we can set it as the only outcome possible, and yield a fully deterministic process which is indistinguishable from the original, random, process. In other words, we can say that a fundamentally random process is a deterministic process which relies on hidden variables which are unreachable for us.
0Houshalter6yYes but what determines the state of the hidden variables?
0estimator6yWe can't say. They are hidden; all our hypotheses about them would be unfalsifiable. Moreover, the fundamentally random and hidden variables viewpoints are indistinguishable by experiment, so choosing one is a matter of convenience, not absolute truth.
0Houshalter6yI'm not asking if the hypothesis is testable which is a different matter. Obviously it's impossible to distinguish pseudo-randomness from randomness, if it's done properly. But what you are suggesting is that even if it is random, it can still be thought of as a deterministic process with seemingly random but fixed hidden variables. I'm asking how that is different than true randomness. A hidden variable in a causal graph, that itself has no cause, is for all intents and purposes "random". In fact that's probably how I would formally define randomness if I had to. If some simple deterministic algorithm is setting all these hidden variables that's a different hypothesis. But if they have no cause, and you have all these variables which can have totally arbitrary values for no reason, then that's randomness. I don't really think it matters which is why I don't care that it's a testable hypothesis. But for some people like OP believe it's really important which is how this issue came up.
0estimator6yHidden variables aren't random; they are fixed, but unknown. Maybe we are using different definitions of randomness here. Yet I can't see why you are comfortable with a hidden deterministic algorithm setting hidden variables; wouldn't such an algorithm itself be random by your definition? There is no point in arguing, which of the hypotheses producing the same results is "really true". We should just pick the simplest one according to the Occam razor. But the simplest hypothesis isn't just the one which involves less objects (like hidden variables), but rather, the one for which our theories fit with minimal stretch. If you agree with the interpretation of probabilities as a measure of uncertainty, then it's simpler to use the fundamentally random processes interpretation which fits into this framework -- the one with hidden variables.
0Houshalter6yI just don't see any distinction between a hidden variable and a random variable. That it's fixed has nothing to do with anything. It's the difference between having a random number generator inside your program, or having a deterministic program which is called with a bunch of randomly generated arguments. Either way you still have to ask the question of where the numbers are coming from, and if they are truly random. If they are the result of some simple deterministic algorithm. If we could, at least in principle, predict it with total accuracy, or if it's impossible to predict no matter how much computational power we have. And I do think there is a practical consequence of it. As you mention, Occam's razor favor's simpler hypotheses. If your hypothesis has a huge number of variables that can have arbitrary values, it has far more complexity than a hypothesis that allows for a random number generator.
0[anonymous]6yWould you agree then that probability doesn't exist because it is just the product of us not reaching those hidden variables, but if we could reach them then everything would be certain? If so, t seems that probability, like free will and time, is also an illusion.
4[anonymous]6yProbability is in the mind. [http://lesswrong.com/lw/oj/probability_is_in_the_mind/]
-2TheAncientGeek6yOr maybe not [http://lesswrong.com/lw/oj/probability_is_in_the_mind/90wd]
0[anonymous]6yQuantum uncertainty and indeterminism? I've never heard these terms, but this weekend at Yosemite I met a guy from Sweden who had come here to get his PhD in physics, and he made some comment along the lines of the movement of waterfalls not being predictable/explainable by physics... so is a waterfall an example of quantum uncertainty or indeterminism? If not, what are some examples?
0TheAncientGeek6yThe typical examples are things like radioactive decay, although there are many others. And, may I repeat, it is a myth that the some barrier prevents quantum indetermimism having macroscopic consequences. If it did, particle physics could not be an experimental science.
2estimator6yNote that fundamentally random processes viewpoint and hidden variables viewpoint are equivalent -- they produce the same predictions -- so choosing one is the matter of convenience. And hidden variables viewpoint is convenient exactly because it allows to think that probabilities is in the mind [http://lesswrong.com/lw/oj/probability_is_in_the_mind/], that is, probabilities are nothing but a measure of uncertainty. It eliminates the only special case -- fundamentally random processes, thus allowing us to apply our uncertainty-measure concept everywhere. Fundamentally random processes are processes which rely on parameters for which we (fundamentally) can't reduce our uncertainty, and that's it. So yes, I would agree.
1[anonymous]6yThx for the complete answer I like your thinking process! I agree that they are equivalent in that they denote a lack of understanding of the underlying mechanics, but in the case of randomness, even though it could be an illusion, I still subjectively (naive view) favor the existence of randomness (and probability) in the base physical mechanics because I fail to see a connection between certainty and our brain's apparent non-bound decision making. Nevertheless I am open to the option that physics is only deterministic and that such a process may recreate our consciousness (I have to think more about that though).
1estimator6yAs others already mentioned, introducing fundamental randomness doesn't help in resolving free will problem -- whether or not physical processes are truly random, you have no control over them. You may want to read LW free will sequence [http://wiki.lesswrong.com/wiki/Free_will].
0TheAncientGeek6yOpinions vary. Naturalistic libertarianism is a thing.
-1TheAncientGeek6yWhich is why discussions of fundamental indetermimism in QM always involve hidden variables. Proponents of fundamental indetermimism are invoking Occams razor. OTOH, you can never have certain evidence that a given law is deterministic, only that it holds in t99%, .or 99.9%of cases.
0Transfuturist6yThat doesn't get rid of randomness, it pushes it into the observer.
0[anonymous]6yMy connection between randomness and free will is that I think free will wouldn't be possible in a deterministic system since everything happens as a consequence of previous events rather than as a consequence decision making. I think that in the two branch universes above it is still random on which side the heads or tails would fall therefore it still seems random together or forked.
4Houshalter6yI don't understand the distinction between "consequence of previous events" and "consequence of decision making". If your decisions aren't a consequence of previous events, then they are just meaningless randomness. Your decisions should ideally be as correlated as possible with your values and with the information you have. The more random your actions, the less likely they are to result in anything desirable. And randomness is very distinct from the old concept of free will. Randomness is not your will. You have no control over it. Rather it controls you.
0[anonymous]6y* Consequence of previous events: when things pass from state to state as a consequence of a causal chain of actions that are not initiated or continued by a living decision maker that purposely provoked them. * Consequence of decision making: when a living being acted on a chain of physical events and modified them according to its will and therefore the pattern of the sequence is not consistent with random mechanical events. I agree with the idea that living things make decision based on the observation of reality and must not initiate actions out of nowhere. When I mention free will on my OP I am not referring to the ideological concept,but just my personal opinion that decision making in our brains must obey to some randomness in order to be free of regular certainty in physics. I don't think that randomness is in our brains,I think there must be randomness in the mechanics of physics.
2Kindly6yWhat makes you think that decision making in our brains is free of "regular certainty in physics"? Deterministic systems such as weather patterns can be unpredictable enough. To be fair, if there's some butterfly-effect nonsense going on where the exact position of a single neuron ends up determining your decision, that's not too different from randomness in the mechanics of physics. But I hope that when I make important decisions, the outcome is stable enough that it wouldn't be influenced by either of those.
1Houshalter6yPeople are not as random as you may think they are. You can test your own randomness here [http://www.loper-os.org/bad-at-entropy/manmach.html]. There is no need for true randomness to create random seeming behavior. Famous example is the weather. Even totally deterministic simulations of the weather are chaotic. Even slight changes to the initial conditions will result in totally different outcomes. Or in cryptography hashing functions, which generate random and irreversible strings from an input. There are a number of examples [https://www.wolframscience.com/nksonline/page-129#previous] of this covered in the book A New Kind of Science, but you can only view a few pages online for free without using incognito mode.
0[anonymous]6yI think my possible argumentative error is: P1: I observe free will in the behavior of living things. P2: Deterministic physical mechanical processes don't permit free will. C: Therefore physics must include random processes. I think I only see a solution of free will in randomness, but maybe there are other solutions ( I will read the Free Will Sequence here on LW!)
0Houshalter6yP1 is wrong because it's impossible to observe free will. If free will equals randomness, and randomness is indistinguishable from non randomness for all practical purposes, then it's impossible to know if you live in a universe with free will or not. However defining free will as randomness is really weird, which is what I tried to argue above. If randomness is determining your actions, that's not your will, and the result is meaningless. You don't gain any useful information by watching a coin flip.
1[anonymous]6yI agree, both P1 and P2 are false because free will is unobservable to begin with. This post and the exchanges with you and others have helped me advance my thinking a lot about these issues. I am reading the Free Will Sequence [http://wiki.lesswrong.com/wiki/Free_will] too.
-1TheAncientGeek6yHow can you know the best way of fulfilling your values if you don't experiment? Is unpredictability never a value in itself?
0Houshalter6yPeople are horrible at being random even when they try. Test yourself here: http://www.loper-os.org/bad-at-entropy/manmach.html [http://www.loper-os.org/bad-at-entropy/manmach.html]
4dxu6yWhat is decision-making but a physical process occurring in your brain? Consider reading Thou Art Physics [http://lesswrong.com/lw/r0/thou_art_physics/].
0TheAncientGeek6ySince when was "physical" a synonym for "deterministic"
2Username6yName one non-deterministic macroscopic process that affects objects on the scale of neurons.
-2TheAncientGeek6yAny process critically dependent on its starting conditions = chaos. Any microscopic event triggered by a device capable of measuring quantum levels events, eg a bomb hooked up to a geiger counter. Typical stochastic devices, such as dice.
3dxu6yThe brain doesn't do this, so how is this relevant to free will? Dice are deterministic. Chaotic behavior != indeterminism.
-3TheAncientGeek6yYou don't know that, since no one does. You don't know that either. A number of random number generators have enough sensitivity to initial conditions to reach the quantum level. Confusing phrased. Classical chaos could exist in a deterministic universe, but it can also exist in an indeterministic universe where classical behaviour is a high level approximation. In that kind of universe, classical chaos acts ad a natural amplifier.
0[anonymous]6yI assume they are using the "physics is deterministic" assumption when they tell me our thought process is a physical process. My OP above questions this and I speculate that there is randomness in base physics (quantum or somewhere else, maybe at macro level too when systems cross certain levels of complexity).
0TheAncientGeek6ySome people seem to think that incompatibilist free will is definitionally the ability to transcend physics, although voluntarists don't usually define it that way. It may be a confusions arising from the fact that if physics is determimistic, an override would be needed to get incompatibilist FW.
0[anonymous]6yEliezer wrote: I agree that decision making is a physical process occurring in our brain, but I think that by calling it "physical" we are also implying that there is certainty in the mechanics of that process and that its just that we can't yet reach it or explain it. What I was trying to say when I wrote "determinism is a special case of randomness" is that there must be non-certain processes in physics and that would explain, in my mind, why we can make arbitrary decisions that seem to change the determinate course of physical processes.
3dxu6yAnd what makes you think our decisions are "arbitrary", and in need of explanation?
1[anonymous]6yThx for the good question! I think that my observation of the existence arbitrary decisions is that as living things we interrupt randomness and cause things to behave in ways that are not the product of free physical mechanics, but the product of what is going on in our minds. Here we come back to the "what goes on in our minds is also the product of physical processes" argument, and I agree, only that it seems not determined, but "decided". The fact that I use the word "seems" confirms that it might be an illusion too.
0TheAncientGeek6yPresumably, he means we can make decisions in the absence of obvious decision theoretic procedures, or strongly weighted evidence, rather than getting stuck like Burridans Ass.
3dxu6yRight, but that's not a reason to question determinism.
0TheAncientGeek6yNo, its a reason to think tthat not all decision making is prima facie deterministic. The evidence for indetermimism is something else.
3dxu6yNot obviously deterministic, no. But deterministic at the bottom level? Almost certainly. Please don't bring up QM. Let's leave the physics to the physicists. (Also, that wasn't my original point. Regardless of whether determinism actually holds, attacking determinism to support naive free will is poorly motivated.)
-1TheAncientGeek6yThe bottom level is quantum. I am a physicist , and my views on free will arent naive.
2dxu6yYou're a physicist? In what field? EDIT: Also, I was calling the OP's view of free will naive, not yours.
2[anonymous]6yI agree my view is naive, but from the standpoint of knowledge of the matter since I am not a scientist and I am new to rationality overall. I am not naive in the sense that I support free will just for the sake of it, for political or idealistic reasons. Personally I prefer the truth rather than a "feel good" moment. I am very open to learn and discuss these issues and I hope LessWrong is a good place for this.
3dxu6yNo problem! Also, just in case you didn't know and thought I was criticizing you for not knowing enough: "naive" has a special meaning around here; it basically means a viewpoint based on an understanding that's no longer supported by the latest developments. For instance, many of Aristotle's views are now considered naive, although they certainly weren't back in his day!
0[anonymous]6yIf the bottom level is quantum, is there a space for randomness or non-causal mechanical processes?
-1TheAncientGeek6yThats subjective randomness being a special case of objective determinism.
1[anonymous]6yThank you, great article. I don't consider myself as proposing the existence of free will as an ideological issue, but I am having trouble connecting a causal mechanical system only (that I would call deterministic). I don't see it makes sense that arbitrary decision making exists (or even us being conscious of this conversation) if it was possible without any effort just by letting events run their course.
1shminux6yEmergent phenomena are like that. You can track them down, but not up. For example, consider a complicated piece of software. Sometimes it seems to act on its own, or hate you, or something. I swear that one Linux distro I tried had a thing against me personally. And this behavior is usually unintended by the programmers. Often it even appears non-deterministic and hard to duplicate. However, one can usually trace the weird behavior to a bunch of "bugs", rather than attribute agency/free will to a piece of code. But it is nearly impossible to predict the weirdness beforehand. Stuff just happens. Apparently even the term "bug" came about because any non-trivial piece of technology appeared to have gremlins inside just trying to mess with you. Given that humans are probably just glorified computers evolved out of meat, it seems unsurprising that we have developed a mind of our own.
0[anonymous]6yI think that I have two possible errors in my argument: 1. Deterministic processes do not permit free thinking. 2. Free thinking needs randomness in its underlying process. I agree with you that behavior in complex systems seems non-deterministic even though the underlying processes are deterministic (like the software example you give above). So our perception of consciousness and even the dichotomy "randomness vs certainty" could be a mental illusion.
1shminux6yI think your error is in not being able to define what free will is. My go to approach to "obvious" and "intuitive" statements is to ask to define the opposite. For example, how do you think it feels to have no free will? Can you give a few concrete examples of "not having free will"?
0TheAncientGeek6yThose are two different questions.
0[anonymous]6yI agree that not to focus on free will first may be a mistake in itself and it makes me ask questions that are irrelevant from the get go. Just in case you last question is not rhetorical: In a potentially mistaken model where free will is considered an objective reality then not having free will does not have any feelings and an example is flowing water in a river, it doesn't think feel, or decide, it just flown governed by gravity, etc. But again, the above answer is useless if free will is an illusion. I will try your method of defining the opposite first!
1shminux6yMy question was not rhetorical. But it was unclear. Water indeed doesn't feel, as far as we know. What would it feel like FOR YOU to not have free will? Would irresistible voices in your head telling you what to do give you that feeling? Would observing your arm flailing about without your input? Would watching yourself reach for your X-Box despite knowing that you should study for a test? Or knowing that someone else can predict your actions and maybe even thoughts before you aware of having them? Think about all these very different no-free-will cases and tell me what not having free will means for you. Not for water.
0[anonymous]6yNot to have free will would feel like when I am not conscious of the fact that free will exists. I would actually operate the same way as usual. Free will is just an idea that appears when I think about determinism and randomness in the universe. Also, I think about free will when deconstructing the universe and trying to understand how it works. This is because as a way to compare "dead" physical mechanics to "non-dead" I use as a reference the supposed free will I have in my mind (or the feeling of free will). Summary: Free will is the name I designate to a group of activities in my mind that result in a decision. But it's not a thing or something that actually exists anywhere, but in my imagination!
0shminux6ySo, you don't think there is any situation where you would feel like your free will has disappeared? None of the cases I described click?
0[anonymous]6yIn all those cases I would feel frustration, anger, and a sense of claustrophobia I think. Maybe a deep depression.

Could you elaborate on what you mean by "special case of randomness"? As far as I can tell, you don't ever really explain this within the post, from which I infer you probably think it obvious enough to not be worth explicitly saying. Whenever an author thinks this, however, it is usually untrue, and in fact I found (and still find) whatever you were trying to say completely non-obvious. I think it would greatly help discussion if you were to put a brief explanation of your idea within the post; that way readers won't be left floundering.

0[anonymous]6yI think I am confusing some terms above (randomness, probability, certainty, etc.) I will rethink and try to explain it by editing.

Why do you want to rescue free will?

0TheAncientGeek6yRescue it from what?
1polymathwannabe6yFrom the reduction of human brains to subatomic particles. Vitalism is a hard beast to kill.
-1TheAncientGeek6yWhy does reduction imply determinism? What does vitalism have to do with free will?
1polymathwannabe6yExplaining mental stuff in terms of non-mental stuff implies that we are atoms and nothing more, and are under the same laws that govern all physical events, so I am no more free to choose to close my eyes than a photon is free to bounce off a half-mirror. Having reduced mental stuff to non-mental stuff (atoms and interactions), the only way to preserve free will is to postulate the existence of some mental fundamental essence which inanimate things don't have, and that is a form of vitalism.
-1TheAncientGeek6yUnder physical laws doesn't mean under deterministic physical laws. Who told you that? Naturalustic libertarians reduce free will to specific combinations of physical determinism and indetermimism.
1polymathwannabe6yYes, they do that. They're deceiving themselves.
0TheAncientGeek6yIs that a fact?
0[anonymous]6yI don't have an attachment to free will I think its a mental construct like time. What I think is that we make decisions and we seem to arbitrarily change the course of things, even if they are physical processes, I think there must be a component of randomness in physics that enables this.

If mathematicians measure randomness with probability, then there must be some things that have a 100% occurrence probability

Er... what? I think you need to state your train of thought in more detail; at the moment it doesn't seem precise enough to engage with.

0[anonymous]6yYes, I think I am confusing randomness, with probability and certainty. I will try to clarify above by editing my post.

It is something like why ask about time travel if time doesn't exist? or, why explore the mechanics of randomness vs determinism if randomness doesn't exist and thus the dichotomy "randomness vs determinism" doesn't exist in the first place?

The conceptual dichotomy still exists, even if reality sides with one horn of the dilemma.

It's important to realise that you are not dealing with a dissolution here. A dissolution roughly means that an "A or B" questionis conceptually invalid. Empirically settling an A-or-B isnt a dissolution, a... (read more)

0[anonymous]6yI agree, I need to understand the concept of dissolution more.

Upvoted for changing your mind.

You are kinda using words in a wonky way. I pattern matched to a plausible set of alternate meanings you might be using. While it doens't have formal connection to what you wrote I am still pursuing that avenue as I think that will more closely match the psychological process behind them better.

When you have that kind of division you have probably made random processes to happen in multitude of ways but each spesific way specified. In contrast if you have system that is underspesified it might behave in any way but not because of some positive statement th... (read more)

-1TheAncientGeek6yWho told you that?
0Slider6yI do not have any other authority to refer to than myself. Feel free to argue to the contrary if the thought doesn't seem obvious.

If you define randomness as less than100% determinism, that doesn't prove anything about the existence of indetermimism, since everything could still be 100% determined. Otoh, thinking that way helpfully gets away from the stumbling block that determinism and indetermimism are metaphysical opposites.

It might be helpful to check out David Bohms "Causality and Chance in Modern Physics" for an account of how the twocan interleave. Among many others.

[-][anonymous]6y 0

I think this article is useful when thinking about determinism and free will:

Suppose to be able to do an experiment where we can put a person in exactly the same mental situation (with the same memories, values, character, mood ...) and suppose we repeat the experiment many times, always with the same initial conditions. What would observe? There are two extreme possibilities: the first is that we see that the person will decide entirely at random. In this case the results will be just governed by chance. Half the time he will make a choice, the other ha

... (read more)
-1TheAncientGeek6yIncomparibilist free will means independence from external circumstances, not internal ones.
0[anonymous]6yOh! Okay. I mentioned this quote to my high school religion teacher, and he seemed to think free will was determined by our internal mind-state, and that our choices would result the same every time, so I guess he probably believed in incompatibilist free will, and that fits with what you're saying... although it doesn't sound very free to me. So how would you describe compatibilist free will then? Is that the belief that our decisions are random, that based on the external and internal circumstances, they could still go either way?
-1TheAncientGeek6yWhy would you want to be free from your own brain state? Compatibilitism: No, See wikipedia,
1[anonymous]6yFrom wikipedia: I'm reading, and having a hard time seeing the difference between compatibilism and hard determinism. Isn't every action done out of some determined motive? Even when we choose which motive to act on, isn't that choice motivated by some other motive? Or is that the difference, that the compatibilist would say the choice to act on a motive is free and not based on another internal motive? I guess it would help me if you could write something that briefly describes all three positions like this (not saying my descriptions are accurate, just an example): Incompatibilist free will = Belief that we'd always choose the same thing, dependent on internal states and independent of external circumstances, and this is freedom Compatibilist free will = Belief that we could choose differently, even with the same internal and external circumstances, and this is freedom Hard determinism = Belief that we'd always choose the same thing, based on the same internal and external circumstances, and this is not freedom
-1TheAncientGeek6yCompatibilism=free will could exist even if determinism is true. Incompatibilism=free will could not exist if determinism is true Hard determinism=incompatibilism+determinism, ie no free will. Compatibilists don't generally deny that actions have motives, they deny that your own motives are a constraint on your own freedom. They typically define freedom as being able to do what you want, irrespective of whether what you want is determined. How aware are we of our real motives? What's the hard evidence for that?
1[anonymous]6yOh. So it really is just a definition thing? I thought the two sides might actually have different beliefs about the outcome of that original thought experiment. So compatibilists think we do have "real motives", but since we're not so aware of them, we might as well keep calling our decision-making process free will. And hard determinists acknowledge the same "real motives" but think that since there are motives driving our decisions that we aren't aware of, we shouldn't call our decision-making process free will. Is this basically the difference between the two?
0TheAncientGeek6yCompatibilism and incompatibilism have different definitions, and various mechanisms have been proposed to fulfill them, which is why I have been using phrases like generally and typically. A incompatibilist libertarian ... someone who takes the could-have-done -otherwise view of free will.... should view the thought experiment as a bit of a have-you-stopped-beating-your-wife question. It funnels them into thinking that if they could have done otherwise under a set of circumstances, they would have done something less connected with their values and thought process. The wise libertarian would want to interpret CHDO on the donut principle, as meaning the ability to have done differently under the same external circumstances but not necessarily given the same brain state. The fact value divide makes it not implausible that thought processes could have some independence from events, although an appropriate causal mechanism would be needed too. Compatibilism is more about definitions than mechanisms. For a compatibilist, you are free if you can do what you want, ie, if no one is impeding you, ie the legal fiction of acting of your in free will. That doesn't demand much in the way of a special mechanism, and so is compatible with determinism. Because compatibilists define free will differently, people talk about "incompatibilist fee will". The problem with intuitive, folk models of decision making is that they reflect the individuals beliefs about FW, so they are unit independent evidence.