Turing's halting problem states, roughly, that there is no computer program which takes as input another computer program and correctly determines what that program will output. It is not a matter of perfect knowledge, measurement error, nondeterminism, randomness, or observational influence. There simply cannot be such a universal computer program which works (or even does something half-sensible) for all (or even most) inputs. In short, it can't exist because the world explodes when you feed the prediction program to itself as its own input.

So computer programs have a no-prediction-machines theorem. So can we say that computer programs (which are well-defined, mechanistic, deterministic) have free will?

If the machine had perfect knowledge of your brain, it would know your knowledge of the machine would affect the outcome, but it would also know the point at which you would cease to consider that as a factor and act anyway becasue of the perfect knowledge of your brain. As in the rock paper scissors example, the human player would know that the machine could predict his move. Eventually he would just throw something, not based on a logical progression or strategy, but on some other criteria. The machine would be able to predict this without putting itself in an infinite loop. Right?

I feel like you're fishing here. I've read the three posts thus far that comprise this argument, as well as your essay on Ebonmusings "The Ghost in the Machine" and throughout both, your agruments sound like they should lead to determanism as the natural conlusion. However, when it comes time to actually make your conclusion, you shift gears, and attempt to say that just because things are predictable doesn't mean they're predicable.

I think the discrepancy here is the confusion of the word "caused" with the word "predictable", the outcome of a fair dice roll is caused, but for the average human it is unpredictable as predicting an outcome means assesing too many variables (the strength of the throw, any wind, the at what angle the table will cause the dice to bounce etc.) at once. Although it is theoretically possible to construct a machine that can account for every single variable in the human psyche, the act of finding the variables and predicting them, adds another variable to the human psyche that the person uses when making the choice and so the machine finds that and causes yet another variable and so on ad infinitum.

It doesn't change the outcome for a computer, so why assume it will change the outcome for us?

Well, for one thing, computers are specifically built to be insensitive to these kinds of minor alterations. They are digital devices, and any influence on them below their activation threshold will not trigger a change in their output.

But the human brain is definitely an analog machine. Rather than being designed to be impervious to minor influences, it uses them opportunistically as input - just like this circuit designed by an evolutionary algorithm, which appears to exploit subtle environmental effects like the minor currents induced by nearby logic cells. If something of this nature were scaled up to the complexity of the human brain, who's to say that it too wouldn't become chaotic and unpredictable?

But still, the biggest aspect is probably the complexity of the brain. I don't know the numbers exactly, but I know that the number of connections and neurons are several orders of magnitude. Also, standard computers don't run like human brains. I believe they HAVE built extremely primitive ones that do, but your standard computer does operate by simple signals. We still aren't entirely sure why a series of signals suddenly becomes the spoken word "blue" or the sensation "pain". Computer follow very exact rules, even ones with some form of learning capability. They don't learn or think anything like we do.

The PM could be generalized to a prediction machine. Each prediction of the future has a chance of changing that future. But some have a less chance than others. Say the PM predicts an earthquake. There is little that we can do to change that so there is a good chance it will happen. However, if it predicts an assassination, then there is a good chance it will not happen (if it is publicized.)

I think we should compare people to computers in this. For example, if I told a computer it would overheat in 10 minutes (due to the PR) and if the computer knew that overheat meant it should ramp up the cooling fan, it may turn on its fan and change the future. But does the computer have free will because it violated predictability?

Mormon; I think Adam's point here is that he accepts the part of determinism that says that stimuli-->outcome, but rejects the idea that that HAS to mean we are predictable machines, which is something dualists have imposed upon determinism. That's the feeling I get, anyway.

However I don't see why it is productive to introduce a distinction between determinism and... well, you don't give it a name, but describe it as the "the reasons for our behavior have to be determined by antecedent causes." That seems to be a definition of determinism. Why do you eschew the label of determinism, and yet call yourself a compatibilist, when the embrace of determinism is a defining feature of compatibilism? Is this an idiosyncratic move on your part, or do other philosophers (Dennet?) claim to be compatibilists while avoiding the label of "determinism"?