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Is this a sound argument?

Free will is a cause that is neither determinism nor stochastic. Causes are either deterministic or stochastic. Free will is an incoherent entity

All incoherent entities do not exist Free will is an incoherent entity Free will does not exist

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    "Causes are either deterministic or stochastic." Citation needed (and definitions for that matter - providing a precise definition of "free will" in particular is a nontrivial task). – Noah Schweber Apr 10 at 19:55
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    It is a valid argument, but its second premise is false, causes may well be mixed. A bigger problem is the "cause". As phrased, it seems to presume a naive notion of causality that leads to the fallacy of the single cause. The folk idea of causes as individual "pushers" is not supported by modern science. How causality is understood would have to be flashed out, and the argument rephrased considerably to make something out of it. But, in the end, some form of dichotomy will still be needed, and beg the question against free will. – Conifold Apr 10 at 20:28
  • To clarify the first sentence of Conifold's comment: an argument is valid if the conclusion follows logically from the premises. But validity has nothing to do with the truth of those premises themselves! – Noah Schweber Apr 11 at 22:48
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No, at least with reasonable definitions. Here's the problem:

Causes are either deterministic or stochastic.

Here are my definitions.

  • Determinism is the notion that every specific effect has a sufficient antecedent cause
  • Stochasticism is the notion that events are fundamentally unpredictable (what this means exactly can be discussed, but this is the rough idea)

This is in my estimation the core of your argument. The problem is that it's a false dilemma. Here's a simple example of another category.

Suppose you have a universe. In this universe you have a box that has a display and a button. Each time you push the button, the display indicates a number from 0 to 9. Suppose that the number that is displayed is independent of the state of the universe at the time. This is perfectly coherent and, by the definition above, it means our universe is not deterministic.

Suppose further that each time you push the button, the number it displays is the next digit in the decimal expansion of 1/phi (due to a law of the universe that it behave this way; i.e., let's ignore the randomness essay here and presume it's not just "luck"). This itself is both coherent and still consistent with the box being indeterministic. But as it's fairly easy to calculate the decimal expansion of 1/phi, this would not be stochastic.

If you agree with me that this box is neither deterministic, nor stochastic, nor incoherent, then that must mean there's a fourth option. So when you say that free will isn't deterministic, nor stochastic, but conclude that it's incoherent, then your argument does not follow because there are other options (at least the one).

Note that the definition of free will per se doesn't come into play here, just this core.

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  • When you say "independent of the state of the universe", do you mean independent of the present state, or independent of the entire physical past (or perhaps the past light cone in relativity) as well? If the latter it still seems deterministic to me, since it's following a deterministic rule where the current digit displayed follows from the past sequence of digits displayed, each of which was a physical event in the universe. – Hypnosifl Apr 11 at 6:38
  • @Hypnosifl "do you mean independent of ..." Independent of antecedent states. "still seems deterministic to me" ...not to me, because there's a causal asymmetry. But, okay, let's roll with this. Let's say number-of-presses is a state, and picking the next digit of a specific number means this is deterministic. So let's just change the number; instead of it being 1/phi, it's a specific uncomputable number. By the same logic, this, too, would be deterministic. But by definition it is fundamentally unpredictable. So you still wind up with a third option; both deterministic and stochastic. – H Walters Apr 11 at 13:05
  • Good point, if you allow rules using arbitrary reals, including "random reals" with no finite program to generate them (or even finite programs on some oracle machine generated from some countable series of Turing jumps from a Turing machine, perhaps), the distinction between a deterministic universe and a stochastic universe seems to disappear, or perhaps one could say it's a matter of philosophical interpretation. But it's not exactly a "third option" either. – Hypnosifl Apr 11 at 18:23
  • Thanks, cool example. Made me think about the scope of the state of the universe and observability... Im tempted to say that only observability matters but I feel like that is inviting error. Maybe I need to better define what's meant by a cause too. We observe events. Some we associate together such that... oh gosh this is tough. Stuff happens. Sometimes we pretend the later are linked with the earlier by varying likelihoods. Free will is not this. What is free will meant to be?! :S :) – kungfuhobbit Apr 11 at 22:40
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“Free will is a cause that is neither deterministic nor stochastic.” Although this notion is somewhat common, I would argue that this distincion (often interpreted as exclusive classification of causes) is incompatible with what we observe:

Yes, there are phenomena that are (as far as we know) fundamentally stochastic, most often associated with subatomic/“quantum” scales. And there are systems we can describe sufficiently accurate so that we view their behavior as “deterministic”, like macroscopical mechanical systems. For some, we may even prove that stochastic effects in the above sense are irrelevant (i.e. cancelled out by a system's stable behavior).

But as systems get more complex, this distinction rapidly loses its meaning:

Just observing a rather trivial system like multiple bodies driven only by their gravitational interaction over long times, yields a system where outcome depends on initial conditions at a scale below the fundamental measurability (→uncertainty relation).

Another example may be fluid dynamics, where we have to rely on a stochastic description (and often heuristic models) to describe the macroscopic behavior, while assuming underlying deterministic behavoir. But again, due to the (in a mathematical sense) unstable behavior of the system it is quite clear that ultimately, fundamentally stochastic effects contribute to the concrete pattern of flow at a certain time.

Hence, causes will be either deterministic or stochastic only for systems of very low complexity. Given the vast variety of real systems where we observe stochastic causes contributing to locally deterministic behavior, I find it highly arbitrary to choose to exclude free will, i.e. the behavior of brains, from this logic and invent something different altogether (“free will”) instead. Brains are certainly very complex systems, where deterministic effects like simple impulse conduction as well as unstable (hence potentially stochastic) effects like decision-making are omnipresent.

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