Tag Archives: Consequence Argument

Free will, part 2 of (5-ish)

As we said last time “alpha is unavoidable for you” means “For every action A you could take, if you did A, alpha would (still) happen / be true”. A key concept here is a would statement, which logicians call a “counterfactual conditional”. For example, if I had written that logicians call a would statement “the cat’s meow”, you would think I was joking. The term “counterfactual” is a bit misleading because there can be would-counterfactuals with factual antecedents. For example if I had written that the Consequence Argument was formulated by Peter van Inwagen, you would have read the name Peter van Inwagen. And I did; and you did. What the would statement adds, beyond the simple statement that I did so write and you did so read, is the idea that there’s a robust connection between those things. A counterfactual is a bigger claim than the “if” from propositional logic (which logicians often symbolize with “⊃” — so A ⊃ B simply means that it’s not the case both that A is true and B is false.) Note that counterfactual antecedents and consequents (the “if…” and “would…” parts, respectively) range over processes, events (including boring events like a particular state obtaining at a particular time), and actions.

The premises of the Consequence Argument that we’ll question are (and here let’s spell out the counterfactuals contained in the shorter versions):

(2) The distant past state of the universe is such that, for every action A you could take, if you did A, that past state would still obtain.

(3) The laws of nature are such that, for every action A you could take, if you did A, those laws would still obtain.

And we won’t question premise (1) from the last post, nor the formulation of scientific determinism from which it follows, but we will take a good hard look at that formulation. It turns out not to say some of the things that we might on first glance think it says.

Laws of nature

As I mentioned last time, premise (3) is controversial among philosophers. There’s a dispute over what kind of thing the “laws of nature” are. On the view called the Best Systems Analysis, laws of nature are just a sort of summary of facts. This view is held by the most zealous fans of Occam’s Razor — or at least, that’s what I think they would claim — because it avoids treating laws of nature as a deeply separate category of facts. (Occam’s Razor says “Entities should not be multiplied without necessity.”) Terrance Tomkow has a good explanation of the Best Systems Analysis at: https://tomkow.typepad.com/tomkowcom/2013/09/the-computational-theory-of-natural-laws.html and https://tomkow.typepad.com/tomkowcom/2014/02/computation-laws-and-supervenience.html

The Best Systems Analysis has a model in Algorithmic Information Theory, for which a very crude model is a .zip file, such as you might create from a .txt document on a computer. The .zip file contains compression rules plus compressed data (and the program that reads and writes zip files, say 7zip, contains additional compression rules). The compression rules (including those in the zip-making program) are like the laws of nature, such as the mass and charge of an electron; the remaining data is like the remaining facts, such as the locations of electrons at particular times. Different programs, say 7zip vs the Windows file compressor, might make somewhat different decisions about how to divide up the totality of information in a text file into “compression rules” vs “raw data”. And of course, if you put a different text file into the zip program, you typically get output containing both different “rules” and different “raw data”. For example, if I have a text file where most lines consist of a lot of spaces, the compressor program might make a rule where one special character represents 9 consecutive spaces and another represents 3 consecutive spaces. Then a line consisting of 13 spaces can be abbreviated with 3 characters. But if the text file instead contains a lot of consecutive z’s and no consecutive spaces, the rules part of the compressed file will contain rules representing z’s instead.

It’s this last point that casts doubt on the immunity of laws of nature to human action. If human actions were distributed differently, the totality of physical facts of the universe would be different, so different “compression rules” might most-efficiently summarize the total physical information. If all that laws of nature are, are just efficient summary rules for physical information, then they depend on all that information: the human related bits included every bit as much as the rest. The individual ground-level facts, including what people are doing, are fundamental, on the Best Systems Analysis. The laws are consequences of those facts, not governors of them.

Now, it would be nice if I could say whether the Best Systems Analysis is correct. But all I can do is register my hazy suspicion that it’s not. (My thoughts on that aren’t even worth setting down.) So it seems we are stuck on this part. But wait! What’s that smell? Yes, it’s the sweet smell of unnecessary work! (Hat tip: Dilbert comic.) There’s a chance we don’t have to decide about Premise 3 of the Consequence Argument, and thus we don’t have to decide about the Best Systems Analysis of laws. We don’t need to evaluate Premise 3 if we can undermine Premise 2 of the Consequence Argument. And we can.

The Past

Let’s look again at Premise 1 of the Consequence Argument, or better yet, at our definition of scientific determinism (abbreviated SD), from which Premise 1 followed:

(SD) Determinism requires a world that (a) has a well-defined state or description, at any given time, and (b) laws of nature that are true at all places and times. If we have all these, then if (a) and (b) together logically entail the state of the world at all other times (or, at least, all times later than that given in (a)), the world is deterministic.

Stanford Encyclopedia of Philosophy entry on “causal determinism”

SD says that the laws plus a complete description can logically entail the state of the world, either symmetrically both into the past and future, or asymmetrically just into the future. But the actual laws of physics that science has given us to this point are time-symmetric in exactly this sense, at least when they are deterministic. Conservation of information in quantum mechanics is a case in point. (There are deterministic interpretations of quantum mechanics, such as the Everett Interpretation, which interpret quantum probabilities as statements of rational expectation in the face of partial ignorance.) Because of conservation of information, the final state of a quantum system plus the environment, after an interaction, must contain the information that the system had beforehand. In other words, from the later state plus the laws of quantum mechanics, the earlier state is logically implied. Scientific determinism is a two-way street.

But now notice: “causality” is supposed to be a one-way street. A cause is not supposed to be itself caused by the very thing it supposedly caused. Let’s make this part of the definition of “cause”: causation is asymmetric, so that “A causes B” and “B causes A” are contraries. It immediately follows that

(Determinism ≠ Causality) The existence of laws of nature that logically entail state B at one time given state A at another, does not suffice to show that A causes B.

Causation is not interdependence, but one-way dependence. For example, a room-temperature cup of water could be caused by leaving a cup of steaming hot water in the room until the temperature equilibrated with the room. Or it could be caused by leaving a cup of ice water in the room for a long time, instead. The effect is guaranteed by the cause, but no particular cause is guaranteed by the later state. Without this kind of asymmetry in the relationship, causality is lacking, as physicist Sean Carroll explains in this 3-minute video. “There’s just a pattern that particles follow,” he says. “Kind of like how the integer after 42 is 43, and the integer before it is 41, but 42 doesn’t cause 41 or 43, there’s just a pattern traced out by those numbers.”

So where does causality come from? I’ll give two answers reflecting different interpretations of “causality” – both of them useful in different ways. On one reasonable interpretation (used by Sean Carroll), causality comes from entropy. On another reasonable interpretation, given by Judea Pearl in his book Causality, causality comes from our division of the world into a system of interest vs exogenous variables.

Now let’s look again at the Consequence Argument’s premise

(2) The distant past state of the universe is such that, for every action A you could take, if you did A, that past state would still obtain.

Is it true? If the “distant past state” is given macroscopically, describing such things as glasses of water and their temperature, then (2) is true, but not adequate for the argument, because (as we’ll see later) the present state of the universe doesn’t follow from the past macroscopic state. But if the “distant past state” is given in microscopic detail, then it is not independent of the present state including what we are doing now.

There is no reason to believe (2), where the states in question are described in microscopic detail. Or rather, there is a reason, but it evaporates once you realize that there’s another explanation for why we never observe the past depending on the present or future. We don’t need to posit a magical “flow of time”, or a universal master/slave relationship between past and future. The idea that the past has power over the future but not vice versa is an overgeneralization from our experience of the macroscopic world: our experience of states and processes large and complex enough for entropy to be well-defined and increasing in only one temporal direction.

All this has gone by way too fast, and there are many points that need further justification and explanation. Along the way, we’ll use modern science to deeply challenge our intuitive conceptions of time and causality, then show how those wrong intuitions about how our universe works have affected our views of the free will “problem”. Scientific determinism isn’t the problem – our misconceptions of it are. The traditional free will problem doesn’t hinge on the definition of “free will”, but of “determinism” and “causality”.

Free will: the argument against (part 1 of 5ish)

Let’s start with some popular versions of what I call “the main type of argument” against free will. Here’s Jerry Coyne, from the conference called Moving Naturalism Forward:

(stolen from Anthony Cashmore) Free will is defined as the belief that there is a component to biological behavior that is something more than the unavoidable consequences of the genetic and environmental history of the individual and the possible stochastic laws of nature.

Jerry Coyne, Free Will and Incompatibilism: Jerry Coyne et al – YouTube, at 2:00

There are two words there that are doing a lot of work: “unavoidable” and “consequences”. The “unavoidable” becomes both more and less clear, in different ways, when Jerry comments on the “stochastic laws of nature” part of the definition.

My definition used to be: If you put yourself in the same situation in the same universe with every molecule in the same place, free will would mean that if you come to a decision point you could make more than one decision. But then I realized that quantum indeterminacy if it acts on the neuronal level could make you make a [conscious and] different decision.

ibid., at 2:22

What gets less clear after this explanation is why the word “unavoidable” is appropriate. when it is hypothesized that human behavior might be different even putting yourself in these highly restricted conditions. And worse, the “same universe with every molecule in place” includes all of you. If something flows from you, that seems an especially poor reason to call it unavoidable. But what gets more clear, I think, is why a non-stochastic (deterministic) view is thought to make behavior “unavoidable”. Genetic and environmental history, after all, can be traced back before you were born. And the universe before your birth doesn’t include you. So let’s forget about stochastic laws of nature at least temporarily, and just get clear on the basic argument, assuming that the laws of nature are deterministic. We will use the scientific meaning (not, say, a theological meaning) of determinism:

Determinism requires a world that (a) has a well-defined state or description, at any given time, and (b) laws of nature that are true at all places and times. If we have all these, then if (a) and (b) together logically entail the state of the world at all other times (or, at least, all times later than that given in (a)), the world is deterministic.

Stanford Encyclopedia of Philosophy https://plato.stanford.edu/entries/determinism-causal/

So we’ll assume now that our universe is deterministic in this sense, and formalize the argument against free will. If we need to see if it generalizes to the case of stochastic laws (teaser: we won’t need to), we can check that later. We can interpret the phrase “consequence of genetic and environmental history” (from Cashmore and Coyne) as the logical entailment mentioned in the definition of determinism. And we can add two plausible premises: the state of the past before your birth is for you unavoidable, and the laws of nature are unavoidable. (To save words later, “the past before your birth” is abbreviated “the distant past”.)

Here’s how we’ll understand “unavoidable”: “Alpha is unavoidable for you” means “For every action A you could take, if you did A, alpha would (still) be true”.

The argument we get is the Consequence Argument, a famous (infamous?) argument in modern philosophy. The original formulation was by Peter van Inwagen, but that relied on an inference rule which was invalid. A better version was later constructed by van Inwagen, David Widerker and Alexander Pruss. It goes like this:

(1) The distant past state of the universe, together with the laws of nature, together logically entail your action now.

(2) The distant past state of the universe is unavoidable (for you).

(3) The laws of nature are unavoidable.

(4) If a proposition X expresses a fact unavoidable for you, and X logically entails Y, then Y is also unavoidable for you.

(5) Therefore, your action now is unavoidable for you.

The argument so formulated actually makes premise (4) a tautology, and I want to continue assuming for the sake of argument that (1) is true. But premise (3) is controversial and (2) even more so. We’ll take them up in the next part.


Pruss, Alexander 2013. Incompatibilism Proved, Canadian Journal of Philosophy, 43/4: 430–437

Van Inwagen, Peter 1983. An Essay on Free Will. Oxford: Clarendon Press.

Widerker, David 1987. On an Argument for Incompatibilism. Analysis, 47/1: 37–41.