Thursday, December 23, 2010

Who's Still Afraid of Determinism? (Part 1)

Daniel Dennett

(Conceptual framework for understanding free will)

Who’s still afraid of determinism?” is an article by Dan Dennett and Christopher Taylor (hereafter “D & T”) on the topic of free will and determinism. As the adverbial use of the word “still” in the title suggests, it is an updated version of an earlier article. In the next two blog posts I want to summarise this paper.

Having read both versions, I can tell you now that the difference between them is slight. The major change is that a section has been added discussing Judea Pearl’s theory of causation. Ironically, I’m going to exclude this from my summary. I do so for two reasons: (i) the value of the discussion is proportional to one’s understanding of Pearl's rather complex theory of causation, which I have no intention of summarising and (ii) the authors argue that Pearl’s theory is not relevant to their overall conclusions so, at least in terms of understanding those conclusions, we do not need to discuss it here.

Anyway, my consideration of D & T’s article will be broken into three parts. The first part goes through the motivations behind the article, as well as the various concepts that D & T employ in their arguments. The second part examines the two main arguments (or theses) put forward by the authors. The third part looks at Van Inwagen's famous Consequence Argument, as well as D & T's responses.

1. The Motivations Behind Incompatibilism
The target of D & T’s argumentative ire is incompatibilism. As noted on a previous occasion, incompatibilism is the claim that either (a) free will is incompatible with causal determinism or (b) causal determinism is incompatible with moral responsibility. D & T’s primary concern is with the moral and existential implications of determinism. It would be a mistake, I think, to interpret them as making claims about the ontological or metaphysical implications of determinism.

As D & T point out, incompatibilism is attractive for two main reasons.

First, most people think that in order for alternative possible futures to be available to them when they act, causal determinism must be false. In other words, they think that determinism implies that they “could not have done otherwise”. This is because, in the words of Van Inwagen, determinism is the thesis that there is only one possible future.

Second, most people think that causal determinism implies that human beings are the empty receptacles of external causal forces. This thereby robs them of any ability to be the true (ultimate) originators of their actions.

D & T’s goal in their article is to show how acceptance of causal determinism neither rules out a meaningful sense of “could have done otherwise”, nor a meaningful sense of causal origination. If they succeed, the burden of proof then shifts to the proponents of incompatibilism. They must explain why their position still remains attractive.

To make their case, D & T begin by setting out some formal concepts.

2. Possible Worlds
The first thing D & T try to do is to get some purchase on the modal concepts of possibility and necessity. Philosophers usually do this by appealing to the idea of different possible worlds. D & T are no different, but they focus on possible worlds that are consistent with a modern scientific view of reality. They do not focus on all logically or metaphysically possible worlds.

Their account builds on a Democritean model of the universe. A Democritean universe is specified by a function ( f ) that assigns a value (0 or 1) to a four-dimensional unit of spacetime (x, y, z, t). If a value of 1 is assigned to (x, y, z) at time t1, then that unit of spacetime is occupied; if a value of 0 is applied to that unit, then it is not occupied.

This brings us to a definition:

  • Def. “Possible world” = Any function of the form : (x, y, z, t) → {0,1}

There are two important sets of such possible worlds:

  • Ω is the set of all possible worlds.

  • Φ is the set of physically possible worlds in which no physical law is broken (i.e. the deterministic worlds).

D & T acknowledge that this Democritean vision is a long way from the universe as described by modern physics, but they think it will suffice as we try to refine our concepts of necessity and possibility.

Within a possible world there will be entities. These are simply connected hypersolids occupying units of spacetime that have coherent and stable clusters of properties. A system of informal predicates such as “is human” and “is alive” will be used to describe such entities.

Some of the predicates ascribe necessary or contingent properties to entities. For example, a sentence of the form “Necessarily, Socrates is mortal” ascribes a necessary property to the entity we call “Socrates”. What does such a sentence really mean? According to D & T, it means roughly the following:

  • In every world f, the sentence “∀x (x is Socrates → x is mortal)” obtains.

The crucial question for discussions of necessity is: how large should the set f be allowed to range? Should it cover Ω, or Φ, or some more restricted set X? D & T think this is a difficult question to answer but they propose that the following notation be used to indicate whenever something is necessary:
  • x ψ
This translates as “the sentence ψ obtains in all worlds in the set X” and would be equivalent to “Necessarily ψ.”

Having developed this understanding of the concept of necessity, the concept of possibility is much easier to define. Take the sentence “Possibly, Socrates has red hair”. This sentence can be rendered formally:

  • There exists (within the set X) a possible world f in which the sentence “∃x (x is Socrates ∧ x has red hair) obtains.

More generally, we can employ the following notation to indicate that something is possible:
  • x ψ
This translates as “the sentence ψ obtains in at least one world within the set X” or "Possibly ψ".

3. Counterfactuals
Counterfactuals are propositions that straddle possible worlds. As noted in another post on this blog, they are often thought to be central to accounts of causation. The following statement is a classic instance of a counterfactual:

  • “If you had tripped Arthur, he would have fallen”

This means, roughly, that in every possible world within the set X, whenever the antecedent (Arthur’s being tripped) holds, so does the consequent (Arthur’s falling). D & T employ the following notation for counterfactuals:

  • x ψ → φ

In this case ψ means “Arthur was tripped” and φ means “Arthur fell”. Two other bits of notation need to added at this stage:

  • → φ"  and "~φ→ ~ψ"

The first of these translates as “If ψ, then φ”. The second translates as “If not-φ, then not-ψ”.

Again, crucial to understanding the scope of counterfactual statements like this is the question: how large should the set X be construed? The answer, according to D & T is that X ought to include:

  • (i) worlds in which ψ holds, not-ψ holds, φ holds and not-φ holds.
  • (ii) worlds that are otherwise very similar to the actual world (i.e. the one in which we live).

Obviously (ii) is a bit of a fudge but D & T argue that a certain vagueness is inherent in even the most rigorous discussions of counterfactuals (they reference their later discussion of Pearl’s theory in this regard).

4. Causation
We come at last to the nature of causation. D & T do not think that a “true” account of causation is possible, so they set their sights a bit lower. They try to develop some conceptual tools for refining our thinking about causation in the real world. We will describe these tools by referring to the following example:

  • “Betty’s tripping Arthur (call this “ψ”) caused Arthur to fall (call this “φ”).”

Our goal now is to describe the concepts that allow us to make causal claims like this.

  • (a) Causal Necessity: ψ is a necessary causal condition for φ if, in every possible world within the set X, whenever ψ does not happen, φ does not happen either. As it happens, ψ is not a necessary condition for φ: Betty’s tripping Arthur is not necessary for his falling, he could fall for other reasons.
  • (b) Causal Sufficiency: ψ is a sufficient condition for φ if, in every possible world within the set X, whenever ψ happens, φ happens. In our example, ψ probably is a sufficient condition for φ: Betty’s tripping Arthur probably does make him fall (but perhaps there are ways in which he can avoid this outcome even after he is tripped).
  • (c) Independence: in making a causal claim, we expect the two sentences ψ and φ to be logically independent. In other words, we expect there to be possible worlds, however remote they might be from our own, in which ψ is true but φ is not.
  • (d) Temporal Priority: in order for one event to cause another, it is usually the case that the cause precedes the effect.
  • (e) Miscellaneous other concepts: there are other concepts to which we appeal when making causal claims. For example, most of the time the cause is active while the object on which it exerts its causal powers is passive. Also, physical contact is often thought to be important in discussions of causation.

After describing these conceptual tools D & T proceed to consider three classic problem cases. I won’t go through these here but I will summarise the main points, which are:

  • (i) When trying to identify “the” cause of an event, sometimes we focus on the necessary conditions, sometimes on the sufficient conditions, and sometimes on other conditions such as temporal priority.
  • (ii) Sometimes there may be no singular “cause” of an event.

Okay that’s enough for now. There's quite a lot to take in here. In the next post we’ll see how these concepts are used in the service of D & T’s arguments. You might like to keep this post open in a separate tab when you read the next part.

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