A note on Richard Taylor's Fatalism

In 1962, Richard Taylor wrote a short and seeming pedestrian paper alleging the logical inevitability of fatalism, the view that we are as powerless over the future as we are about the past [1]. This is the philosophical disposition that accompanies a recognition that free will is impossible, and so Taylor's proof appears to decide the contentious debate over free will in favor of hard incompatibilism -- that free will and moral responsibility are illusions. The contemporary dialogue over free will hinges on the primacy of physical causality in constraining future events: Taylor's proof would seem to settle the issue on the basis of logic alone, without recourse to arguments surrounding the regularity of physical law, the causal closure of the universe, and so on. The initial response to Taylor's claim is therefore typically one of suspicion and skepticism: something is obviously wrong with the argument. But what? Has some subtle error led Taylor astray?

Taylor bases his argument on six innocent assumptions: (1) the law of the excluded middle: that a proposition is either true or false, (2) that a condition \({\color{black}{A}}\) is sufficient for a condition \({\color{black}{B}}\) if the occurrence of \({\color{black}{A}}\) necessitates the occurrence of \({\color{black}{B}}\), (3) that a condition \({\color{black}{A}}\) is necessary for a condition \({\color{black}{B}}\) if the occurrence of \({\color{black}{B}}\) necessitates the occurrence of \({\color{black}{A}}\), (4) that if \({\color{black}{A}}\) is sufficient for \({\color{black}{B}}\), \({\color{black}{B}}\) is necessary for \({\color{black}{A}}\) (not really an independent assumption...it follows from (2) and (3)), (5) that "no agent can perform any given act if there is lacking, at the same or any other time, some condition necessary for the occurrence of that act'', and (6) that time cannot be efficacious, that it cannot in itself affect the capacities of anything. The first five of these are self-evident truths, and the last likewise doesn't raise any eyebrows. Nonetheless, some philosophers have closely examined these assumptions for cracks in the foundation, but I'm not aware of any resounding progress on this this front [2]. I will therefore accept Taylor's assumptions as is, and instead look for a misstep in his argument.

The setting of Taylor's deceptively simple argument is a Navy Commander contemplating an order to battle. Consider two acts \({\color{black}{O}}\) and \({\color{black}{O'}}\): the first, \({\color{black}{O}}\), is an order from the Commander to the fleet that ensures that a naval battle will occur tomorrow, while the second, \({\color{black}{O'}}\), is an order that ensures that no naval battle occurs. There are likewise two outcomes: \({\color{black}{Q}}\), that a naval battle occurs tomorrow, and \({\color{black}{Q'}}\), that a naval battle does not occur tomorrow. Acts \({\color{black}{O}}\) and \({\color{black}{O'}}\) are sufficient for \({\color{black}{Q}}\) and \({\color{black}{Q'}}\), respectively. Events \({\color{black}{O}}\) and \({\color{black}{O'}}\) are clearly mutually exclusive, as are \({\color{black}{Q}}\) and \({\color{black}{Q'}}\). Taylor seeks to evaluate the truth of the following simple proposition:

Proposition: It is within the Commander's power to do \(O\), and it is within the Commander's power to do \(O'\).

In other words, he can choose freely between the two alternatives -- a noncontroversial assertion. But, consider the formal argument:

1. If \(Q\) is true, then it is not within the Commander's power to do \(O'\). (This is because if \(O'\) is true, it is necessary that \(Q'\) is true, but then \(Q\) would be false since \(Q\) and \(Q'\) cannot both be true.)

2. But if \(Q'\) is true, it is not within the Commander's power to do \(O\).

3. Either \(Q\) or \(Q'\) is true.

4. It is therefore either within the Commander's power to do \(O\) or it is within the Commander's power to do \(O'\).

Step 4 invalidates the proposition that the Commander has the power to do \(O\) and he has the power to do \(O'\). Except that this argument is flawed, and the problem lies in steps 1 and 2. The problem is that Taylor has no right to call into question the power of an agent to do this or to do that based solely on the occurrence or non-occurrence of a future event. Given that \(Q\) occurs, all we can say is that order \(O'\) was not given (because if \(O'\) was given then \(Q'\) would occur) -- we cannot make the stronger claim that it was not in the Commander's power to have done \(O'\).

We can formalize this as a proof that parallels Taylor's. We introduce two states, \({\color{black}{A}}\) and \({\color{black}{A'}}\): if \({\color{black}{A}}\) is true, then it is within the Commander's power to do \({\color{black}{O}}\), while if \({\color{black}{A'}}\) is true, then it is within the Commander's power to do \({\color{black}{O'}}\). We've not added anything to Taylor's set-up; we're just reformulating his proposition to read:

Proposition: Both \(A\) and \(A'\) are true.

If order \(O\) is given, then clearly \(A\) is true -- it must have been within the Commander's power to issue the order. In other words, \(A\) is necessary for \(O\). However, importantly, \(A\) is not sufficient for \(O\): just because it might be within the Commander's power to issue the order does not compel him to do so. And likewise for \(A'\) and \(O'\). Now, let's examine Taylor's argument in terms of \({\color{black}{A}}\) and \({\color{black}{A'}}\). First, consider the more conservative (and I think correct) version of Taylor's first assertion,

1. If \(Q\) is true, then order \(O'\) was not given.

This is all we really know about the state of affairs of the Commander -- that if the battle occurs then the appropriate order must have been given -- it does not necessarily imply that the Commander lacked the power to give the order. Since \(Q\) is true, then order \(O\) was given. This means that \(A\) is true. But though order \(O'\) was not given, \(A'\) might still be true because the issuance of \(O'\) is not necessary for the truth of \(A'\) (we said above that \(A'\) is not sufficient for \(O'\), which is the same thing by assumption (4)). So, we can say

1. If \(Q\) is true, then order \(O'\) was not given. \(A'\) might or might not be true.

The remaining steps of the argument become:

2. If \(Q'\) is true, then order \(O\) was not given. \(A\) might or might not be true.

3. Either \(Q\) or \(Q'\) is true.

4. \(A\) and \(A'\) might or might not both be true.

What this means is that Taylor's argument is insufficient to determine the truth of the proposition. This is expected, since the truth or falsity of the proposition would disprove or prove the existence of free will, which is a question that is intuitively expected to depend crucially on facts about physics and the nature of the universe. We don't expect logic to have much to say on this issue, and a re-examination of Taylor's argument reveals that the occurrences of certain events imply nothing about the power -- the potential -- to cause the precipitating, antecedent events.

[1] Taylor, Richard. "Fatalism.'' The Philosophical Review (1962).
[2] Fate, Time, and Language: An Essay on Free Will. David Foster Wallace, Columbia University Press (2010).

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