8. Logical fatalism

Suppose you wagered earlier today that the Irish would win a certain football match and are anxious to know the result.

The match itself is over and it’s only the result that you don’t know.

Despite your anxiety, you decide to wait a while before checking the result because you believe that the Irish will prove more likely to have won if you postpone the checking for a few hours; rushing to check the result will only “jinx it.”

You inherited this curious attitude from your father, say.

Many would call this superstition, of course, since whether you check the result now or later can’t possibly make a difference, given that the match is already over. In fact, there’s a fairly simple proof of this, isn’t there? Thus:


Many would consider this piece of reasoning to be obviously correct, indeed entirely trivial. We might call them fatalists about the past.

But the English philosopher Michael Dummett observed that if we apply the same style of reasoning to the future, it smacks of sophistry.

In Dummett’s example, it’s wartime London, the bomb siren goes off, and the whistle of an approaching bomb is heard. Everyone else rushes for the bomb shelter, or otherwise takes precautions, whereas you find yourself entertaining the following piece of reasoning:


This is exactly the same style of reasoning, but hardly anyone would endorse it this time. Indeed, it must surely be flawed because it yields the outrageous conclusion that it’s pointless to take precautions against the bomb. For all that, the reasoning seemed impeccable in the previous case, where the conclusion happened to look agreeable.

What should we make of this?

Well, one possibility is that there is some difference between past and future which explains why the football argument, directed as it is towards the past, can remain correct even though the bomb argument, directed towards the future, is completely specious. The question then is what this difference might be.

But another possibility—the niggling possibility—is that this is yet another case where a subtle logical error goes unnoticed if the conclusion looks innocuous, and is brought to light only when the conclusion seems crazy. As we saw in the last section, this hazard is quite real and possibly even widespread. On this view, the football argument is really as bad as the bomb argument, despite seeming to be “obviously correct” at the start.

To see where the truth lies, let’s uncover the purported error in Dummett’s bomb argument and then consider whether it also infects the football argument.


The bomb argument was well-known to the ancient Greeks, you will not be surprised to hear, though not, of course, in terms of sheltering from an air raid.

The Stoic philosopher Chrysippus (c. 250 B.C.) considered instead a sick man, reasoning in the same style, wondering whether to see a doctor:


This style of reasoning was known as the Idle Argument in Chrysippus’s day and is reasonably deemed “paradoxical” because of its slippery logic and scandalous conclusion. All the same, most people tend to agree that we should reject the reasoning, the only question being how, rather than swallow the conclusion.

Philosophers also speak here of the puzzle of fatalism, or sometimes that of logical fatalism, to underscore that purely logical considerations can seemingly support a fatalistic outlook, the contrast being with factual considerations such as those of cause and effect, capable also of supporting fatalism, but in a different way. Paradoxes of logical fatalism were in fact generated in various ingenious ways by philosophers of antiquity—see this Stanford encyclopedia entry for a catalogue—but the Idle Argument is a particularly accessible one.

So where does the Idle Argument go wrong? I’m about to reveal a likely answer, in case you’d like to mull it over before reading on.


I’ll explain the answer in terms of Dummett’s bomb argument, although similar things may be said of Chrysippus’s doctor argument.

In terms of the bomb argument, the fallacy may be traced to the yellow bit highlighted below, occurring in the third premise of the argument:


Note that the yellow bit is a complete sentence in its own right, namely:

The bomb won’t kill me regardless of whether I take precautions.

This sentence looks rather harmless but is in fact ambiguous in a subtle way, which proves to be the root of the problem. Thus, read in one way—a so-called “thick” way—the sentence implies that it is unnecessary to take precautions against the bomb, as indeed the reasoning above proceeds immediately to infer. (See just after the yellow bit.)

In this same “thick” sense, we might say, of a woman in love, ‘She’ll marry him regardless of whether he’s rich,’ implying in the same way that his being rich is unnecessary to win her hand. The clause, ‘regardless of whether he’s rich,’ is here helpfully glossed, ‘whether he’s rich or poor; she doesn’t care.’

Read in another way, however—a “thin” way—the implication in question is quite absent. For instance, knowing only that she’ll marry him, e.g., because of an announcement in a bulletin, but knowing nothing of his wealth, or even whether she loves him, we can still sensibly say, ‘She’ll marry him regardless of whether he’s rich.’ This employs the same form of words, but is now curiously neutral on whether he needs to be rich to win her hand. The clause, ‘regardless of whether he’s rich,’ is here more aptly glossed, ‘whether he’s rich or poor; we don’t know.’ In this case, unlike the previous one, it remains open that she is in fact marrying him for his money.

Once you notice this ambiguity, it is not hard to see that the premise in question—the third premise shown above—starts off using the yellow sentence in the thin way:

If the bomb won’t kill me, then the bomb won’t kill me regardless of whether I take precautions …

this being the only way to justify this opening claim, but then surreptitiously switches to using it in the thick way:

… the bomb won’t kill me regardless of whether I take precautions; so any precautions I take will be unnecessary.

the switch now being required to justify this closing claim. This, of course, is the fallacy of equivocation: that of changing meanings midway through an argument. The intent was clearly to merge the two claims just shown and derive:

If the bomb won’t kill me, then any precautions I take will be unnecessary

this being a key claim of the larger argument. But the derivation is now seen to be fallacious, based as it is on an equivocation. (This is essentially the diagnosis given by Dummett himself.)

Relative to the key claim just shown, we may also protest directly that if the bomb won’t kill me, then this may be because of the precautions I take, in which case the precautions can hardly be “unnecessary.” (Chrysippus makes this point relative to his doctor argument.) The purpose of the longer analysis above, however, was to show where the sneaky “proof” that such precautions are unnecessary goes wrong.


Turning our attention back now to the football argument, we find that it is fallacious in exactly the same way, notwithstanding its direction towards the past.

Thus, the yellow bit below is ambiguous in exactly the same way as before:


And the key claim:

If Ireland already won, then any waiting that you do will be unnecessary

rests illegitimately upon the resulting equivocation. All of this is exactly as before.

Relative to this key claim, we may also protest directly that if Ireland already won, this may be because of the waiting you are about to do, in which case the waiting can hardly be “unnecessary.” No doubt, this would be to countenance some form of backwards causation, or backwards influence: the idea that you can do something now to bring it about, or make it more likely, that something has already happened. As before, it might be felt that such an idea is nonsensical, or otherwise impossible. But it would beg the question to raise this objection here because that, after all, was the whole point of the football argument to show. That’s how we got started.

So, on pain of begging the question, the football argument does not succeed in showing that affecting the past is impossible any more than the bomb argument succeeds in showing that affecting the future is impossible. There may well be other reasons to think that it is impossible to affect the past, but the football argument is not it.

Considerably more may be said of the large and difficult topic of affecting the past and backwards causation in general, but, regrettably, we can’t manage that here. For our purposes, let’s just take away what we can from the discussion above.


We were looking for cases where it has not yet dawned upon us that a certain style of reasoning is flawed, raising the risk that we would employ it in practice, mistakenly believing in its validity.

For those who have never encountered the paradoxes of fatalism, the Idle Argument is likely to be an example, especially as applied to the past. A realistic example of this is provided again by Dummett and we can end with it.

Imagine that a ship has sunk and a loved one of yours was on board. There were only a few survivors, but the authorities have yet to release their names. While waiting anxiously for news, you utter a prayer to God that your beloved was among the survivors. Among religious people, at least, this would be a natural thing to do. And yet it is easy to be tempted by the Idle Argument here and castigate such “retrospective” prayer as being pointless. After all, if your beloved survived, prayer is unnecessary; whereas, if she didn’t survive, prayer will be ineffective. Right?

Indeed, we learn from Dummett that orthodox Jewish theologians are said to hold that retrospective prayer is pointless for essentially these reasons. If our foregoing analysis has been right, then this is mistaken reasoning, although it would be difficult to blame anyone, even learned theologians, for employing such false logic, because, as we saw at the start, anyone can succumb to it. All the same, as this example shows, the consequences of falling into this error can be potentially significant.

Incidentally, this example also illustrates how we can “make sense” of doing something now to bring about a past event. Not that everyone who has ever said a retrospective prayer was thinking as such, but the idea is this. Since God is omniscient and can see what the future will bring, he would have foreseen, at the time of the accident, that you would subsequently pray, and could thus have granted your prayer in advance. Considered in this light, your beloved really may have survived because of your subsequent prayer, something which may otherwise seem unintelligible.

In contrast, it must be admitted that it is harder to make sense of how waiting a few hours before checking the result of a football match can bring it about that your team already won. Anyone who thinks that such a thing is possible therefore owes us an explanation of sorts; a way of understanding what is going on here. Such a thing may or may not be possible in the end—the matter is unsettled—but the point, nevertheless, is that the Idle Argument doesn’t so far rule it out.

So much for our exploration of logical fatalism. This leads us nicely to our final paradox, which is a bewildering conundrum known as Newcomb’s paradox. This too involves the contentious idea of doing something now to make it more likely that something desirable has already happened—though in an interestingly different way from anything we have seen above. This time, it’s really paradoxical because philosophers are completely divided on how to make sense of the situation.