In his book, "Inference to the Best Explanation", Peter Lipton lays out a response to Stanford's problem of unconceived alternatives (also referred to as the problem of underconsideration) by saying that we can (in principle) compare some hypothesis to its contradictory to discover that the hypothesis is likely true and in this situation one doesn't need to compare all alternatives.

Something about this response isn't clicking with me. I actually do accept inference to the best explanation (or just 'explanation') as a valid form of inference. Could someone better elaborate on or explain Lipton's point for me such that it might click? I'm finding it hard to consider this solution in terms of an example.


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    someone should reply with examples from physics... – user34654 Aug 26 '18 at 12:47

Lipton responds to the point in a way that may help. I have quoted more thanI would normally but have deleted text where possible and put in bold Lipton's key moves. I have also added 'optional' text in which Lipton deals with potential objections :

I will focus especially on the argument from 'underconsideration'. This argument has two premises. The ranking premise states that the testing of theories yields only a comparative warrant.* Scientists can rank the competing theories they have generated with respect to likelihood of truth. The premise grants that this process is known to be highly reliable, so that the more probable theory is always ranked ahead of a less probable competitor and the truth, if it is among the theories generated, is likely to be ranked first, but the warrant remains comparative. In short, testing enables scientists to say which of the competing theories they have generated is likeliest to be correct, but does not itself reveal how likely the likeliest theory is. **The second premise of the argument, the no-privilege premise, states that scientists have no reason to suppose that the process by which they generate theories for testing makes it likely that a true theory will be among those generated. It always remains possible that the truth lies rather among those theories nobody has considered, and there is no way of judging how likely this is. The conclusion of the argument is that, while the best of the generated theories may be true, scientists can never have good reason to believe this. They know which of the competing theories they have tested is likeliest to be true, but they have no way of judging the likelihood that any of those theories is true. On this view, to believe that the best available theory is true would be rather like believing that Jones will win the Olympics when all one knows is that he is the fastest miler in Britain.


Let us now consider the argument from underconsideration in its own right.


The most straightforward way to eliminate a gap between comparative and absolute evaluation would be by exhaustion. If the scientist could generate all possible competitors in the relevant domain, and he knew this, then he would know that the truth is among them. Given the reliability that the ranking premise grants, he would also know that the best of them is probably true. This brute-force solution, however, seems hopeless, since it takes a wildly exaggerated view of the scientist's abilities. Even granting that we can make sense of the notion of all possible competitors, how could the scientists possibly generate them all?

But collapsing the distinction between relative and absolute evaluation does not require exhaustion. The scientist does not have to know that he has considered all the competitors, only that one of those he has considered must be true, and for this he needs only a pair of contradictories, not the full set of contraries. It is enough that the scientist consider a theory and its negation, or the claim that a theory has a probability greater that one-half and the claim that it does not, or the claim that X is a cause of some phenomenon and the claim that it isn't, or the claim that an entity or process with specified properties exists or it doesn't. Since scientists are plainly capable of considering contradictories and the ranking premise entails that, when they do, they will be able to determine which is true, the argument from underconsideration fails.

This is the gist of Lipton's reply. If you want to read beyond this, I include his consideration of two possible replies.

The sceptic has two natural replies to this objection from contradictories. The first is to modify and restrict the ranking premise, so it concedes only the ability to rank contraries, not contradictories. But while the original ranking premise is epistemically over- generous, it is not clearly over-generous in this way. Scientists do, for example, compare the likelihood of the existence and non- existence of entities, causes and processes. So the sceptic would owe us some argument for denying that these comparisons yield reliable rankings while accepting the reliability of the comparisons of contraries. Moreover, it is not clear that the sceptic can even produce a coherent version of this restricted doctrine. The problem is that a pair of contraries entails a pair of contradictories. To give a trivial example, (P&Q) and -P are contraries, but the first entails P, which is the contradictory of -P. Indeed, all pairs of contraries entail a pair of contradictories, since one member of such a pair always entails the negation of the other. Suppose then that we wish to rank the contradictories TI and -Ti. If we find a contrary to TI (say T2) that is ranked ahead of TI, then -Ti is ranked ahead of T 1, since T2 entails -T 1. Alternatively, if we find a contrary to -T I (say T3) that is ranked ahead of -TI, then Ti is ranked ahead of -T1, since T3 entails TI. So it is not clear how to ban the ranking of contradictories while allowing the ranking of contraries.

The second natural reply the sceptic might make to the objection from contradictories would concede contradictory ranking. For in most cases, only one of a pair of contradictories would mark a significant scientific discovery. Not to put too fine a point on it, usually one member of the pair will be interesting, the other boring. Thus if the pair consists of the claim that all planets move in ellipses and the claim that some don't, only the former claim is interesting. Consequently, the sceptic may concede contradictory ranking but maintain that the result will almost always be that the boring hypothesis is ranked above the interesting one. In short, he will claim that the best theory is almost always boring, so the scientist will almost never be in a position rationally to believe an interesting theory.

This concession substantially changes the character of the argument from underconsideration, however, and it is a change for the worse. Like most important sceptical arguments, what made the original argument from underconsideration interesting was the idea that it might rule out reasons for belief, even in cases where the belief is in fact true. (Compare Hume's general argument against induction: he does not argue that the future will not resemble the past, but that, even if it will, this is unknowable.) With the con- cession, however, the argument from underconsideration reduces to the claim that scientists are unlikely to think of the truth. The idea that scientists are only capable of relative evaluation no longer plays any role in the argument, since ranking of contradictory theories has collapsed the distinction between relative and absolute evaluation, and the argument reduces to the observation that scientists are unlikely to think of interesting truths, since they are hidden behind so many interesting falsehoods.

So the revised argument is substantially less interesting than the original. But the situation is worse than this. For scientists do in fact often rank interesting claims ahead of their boring contradictories. The revised argument thus faces a dilemma. If it continues to grant that scientists are reliable rankers, then the fact that interesting claims often come out ahead refutes the claim that scientists do not generate interesting truths. If, on the other hand, reliable ranking is now denied, we have lost all sense of the original strategy of showing. how even granting scientists substantial inductive powers would be insufficient for rational belief.


P. Lipton, 'Is the Best Good Enough?', Proceedings of the Aristotelian Society, New Series, Vol. 93 (1993), pp. 89-104 : 89-96 passim.

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  • It is enough that the scientist consider a theory and its negation, or the claim that a theory has a probability greater that one-half and the claim that it does not – user34654 Aug 26 '18 at 13:43
  • so the existence of unconsidered alternatives is a valid skeptical argument supposing that they affect the ranking of theories by a scientist. seems like they could. but yeah i get the argument, induction from being able to rank actual theories, to being able to rank their negation. right? – user34654 Aug 26 '18 at 13:51
  • So is he saying that the hypothesis (for a simple example) "Atoms are responsible for pressure change in gases" being more probable than "Atoms are not responsible for pressure change is gases" gives us reason to be confident that atoms are in fact responsible for pressure change in gases? – Joe Lee-Doktor Aug 26 '18 at 16:42
  • @Joe Lee-Doktor. If we change 'gives us reason to be confident' to 'gives us good reason to believe', then yes I think you have pinned his position. (a) We have a theory and know that either the theory or its contradictory is true. (b) We can use the ranking premise to prefer the theory or its contradictory. I think this does block the view that 'while the best of the generated theories may be true, scientists can never have good reason to believe this.' We can have good (not conclusive) reason to believe that the best of the generated theories is true, given (a) and (b). Are you persuaded ? – Geoffrey Thomas Aug 27 '18 at 7:41
  • @GeoffreyThomas I... think I am. I can see that a theory is more probable than its contradictory given repeated empirical success. What I'm failing to grasp, I think, is how this 'comes into play' with like the pessimistic induction. I also think I'm confused because couldn't the contradictory hypothesis 'contain' some perfectly good alternative? Would you mind giving this theory vs contradictory reasoning in terms of some example and show how we come to prefer the theory over its contradictory or something? – Joe Lee-Doktor Aug 27 '18 at 9:43

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