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The No-Miracles Argument

The no-miracles argument states that in certain circumstances if A and B are competing hypotheses and if event e is more likely on A than on B, then A is more likely to be true.

It seems to me that arguments of this kind are used in everyday reasoning, as in the following example: a bag is known to contain 100 balls, black or white. I draw 99 without replacement and they all turn out to be black, whereupon I reason as follows: on the hypothesis of 100 black balls originally in the bag, it is certain that the first 99 will be black; on the hypothesis of 99 black balls and a white ball, the probability of the first 99 balls being black is 1 in 100, which is very low. Therefore, it is likely that there were originally 100 black balls in the bag, which is to say that the remaining ball is black.

Here is an example concerning the inference to another person’s sensations: imagine that I touch a hot-plate and burn my fingers and cry out. Now I observe another person approach the plate and go to touch it, whereupon I predict that he also will cry out. Suppose my prediction is fulfilled; then I may argue as follows: on the hypothesis that he did not feel pain there is no reason to assume any causal connection between his touching the plate and exhibiting pain behaviour. In my case the causal connection is via my pain, but if the hypothesis is that he did not feel pain, then there was no reason to expect him to cry out, this being just one out of hundreds of different forms of behaviour he could have displayed. So it was purely by chance that my prediction was correct, the probability of which was very low indeed. But on the hypothesis that he did feel pain, it was very likely that he would cry out and so on, and the reason is that such behaviour is an involuntary reaction to intense pain.

I think that the least that this argument has to offer is that it is more subtle and more substantial than the basic argument from analogy. A weakness, perhaps, is that it seems to work only within a framework in which other minds are presupposed. In that case perhaps the point of the argument is not to justify our knowledge of other minds but only to establish and justify particular inferences as to their contents.

      What I shall now try to show is that the no-miracles argument is essential to the justification of memory, and in two ways: firstly, it is essential in the sense that there are circumstances, as we shall see, in which it provides the only justification of particular memories; secondly, it is essential in that it is only by reference to it that we are able to account for the evidential force of successful prediction in the confirmation of memories.

      The best way to show this, perhaps, is to explore a particular example. Suppose that I find myself in total darkness, as if in a basement or cave, and that I am restrained in some way or other and unable to investigate my surroundings. Now imagine that I close my eyes and that I seem to remember that a glowing white disc appeared in front of me and disappeared only when I closed them. Expecting it to reappear, I open my eyes and find my expectation confirmed. I now reason as follows: my correctly expecting to see the white disc would be extremely unlikely if the disc had not previously been there, so that my memory of it was false. On that hypothesis I had no more reason to expect a white disc than to expect any of an infinite number of possible colours and shapes. It would be as if someone had instructed me to close my eyes and guess which of the natural numbers he was about to write down. There has to be an explanation for my success, this being part of the common ground of reasoning, and the only candidate worth considering is that my memory of the disc was correct. But this explanation is compelling.

      Despite the force of such explanations, we still have to consider objections to our claim that the no-miracles argument is essential.  Suppose it is objected that if any confirmation is needed then this may be furnished by an inductive appeal to the reliability of memory. Thus, even before we open our eyes and see the expected white disc we believe that our memory is correct, or, since memory is a form of belief, we believe that previously we were looking at a white disc, one effect of which was to cause the memory. And the source of this belief, with regard to its justification, is the whole of our experience of memory turning out to be correct, which is to say that particular memories are justified inductively.

       Now, the one thing that is clear is that we do fall back on induction in support of particular memory claims, and also that we reason in terms of it when arriving at a memory belief. Suppose, for instance, that I suspect myself of incipient dementia, having noticed that I increasingly mis-remember recent events. Then I may lose confidence in any particular memory, especially if it conflicts with other evidence or is uncorroborated. The other extreme is that in which my confidence is boosted by past successes; it could be, for instance, that I seem to remember seeing a white disc but that it does not appear when I open my eyes. I now reason that I have an excellent memory for recent events, therefore it is likely that this present memory is correct.

      It has to be acknowledged, then, that with my eyes closed I could justify my memory belief with regard to the white disc by appealing to the general reliability of my memory. As against this, consider the claim that this appeal begs the question, since we have to remember that most of our memories have been correct. To this it may be replied that it is only a particular memory that is in question, not our general memory or our knowledge of the past in a wider sense. The confirmation of any proposition depends on other propositions remaining unconfirmed: there is no question here of being accountable to the radical sceptic but only of defending our beliefs in accordance with ordinary standards of reasoning.

      Dismissing the objection, then, and admitting that with our eyes closed we may appeal to the excellence of our memory, let us now consider the claim that such an appeal is all that is required, so that the no-miracles argument has no essential role, not even when I open my eyes and find that my expectation of seeing the white disc has been met. On this view one has to account in inductive terms for the evidential force of my seeing what I expected to see. In what sense does my seeing the white disc confirm my memory of it? Consider the following attempt at an answer: the disc may be taken to be a long-lasting physical object that very likely existed before I closed my eyes, so that I saw it and truly remembered it. But this won’t do: first of all, there need be no such likelihood, as is obvious if we think of the disc as an electric light, then ask whether its now being switched on is a strong indication of its previous state. It would have to be strongly indicated because the no-miracles argument would bring to my memory of the disc a great deal of certainty if I could use it, thereby setting a benchmark for the argument from reliability.

      Not only is there no such likelihood but it is also to be noted that the no-miracles argument does not depend on its being the case that the white disc appearing when I open my eyes is evidence of its existing before I closed them. Consider the following example, which does not involve closing and opening my eyes: suppose that I am in darkness as before and that it has just been pierced by a flash of light, I think, though I am not sure whether I remember or imagine it. What tips the balance decisively in favour of memory, however, is that a flash of light, the second if the first occurred, suddenly splits the darkness in the same position in my visual field. If I were now required to justify my new-found certainty, then it is clear that I could invoke the no-miracles argument. What I could not do, however, is to claim independently of that argument that the later event is evidence in itself of the occurrence of a similar earlier event: if I am exposed to a flash of light, completely outside any explanatory framework, then I have no reason to believe that it had a predecessor. Nor is there any reason to believe that my certainty may be accounted for in terms of the reliability of my memory: the fact of its being reliable did not save me from the initial uncertainty as to whether or not I had imagined a flash of light. The only possibility, as far as I can see, is that the second flash of light has evidential force by virtue of the no-miracles argument.

      It may be worth taking a different approach to the same question to see if we arrive at the same answer. If previous arguments were correct, then before opening my eyes I am able to justify the particular memory in terms of my memory generally being reliable. What I cannot do is to assert that no justification is required. But then, the same applies to the general claim that my memory is reliable, which also requires to be justified, as is evident from the fact that not everyone has a good memory. This is to imply not that the general statement must be defended on each occasion of its use but only that a justification should be available if required. I have already agreed that it is not question-begging to justify a particular memory by appealing to the general case. All that is now being said is that having made that appeal, we could then be asked for evidence in support of our having a good memory.

      Suppose that this is what happens, which is to say that I am asked how I know that my memory is reliable. Then it is at this point that predictions arising from memory come into their own, the way forward being to confirm that reliability by adducing cases in which it is instantiated. All I need do, then, in the case of the white disc, is to open my eyes in order to establish that the disc is there. If it is, then I am now able to deploy the no-miracles argument and to show by means of it that almost certainly my memory is correct.

      What is demonstrated here, I think, is that it must be possible to justify particular memories other than on the basis of the general reliability of one’s memory, and the reason is that some other basis must be found if one’s general memory is itself in question. The process of confirmation of memories involves expectation or prediction, as in the case of the white disc, or the recognition of a later event as being similar to an earlier event the memory of which is in question, as in the case of the flash of light. In both cases the no-miracles argument establishes the soundness of the particular memory. I conclude that the no-miracles argument has an essential role. Since all reasoning and belief involves memory, the inference to be drawn is that the argument is essential to all knowledge.

      Finally, it is worth mentioning the possibility that processes of reasoning accord with an underlying logic. When an expectation or prediction derived from a particular memory turns out to be correct, this in itself may provide a high degree of confirmation of the memory. Such a high degree, in fact, that one wonders whether it points to an underlying logic involving the no-miracles argument. The difficulty, of course, is that of trying to clarify what could be meant. There is also a related question as to whether there are classes of propositions or arguments that require less support than others and in that sense are more basic. We argue from the reliability of our memory, and also we have to argue for it, because not everyone has a good memory. But what about the no-miracles argument itself – does that also need to be defended in terms that go beyond it?