Induction and the A-theory

According to the A-theory of time, there is an objective difference between past, present and future. What the difference consists in depends on the particular A-theory one has. The growing block theorist thinks the difference is that there are no future events, but there are past and present ones. The presentist thinks there are no past and future events, but there are present ones. The spotlighter thinks that one moment, the present one, has a special property of presentness (it is in the moving temporal spotlight).

I will argue that the A-theory decreases the strength of many simple inductive inferences in a way that is implausible. Suppose I engage in simple induction. I observe many ravens. They all are black. I am then asked about Smitty, a raven whose color I have not yet observed. I say he's black. This inductive inference presupposes that the observed sample was not biased in some significant way. But suppose now that I knew that the unobserved raven had some natural property P that the observed ravens do not have. Unless P were the property of being unobserved or something like it (the strength of inductive inference in general already takes this difference into account), or unless we had evidence that the possession of P is irrelevant to properties like blackness, this would weaken the inference. Suppose, for instance, all the ravens I observed were male, and the unobserved raven were female. I would have good reason to take the inference to be significantly weaker in this case. Moreover, the more "significant" the property P, the more it weakens the simple induction.

Now, consider two special cases of induction: induction from past events to present or future events. Our observed sample consists of a set of past events. For instance, we've observed strikings of matches, and noted that they are all followed by the match's bursting into flame. We are told (Case 1) that George will strike a match, or (Case 2) that he is now striking one. How strongly should we expect that the match will burst into flame?

If the A-theory is true, then George's striking the match is significantly different from the observed strikings. The observed strikings were all past. George's striking is future or present. This is a particularly significant difference on Case 1 for growing block theories, on which the observed strikings fall within the realm of the real while George's striking does not, and on Case 2 for presentists, on which the observed strikings fall outside the realm of the real while the George's striking is real. On these two theories, this is even more significant a difference than finding out that the unobserved raven was of a different sex from the observed ones, because there is an ontological difference between the observed strikings and the unobserved one.

Note that this temporal difference between the observed cases and the unobserved one here is not a general difference of a sort that induction automatically takes into account, such as the bare difference between observed and unobserved. It is quite possible to do induction based on past observed events and draw a conclusion about an unobserved past event, and that kind of inductive inference will be unaffected by this argument. So this is not a general sceptical argument. Moreover, the argument simply makes use of a principle—viz., that disanalogies between observed and unobserved cases weaken inductive inferences—that is intrinsic to inductive practice, rather than making use of any sceptical hypotheses.

Could one argue that the temporal difference is one that we know is insignificant vis-à-vis induction? If the unobserved raven had an even number of feathers and the observed ones all had an odd number of feathers, we wouldn't take this to weaken the induction, particularly in light of the fact that we know that the parity of the number of feathers changes faster in birds than their color (they keep on losing feathers). Some properties, we know, are insignificant. Is the temporal difference like that?

If it is, the onus is on the A-theorist who wants to keep past-present and past-future induction unweakened to show that it is. I do not know of any good a priori arguments here. Could we know this inductively? I think not. For consider what an inductive argument would look like. Maybe it would say: "We have found in the past that inductive inferences from past to future or present were just as likely to succeed as inductive inferences from past to past, so we should conclude that inductive inferences from past to future or present are just as likely to succeed as inductive inferences from past to past." But this inductive argument would be precisely an instance of those inferences whose force is weakened by my argument. So even if this inductive inference weakens my weakening, inductive arguments from past to present/future will still be weaker than ones from past to past.

If this argument works, it shows that if A-theory holds, then induction from past to present or past to future is significantly weaker than induction from past to past. But our inductive practices do not take into account any such difference. If our inductive practices are nonetheless correct, then the A-theory is false.

All this is particularly problematic on presentism for the following reason. One way to understand presentism is to say that the most basic propositions are propositions about the present. However, we have two modal operators (actually a continuous family of them describing different degrees of pastness and futurity, but I will neglect this for simplicity), "Pastly" and "Futurely", which shift the proposition's tense (as it were: strictly speaking, tense is linguistic rather than propositional). Now in inductive reasoning from past to past, we reason from claims that start with a "Pastly" modal operator to ones that also have it. This is unproblematic. But to reason inductively from claims that start with a "Pastly" modal operator to ones that have no such modal operator or that start with a "Futurely" modal operator is very fishy. The modal operators "Pastly" and "Futurely" for the presentist are like the modal operators "In a novel" and "Possibly"—they are potentially truth-canceling (something that holds pastly, futurely, in a novel or possibly need not hold). But to make inductive inferences from what happens possibly to what happens actually, or from what happens in a novel to what happens in the real world, or from what happens possibly to what happens in a novel, or even from what happens in a novel to what happens possibly, is dangerous. (The last is the safest, except when one is dealing with time-travel novels.)