Friday, February 22, 2008

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.)

13 comments:

Anonymous said...

Alex,

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.

I think I would say that presentness (pastness, futurity) is irrelevant to blackness as it is causally irrelevant to any property. Naturalness requires causal relevance.

An A-theory I like will also analyze pastness and futurity. It won't face your objection. To say x is past is to say it is earlier than the present, it's future iff it's later than the present. Presentness is primitive and intrinsic. Anyway, it's not clear to me how the problem is a problem on this view.

-Christian

Alexander R Pruss said...

Christian:

1. How do you know presentness is causally irrelevant to properties? A priori or a posteriori?

2. It seems that presentness is causally relevant. For while a present blackness can't be caused by a future blackness, a present blackness can be caused by a present or past blackness (say).

3. I don't think the view you mention escapes the criticism. All the observed events are earlier than the present, and hence lack presentness. The unobserved case is present. This seems to be an objective difference between the observed and unobserved cases.

Anonymous said...

I'd say a priori. Right theory of causation + right theory of time = presentness is causally irrelevant. The former are a priori (don't ask me for the derivation, please).

So I deny the seeming in 2. I'd say that present things cause, not because they are present, but because they have other properties. Perhaps things are earlier than other because of causation via causal theories of time's direction. But I'm not sure.

I also think all events have presentness tenselessly, but are in time by now having presentness, by having properties in a certain way, not by having certain properties. They are past in virtue of being earlier than events that now have properties. I realize this is idiosyncratic, but I think it's right, right now.

I agree there is an objective difference between the observed and unobserved cases. What I don't see is why being earlier than the present is relevantly different from being later than the present. It's true that induction into the past, like you say, is induction to objects that share the property of being earlier than the present, induction into the future is to objects that lack it. I'm not yet feeling the intuition that this makes a difference, that is, any more of a difference than that induction is from observed to unobserved, or from things close to me to things far away.

Maybe I could get you to tell me why you think the B-theorists does not have the same problem?

-c

Alexander R Pruss said...

It seems that just as details of spatial arrangement are causally relevant (a source of heat can only cause water to boil when the source of heat is physically near the water), so are details of temporal arrangement. For instance, some causes have effects precisely a certain amount of time later (setting an alarm for 10 hours ahead causes a noise in 10 hours). I suppose you could argue that what is causally relevant are B-relations like "being 10 hours earlier than", but A-determinations are causally irrelevant. But that would seem to me to be ad hoc, unless you have an argument. Maybe you do, given your theory. But I can't follow the account, given your brevity.

I don't think my argument requires the A-determinations to be actual properties. It works fine on the modal rendering I offer at the end, for instance.

As for the B-theorist, she might escape the argument because the difference between past, present and future events is just a difference in how the events are related to the observer or, alternately, are merely indexical. But merely indexical differences, or differences in relation to the observer are already accounted for in inductive reasoning.

Anonymous said...

As for the B-theorist, she might escape the argument because the difference between past, present and future events is just a difference in how the events are related to the observer or, alternately, are merely indexical. But merely indexical differences, or differences in relation to the observer are already accounted for in inductive reasoning.

I see now. The A-theory I'm suggesting is one according to which presentness is indexical. So the A-theory, like the B-theory your describing, will also have accounted for the differences in inductive reasoning. But like I said, this is idiosyncratic. The standard A-theory accepts primitve future and past tense properties, I don't think an A-theorist should accept this.

Alexander R Pruss said...

Christian:

If presentness is indexical, then I don't see how what you have is an A-theory. Do you think there is an observer independent fact about the world what time is present?

Anonymous said...

I know this is a bit afield, but I have a view in mind like E.J. Lowe's (with a modification).

Roughly, one accepts primitive tensed predication and accepts that 'now' is both referential and descriptive. It refers to the time of utterance (varying from context to context) "and" describes the property had at that time as present. We then analyze the past and future in terms of it.

We capture B-theorists intuitions of analyzablility and the A-theorists intuitions of primitive presentness, and we do this allowing the variability that appears to accompany 'now'. And we avoid McTaggart's argument and awful 'at t' locutions.

Alexander R Pruss said...

It doesn't, then, sound indexical, because of that extra bit of descriptivity...

Anonymous said...

The problem seems a false one. We don't observe anything in the future, only what has already happened. So all induction is from past to past.

Alexander R Pruss said...

We make inductive predictions about the future. Let's say we have good reason to think that tomorrow you will strike a match. I conclude that it will probably catch on fire.

Anonymous said...

Alex,

Since it could be confusing, the above comment wasn't my own. Responding to your earlier point, though, the extra bit of descriptivity doesn't make the theory purely indexical. I agree. There may be some other interesting issues here too. Some respond to the problem of induction by restricting projectable predicates to non-temporally relativized ones. Such predicates wouldn't express properties that figure in laws. So, if the A-theorists accepts that her predicates are so relativized, she may have another way to sidestep the objection.

-christian

David said...

If you are right that there is a problem for the A-theorist, isn't there also a parallel problem for the B-theorist who reasons from past to future? Future events, for him, have a different property from past events: they occupy a different part of the B series. You might respond that this isn't an ontological difference; but this shows only that the problem isn't as severe for the B-theorist, not that there isn't a problem at all.

Alexander R Pruss said...

Nice question. On the B-theory, the difference between a past and a future time is a merely numerical difference, and the same kind of numerical difference is already found between different past times. Merely numerical difference is always an issue with regard to any induction, so I think that's already taken into account.