B-Theory, Language and Ethics
Alexander R. Pruss
Department of Philosophy
December 28, 2006
The A-theory of time states that there is an absolute fact of the matter about what events are, respectively, in the past, present and future. The B-theory says that all there is to temporality are the relations of earlier-than, later-than and simultaneous-with, and the past, present and future are merely relative.
There are two major arguments for the A-theory. The first is that the A-theory is more faithful to our lives as agents, thrown into temporality, caring about things in temporally asymmetric ways, worrying about future pains in ways we do not worry about past ones, or deliberating about the future and never about the past. This is the humanistic argument.
The second argument is based on the generally accepted claim that A-sentences, namely sentences that overtly involve tense or other determinations of events as past, present and future, cannot be translated into B-sentences, namely sentences that involve at most relative temporal determinations. Because some of these A-sentences are true, there must be facts in reality that the B-theory misses. I will show, however, that on the assumption that A-sentences can be translated into what I shall call “canonical A-sentences”, the B-theorist can consistently hold that A-sentences can be translated into a language, X-English, that does not carry any A-theoretic commitments.
An important fact to keep in mind is that the A-theory is prima facie ontologically richer than the B-theory. Whereas the B-theory only recognizes temporal relations between events or times, the A-theory adds to relational facts an absolute fact about what events are now or which time is now. The greater ontological parsimony of the B-theory is a major argument in favor of it. If the arguments for the A-theory fail, then the B-theory should be accepted.
What seems to be at the root of the variance in the ethical attitudes towards events in time is that they treat time as anisotropic, as if there were a significant ontological difference between forwards and backwards, in a way in which there is no significant ontological difference between what is in front of me and what is behind me. We are worried about future physical pains but not past ones. We deliberate about future actions but not past ones. We punish past actions but not future ones. We criticize people who excessively dwell in the past and the future instead of in the present. Improvement is better than deterioration: it is better to live years of vice followed by years of virtue than years of virtue followed by years of vice (Thucydides has Sthenaleidas say of the Athenians that “if they behaved well against the Mede then, but ill towards us now, they deserve double punishment for having ceased to be good and for having become bad”). And because we do not wish to live our lives without examination, we should not say that the difference between our relations to the past, the present and the future is something that we simply project onto reality.
Thus, one form of the humanistic objection to the B-theory is that it is unable to justify the complex differences in our attitudes towards the past, present and future. But now note that the A-theory as such is no better able to do so. By the theory as such, or the unelaborated theory, I simply mean the basic A-theoretic claim that the past/present/future distinction is ontologically absolute, rather than an elaborated metaphysical account of what the distinction consists in. Likewise, the unelaborated B-theory says that the distinction is merely relative, but is not committed to any particular analysis of the relations involved.
Now, both the A- and the B-theories distinguish between past, present and future events. The B-theory makes the distinction be only relational, but that is not a problem. For, in general, what attitudes are appropriate towards and event or person depends on how one is related to that event or person. It is appropriate to feel differently about the death of one’s own spouse than about the death of someone’s spouse, even though the relevant distinction is merely relational. Likewise, it can be appropriate to feel differently about present pain than about non-present pain, even if the distinction is merely relational. To gauge the appropriateness of the attitudes of a person x at time t to an event or person y we should make use of not just the absolute properties of y, but also the relation that y has to x and t. Saying that a justification is agent- and time-relative does not make it any less objective. It is an objective fact that everyone ought to feel differently about the death of their own spouse than about the death of someone else’s spouse. And likewise it could be an objective fact that everyone ought to feel differently about present pain than about non-present pain.
It is certainly true that our attitudes ought to be grounded in objective fact. But because they are our attitudes, that grounding should make reference to us and our relation to whatever the attitudes concern. This is just as in the case of our sensory perceptions. Just as I should feel worse about my daughter’s illness than about the illness of a stranger, so too an elephant in this room should be perceived differently from an elephant in another building—one in this room should look gray to me, but one in another building should not appear to me at all (a stronger claim than one that I would make in the case of the illness). This is a genuine normative requirement. If I “see” things that aren’t around me, my eyes aren’t conveying true information. It would be just as much a hallucination to have a visual perception of an existent entity that isn’t presently in my field of view, such as a the male lion in the National Zoo, as would be to perceive a completely non-existent entity such as a unicorn. And just as it is inappropriate to see things that aren’t appropriately related to the “here”, so it is inappropriate to see things that aren’t appropriately related to the “now”: for instance, there is a medical condition that causes people to periodically get visual images of things they used to be in the presence of, and such a condition is clearly a deficiency.
Thus, there is nothing objectionably subjectivistic in a B-theorist’s insistence that our attitudes at t towards events should be partially grounded in the relation we-at-t have to these events. Our senses provide genuine objective information, but also locate us-now with respect to what we perceive, and our emotions likewise locate us-now.
The mistake of thinking that a B-theory would not justify differential emotional attitudes towards past, present and future is very much like the mistake in ethics of thinking that my being ontologically on part with everyone else would justify something like the utilitarian conviction that I should strive to maximize every person’s welfare equally, completely independently of her relation to me.
However, the A-theorist may insist that while the B-theorist distinguishes between an earlier-than and a later-than relation, there is no room given a B-theory for an objective difference between these two. Now, it is true to say that an unadorned B-theory does not say what makes the earlier-than relation be the earlier-than relation rather than the later-than relation. Here an “unadorned A- or B-theory” is just a statement that there either is or is not (respectively) a fact of the matter about absolute past, present and future determinations. But neither does an unadorned A-theory say what makes the future be the future rather than the past. And of course it will not do for the critic of the B-theory who accepts an unelaborated A-theory to say that what grounds the appropriateness of fearing future rather than past pains is just that they are future, since the B-theorist can say that part of what grounds the appropriateness of fearing at time t a pain P is just that the pain is later-than t.
Thus, unelaborated A-theories and B-theories are on par with respect to anisotropy. Both can say that there is an anisotropy, but neither gives us a grounding for it. Next, observe that a number of particular ways of expanding on the A- or B-theory to make sense of the anisotropy work equally well, or equally poorly, for both the A-theory and the B-theory. Just as the A-theorist may say that the difference between the future and the past is primitive, so too the B-theorist can say that later-than is a primitively distinguished relation. Both the A-theorist and the B-theorist can try to ground the anisotropy of time in physics, say in some yet-to-be-discovered anisotropy in the laws of nature, or in the unidirectional increase of entropy, or in David Lewis’s account of counterfactuals. None of these solutions are completely satisfactory, but they can all be attempted equally well by both A- and B-theorists. It does not appear that the A-theorist’s position is at all preferable to the B-theorist’s on the above considerations.
Now, one might think that an adorned A-theory can do what an unadorned one cannot, where an adorned A-theory says something about the ontological significance of the past, present and future distinction. But note that two of the most popular adorned A-theories, namely presentism and anti-futurism, do not solve the problem, but actually make it greater. Presentism holds that only things and events that are now present are actual. Anti-futurism denies ontological status to some or all future things and events.
Given presentism, it is unclear why we should punish unreal past misdeeds rather than equally unreal future ones, why unreal future pains should worry us while no less real past ones should not, and so on. Presentism places the past and future ontologically on par—neither is real. Strong anti-futurism, the denial of the existence of any future things and events, is just as unhelpful. Why it is better to have a real past of vice and be facing an unreal future of virtue than to have a real past of virtue and be facing an unreal future of virtue is a deep puzzle. Surely if anything we should worry about past pains, since these are real, while future ones do not exist.
Weak anti-futurism denies the existence of some putative future things and events, typically future contingents, namely things and events whose existence does not follow necessarily from the laws and the present state of the universe. Thus Aristotle as a weak anti-futurist insists that neither the occurrence nor the non-occurrence of tomorrow’s sea battle is a fact, the sea battle being a future contingent.
Weak anti-futurism does better with regard to physical pains than strong anti-futurism or presentism. Future pains being contingent are within the potential realm of what we can affect, and hence it makes sense to worry about them, whereas the past ones are fixed, and beyond worry. But note that what does all the work here is not the denial of the reality of the future pains, but the claim that we can affect the future, a claim that every sane A- and B-theorist shares. Moreover, the weak anti-futurist cannot explain the appropriateness of the dread of certain future evils and the inappropriateness of having such dread towards the past ones. Furthermore, weak anti-futurism cannot explain why it is that the opposite anisotropy is often present for psychological pains—past psychological pains seem to concern us more than future ones. Weak anti-futu
Moreover, interestingly, there are partial exceptions to the anisotropy of our concerns. Suppose I read on the Internet that somebody somewhere on the other side of the world is being tortured in a particularly brutal way at 11 am today. Surely, I do not need to look at my watch and figure out the respective time-zone of the execution and my watch to know whether this was in the past or is yet to come, and hence how I should feel about this. But in my own case, obviously I would need to know whether it is in the future or the past to know the sort of attitude that I should take (to fill this out in the first person case, one of course needs to introduce amnesia, as in Parfit).
In other words, the less personally concerned we are in something, the less it seems to matter whether it is in the past or the future. If there were deep ontological differences between past, present and future, then, rationally speaking, there should surely also be a corresponding difference in my attitudes towards someone else’s future and past pains. The lack of such a difference strongly suggests that the particularly anisotropic attitudes are grounded in a difference in the relation of future and past events to me-now, rather than in some deep ontological difference between future and past events.
Suppose, on the other hand, that we adopt a particular adorned B-theory, namely a causal one that says that either time is grounded in causation, or more weakly that the order of time supervenes on the typical order of causation. Then, I claim, we can say something positive about humanistic anisotropies. I will be extremely brief and dogmatic here, since my intention is to give a suggestive sketch. I will rely on the idea that the justification of an attitude that I now have something crucially depends on the thing’s relation to me-now.
Sometimes future events have present causes. These causes may not be deterministic, but present events are at least the initiators of chains of causes that lead to future events. The roots of future physical pains or of a future non-existence are now here. Moreover, the cause of something bad is, in a sense, bad. Since it makes sense to feel more strongly about what is present now since the present is more closely related to one than the past or the future, and since the roots of future pains are here, it is appropriate to feel badly because of them. Admittedly, what we fear or dread are the future evils, but it is quite possible that what justifies dread—the attitude towards an inevitable future evil—is the present existence of the causes of the inevitable evil, and what justifies fear is the possibility of the present existence of conditions leading up to the evil.
Note that here is where there is a difference between physical pain and psychological suffering. For while past psychological suffering tends to have bad present effects, broken relationships, trauma, etc., and these bad present effects may justify certain present emotional attitudes, purely physical pain (a theoretical idealization, of course) once it is over and done with may leave fewer sequelae. Presentism and anti-futurism were not helpful here, but causal considerations remove the mystery.
While it is prima facie a bad fact about x that it is a partial cause of bad outcomes, it is not bad, even prima facie, that x comes in part from bad causes. It is tragic when a good leads to evil, but a cause for rejoicing when evil leads to good, unless somehow this good is still an intimate part of the evil (as in a criminal’s enjoyment of the fruits of crime). This may be because we rightly see the effect in the cause, and so when good comes from evil, this shows that the cause was not as bad as one might have thought, while when evil comes from good, this shows that things were worse than one might have thought. What makes vice followed by virtue better than virtue followed by vice is the causal connection: when vice gives birth to virtue we rejoice, while the decline of virtue into vice is reason to mourn. Note that if the transition occurs through an accident causing amnesia, our intuition about the relative values of the two options is weaker. Alternately, one might say that when good comes from evil, the evil has been frustrated, its evil powers thwarted and made impotent.
The future is open in the sense that what is done now affects the future. The future is the area of our causal activity’s effects while the past is not. This is why we can speak of us being thrown in respect of the past and the future as open to our actions. This gives us another reason for those who believe that death is the end of our existence to dread it. Because our projects are causal in nature, because we now want to accomplish something, a future non-existence cuts short our plans, limits our ability to cause effects in the future, in a way in which a past non-existence does not.
It is just to punish past but not future crimes because only in doing can the punishment be the effect of the crime. We feel satisfaction when a criminal’s designs are frustrated. They are frustrated when they do not give the criminal what she wants. The criminal wanted a life of opulence, but instead her fraud results in her spending years in a prison cell. We feel that it is “poetic justice” when a criminal receives suffering that “fits the crime”, and find it particularly poetic when the suffering is the result of the crime, as when the poisoner drinks her own poison.
Now, all these causal claims can be made by most A-theorists. However, if an A-theorist makes them, then either she will be a causal A-theorist, thinking that the anisotropy of time is grounded in causation—a rare but not impossible view—or else her theory will be less parsimonious than the B-theoretic account, in that one thing, causal asymmetry, will ground various ethical intuitions while another will ground the anisotropy of time itself. Moreover, as a B-theorist, she will be able to give a simpler account of how extended discourse works—facts and knowledge will not slip away as they would on the B-theory. I shall show this now.
It is generally accepted that there is no way of translating A-sentences into B-sentences. I shall argue that this is false, if you grant me a simplifying assumption.
The simplifying assumption is that every A-sentence can be translated into a canonical A-sentence. A canonical A-sentence is a sentence of the form F(now), where F is B-linguistic formula open in t, and “now” is used grammatically as a noun referring to a time, in a context where “now” refers to the speaker present. A canonical A-sentence thus involves only tenseless verbs, and does not involve the terms “past” and “future”. The only A-term in it is the word “now”. It is a precise kind of “now”—it is of noun-type.
To make my claim plausible, observe that a sentence that says that E is past can be translated into a sentence that says that E is earlier than now. More complex tense embedding can be handled without undue difficult. Thus, the optimistic claim that one future day war in the middle east will all be past translates into the claim that there is (timeless) a day d later than now such that there is (timeless) war in the middle east at some time prior to d but at no time later than d. The adverbial use of “now” as in “It is now raining” is to be replaced by “It is (timeless) raining at (the) now.” The translations can be complex, and the resulting language somewhat forced, but that should not be seriously problematic. I shall call this the “Canonicity Assumption”.
The second step in my argument is to consider some general facts about demonstratives and ontological commitment, and then construct the language X-English into which canonical A-sentences of English can be translated. Suppose I wish to tell you about an indexical that you do not know, either because you do not know the language it is in or because it is an indexical I have just made up. I then tell you that all there is the term in question is its being a directly referential (and hence rigidly referring) pure indexical defined by the answers to the following three questions:
· [Recognize] How to recognize tokens of the demonstrative?
· [Role] What grammatical and syntactic role does the demonstrative serve?
· [Reference] By what rule does a token of the demonstrative determine its referent?
I claim that this suffices to explicate or introduce the indexical. This is the “Introduction Assumption”.
I am not endorsing here Kaplan’s semantic claims about character and content. Nor am I claiming that all indexicals can be introduced in this way. All I am claiming is that it is possible to introduce a word by answering the Recognize, Role and Reference questions and by insisting that it is a directly referential pure indexical. For instance, I might introduce the word “xind” by pronouncing it clearly (Recognize), saying that it is always used adjectivally (Role), explaining that it refers to being located at a position just behind the speaker’s right shoulder (Reference), and then affirming that this together with its directly referential pure indexicality is all there is to the word—there are no further connotations, uses, etc.
I now need a crucial ontological thesis. This is that if a term is introduced by a purely indexical Recognize/Role/Reference specification, then the contribution to the ontological commitment arising from the use of the term is at most to the existence of the referent of that term. Thus, the use of “xind” commits us only to there being a place behind the speaker’s right shoulder. This is the “Ontological Commitment Assumption.”
I now claim that the Canonicity and Ontological Commitment Assumptions make it highly plausible that A-language can be translated into sentences whose ontological commitment does not go beyond the ontological commitment of B-sentences.
To do this, let X-English be an extension of English containing a new word pronounced “xow” (Recognize), playing the role of a noun (Role), which always refers to the time of the tokening of the sentence in which it is contained (Reference). (There is some vagueness as to whether it refers to an interval of time, or to some specific point of time during the tokening. This vagueness is deliberate.)
Now translate a canonical A-sentence into a sentence of X-English by replacing F(now), where F is a B-formula, with F(xow). It is highly plausible that this is indeed a good translation—this is the Translation Claim. For F(xow) carries exactly the same pragmatic content as F(now). Learning that it is raining at xow justifies us in exactly the same actions as learning that it is raining now, since it is an a priori truth that simultaneous tokenings of “now” and “xow” have the same reference (modulo the same vagueness in temporal determination). Xow-sentences can play exactly the same role in our ethical and scientific lives as canonical A-sentences do. We could take an agent speaking in canonical A-sentences, replace all of these by the corresponding xow-sentences, and all the same actions would be equally comprehensible and justifiable. If Wittgenstein is right that meaning is defined by the norms of use, then F(now) and F(xow) are synonymous.
Imagine an island of English speakers who have a restricted grammar that prohibits the from using non-canonical A-sentences. Suppose that a clever philosopher introduces half of these speakers to the term “xow” just as I introduced you to it, and pays them off to use that term instead of “now”, and makes them promise to keep the whole story secret. They quickly see that the term “xow” is equally well adapted to their ethical and scientific lives, and are willing to go for it. Other speakers on the island erroneously think that the xow-speakers are merely mispronouncing the word “now”, and the xow-speakers never explain that this is not so. Now-speakers introduce their children to now-language, xow-speakers introduce theirs to xow-language. Moreover, the xow-speakers do not tell even their children the story behind the introduction of the word “xow”. After all, we do not define indexicals when we teach them to our children—we teach the indexicals by using them.
The xow-speakers thus teach their children the use of “xow” by exactly the same methods by which the now-speakers teach their children the use of “now”. It is highly plausible that the children are meaning the same thing as the parents by the respective words “now” and “xow”. But since the xow-children were introduced to “xow” in exactly the way that the now-children were introduced to “now” it is highly plausible that they mean the same thing by the respective words, and hence by transitivity that so do their parents. After all, both sets of children live on the same island, making reference to the same times by their language, and it is implausible that any Kripkean H2O/XYZ distinction is going to be available here to show that “now” and “xow” are not synonymous. Moreover, we may suppose that as generations pass, xow- and now-speakers intermarry, and the pronunciations converge, so that after several generations everybody is saying “nsow”. Ockham’s razor dictates against trying to give an answer to the question of when the meanings converged and which meaning they converged on—it seems much simpler just to suppose that the meanings were always the same.
If I am right, then any A-sentence can be translated into a canonical A-sentence by the Canonicity Assumption. Any canonical A-sentence can be translated into a xow-sentence by the Translation Claim. And xow-sentences are of the form F(xow) where F is a B-formula. By the Ontological Commitment Assumption, F(xow) carries only the B-theoretic commitments of F together with the commitment to the existence of a referent of “xow”. But the B-theorist need have no problem in affirming the existence of a referent of “xow”—that referent is a point or interval in time. Hence F(xow)’s ontological commitments are compatible with the B-theory.
It is worth noting here that the pitfalls of older proposals of translating A-sentences into B-sentences, namely the token-reflexive and replacement-by-a-time methods, no longer apply. The token-reflexive method replaced “now” with “the time simultaneous with this utterance”. This led to the absurdity of translating “It might have been the case that there are no utterances now” as something like “It might have been the case that this utterance is simultaneous with no utterance”. No such problem here: we simply say that “It might have been the case that there are no utterances simultaneous with xow.” It is true that “xow” refers to the time of the utterance, but it does so rigidly, and without ontological commitment to an utterance being made. We can likewise say without absurdity, while pointing: “This place might not have been pointed at.” (The “xow” plays the role of “this”, and the uttering plays the role of the pointing.)
The replacement-by-a-time method replaced “It is snowing now” with something like: “It is snowing on December 28, 2006” (if that was when the utterance was made). This led to the absurdity of replacing the informative “It is now December 28, 2006” with the boring tautology “It is December 28, 2006 on December 28, 2006.” Again, using “xow” we can just say: “It is December 28, 2006 at xow.” This is informative, just as it is informative to say, while pointing, “This place is room [replace with actual room number].”
Since the translation of a sentence carries the same ontological commitments as the original, it follows that A-sentences do not ontologically commit us to anything beyond what the B-theory can countenance. Moreover, the anisotropy in our ethical lives makes at least as much sense on a B-theory as on an A-theory, and makes more sense on a causal B-theory than presentism and anti-futurism. Given that the B-theory is ontologically less committal than the A-theory, we not only have answers to the humanistic and linguistic arguments.
 For an extended, entertaining and enlightening discussion of such disanalogies, see Richard M. Gale, “Disanalogies between Time and Space”, Process Studies 25 (1996), 72–89.
 It seems as if this might be the way in which Gale (ibid.) argues for the A-theory.
 Of course there are non-relational differences. Perhaps one’s own spouse is smarter than the spouse of someone else. But such differences are plainly not what grounds the difference in attitudes that I am interested in.
 This observation seems sufficient to vitiate one of the main arguments against the B-theory in Cockburn (op. cit.).
 We know of a Charge-Parity-Time reversal violation, but this does not seem like at all the sort of thing that could ground the humanistic intuitions in question.
 See the discussion by Larry Sklar (Physics and Chance: Philosophical Issues in the Foundations of Statistical Mechanics. Cambridge: Cambridge University Press, 1993, pp. 397–404).
 See David Lewis, “Counterfactual Dependence and Time’s Arrow”, Noûs 13 (1979), 455–476. This has been criticized recently by Adam Elga (“Statistical mechanics and the asymmetry of counterfactual dependence”, Philosophy of Science, supplement to volume 68 , PSA 2000, S313–S324) and by Alexander Pruss (“David Lewis’`s Counterfactual Arrow of Time”, Noûs ). A forthcoming article by Barry Loewer (“Counterfactuals and The Second Law”, in: Causation and Counterfactuals, ed. Huw Price, Oxford: Oxford University Press, forthcoming) defends the approach.
 For a now-classic discussion of the asymmetry in the fear of death, see the first essay in Thomas Nagel, Mortal Questions, New York: Cambridge University Press, 1979.