Friday, May 7, 2010

Translating A-sentences to B-sentences

I won't spell out a full method here, but I will give an example.

  1. It was sunny five minutes ago.
  2. It is sunny five minutes prior to t0 (where I let t0 be the time of this utterance).
This translation method makes use of a communicative tool that is always available to us—to stipulate new terms or symbols. Note that the parenthetical phrase is not a part of the assertion and while it is grammatically declarative, this is a declarative of stipulation rather than a declarative of assertion. In fact, the parenthetical functions exactly like prefixing with the grammatically imperative sentence: "Let t0 be the time of this two-sentence utterance."

This avoids the standard problems with the token-reflexive method of translating A-sentences to B-sentences, such as the problem that we don't want the B-sentence to entail the existence of an utterance when the A-sentence does not. Indeed, (2) does not entail the existence of an utterance or of myself. In embeddings, the parenthetical remark functions in the wide scope. For instance:

  1. It might have been that there are no speakers now.
  2. It might have been that there are no speakers at t0 (where I let t0 be the time of this utterance).
(I don't translate "It might have been" because it is just a colloquial way of writing the box operator rather than something for a theory of time to take account of.) There is no absurd claim that there might have been no speakers at the time of this utterance, but only that there might have been no speakers at t0.

In English, and I assume in many other natural languages, we have two ways of picking out what was said: sometimes we pick out the sentence and sometimes the proposition. Thus:

  1. A: It is sunny now. B: I hope you will always remember that.
  2. A: It is sunny now. B (after a pause): That's no longer true.
In (5), B is picking out A's proposition, and hoping A will remember it. (Maybe it's a romantic moment.) In (6), maybe it has started raining, and B is picking out A's sentence, and saying it's no longer true. Now, here are my translations of (5) and (6):
  1. A: It is sunny at t0 (where I let t0 be the time of this utterance). B: At t1, I hope that after t1 you always remember that (where I let t1 be the time of this utterance).
  2. A: It is sunny at t0 (where I let t0 be the time of this utterance). B (after a pause): At t1 a restatement of your whole sentence, including the stipulative portion, is no longer true (where I let t1 be the time of this utterance).
The stipulative parenthesis is wide-scoped for purposes of embedding, including in "is true".

So, we can translate A-sentences into B-sentences. Since the B-theory is simpler than the A-theory, and fits better with science and theology, we should all become B-theorists at t0 (where I let t0 be the time of this utterance).

32 comments:

Dan Johnson said...

Alex, this is close to what I say in my dissertation (in the part I haven't sent to you yet). I think a few things need to be different, though.

First, paraphrase/translation (I take these to be the same) is a relation between sentences. The following is a condition on paraphrase: if sentence A is a paraphrase/translation of sentence B, then utterances of sentence A are true in all and only the same circumstances as utterances of sentence B.

But your translations fail that test. If I utter sentence C, "It is raining now," you translate as sentence D, "It is raining at t0." But then when I utter sentence C five minutes later, suppose it is false, but sentence D is still true. So the translations you provide for sentences employing tense or A-determinations are not good translations.

Here is how I think your point can be salvaged, though. The first step is this. Suppose that words like "now," "present," "future," and tensed copulas function as indexicals, as B-theorists have long claimed. Then your sentence (1), though it cannot be translated into sentence (2), expresses the same proposition as sentence (2). The distinctive thing about indexicals is that sentences employing them express different propositions when they are uttered in different situations.

The second step is this. Deny that you need a translation/paraphrase to get out of ontological commitment. Instead, you need an ontological explanation (in my sense) -- which is a relation between propositions, NOT sentences. The B-theorist can give ontological explanations of the propositions expressed by A-sentences, explanations that do not make use of tense or A-determinations.

In sum, even though the B-theorist cannot give TRANSLATIONS of A-sentences that don't employ A-determinations, they can give ONTOLOGICAL EXPLANATIONS of the propositions expressed by A-sentences that don't employ A-determinations. This is exactly what they need to do to get out of ontological commitment to A-properties.

And B-theorists should not expect to be able to give paraphrases/translations of A-sentences that reduce the A-determinations out -- you generally can't give genuine paraphrases of any sentences involving indexicals that get rid of an indexical element because the sentences need to be able to express different propositions when uttered in different circumstances. The B-theoretic strategies up until now have generally tried to replace temporal indexicals (A-determinations) with other indexicals ("this" utterance) but that hasn't worked either because they are different sorts of indexicals.

Does that sound good to you?

Dan Johnson said...

Addendum: I actually think that what you say in the second half of your post (that the sentence "it is sunny now" is no longer true but the proposition expressed by the sentence remains true) is in tension with what you say in the top half (that the eternally-true sentence is actually a translation of the sentence that is false when uttered at a different time).

Now, maybe you were thinking that you were giving a translation of a sentence token rather than a sentence type. But I don't know how it is even possible to give translations of sentence-tokens unless you are giving a translation of the type that the token instantiates -- because your translation will be a different token.

Alexander R Pruss said...

Dan:

The parentheticals should be reckoned with the translation for the purposes of evaluation of the translation. Thus, I translate "It is raining now" as "It is raining at t0 (let t0 be the time of this utterance)."

There is one tricky point I haven't figured out--what does "this" refer to in the translating utterance? The same issue comes up in general in translations of self-referential sentences. Consider English*, which is just like English, except the word that means sentence is "abacadafagahajakalamanaparasatawaxaza". Then consider the English* sentence "This abacadafagahajakalamanaparasatawaxaza contains a very long word." The English translation of this would seem to be "This sentence contains a very long word." But the English* sentence is true while the English one is false. Isn't that weird? This suggests something may be wrong with your criterion for translation.

But maybe "This" in a translation refers back to the original utterance. I think that's kind of how we handle indexicals in translation. If you say in French "Je suis americain", and I am to simultaneously translate you into English, I will say: "I am American", but my "I" refers to you, not to me.

Likewise, if you say "Cette phrase est en francais", I should translate as "This phrase is in French", and then take the "This" to refer back to the original. That's at least what I'd do if I was subtitling or dubbing a movie.

I think it's because translatese is understood differently from non-translatese.

Dan Johnson said...
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Dan Johnson said...

I don't think that self-referential sentences pose a problem for my criterion. My criterion just says this: if A translates B, then utterances of A and B would be true in all and only the same situations. But with self-referential sentences, the situations are relevantly different: when A is uttered, A is part of the relevant situation that determines the truth of the sentence; but when B is uttered, A is not part of the situation. The key is this: A and B remain different sentences, and so they can make it so that the situations are relevantly different.

Alexander R Pruss said...

That's true: we should distinguish the context that the uttering itself creates from the context of the utterance. And a translation itself creates a different context for itself.

Dan Johnson said...

I think I'm beginning to get your move better now. Two comments:

It seems that your method of translating is compatible with my point that it is really the propositions that matter for ontological commitment, and B-theorists can handle the propositions even if they can't translate the sentences. Notice though that it is still true that seeking out translations isn't that important; it is the propositions that matter, and ontological explanations of those propositions. The B-theorist could go with a translation of A-determinations into other sorts of indexicals ("this"), as the token-reflexive folks do and as you do; or you could just claim straight out that the A-determinations function as indexicals themselves without translating them into other indexicals. Either way works for the B-theorist.

Second, a question: can you handle nested temporal operators? "In two years my dissertation defense will be a thing of the past." I know that this is a problem for the token-reflexive folks.

Justin Martyr said...

Since the B-theory is simpler than the A-theory, and fits better with science and theology, we should all become B-theorists at t0 (where I let t0 be the time of this utterance).

1. Evidence counts for more than simplicity. The fact of temporal becoming is a powerful empirical observation that is inconsistent with the B-Theory.

2. Simplicity is only one aspect of making a good inference. Explanatory scope also matters. Right now physicists have a bit of problem in trying to harmonize quantum mechanics and relativity. My outsider's understanding is that most physicists take quantum mechanics to be fundamental, not relativity. They subscribe to relativity simply out of positivism.

(and we can pretty easily say that presentism defeats McTaggert's paradox)

Justin Martyr said...

I should have clarified above that being able to coherently talk about events that come before or after each other in time is not a substitute for explaining temporal becoming. E.g. I can move left and right through space, but I cannot move forwards and backwards through time.

Alexander R Pruss said...

Dan:

Yes, there is the direct indexical move. I think it's taken the philosophy of time literature way too long to catch up with Kaplan's work on indexicals.

"In two years my dissertation defense will be a thing of the past." -- "There is such a time as t0 + 2 years, and my dissertation defense is prior to that time (where t0 is the present time)."

JM:

I am afraid I don't know what you mean by "temporal becoming". I've heard that term, and I've heard people try to explain it. But I don't get it. Here are a few options:

1. Temporal becoming just is the A-theory's correctness or the truth of presentism. Well, then, the argument is question-begging.

2. Temporal becoming is the objective difference between later and earlier. Well, this is just as hard to explain for the non-open-future presentist and the moving-spotlighter as for the B-theorist. I say that the direction of time is just the predominant direction of causation, and I think this is also the best the non-open-future presentist or the moving spotlighter can say. Granted, here, the open future presentist and the growing block theorist have other options, but what I just said is enough to show that the direction of time is not per se concerned with the A/B debate.

3. Temporal becoming is some sort of a motion through time. But what is motion? I know of two stories. One is just the at-at story. Motion is just being at x0 at t0 and at x1 at t1. Well, then, anything that exists at both t0 and t1 moves through time--it is at t0 at t0 and at t1 at t1. (This may be argued to require endurantism, but a B-theorist can be an endurantist.) And this is independent of the A/B debate. The second story supplements the at-at story with some sort of causal stuff. But again that's independent of the A/B debate.

4. Temporal becoming is [insert your favorite metaphor here, like the river of time]. Then things will depend on how the metaphor is to be cashed out and on judgments whether a given theory does or does not fit with the metaphor.

Dan Johnson said...
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Dan Johnson said...

Alex,

That is a nice way to handle the nested temporal operators. Notice, though, that you must eschew any wooden requirement for translating "past," "present," and "future," because these individual words have to be translated somewhat differently when they are nested than when they aren't. In other words, you can't say that "is past" is always translated "is prior to time t0, where t0 is the time of this utterance" -- because then you can't have the translation of the nested operators that you want.

I don't think that is a problem for you, though. It just means that words can't be woodenly replaced in translation; you have to take into account the surrounding context.

Justin Martyr said...

Alex,

Thank you for the kindness of a reply.

I suppose I would take option #3 - motion through time. But I would add a restriction that this motion only happens in one direction. Why can I move left or right through space, but not forwards and backwards through time?

I suppose this is where the B-Theorist might add "some causal stuff" (to use your phrase from your comment to me). But correct me if I'm wrong, but that causal stuff does not follow from relativity. That means that B-Theorists also need to add an epicycle to relativity.

Alexander R Pruss said...

Sure, the causal stuff doesn't follow from relativity, but it is compatible with it, and we need causation anyway for lots of stuff (e.g., agency).

As for the forwards/backwards thing, even on the at-at theory, temporal motion is unidirectional. At t0, one is at t0, and at t1, one is at t1. Therefore one's velocity of temporal motion is (t1-t0)/(t1-t0) = +1, and hence is always positive. On the other hand, one's velocity of spatial motion will be (x1-x0)/(t1-t0) which may be negative, zero or positive.

Drew said...

I'm curious about how you reconcile this theory with actual infinites.

Do you believe that the future will be unending?

Do you believe that actual infinites are possible?

As you noted in a previous post, the existence of actual infinites has to contend with the Grim Reaper paradox. If actual infinites could exist, then the Grim Reaper paradox could happen, which is absurd.

But if actual infinites are impossible, then the B-theorist has to abandon any notion that the future will go on forever. Time has to have some sort of back edge to it, which also seems absurd.

Alexander R Pruss said...

1. I think the future is unending and infinite.

2. I am troubled by actual infinites. However, there are two sorts of arguments I have against them. First, some probabilistic arguments. Second, Grim Reaper arguments. I don't know exactly what to do with the probabilistic arguments, but they apply just as much given presentism and an infinite future. It may be that these probabilistic worries are less compelling given a future-directed sequence. Second, the Grim Reaper arguments only establish the following thesis: No object or event can an infinite number of objects or events in its causal history. To be honest, I don't know what more to say. There is a tension in my views.

Alexander R Pruss said...

Maybe what I should say is something like this:

A. It is not possible for an object or event to have an infinite number of objects or events in its causal history.

B. While it is possible to have infinite multiverses, in these multiverses, and in infinitary situations analogous to them, non-deductive reasoning breaks down. (In particular, if a scientific theory holds that we are in an infinite multiverse, it is self-defeating.)

I think A and B may be all I need.

Drew said...

I would definitely deny that there is any infinite problem with actual infintes and presentism. Under presentism, the number of causal events in history will always be finite. Even if it is unending, there is no point where it will be infinite.

I'm glad you admit there is a tension in your views. If it is true, then we do have an infinite number of objects in our causal history. So why not abandon the B-theory? Our experience indicates that we live in a 3 dimensional universe where objective change occurs, not a static 4 dimensional universe. We don't experience time in the same way we experience height, width, and depth. And unidirectional causality fits the A-theory much better than the B-theory (under which, why would we have any reason to suspect causality in the first place).

Alexander R Pruss said...

Drew:

Future history includes an infinite number of events, but past history does not.

On presentism, if the future is infinite, there will still be infinitely many facts like: in one day, somebody will exist; in two days, somebody will exist; .... That's all that's needed to generate the probabilistic problems.

"Our experience indicates that we live in a 3 dimensional universe where objective change occurs, not a static 4 dimensional universe."

I don't see why the B-theoretic view should count as "static". That characterization begs the question.

"We don't experience time in the same way we experience height, width, and depth."

Right, and time is not the same as height, width and depth. For instance, time gets a minus sign in the metric.

"And unidirectional causality fits the A-theory much better than the B-theory (under which, why would we have any reason to suspect causality in the first place)."

Presentism as such is fully symmetric between past and future: it simply says that only present events and things are real. Moreover, I don't see any reason to believe in causality given A-theory that isn't also a reason to believe in causality given B-theory.

Drew said...

On presentism the future is not infinite. It is unending, but at no point does it reach actual infinity. Such questions as "how many events will occur in the future" returns an answer of potential infinity, but not actual infinity. Or you could label the answer as "undefined" or claim that the question is as meaningless as "what is north of the north pole." All options are open to the presentist, but not to the B-theorist.

And how can the B-theory be dynamic and undergo objective change, unless it is combined somehow with the A-theory? But these ideas like the constructing block theory seem to posit two dimensions of time. We have the timeline itself, where multiple times are equally real, but then we have this objective change happening in a dynamic dimension of time. How is this second dimension not presentist?

Alexander R Pruss said...

According to the B-theorist, objective change just is a matter of things being one way at one time and another way at another time (perhaps with a causal tie).

On presentism, surely the following questions should make sense:
1. Will anyone exist tomorrow?
2. Will anyone exist the day after tomorrow?
3. Will anyone exist the day after the day after tomorrow?
...
And if theism is true, and God is in time (hard to see how he would not be on time given presentism), then the answer to each question is affirmative. Therefore, for any finite number N, there will be at least N future days. But if for every finite N there will be at least N Fs, then there will be infinitely many Fs.

Drew said...

No. There will be an undefined number of F's, or there will be a potential infinite number of F's, or asking someone to define the number of F's without placing a limit makes it incoherent. No need for actual infinites here.

Alexander R Pruss said...

Do you grant that for every finite N there will be more than N events?

But that seems to be just what "There will be infinitely many events" means.

Marc said...

Dr. Pruss:

And if theism is true, and God is in time (hard to see how he would not be on time given presentism), then the answer to each question is affirmative. Therefore, for any finite number N, there will be at least N future days. But if for every finite N there will be at least N Fs, then there will be infinitely many Fs.

This resembles one of the objections which Morriston raises against Craig, but I don't think it succeeds. I'm suspicious of the coherence of future-oriented statements of the form: there will be infinitely many Fs. It seems to me unusual to hold that while there will be no temporal point at which some future state of affairs obtains, it will obtain nonetheless.

Here's a familiar scenario to illustrate the problem. Suppose that Jones is standing 10 feet from a wall. Whenever authorized, he proceeds incrementally toward the wall by decreasing his current distance by one-half. Jones receives his authorization from God who tells him to proceed forward once a single day has elapsed. Unfortunately for Jones, he'll never finish his project and reach the wall. However, given absolute convergence, if there will be an actually infinite number of future days and Jones proceeds forward at the end of each day--i.e., there's a one-to-one correspondence--then it seems he'll eventually reach the wall. But to reach the wall, he'd have to simultaneously traverse one-half of his current distance to the wall as well as the entire distance, which is impossible.

Now perhaps there's a (cardinality?) problem with the illustration itself, but it appears to diffuse Morriston's objection.

Alexander R Pruss said...

"It seems to me unusual to hold that while there will be no temporal point at which some future state of affairs obtains, it will obtain nonetheless."

The statement "There will be exactly three world wars" seems to make perfect sense, even if there is no future time at which there will be exactly three.

What does the statement mean? Well, on the eternalist's view, it just means that there are three world wars that are in the future. On the presentist's view, it's rather complicated to express the statement, but it had better make sense if presentism is plausible (David Lewis has a paper showing how to express things like that). For exactly the same issue comes up with regard to the past, and surely "There were exactly two world wars" is true.

Drew said...

Even if I granted the statement "there will be an infinite number of future events" does this mean that presentism affirms the existence of actual infinites?

I think not.

This is for the presentist, an admission to potential infinites, but under presentism, an infinite number of events will never be actualized. The number of events will always be finite but growing.

And even if I answer "infinite" to the question as to how many events will happen, that doesn't commit me to actual infinites any more than being asked the question "how many children does the average American family have" and answering "2.5" This isn't an an admission that there is any such thing as an average family or that there is such a thing as having 2.5 children.

Alexander R Pruss said...

Agreed. But the infinites don't have to be actual to generate the probabilistic problems that worry me.

Marc said...

The statement "There will be exactly three world wars" seems to make perfect sense, even if there is no future time at which there will be exactly three.

What does the statement mean? Well, on the eternalist's view, it just means that there are three world wars that are in the future.


What exactly is designated by the words "will be" if not something like "will happen" or "will obtain"? Regarding your statement, if there's no future time at which there will be exactly three world wars, that seems to deprive the statement of (part of) its essential meaning. How do we account for something's being in the future yet never becoming present, even if it's allegedly infinitely distant from now?

Alexander R Pruss said...

Surely it makes perfect sense that so far, there were two world wars. Yet there was never a time at which there were two world wars.

Marc said...

Surely it makes perfect sense that so far, there were two world wars.

Agreed.

Yet there was never a time at which there were two world wars.

I guess I'm unclear about what you mean here. I wonder if I'm misunderstanding your terminology. (You're probably speaking more precisely than I am. =) )

If t = the year 2010, isn't it true at t that there were two world words? And, if t = the year 1900, it's false at t that there were two world wars?

Alexander R Pruss said...

There is no time at which two world wars are present. I thought that was your worry about an infinity of future events--that there is no time at which there are infinitely many events.

At t = 1900, it is true that there will be at least two world wars, unless one combines the presentism with open futurism.

Marc said...

Thanks for the clarification, and apologies for my imprecision. I'll try to better express my worry about an infinity of future events.

You suggested earlier to Drew that "there will be infinitely many Fs." Statements of this sort give rise to my worry, as I don't understand what could serve as their truth conditions. Such conditions seem unavailable.

At t = 1900, it's true to say that there will be at least two world wars because there will be another time (say, when t = 2010) when the world's history includes the obtaining of two world wars. In 1900, the two world wars are in the future because they will happen. But how do we coherently say that an infinite number of events will happen? Stipulating that the past isn't actually infinite, there will never be a time in the future at which the world's history includes an actual infinite number of events.

If so, it doesn't appear meaningful to say, for example, "there will be infinitely many Fs" in the future.