## Friday, January 18, 2013

### More on the Principle of Sufficient Reason and A-theory

Update: My comment of Jan. 19, 2013 may contain a satisfactory answer.

In an earlier post, I argued that asking why it's 2013 presently forces the A-theorist to deny the Principle of Sufficient Reason (PSR). Let me expand on that argument. Here's a thought about my main argument.

Suppose the PSR is true. With the typical A-theorist, consider the proposition q that it is 2013 presently to be a contingent proposition that changes in truth value—it was false a couple of weeks ago and will be false again in a year but is now true. Let p be the ultimate explanation of q. For if PSR is true, there are ultimate explanations. Cf. my PSR book. Then either p is a proposition that is true at all times or it is a proposition only true at some times.

But it is incredible what proposition that is true at all times (in 2012, in 94994 BC, etc.) would explain why it is 2013 presently.

But if p is true at some but not all times, then p can't be an ultimate explanation, because it is unexplained why p is presently true, rather than this being one of those times where p is false.

So, either way, we get a contradiction.

The typical B-theorist, on the other hand, will say that all true propositions are eternally true, so q, if there is such a proposition at all, is eternally true, and there is no difficulty about explaining it with another eternally true proposition.

Objection: But Pruss has argued at length (say, in the PSR book or here) that it is possible to explain a contingent proposition with a necessary one. So why can't one explain a non-eternal truth with an eternal one, explaining q with an eternal truth p?

Response: I just don't see any plausible way to do it, that's all. I wish I had something more rigorous to say here.

elliottroland said...

I made a comment on your earlier post, but I think it might've been missed because of all the other comments, so I thought I'd make the same comment here in a hope of getting a response from you Dr. Pruss :)

I suppose I could phrase it like this: "It is now 2013" is explained by (or even equivalent to) a fact of the form "N years have elapsed since the beginning of time". Now it seems plausible to me, that if the A-theorist can explain why time elapses at all, then she can explain why N years have elapsed in a similar fashion.

Now if the A-theorist holds to a relational view of time, then time elapsing can be explained with reference to events that happen (which themselves can be explained, according to the PSR). And if she holds to a substantial view of time then I imagine she could explain it with reference to whatever mechanism causes time to elapse (God, perhaps?) Do you see a problem with explaining why N years have elapsed along these lines?

I have three further questions: 1. Do B-theorists typically take B-theory to be necessarily true? Because, if not, given that the PSR must be necessarily true and A-theory is possibly true, if follows that the PSR is false. I don't like this, because I believe the PSR :P

2. On A-theory, is there more to the proposition "The present year is 2013" other than a sort-of identity? Because if not, then to explain that proposition is to explain "The present year in 2013 is 2013", which is necessarily true. (Please forgive me if that was a stupid question)

3. With regard to your earlier post, to explain why "God created time N years ago" is it sufficient to explain why "God created time N years ago" (as opposed to, say, him creating just an apple)? I seem to recall you having a post a while back where you italicized different parts of the proposition (I think it was about contrastive explanations), but I can't quite remember the conclusion of that post.

Heath White said...

This objection is the one I was going to raise.

Put it this way. Necessary truths are a subset of eternal truths and non-eternal truths are a subset of contingent truths. Your position is that (1) Necessary truths can explain contingent truths, but (2) Eternal truths cannot explain non-eternal truths.

It follows that (3) Necessary truths cannot explain non-eternal truths. If we add the PSR (4) that all contingent truths have an explanation, then we get (5) no contingent truths are non-eternal, i.e. B-theory.

But how to defend the combination of (1) and (2)? You want to say that “A.P. invented a new argument for B-theory prior to this assertion” is explained by some necessary N, while “A.P. invented a new argument for B-theory in the past” cannot be explained by N. I am not clear on why the first attempt at explanation works but the second fails.

(Maybe the following? If N could explain “A.P. invented a new argument for B-theory in the past” it would also have to explain “A.P. invents a new argument for B-theory in the present” and “A.P. will invent a new argument for B-theory in the future.” But that is impossible.

Reply: According to the libertarian+PSR advocate, if N can explain “A.P. freely mows his lawn” it can also explain “A.P. freely refrains from mowing his lawn.” That seems just as impossible.)

Alexander R Pruss said...

Elliott:

But why have N years elapsed? (Rather than N+1 or N-1, say.) Because time began N years ago? But why did it begin N years ago? :-)

Heath:

I think that when a reason R favors an action A, and A is done for R, that explains A. If it's a necessary truth that the agent (in this case, of course, God) has reason R and A is contingent, then this is a case of a necessary truth explaining a contingent truth. This is true even if it's also a necessary truth that the agent has a reason R' against A, that would have explained non-A had the agent acted on it.

I did not mean to commit myself in this post to the general thesis that no eternal truth can explain a non-eternal truth. I thought about that thesis, and there seems to be a counterexample. Suppose God necessarily has very good reason R to ensure that some event type E is only very rarely exemplified, and suppose that that E is exemplified at some time but not at present. Then R explains why E is only very rarely exemplified as well as why it's not exemplified now. It's a stochastic kind of explanation.

So the referent of "it" in my "Response" isn't "explain[ing] a non-eternal truth with an eternal one" but "explaining q [that it's 2013 presently] with an eternal truth p". I just didn't see how to pull that off.

Maybe there is a way. Could one say this? Because 2013 is such a great year (after all, the events in every year give praise to God), God necessarily had reason to create it and make it present. And every year is made present by God when it is present.

Jonathan D. Jacobs said...

What is the B-theorist's answer to the question, "Why did God create the world N years ago rather than N-1?"

Jonathan D. Jacobs said...

What would the problem be with a Ross Cameron style answer to this issue. Let the world have both an age and a temporal distributional property. A temporal distributional property is the property of being thus-and-so across time (i.e., being such that at time n, things were so-and-so, at time n+1, things were thus-and-such, etc.). These are features the world presently has, so it's consistent with presentism. And so long as we have an explanation (a theistic one?) for why the world has those properties, then it's consistent with PSR. And, it seems to me, whatever explanation a B-theorist gives for why the world has such a distributional property will suffice for the A-theorist. Or am I missing something?

Alexander R Pruss said...

Jon:

Well, the B-theorist will take this to express the same proposition as "Why is it that God creates the world N, rather than N-1 or N+1, years before t1", where t1 rigidly refers to some time.

Now, it could be that times are individuated by how far they are from beginning. So, then, <God creates the world N years before t1> is entailed by: <God creates the world N years before the time that is N years after the beginning>. And this, in turn, is entailed by: <God created a world that has a temporal beginning and that will last at least N years.> (We need the latter contingent fact, or else there might be no time that is N years after the beginning.)

Alexander R Pruss said...

Jon:

As to the Cameron-style answer, how do we ultimately explain why the world has age N?

Our ultimate explanation will either be eternally true or non-eternally true. If it's non-eternally true, then we're going to have more questions of a similar sort, and it won't be ultimate. (E.g., "the world has age N because N years ago God created it". But why did God create N years ago.) If it's eternally true, it's hard to see what it is going to be, unless something like the answer I offered in my response to Heath works. And I am becoming more friendly to that answer the more I think about it.

Elliott:

Ad 1: I would think B-theorists think it's impossible to have a world governed by an A-theory.

Ad 2: On the B-theory, the statement may be just an identity conjoined with an eternal claim that time includes 2013. But on the A-theory it can't be just an identity, because identities are eternal, and I mean this to be a non-eternal truth. Think of concrete ways of spelling it out on particular A-theories: "2013 is on the leading edge of reality" (growing block), "2013 is lit up" (moving spotlight) or "2013 is the year that includes all events" (presentism).

Ad 3: That's an interesting suggestion. I wonder if my present argument requires not just explanations but contrastive ones.

elliottroland said...

Dr. Pruss, assuming I held a relational view of time couldn't I say that N years have elapsed because the earliest and latest events are separated by N years? Or, the latest events occur N years after the beginning of time (since, on the relational view of time, time is reduced to events)?

You might then ask why such-and-such event happens N years after the beginning of time. But since this is a tenseless question, the A-theorist can just use whatever answer the B-theorist uses. I suppose, we could explain this in terms of the preceding events, and their preceding events, and so on... which seems as possible on A-theory as it is on B-theory.

elliottroland said...

Also, thanks for the answers to my other questions.

1. Yeah, now that I think about it, A- and B-theory seem to be theories about the very nature of time. And time would necessarily have its nature.

2. Does the proposition "Barack Obama is president" not represent a non-eternal identity? Or are we speaking of a different sort of identity?

3. If your argument does require contrastive explanations, then am I right in thinking that the A-theorist needn't necessarily deny the PSR? (just trying to get a handle on the dialectical situation here)

Alexander R Pruss said...

Elliott:

Doesn't "latest" basically mean "present" here? And if so, then the proposed explanation is just that the beginning and the present are separated by N years. And we're back to where we were.

Ad 2: I was thinking of identities involving rigid designators. "The president" isn't rigid, as its referent differs between worlds (and times). Identities involving definite descriptions certainly tend to call out for explanation.

Ad 3: Maybe. There is a question of just how weak this PSR would be.

Michael Gonzalez said...

Pruss,

The eternal truth is that, over an infinite amount of time from the beginning of time onward, all points in time will eventually be instantiated. So, "14 billion years after beginning" is a time that will eventually be instantiated. The only contingent fact here is that you asked the question now, instead of last year. And the PSR dictates that there are reasons why you asked it now and not at some other time. But, as such, it is no problem for A-theory.

As to "why did God begin the Universe N years ago?", I really think one has to look at it from the other direction. God didn't create with a view to when you would ask this question; He created at the very first instant of time. Absolutely zero time had elapsed prior to that point. So there were no other times at which He could have created; in other words He didn't choose from among any options.

Finally, if you consider Kalam-style arguments, you realize that the very existence of a finite Universe (finite in time, and having an absolute beginning, that is) necessitates the existence of a Cause who is a free agent. Otherwise the timeless state could not alter. I often say, tongue-in-cheek, that God was a B-theorist until He made the first change via His free will to do so. As such, He is now dynamically in time (I agree with Craig on this one). It seems to me that a B-theorist would have more of a problem answering "why is the space-time block only this big?" -- that is to say, why does time extend only from this point on -- than the A-theorist has in answering "why did the Universe begin to exist only when it began to exist, and not at some other time?".

Alexander R Pruss said...

Michael:

Does the fact that something happens at some time explain why it is happening now (rather than, say, yesterday or tomorrow)? Maybe, but it's not clear.

"So there were no other times at which He could have created; in other words He didn't choose from among any options."

Suppose that right now is the moment of creation. Then the following is true: God is presently creating. But why is he creating presently, rather than, say, yesterday? After all, the proposition that God was creating yesterday is metaphysically possible, and indeed will be true tomorrow.

You say that he couldn't have created yesterday, because there was no yesterday, if this is the first moment. But now I ask: Why was there there no yesterday? After all, the proposition that there is a yesterday is metaphysically possible, and indeed will be true tomorrow. So why isn't it true presently?

Well, maybe because presently it's the beginning of time. But that takes us back full circle.

Alexander R Pruss said...

I should note that I am using "yesterday" as a definite description rather than rigid designator here.

Michael Gonzalez said...

Dr. Pruss:

"Does the fact that something happens at some time explain why it is happening now (rather than, say, yesterday or tomorrow)? Maybe, but it's not clear."

The answer is that, on an A-theory, things ONLY happen "now". That is to say: for any X, if X is happening, it is happening "now". So, to ask, why is X happening "now" is not meaningful (or, at least, it's redundant). It reduces to "why is X happening?", which isn't the question you mean to ask. Thus, it is 2013 "now", because you're asking the question "now". And the only contingent fact to be considered is "why did Alexander Pruss ask that question in 2013 instead of 2012?".

"After all, the proposition that God was creating yesterday is metaphysically possible, and indeed will be true tomorrow.
"

At the first moment of time, the proposition "God was creating yesterday" is actually metaphysically impossible. The full statement would be "God was creating at a time prior to time" which is a self-contradiction.

Or, let me put it another way: It is metaphysically impossible that X should occur at a point earlier than the earliest possible point.

I think the elephant in the room is that "yesterday" is a moving target (just as "now" is). "Yesterday" (or N-1, etc) does not denote a particular time, but a time relative to when you're asking the question.

Michael Gonzalez said...

"I should note that I am using "yesterday" as a definite description rather than rigid designator here."

I suspected. But the point remains: "Yesterday" is relative to when you ask the question. And the PSR applies perfetly to the contingent fact "Pruss asked the question in 2013 rather than 2012".

Michael Gonzalez said...

Finally, Dr. Pruss, I am genuinely curious how the B-theorist answers the symmetrical question: "Why is the space-time block only as large as it is?". I'm presuming that the Universe is finite, and thus time has a "beginning point" (analgous to a block of cheese having a "farthest left edge"), even if it has no ending point. So the question of "why is the beginning edge here, rather than farther left?" seems rather more damning of the B-Theory than your question is of A-Theory.

But perhaps I'm not seeing it correctly.

Alexander R Pruss said...

I think you're actually starting to talk like a B-theorist here. It is the B-theorist who interprets tensed utterances as relative to the time of utterance.

How can what is metaphysically possible change? The metaphysically necessary can't change, since the metaphysically necessary is what is necessary no matter what. But something is possible if and only if its denial is not necessary.

As for the analogous question for the B-theorist, if we consider two times identical provided that they are equidistant form the beginning of time, then set of times couldn't have gone further back than it did.

elliottroland said...

Dr. Pruss:

I'm not sure "latest" and "present" are the same thing here. I could take any set of events (say, those between 2004 and 2005) and ask which the latest one is. All this would be is the last element, when these events are ordered temporally. Now, how is this any different if I consider the set of all events that have happened? I seem to be no more committed to equating the latest event in that set with the present as I was with the case of the smaller set.

I guess we could look at it like this: consider some time interval of seconds [t0, t1]. What is the explanation that t1-t0 seconds elapsed in this interval? Well, because there were events at t0 and at t1 which were separated by a span of t1-t0 seconds (which a bunch of other events between, no doubt). I'm not sure if that was worded entirely correctly from the relational view of time, but hopefully it was clear enough to get my point across. Perhaps, similarly, to explain why N years have elapsed, I could start with all the events that have taken place, ordered temporally, and say, "time began, then e1 happened, then e2 happened, then e3, ..., then eK happened" where eK is the last event that has happened. This would explain why N years have elapsed. To explain why only N years have elapsed, I could say that {e1, ..., eK} are all the events that have ever happened.

We might ask why only these events have happened and no more, but I imagine we could answer this question the same way the B-theorist would explain why only these events have happened (and no more) prior to some point in time in 2013.

Michael Gonzalez said...
This comment has been removed by the author.
Michael Gonzalez said...

"It is the B-theorist who interprets tensed utterances as relative to the time of utterance."

I think all people have to interpret a tensed utterance relative to the time of utterance. How could it be otherwise. If you ask "why did God create the Universe 14 billion years ago?" at a time when the Universe is actually only 13 billion years old, your question will have quite a different answer than it would have if you asked it now! LOL. Honestly, it seems to me that the only contingent fact here is when you asked the question, not when the Universe began. The Universe began at the first instant of time, and it could not have been otherwise. Or, in other words, the first point in time must always occur at the first point in time.

"How can what is metaphysically possible change?"

It doesn't change. It is ALWAYS the case that "nothing can come before the first point in time, since 'before' is a function of time". Therefore, there were no prior points at which God could have created the world; He could only create it at the first point in time (this is rather tautologous). Ergo, it is a necessary truth that "If God creates the Universe, He does so at the first instant in time". So, when the Universe was created is not a contingent fact. The relation between that point and "now" is a contingent fact, but only because "now" is contingent on when you choose to ask the question. So, we're right back to what I've been saying: The only contingent fact to be explained is why you asked the question today, instead of at some other time.

Think of it this way: Forgetting the beginning of time, let's just say that Christ had to be crucified at a particular time in history. Let's just say that this was a necessary truth (perhaps the fulfillment of prophecy, or something). Now, let's say that a Medieval philosopher asks "Why was Christ crucified 1,000 years ago, instead of 1,001?". The answer is not with reference to the necessary truth of the crucifixion date. The answer need only reference that when the philosopher asks the question is utterly contingent (and, of course, there are explanations as to why the philosopher asked the question THEN rather than at some other time).

Do you see what I'm getting at?

Michael Gonzalez said...

"...if we consider two times identical provided that they are equidistant form the beginning of time, then set of times couldn't have gone further back than it did."

But, my question is why is the present moment not farther away from the edge (the beginning of time)? It is a contingent fact that this point in time is this far away from the boundary; so what explanation is there such that the boundary could not have been farther "to the left" of this point in time?

To put it another way: Aren't there possible worlds where the event of my posting this comment occurs much farther "to the right" of the boundary at the beginning of time? If there are such possible worlds (and, surely there must be, since my posting this silly question can hardly be a necessary truth!), then it follows that there is an explanation for why the gap is this large and not larger.

Alexander R Pruss said...

" It is a contingent fact that this point in time is this far away from the boundary"

No: it is a necessary truth that this point is this far away from the boundary. It would be a different point at a different point.

"I think all people have to interpret a tensed utterance relative to the time of utterance."

What I mean is this. A B-theorist interprets the sentence "It is raining" as expressing some proposition like <It is raining at t0> where t0 is the time of utterance. This proposition does not change truth value over time. The typical A-theorist interprets the same sentence as expressing a tensed proposition whose truth-value changes--on rainy days it's true and on cloudy days it's not.

Michael Gonzalez said...

Honestly, I think the A-theorist can say the very same things your B-theorist says on these particular matters. Just as the B-theorist does not say "it is raining at every time", so the A-theorist says the proposition "it is raining" is only true at on rainy days. And, just as the B-theorist says that "this point" is necessarily a certain distance from the boundary, so the A-theorist says that this moment is necessarily a certain amount of time removed from the absolute beginning. Time progresses at a steady rate, and we arrive at this moment "right on time", so to speak.

The central point is unchanged: Time had to begin at its beginning, and any point in time will be as far away from that point as the progression of time requires. The only contingent fact is that you asked the question today, rather than some other day. And that is easily explained in terms of influences, motivations, inclinations of your personality, etc.