## Saturday, April 4, 2009

### Infinite causal regress

Could everything in existence be explained by an infinite causal regress? I've argued in print that the answer is negative. Here is another thought in favor of the negative answer.

Suppose we have a world where there is an infinite regress of past states and that there is some numerical time-varying property Q(t) in the universe (say, entropy or temperature or charge or volume) that keeps on changing in such a way that the property's having one the value it does in one year determines the value it has in another. Now, consider the claim that the limit of Q(t) as t goes to minus infinity is, say, q0. (Of course, Q(t) might not in fact converge to anything, but since we're stipulating, we can stipulate that it does.) If the regress explains everything, it explains why it was that the limit is q0. But even if a regress explains something, it surely doesn't explain the boundary values at the beginning of the regress, and q0 is precisely such a boundary value. It would be almost as absurd to say that the limit of the temperature in a room tended to 11.0 degrees as t approached noon from above because it was 11.1 at 12:10, and 11.06 at 12:05, and 11.05 at 12:05, and 11.01 at 12:01, and so on, as it would be to say that the temperature of the room was 11.0 degrees at noon because it had such-and-such values after noon.

Suppose that we still insist that the boundary value q0 is explained by the regress. Now suppose that we find another explanation, say in terms of an atemporal being creating the universe. What should we say? That we have two explanations of the same phenomenon, each on its own sufficient? That can happen, but surely that's not what is happening here. The right thing to say is that the regressive explanation of the boundary condition is no explanation at all.

#### 15 comments:

Anonymous said...

It seems to me that even if we can't prove that there's no infinite regress of explanations or that there are explanations, it would be foolish to believe that there are infinitely many explanations or that there are none. This kind of epistemology would not be satisfying.

We can only be confident in our knowledge if we can say "Ok, our explanation ends here and that's why: ..."

Vlastimil Vohánka said...

Alex,

Q. Smith, as I repeatedly noted, is a quite able defensor of infinite regresses. But not only of them.

In some texts, he defends the view that some things, though coming to existence, have no cause.

In other, he defends that something can cause itself.

In other, that the universe was caused by a concrete timeless point.

In other, he suggests causal regresses:

-- the universe is caused by another universe, this by yet another one, etc.

-- the universe has a first temporal interval (say, the first minute), comprising infinity of times, sliced like the series 1/2, 1/4, 1/8, etc; there is no first time, in a sense; every time has a causal explanation in another, causally and temporally preceding, time.

-- the universe has the first time
comprising infinity of particles related by a linear simultaneous causation (cf. www.reasonablefaith.org/site/News2?page=NewsArticle&id=5277 ); every particle has a causal explanation in another, causally preceding and simultaneous, particle.

What would you say to the last two scenarios? It does not seem your present critique apply to them.

Alexander R Pruss said...

Neither of these last two scenarios is explanatory of why the whole exists.

Alexander R Pruss said...

Moreover, the second last scenario falls prey to the objection in this post.

Vlastimil Vohánka said...

Alex,

I still can't see why the whole is not explained. We've already discussed it via e-mail. I'm still unclear about that.

As for the alleged application of your point in this post to the second last scenario:

How is

temperature of the room is 11.0 degrees at 12:00 because it has such-and-such values AFTER 12:00

analogical to

there are particles existing at 12:00 because of the particles existing BEFORE 12:00, and ultimately because of the infinity of particles related by a linear simultaneous causation at t0?

Alexander R Pruss said...

I just don't see how there is any explanation in the circular cases. Smith gives examples, but none of these examples seem at all compelling.

The temperature case is analogous to an infinite regress situation, not a circularity.

Vlastimil Vohánka said...

Yes, I concede there is no explanation in the circular cases.

Still, the regress cases are not clearly problematic, to my current knowledge.

I'll try again. This sentence in your post seems crucial to me:

"It would be almost as absurd to say that the limit of the temperature in a room tended to 11.0 degrees as t approached noon from above because it was 11.1 at 12:10, and 11.06 at 12:06, and 11.05 at 12:05, and 11.01 at 12:01, and so on, as it would be to say that the temperature of the room was 11.0 degrees at noon because it had such-and-such values after noon."

But how is it relevantly analogical to the three causal regresses by Smith?

In the first case, each universe is causally explained by a causally preceding, not subsequent, universe.

In the second case, each time is explained by a causally and temporally preceding, not subsequent, time.

In the third case, each time, except the 1st time t(0), is explained by a causally and temporally preceding, not subsequent, time, and each particle existing at the 1st time t(0) is explained by a causally preceding and simultaneous particle (as there are infinitely many particles at t(0)).

Alexander R Pruss said...

Let's leave the third case alone for now.

In the first two cases, let p be a claim about a limiting condition at the initial time. Maybe, it's a claim that the temperature goes to T7 as time goes to t0. It is absurd that the fact that the boundary value of temperature as t goes to t0 is explained in terms of the regress after t0.

Vlastimil Vohánka said...

"let p be a claim about a limiting condition at the initial time."

As I remember, Smith would say there is no initial time in the 2nd case, as there is no smallest number in the series 1/2, 1/4, 1/8, ...

"the boundary value ... as t goes to t0 is explained in terms of the regress after t0."

But why is such a claim essential to Smith (and causal regresses generally)? Why does he have to make such a claim?

"Maybe, it's a claim that the temperature goes to T7 as time goes to t0."

Would your objection apply if the temperature (or other numerical time-varying property) went to being undefined at t(0)? Cf. Smith:

"the Big Bang singularity is metaphorically said that if it did exist, it would have infinite temperature. It would be infinitely hot. But temperature is the motion of molecules, or particles against each other. But ... Nothing is moving. So it can't have infinite temperature. Temperature doesn't apply to it at all."
www.reasonablefaith.org/site/News2?page=NewsArticle&id=5277#1

Alexander R Pruss said...

Even if there is no t0, one can talk of the limit at t0.
The boundary value at t0 is an abstraction from the values at times shortly after t0. If those values are explained by the regress, so is the boundary value.
Even if the limit is undefined, that fact calls for an explanation, and the same considerations apply. (Technical move: For every free ultrafilter, there will be convergence, perhaps to an infinite value. That convergence is to be explained.)

Kyle said...

Even if there is no t0, one can talk of the limit at t0.

I agree with this, but I am no longer sure that it is odd to speak about the boundary value being explained by the values of the times that occur after t0.

If t0 did not reallt exist then why not say that it is explained by the sequence?

Alexander R Pruss said...

Kyle: Hmm. I guess I'm used to using boundary values to explain later behavior, so it sounds wrong to me. But I see your point. (Maybe I will simply have to retreat to the fact that the sequence as a whole has no explanation.)

Vlastimil Vohánka said...

Thanks. Now I understand better.

As for the view that the limit of the converging cosmological series does not really exist, cf. www.reasonablefaith.org/site/News2?page=NewsArticle&id=5277#3

Ibid Smith opts for a series of discrete temporal intervals (events), with a first interval comprising infinity of such particles that each particle has a causal explanation in another, causally preceding and simultaneous, particle.

That's the 3rd causal regress scenario Alex wanted to leave alone.

Hassan Abdillah said...

Dr. Pruss,

I'm a microbiology undergraduate from Bangladesh who is extremely interested in Natural Theology. The Leibnizian Cosmological Argument strikes me as one of the most impressive arguments for the existence of God. Unfortunately, all the treatments of the topic I've run into thus far are either too basic (Reasonable Faith by Dr. Craig) or too advanced (your essay in the Blackwell Companion to Natural theology). I've been especially troubled by the question you discuss in this post i.e. whether all of contingent existence can be explained by an infinite causal regress. However due to my lack of training in philosophy or mathematics, I couldn't get past the jargon. Could you suggest an intermediate reference text to learn more about the issue?

If such treatments are unavailable, then could you either (or both):

a) Explain how, in your opinion, every contingent thing cannot be explained in terms of an infinite causal regress, in simple terms? I think the impossibility only arises when we think of all contingent objects as a whole, but what if a metaphysician argues that a "whole" is not a separate existence over and above it's constituents (e.g. every sand grain in the heap exists, but there is no entity as the "heap" itself). Dr. Craig argues, even if all the things in the infinite causal chain is contingent, this still doesn't explain why the whole chain is there. But why think of the "whole chain" as an entity to begin with? Can the "whole chain" not be explained in terms of the collective explanation of each one of its constituents?

b) Suggest some basic-to-intermediate texts in philosophy or mathematics which would enable me to comprehend your essay in the Blackwell or other such advanced treatments of the issue.

I would be extremely grateful for your considerations.

Many thanks,
Hassan

Alexander R Pruss said...

I agree that "the whole sequence" isn't an entity over and beyond the parts. Nonetheless, the whole sequence calls out for an explanation.

See my blog post for today for more...