A theist and an atheist enter into a friendly dialogue about all things science, philosophy, theology, and where they overlap.

Wednesday, October 9, 2013

A Criticism of Cosmological Atheology

By Miles Donahue

I. Introduction

In less than 24 hours after publishing “General Relativity Proves What, You Say?: A Response to L. A. Mitchell”, Mr. Mitchell wrote an eight page counter-response [1]. In this article, I’ll review key terms used in the argument, criticize his responses to my refutation, expand on my original criticisms, and end with concluding thoughts. I take it as given that he and I are expected to maintain an appropriate level of respect and cordiality towards one another as we discuss these issues and arguments.

II. A First State of Time

Mitchell only stated disagreement with my definition of one of the four key terms used in the entailment argument, so I will assume he agrees with the other three. He disagrees with my definition of a first state of time:

First state of time - the very first interval of time, whether a closed interval or a half-open interval; such an interval can be modeled algebraically as 0 < t ≤ 1.

But the careful reader will notice that although he disagreed with my definition of the term, he didn’t provide an alternative definition which evaded his objection, so we simply have to wonder what Mitchell means by “first state of time”. Nevertheless, what objections does Mitchell raise to my definition? He claims that, “There is an earlier interval than this interval [0 < t ≤ 1], which is the interval 0 < t ≤ .9. This is an earlier interval than 0 < t ≤ 1 because it does not contain states of time which correspond to the real numbers between .9 and 1.” This response strikes me as misconceived, on three counts.

First, a first interval of time will differ from context to context, based on what unit of measure is being used (e.g., hours, minutes, seconds, etc.), and this isn’t inconsistent with saying that a first interval of time has parts. Indeed, any interval of time in any event can be subdivided into smaller parts. Thus, the first interval of a second in the history of the universe can be subdivided into the first nano-second, being followed by other nano-seconds, or what have you. Second, the interval 0 < ≤ .9 is in no sense earlier than 0 < t ≤ 1. If it was, then the inequality 0 < ≤ .9 < 0 < t ≤ 1, would be true, and clearly it’s not. [2] Rather, “0 < ≤ .9” is simply a part of “0 < t ≤ 1”. Third, his objection applies equally to his original definition of the term. Recall that Mitchel defined “first state of time” as “a line segment with a maximum value and a minimum value.” He gave the following picture to represent the idea.


But then if we grant Mitchell’s objection, his definition goes out the window, for we can subdivide interval AB into AM (where M is halfway between A and B), and AM would be earlier than AB, according to Mitchell, and thus AB would not represent the first state of time, which contradicts his original definition.

III. Quantum Gravity

Here there was some substantial interaction with my objections. The reader will recall that I raised two objections to the entailment argument based on quantum gravity: (i) General Relativity is an incomplete theory of the world, and (ii) certain quantum theories of gravity imply the falsehood of premise (1). With regard to (i), the reader needs to understand that Quantum Mechanics, the other pillar of modern day physics, is incompatible with General Relativity. But they’re equally successful theories, and thus we must seek a deeper theory of the world, a quantum theory of gravity which marries General Relativity with Quantum Mechanics. And it seems to me that to try to argue that because a theory we know to be incomplete, a theory we know will need changes, implies the truth of premise (1) therefore premise (1) is true just isn't an argument for (1), because we don’t know whether premise (1) will remain true in light of a quantum theory of gravity. This isn’t just musing about possibilities; rather I’m claiming that we have no reason to prefer one possibility (every state of the universe is caused by a previous state) over the another (every state of the universe is not caused by a previous state). We must therefore be agnostic about the truth of the premise. [3] So far as I can see, Mitchell raised no counter-objections to (i), so the criticism goes through.

Concerning (ii), I argued that a certain theory of quantum gravity implied that premise (1) was false, because on this theory you can’t divide the first interval of the history of the universe into neat stacks of universe-states which each explain each other. Mitchell raises two objections to (ii). First, he claims that he can’t assess the evidence for this theory of quantum gravity because I didn’t name the approach to QG I was talking about, and therefore it can’t be considered an argument. I simply beg to differ. Look at the first line of the my quote from William Lane Craig, “A typical approach to marrying quantum theory to General Relativity involves describing the evolution of spacetime as a path integral (a sum over all possible paths) in superspace…” This clearly identifies the theory of quantum gravity I’m talking about, namely, Feynman’s “sum-over-histories”. Stephen Weinstein and Dean Rickles, both philosophers of science, comment:

“…the peculiar nature of general relativity and quantum gravity, with respect to the treatment of time, resurfaces in arguably the most covariant of approaches, the Feynman path-integral approach. In this case that central task is to compute the amplitude for going from an initial state to a final state (where these states will be given in terms of boundary data on a pair of initial and final hypersurfaces). The computation of this propagator proceeds à la sum-over-histories: one counts to the number of possible spacetimes that might interpolate between the initial and final hypersurfaces.” [4]

Second, Mitchell claims that my failure to explicitly name the particular theory of quantum gravity I’m talking about, “leads to doubt about the validity of the model. If [I] will not even name the model, then this suggests that there is some flaw which could be brought up if [Mitchell] knew what it was.” Let me assure Mitchell that I would never put forward an argument, or an objection to an argument, if I didn't think it was sound, and I hope to have demonstrated as much in this particular case.

Mitchell spends a great deal of time arguing against quantum theories of gravity. The essence of his argument is summed up as follows:
  1. Quantum gravity models require the Minkowski interpretation of special relativity.
  2. The Minkowski interpretation of special relativity is false.
  3. Quantum gravity models are false.
I agree that the argument is logically valid, and that premise (2) is true, so the only question is whether premise (1) is true. In raising the objection to premise (1) that I am, Mitchell asserts that I’m contradicting my own worldview, and that this somehow implies I’m giving a contradictory argument. I’m not sure what relevance this has, if it’s not to be a thinly veiled ad hominem argument. Suffice it to say that concerns about my personal worldview are irrelevant to the truth of the arguments I give. In defense of (1), all Mitchell really says is this, “Mainstream quantum gravity is based on Einstein’s general theory of relativity, which in turn is based on the Minkowski interpretation of special relativity.” I have no desire to disagree. The problem, though, is that because General Relativity and Quantum Mechanics are incomplete theories of nature, a quantum theory of gravity will have to sacrifice certain aspects of both in order to make them cohere. As Weinstein and Rickles comment,

“These various approaches can be catalogued in various ways, depending on the relative weight assigned to general relativity and quantum field theory. Some approaches view general relativity as in need of correction and quantum field theory as generally applicable, while others view quantum field theory as problematic and general relativity as having a more universal status. Still others view the theories in a more even-handed manner, perhaps with both simply amounting to distinct limits of a deeper theory.” [5]

Thus, it’s entirely fallacious to argue that because General Relativity implies the ontology or structure of Minkowskian relativity, therefore a quantum theory of gravity will do so as well. The latter just doesn’t follow from the former. One might also add that some physicists have argued that a quantum theory of gravity might actually imply presentism, the view that only the present exists, which is antithetical to Minkowskian relativity. [6] The premise, “Quantum gravity models require the Minkowski interpretation of special relativity” just ain’t necessarily so, and might actually be shown to be false as theories of quantum gravity develop.

I conclude, then, that premise (1), “Every state of the universe is sufficiently caused by a previous state”, has not been shown to be true, and thus the entailment argument is not a good argument for atheism. [7]

IV. Examining the Entailment Argument

The reader will recall that I raised two main objections to the entailment argument, (i) we can construct parallel arguments which lead to false conclusions, and (ii) reference to the various states of the universe cannot answer the question of why the universe began to exist. First, I gave two examples of things coming into being without a first state of their existence, and yet having external causes: Mitchell’s truncated life [8], and the motion of a tennis ball. Turning to Mitchell’s truncated life, I'll sketch the premises of this parody argument so that the reader will see the parallel that exists between it and the entailment argument for atheism:
  1. Every state of Mitchell’s truncated life is sufficiently caused by a previous state. 
  2. An external cause of the Mitchell’s truncated life can only exist if there is a state of his truncated life that was not sufficiently caused by a previous state of his life. 
  3. Therefore, Mitchell’s truncated life has no external cause. 
Or consider the entailment argument based on the motion of a tennis ball. As before, we can summarize the argument to see its parallel to the original entailment argument:
  1. Every state of the motion of the tennis ball is sufficiently explained in a previous state. 
  2. An external cause of the tennis ball can only exist if there is a state of the motion of the tennis ball that was not sufficiently caused by a previous state of the ball. 
  3. Therefore, motion of the tennis ball has no external cause. 
It seems quite obvious that the above two entailment argument parodies and the original entailment argument are parallel, so that if one is valid, all three are valid, and if one is invalid, all three are invalid. Similarly, if one contains a false premise, all three contain a false premise. They stand or fall together. Nevertheless, Mitchell objects,

“The deletion of the first instant of my birth is arbitrary and there are no reasons to do so. The key difference between the two deletions is that a first instant of the universe is physically impossible, while a first instant of my birth is physically possible.”

I think this misunderstands the argument. What I was saying in the first parody argument based on Mitchell's life is that the same reasoning used to conclude that the universe cannot have an external cause can be used to show that Mitchell’s truncated life doesn’t have an external cause. Remember, we’re just considering a segment of Mitchell’s life, not his entire life. Mitchell's truncated life doesn't include that first instant because it's simply not part of the interval of his life we're considering. The first instant is still there, but the interval of time including that instant is longer than the interval of time containing Mitchell’s truncated life. Indeed, in any closed interval of time, a half-open interval of time is still there, so to speak, it’s just that the half-open interval of time is shorter than the closed interval of time. The first instant of his life isn't deleted; when considering Mitchell's truncated life, it simply isn't there to begin with. There may be a first state of Mitchell's entire life, but there is not a first state of Mitchell's truncated life.

He also states,

“Vallicella seems to think that the argument reasons that since there is a continuum of half-open states, there cannot be an external cause. Rather, the reasoning is that a first instant is physically impossible, ergo there is a continuum of half-open states, ergo there is no external cause. Vallicella’s parody cannot be equal to Smith’s argument because it cannot contain the false premise ‘the first instant of my birth is physically impossible’.”

Now this remark is very interesting, because if you look at the original entailment argument in either formulation, it itself doesn’t contain the premise “the first state of the universe is physically impossible.” Rather, that statement is used as evidence for premise (1). But so what? The evidence for premise (1) of the first parody entailment argument is simply that we’re considering the half-open interval of time between Mitchell's birth and some arbitrary point in time; there cannot be a first state of his truncated life, by definition, because it's contained in a half-open interval of time. But interestingly, the reason premise (1) of the second parody argument is true is because it’s physically impossible for there to be a first state of the ball’s motion, for reasons I explained in my previous article. So even if the first parody argument is shown not to be parallel to the original entailment argument, the second argument based on motion would.

The reasoning in all three entailment arguments is this: (i) there is no first state of X, thus (ii) there is a half-open continuum of time between the beginning of X and some arbitrary point in time, and therefore (iii) there is no external cause of X. In all three entailment arguments there cannot be a first state of that thing, for various reasons. I conclude that all three entailment arguments are parallel to each other, and so if one is sound, all three are sound. Conversely, if one is unsound, all three are unsound. But the above two parody arguments are unsound; each entity being considered has an external cause. Thus, the original entailment argument for atheism is also unsound.

I’m mystified when Mitchell says that the third parody argument concerning the motion of the tennis ball “can be solved through invoking supertasks.” I have no idea how this consideration shows the third argument not to be parallel, or how it shows that the motion of the tennis ball has a first state. I’m not asking how the tennis ball could have started moving; rather I’m showing that the motion of the tennis ball could not have a first state, and thus should not have an external cause, if the reasoning of the original entailment argument were correct. I have no idea what the argument about supertasks is supposed to be.

Mitchell rightly points out that, “My argument is not that we can explain the universe by saying that each state of the universe is caused by a previous state, although I think that’s true. The argument only seeks to eliminate a certain type of cause from the different causes that we can consider.” But then he seems to have forgotten this when he quotes Quentin Smith who argues that the universe is self-caused. It doesn’t matter if my parody arguments don’t show that universe isn’t self-caused; they weren’t intended to. Rather, what they show is that Mitchell’s entailment argument doesn’t establish the conclusion that the universe doesn’t have an external cause. At this point in the argument, for all we know the universe might be self-caused, or it might have an external cause. The argument for a self-caused universe and the argument that the universe cannot have an external cause are two different arguments, and we need to keep them distinct. For these reasons, I will simply ignore the arguments given by Quentin Smith, Robin Collins, and Paul Draper, because they concern a different argument than Mitchell’s entailment argument.

Second, I argued that reference to the various states of the universe cannot explain why the universe began to exist, and so there must be an external cause of the universe to explain why it began to exist rather than existing eternally. The argument, stated explicitly is as follows:
  1. Whatever begins to exist has either an internal cause or an external cause.
  2. The universe began to exist.
  3. Therefore, the universe has either an internal cause or an external cause.
  4. The universe cannot have an internal cause.
  5. Therefore, the universe has an external cause.
Mitchell and I agree that premise (2) is true, so the whole debate comes down to whether premises (1) and (4) are true. With regard to (1), let me give three lines of evidence for its truth [9].

First, something cannot come from nothing. This seems obvious, when you think about it. The potential for something’s existence is always logged in something else. The potential for a boat is logged in previously existing wood. For something to come into being from nothing, the potentiality for its existence couldn’t be logged in anything, and therefore there is no potentiality for its existence. But if something came into being without a cause, it would come from nothing. Therefore, whatever comes into being must have some sort of cause.

Second, if something could come into being out of nothing, then it becomes inexplicable why anything and everything don’t come into being out of nothing. If universes can come into being out of nothing, why can’t horses and potatoes likewise do so? If they can, then why don’t they? Why aren’t lions and tigers and bears coming into being right now, if it’s possible that they can? If you affirm that something came into being without a cause, not only can you not explain why that being exists, you cannot explain why an infinity of infinity of begins do not exist. That, at least to me, is too high a price to pay for a denial of premise (1).

Third, common experience confirms and never falsifies premise (1). We constantly observe that things which come into being have causes, and never observe things beginning to exist without causes. Therefore, we can make an inductive generalization that whatever begins to exist has a cause. Now, I’m inclined to view this third point as mere support for premise (1), not the basis of its truth. The first and second lines of evidence serve as the foundation for (1), and point three could be thought of as a supporting beam.

Concerning the truth of premise (4), I’ll refer back to what I said in the previous article:

“…we can show that the universe not only could have an external cause if its earliest interval is half-open, but needs an external cause, because the question, “Why did the universe begin to exist?” is still left unanswered, even if the universe’s earliest interval is half-open. Pointing out that each state of the universe is caused by a previous state might show give an explanation as to why the universe exists, but not as to why the universe began to exist….If the universe were eternal, then every state of the universe would have an explanation in terms of a previous state as well, so merely showing that every state of the universe has an explanation in terms of a previous state wouldn’t go one inch in explaining why the universe began to exist, instead of existing eternally.” [10]

I conclude that the universe has an external cause, implying the falsehood of the entailment argument for atheism, leading as it does to a false conclusion.

Despite all that’s been said, there’s still the question, “if the first temporal interval of the universe of the universe is half-open, then every state of the universe is caused by a previous state, so where, so to speak, does God cause the universe to come into being? Which state of the universe does God cause?” I'll sketch two responses to the question. First, God can still create the universe at first instant of metaphysical time, even in physical time has no first instant. This argument is given, ironically, by Paul Draper and Quentin Smith:
"What he [Robin Collins] means to suggest is that God's creative act might be a part of the complete causal history of any universe state, even if the universe did not exist at t0 [the first instant of time] and so did not have any first moment of existence. (Similarly, the exploding gunpowder is a part of the complete causal history of any flight state even if the flight of the cannonball did not exist at t1 and had no first moment of existence)...Collins could best state his case by supposing that there is a metaphysical time series in which God exists and that any physical time correlates to a metaphysical time. He could then argue that, even though there is no t0, there is a metaphysical time T0 at which there is a divine creative act that causally originates the physical time series and all the universe states in this physical time series. In other words, Collins could plausibly claim that, even if the physical causal history of the universe has no first moment, it is possible that the complete (metaphysical and physical) causal history of the universe does..." [11]
Even if the physical time series of our universe had no first instant and thus no state of the universe lacking a previous state, God can still act at a first instant of metaphysical time to originate the series of universe-states. Second, no answer to the question needs to be given, for as we've seen, the motion of a tennis ball, and all motion in general, lacks a first instant and yet has an external cause. I'm content to say that God creates the universe in the same way that motion is caused to occur. Explaining exactly what that means and how that is to be worked out isn't needed in order to see that it's possible, and that's enough to see that Mitchell's entailment argument for atheism isn't a good one.

William Vallicella makes some helpful comments:

“Somehow the external cause has to 'hook onto' the rolling-ball process. How? The last instantaneous state of the pushing cannot hook onto the first state of the rolling-ball process, for there is no first state. This suggests that the last state of the pushing connects to an entire causal sequence, namely the sequence of rolling-ball states. Thus a whole sequence would somehow be the effect of a cause. If so, the sequence or succession would not be logically supervenient upon its members, an 'ontological free lunch,' but something in addition to its members….If something like this could be worked out in detail -clearly not a task for the present occasion!-then the way would be clear for the theist to argue that the entire universe is a sequence of states that is the effect of a cause.” [12]

V. Implications of Cosmological Atheology

Mitchell outlines two implications of the entailment argument that would still stand, were it shown to have premises with possible exceptions. First, Mitchell claims that the kalam cosmological argument for the existence of God would still be undermined. I’ll save my response to this point for when Mitchell and I discuss the kalam cosmological argument, and this will be happening shortly. 

Second, Mitchell contends that the entailment argument for atheism would still be a probabilistic argument for atheism. There are three problems here. First, I really don't understand how, in Paul Draper's words, "...Smith showed in 'A Cosmological  Argument for a Self-Caused Universe,' not just that a self-caused universe is possible, but also that its actuality is supported by our best scientific cosmology." [15] If what I've said it sound, and if what Draper himself said previously in the article is sound, then Quentin Smith, and by extension Mitchell, did not show that the universe being self-caused is supported by our best scientific evidence. My arguments above dismantle such a conclusion, at least in my estimation. Second, I'm skeptical of any claims about what God would do if He existed. How in the world can we know such fantastical things as what the omnipotent, omniscient God would do in some situation? More specifically, how could we know that it's improbable that God would create a universe like this one? Third, and most importantly, the second implication of the entailment argument concerns Quentin Smith’s entailment argument for a self-caused universe, not Mitchell’s entailment argument for eliminating an external cause of the universe. Mitchell has not shown that his argument still works as a probabilistic argument for atheism, and I'm perfectly  justified in dismissing Paul Draper and Smith’s comments here, because they don’t concern the argument Mitchell and I are discussing.

VI. Conclusion

1. The fact that General Relativity is an incomplete theory of nature undermines our warrant for thinking premise (1) is true, and Feynman’s “sum-over-histories” approach to quantum gravity implies the falsehood of premise (1).

2. 0 < t ≤ 1 does represent the first interval of time, though it will differ from context to context depending on the unit of measure being used. 0 < t ≤ 0.9 isn’t earlier than 0 < t ≤ 1, but is merely a part of it. 

3. The three parody arguments I gave are parallel to Mitchell’s entailment argument. They might not be parallel to Smith’s, but we’re not discussing Smith’s argument. Because the parody arguments are unsound, Mitchell's entailment argument must be unsound.

4. Mitchell has not shown that his argument is still a probabilistic argument against God. Remember, we’re discussing Mitchell’s argument, not Smith’s. As for the KCA, those comments will have to hold off until later.

Notes


  1. Mitchell, L. A., “A Defense of Cosmological Atheology”, Doubting Dave, (n.d.) (September 8th, 2013) <http://doubtingdave.com/a-defense-of-cosmological-atheology/>
  2. Remember, “<” means earlier than.
  3. Thus, I’m giving what philosophers call an undercutting defeater of premise (1). That is, I’m removing an warrant for thinking that its true.
  4. Weinstein, Steven and Rickles, Dean, "Quantum Gravity", The Stanford Encyclopedia of Philosophy (Spring 2011 Edition), Edward N. Zalta (ed.), URL = .
  5. Ibid.
  6. Monton, B., 2006, “Presentism and quantum gravity,” in D. Dieks, ed., The Ontology of Spacetime II, Amsterdam: Elsevier, 263–280.
  7. I take it as given that in order for an argument to be a good one, each premise of that argument must be shown to be more plausibly true than false. Premise (1) of the entailment argument has not been shown to be more plausibly true than false.
  8. Because the parody argument based on Mitchell's life and the parody argument based on a segment of the history of the universe are very similar, I'll skip over discussion of the latter. But the reader will understand that remarks concerning the former also apply to the latter as well.
  9. I originally wrote the following three paragraphs here: http://www.debate.org/debates/The-Kalam-Cosmological-Argument-is-Sound/17/
  10. Donahue, Miles. “General Relativity Proves What, You Say?: A Response to L. A. Mitchell.” (n.d.): n. pag. Science, Philosophy, and God. Web. 9 October 2013.
  11. Smith, Quentin, and Paul Draper. “Collins on Cannons and Cosmology.” (n.d.): n. pag. Internet Infidels Library. Web. 13 Oct. 2013. 
  12. Vallicella, William. “Could the Universe Cause Itself to Exist?” Philosophy 75 (2000), 609.
  13. Smith, Quentin, and Paul Draper. “Collins on Cannons and Cosmology.” (n.d.): n. pag. Internet Infidels Library. Web. 13 Oct. 2013. 

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