I. Introduction
In his paper A Latin Trinity, Brian Leftow addresses two central problems with time-travel. First, he assesses a retro-suicide case and, secondly, a causal loop case. In this paper, I explain and evaluate his response to the causal loop case. I then show that his solution is not strong enough to warrant acceptance of the metaphysical possibility of time travel. My response to Leftow will not show time travel to be impossible, only that Leftow’s argument for its possibility is not a good one.
II. A Brief Summary of Leftow’s Paper
1. The Trinity
A Latin Trinity’s central aim is to provide a coherent account of the Christian conception of the Godhead, which is important to note, since it is not a paper concerned (primarily) with time-travel. Rather, Leftow intends to resolve the following objection:
(1) The Father is God.
(2) The Son is God.
(3) [/:.] The Father is the Son. (Symmetry & Transitivity)
(4) Some things are true of the Father, but not of the Son.
(5) [/:.] The Father is not the Son. (Leibniz’s Law)
(6) /:. The Father is the Son and the Father is not the Son. (3,4,Conj)
This line of thought leads to a contradiction, which supports the claim that the Trinity is an incoherent doctrine of Christianity. Any Christian-minded person wants avoid this conclusion, like Leftow.
In Leftow’s attempt to resolve the contradiction, he appeals to an analogy related to time-travel. He argues that the Trinity is something like this, but not this:
All the Rockettes but one, Jane, called in sick that morning. So Jane came to work with a time machine her nephew had put together for the school science fair. Jane ran on-stage to her position at the left of the chorus line, linked up, kicked her way through the number, then ran off. She changed her makeup, donned a wig, then stepped into her nephew’s Wells-o-matic, to emerge in the past, just before the Rockettes went on. She ran on-stage from a point just to the right of her first entry, stepped into line second from the chorus line’s left, smiled and whispered a quip to the woman on her right, kicked her way through the number, then ran off. She then changed her makeup again… Can one person thus be wholly in many places at once? The short answer is: she is in many places at the same point in our lives, but not the same point in hers. If Jane travels in time, distinct segments of her life coincide with the same segment of ours. To put this another way, Jane’s personal timeline intersects one point in ours repeatedly. (80)
Like the dancers in the example, the Father, Son, and Holy Spirit are “intersected” somehow; three instances of one substance (ousia).
2. Time-Travel
For the purposes of this paper, I will be assessing Leftow’s metaphysical defense of the possibility of time-travel. This is directly related to his paper, considering that he uses this argument by analogy for his conception of the Trinity. But, I only focus on his arguments regarding time-travel, not his overarching argument for a Latin Trinity.
Leftow focuses on what he calls “the strongest objections” to time-travel: retro-suicide and causal loops. He first summarizes both paradoxes, then offers reason to deny them as strong objections. For the remainder of the paper, I explain and evaluate his assessment of the causal loop case.
III. Jane and Causal Loops
1. The Problem
Staying with the Rockettes example, Leftow considers a case where the rightmost-Jane knifes the next-left-Jane. The knife wound does not kill next-left-Jane, but she makes sure she won’t be stabbed again. Before entering the time machine, next-left-Jane picks up a knife to defend herself with, just in case. Now taking the place of rightmost-Jane, she unsheathes her protective knife under the suspicion that the dancer to her left is going to attack. After one fast moment, the person to her left is stabbed. In stabbing the dancer, rightmost-Jane stabs next-left-Jane.
Leftow states the problem: “The puzzle is that globally, each event seems its own full explanation — since in tracing its ancestry, we find our way around the loop to the event itself — and that since nothing can explain its own occurring, it seems that globally, each event has no full explanation at all, despite having a local causal explanation”. The supposition, then, is that there is no global explanation of the event, yet there is a local causal explanation. In other words, Jane’s having the knife is a reaction to being stabbed by herself; but in trying to defend herself, Jane is the one that stabs herself.
First, let’s make doubly sure that this is a case of a causal loop. According to Ryan Wasserman, “a series of events, <e1, e2, e3… en>, is a causal loop =df (i) e1 is a cause of e2, which is a cause of e3, which is a cause of… en and (ii) en is a cause of e1”. It is clear from this definition that our story is a case of a causal loop: rightmost-Jane stabs next-left-Jane (e1), this causes her to have a predisposition to defend herself (e2), which causes her to pick up a knife (e3), which leads her to stab next-left-Jane (e1). So, (e1) causes (e2), which cause (e3), which causes (e1).
2. A Principle of Sufficient Reason
Leftow’s defense of the possibility of causal loops appeals to the common debate of principles of sufficient reason (PSR). Firstly, for sake of clarity, let us define what is meant by a principle of sufficient reason. In essence, PSR supposes that there is always an answer to “why” questions. No matter the strangeness of the scenario, there must be an explanation for its being the way it is. It can be defined like this:
PSR: Every thing and event must have a reason or cause.
This formulation of PSR is too general, though, which leads to its falsity. For example, under this PSR, a necessary being must have a cause, but necessary beings have no causes. A more robust PSR would not allow for such an objection. This leads us here:
PSR*: Every contingent thing and event must have a reason or cause.
Under PSR*, we avoid the objection, for only contingent things must have reason or cause; necessary things are not held to the principle.
3. Leftow’s Solution and PSR
Leftow claims that causal loops are “impossible only if some fairly strong PSR is a necessary truth. If one is, of course, one can run powerful arguments for the existence of God. So atheists, at least, might not wish to push this sort of objection.” He think theists shouldn’t push the objection, either, for with a PSR “strong enough to yield God, an explanation of the entire loop’s existence is available from outside the loop. It is that God brought it into existence: the reason Jane has a wound is that God brought this about, by conserving the entire loop”.
His response to the objection is two-fold. In order to suggest that causal loops are impossible would appeal to a strong PSR. Atheists would not want to appeal to such a strong PSR, for this would open up the possibility of strong arguments for God; theists, with a strong PSR, couldn’t rule them out either, for they could just attribute the existence of causal loops to God’s agency in the world. Leftow concludes, “I claim that an intuitively plausible PSR strong enough to rule loops out will rule God in. But with God ruled in, loops become compatible with the PSR after all”.
3. A Response to Leftow
A proper response to Leftow will do two things: (i) it will show that either atheists do not need a strong PSR to argue that causal loops deny the possibility of time travel or that a strong PSR would not rule in the possibility of God, and (ii) it will show that theists would need a better explanation than simply, “God made it so” to rule in causal loops. I intend to do both.
(i) Atheists do not need a strong PSR to rule out causal loops
PSR* states that every contingent thing and event has a cause or reason for existence. Leftow makes the claim that one must rely on such a principle to rule out causal loops; but relying on this principle would rule in strong arguments for God’s existence. So, atheists would not want to use PSR* to argue against the possibility of causal loops. His argument hinges on a hidden premise, though; namely, that the only way to deny the possibility of causal loops is with PSR*. I suggest that this premise is mistaken.
Before stating how I deny causal loops, it is important to understand how principles of sufficient reason are often denied. PSR* is a universal claim. Because of this, all that one needs to do is find a single example where the principle does not hold. Such an example is radioactive decay. If you have two atoms of 228-Th (in a chain of Thorium decay), then in 1.9 years one of the atoms will give off a proton(s) to become 224-Ra. By PSR*, there should be some reason for one of the atoms decaying and the other not. But, contemporary physics is telling us that no such reason exists; the decay is arbitrary. Therefore, there are at least some things that do not have reason or cause for their occurrence.
What does one say about causal loops, then? It is possible that causal loops are something like radioactive decay: they have no reason or cause for their occurrence. But this is not the case. Causal loops do not exist arbitrarily; they do not come about by cause-less means. Rather, the problem with causal loops is that the individual events in the loop bring about themselves. It is impossible for an event to be brought about by itself. So, causal loops are impossible. This version of the causal loop argument avoids the use of PSR* and still denies the possibility of causal loops.
And, thus, atheists can avoid embracing a strong PSR, causal loops, and time travel.
(ii) Theists need to rely on PSR, not God
The first objection of Leftow’s fails. One can have an argument against causal loops without relying on PSR*; thus, not ruling in strong PSR arguments for God’s existence. But, for the sake of discussion, let us suppose that one had to rely on PSR* to defeat the possibility of causal loops. PSR* would then rule in God, which would be an explanation for the possibility of causal loops. This line of thought fails, as well.
Though God is, by definition, omnipotent, there are still impossibilities for him. Firstly, God cannot create a round-square, for it is a contradiction, by definition. Secondly, God cannot override necessary truths, such as Leibniz’s Law, modus ponens, etc…, for they are necessary. Thirdly, God cannot make metaphysically impossible occurrences possible, for they are impossible. What is noteworthy, however, is that causal loops fall under the third limit on God’s power; they are (if one grants PSR*, or something of the like) a metaphysical impossibility. If God cannot make metaphysically impossible occurrences possible, and causal loops are metaphysically impossible, then God cannot make a causal loop possible. So, God cannot make a causal loop possible. From this, theists are able to deny the possibility of causal loops, retain the existence of God, and keep PSR*. In this way, Leftow’s second argument comes undone.
IV. Conclusion
The intention of this paper has been to show that Brian Leftow’s defense of causal loops is flawed. His argument has two sub-arguments, one directed toward atheists, the other directed toward theists. Both sub-arguments have been shown to fail. Leftow’s first argument fails, for it does not establish that PSR* is the only tool to deny the possibility of causal loops; his second argument fails, for God is unable to uphold metaphysical impossibilities. Their failure is not only worrisome for the possibility of time travel, but for Leftow’s larger project of establishing a coherent account of the Trinity.
Works Cited
Leftow, Brian. “A Latin Trinity.” Oxford Readings in Philosophical Theology. Oxford: Oxford UP, 2009. N. pag. Print.
Melamed, Yitzhak and Lin, Martin, “Principle of Sufficient Reason”, The Stanford Encyclopedia of Philosophy (Spring 2014 Edition), Edward N. Zalta (ed.), URL = <http://plato.stanford.edu/archives/spr2014/entries/sufficient-reason/>.
Wasserman, Ryan. The Paradoxes of Time Travel. Forthcoming.
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