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Sunday, March 4, 2012

premise (1) of Rasmussen's new argument for a necessary being

Joshua Rasmussen in his "New Argument for a Necessary Being" (2011), argues that

(1) Normally, for any intrinsic property p that (i) can begin to be exemplified and (ii) can be exemplified by something that has a cause, there can be a cause of p's beginning to be exemplified. (p1)


Rasmussen takes care to add the "normally" operator since he views (1) as a general "rule of thumb," and not a hard and fast principle which can never admit counter-examples. In particular he believes that

for any given property we consider, we have a reason to think (1) applies to it, unless we have reason to think that the property in question is an exception to the general rule. (p2)


His evidence for (1) takes two forms: First, he argues that (1) is supported by intuition. In particular he asks us to imagine an individual instance of (1), whereby some arbitrary property p begins to be exemplified. Quite naturally, we should wonder if this event had a cause, which inclines us towards thinking that it at least can have a cause. Second, he suggests the following abductive argument: when we imagine various examples of intrinsic properties beginning to be exemplified, especially those involving the appearance of new kinds of objects, we find that we can coherently imagine them to have a cause, and infer (1) as the best explanation for this power of our imagination. I regard both of these arguments as inadequate for supporting (1).

The first is an argument from intuition. As with all such arguments, they will only have force insofar as we have reason to trust the underlying intuitions. So for instance if I intuit that my wife's body language indicates unhappiness, this holds inductive support based on my experience with her, and also my previous success in thusly gauging her mood. More broadly, it has support from my experience with other people in general. The further removed my intuition from supporting experience, the less bearing it has on what I should believe. So I'm less inclined to trust my intuition regarding the mood of, say, an orangutan, and still less so of a hypothetical extraterrestrial being. If I realize that I have no experience at all to guide me in an intuition, and I have no other reason to trust it, then the rational position in that case should be skepticism.

Now when Rasmussen asks us to imagine our reaction to the instantiation of an arbitrary intrinsic property, we do indeed look to experience to judge our reaction. He is quite correct that we would naturally be inclined to think that such an event can have a cause. However the sense in which this is true is not the sense in which he needs it to be true for his argument. For Rasmussen is discussing broad logical possibility, but our inclinations in this matter involve only epistemic possibility (or something like it). That is to say, usually we should not be surprised to learn that some observed event has a cause. However this does not require us to suppose in advance that it is logically possible. To illustrate, suppose we are given a large odd natural number, say 3559. In that case we might not be surprised to learn that it is prime, or alternatively that it is not prime. However clearly each option is either broadly logically necessary or impossible. The open-ended possibility we detect for 3559 to be prime versus not prime is based on our own epistemic situation. In other words, for all we know, 3559 is prime, and for all we know it is not. Similarly, for all we know, the beginning of the exemplification of an arbitrary intrinsic property had a cause. This is all I take Rasmussen's thought experiment to show, but it does not follow from this that such beginnings are broadly logically possible.

Regarding his second argument, I don't typically regard purely logical truths as helping to explain actual states of affairs. So for example, if we wish to explain why a piece of plastic has four corners, we might suggest that it is because the manufacturer's mold had four corners, and that in the manufacturing process the plastic must take the shape of the mold. However if you asked me why it was four corners and I replied, "because it is rectangular, and rectangles always have four corners," then you would rightly complain that I had not properly answered your question. So if Rasmussen wonders why we should be able to coherently imagine certain events having causes, a purely logical statement like (1) will not provide the sort of explanation we ordinarily would seek.

Meanwhile, explanations of the other sort, that is, purely logical explanations, seem incompatible with abductive inference. For example, recall the following abductive argument from Aristotle's On The Heavens

Again, our observations of the stars make it evident, not only that the earth is circular, but also that it is a circle of no great size. For quite a small change of position to south or north causes a manifest alteration of the horizon. (2.14)


In a physical context, where certain shapes like spheres are evidently more common than others, this is a more or less reasonable inference. The same sort of argument will not do in a purely logical context, however, where we have no means of assigning a high likelihood to the occurrence of a sphere over that of other three-dimensional objects which would result in the same difference of perspectives along their surfaces. In the same way, we have no means of assigning an a priori likelihood to (1) over competing explanations (or nonexplanations), which prevents us from running a successful abductive argument.

Adding further difficulty, Rasmussen provides a counter-example to the imaginative procedure he asks us to perform. For the ultimate aim of his argument is to plug in property c for p in (1), where c is the property of being a contingent concrete particular (p1). However I cannot imagine in any robust sense property c beginning to be exemplified, and even if I could, I would not know how to proceed to imagine it to be caused. For I do not know what could constitute a context of entirely necessary affairs in which to frame such a cause. This consideration, then, casts doubt on the truth of (1) as applied to the case of property c.

As an analogy, suppose we observe that f(x)=x2 is uniformly continuous on any bounded interval. We might be tempted to think that a good explanation for this is that it is uniformly continuous on R (the whole real line). Of course in this case the suggested explanation is quite false. Indeed we might be moved to doubt our explanation if we realize that the usual method of showing that a function continuous on R is uniformly continuous on such intervals appeals explicitly to boundedness. Since R is unbounded, this would leave us without any reason to suppose f is uniformly continuous on R, even if we didn't already have reasons to think it false.

Finally, the second argument only tracks if we take our imagination to be a reliable guide to broad logical possibility. For without that supposition, then even if we can imagine an event having a cause it will not follow that we have imagined something broadly logically possible, and hence we will have no basis to apply an abductive argument. On the other hand, if we do take our imagination to be a reliable guide to broad logical possibility, then since can imagine the nonexistence of a necessary being, we have as much reason to think it broadly logically possible as we would to abductively infer (1). In this way, Rasmussen's second argument for (1) comes at the cost of undermining the conclusion he ultimately wishes to draw, namely the existence of a necessary being.

So I can find no good support for Rasmussen's premise (1), despite the arguments he suggests. Indeed for the reasons outlined here I think Rasmussen himself should give up his belief in (1), unless he can produce a satisfactory replacement argument for its truth.

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