Sunday, 11 May 2014

Contingency and the Fallacy of Composition

(Intended to be part 1 of a short series on contingency arguments)

The Argument from Contingency

Sketched out, the Argument from Contingency is along these lines:

  1. Things are either logically necessary or contingent.
  2. Contingent things require an explanation, which must ultimately lead to a necessary thing (rather than a loop of contingent things or an infinite regress).
  3. Contingent things exist.
  4. Therefore at least one necessary thing exists.
  5. Everything in the physical universe is contingent.
  6. Therefore the physical universe itself is also contingent.
  7. Therefore the necessary thing is separate from the physical universe, and the theist then asserts it to be God.

Every step of this argument is open to serious criticism, but for the purposes of this post I'm going to focus on steps 5 and 6.

The Fallacy of Composition

  1. Every part of X has property P.
  2. Therefore X has property P.

This fallacy (and its converse, the Fallacy of Division) has been known since antiquity, but remains a common sight in religious arguments; the other common place to find it is in arguments against physicalism of mind (e.g. in the form “neurons can't do X, therefore minds can't do X unless they're made of something in addition to neurons”).

Of course, in saying that the argument is a fallacy, we are not saying that the conclusion is false (that would be committing the Fallacy Fallacy).

We can clearly see that steps 5 and 6 of the contingency argument are a naked instance of the fallacy. In a sane world, that would end the matter; we'd just send the argument back to its proponents marked “fallacy of composition committed here” and expect them to either fix it or abandon it. Needless to say, here in the real world, that tends not to be what happens.

“Not always a fallacy”

The first kind of bad response to pointing out the fallacy is to claim that the composition argument is “not always a fallacy”. This argument has been used by, for example, Feser in a post reproduced on SN last year (saying that it “depends on the subject matter”). Obviously, this misses the point of why we call it a fallacy in the first place: an argument is fallacious even if it only sometimes gives the wrong answer.

What that means is that if we want to infer a property from part to whole, we have to show the missing step that demonstrates that for the property under discussion, for the kinds of objects under discussion, the property of the whole is dependent on the parts in an appropriate way to complete the argument. For example, Feser uses this argument (paraphrased):

  1. I have a wall of ordinary Lego bricks; each individual brick is red.
  2. Therefore the wall is red.

This argument is incomplete; the truth of the conclusion depends on several unstated terms. When dealing with human-scale objects like Lego bricks it's very easy to overlook the significance of these; they are obvious from experience. But it's exactly those unstated terms which delimit the scope of the conclusion's validity, and therefore we cannot afford to omit them. Here is a corrected version:

  1. I have a wall of ordinary Lego bricks; each individual brick is red.
  2. Ordinary Lego bricks are centimeter-scale objects without optically relevant sub-millimeter surface features on the side surfaces.
  3. At about millimeter-scale and above, surface colours compose in the obvious simple way (i.e. a red patch next to another red patch makes a larger red patch)
  4. Therefore the wall is red.

The additional conditions we had to add to account for the (non-trivial) behaviour of light at small scales show us how far we can rely on the argument and where it would break down.

Where there's a valid inference from part to whole in this way, it is always possible to add the required additional terms to the argument. Failing to do so, leaving the naked fallacy and then inventing excuses for doing so, is just an attempt to hide the flaw in the argument rather than fix it.

Weak Analogies

Sometimes the proponent of a composition argument attempts to fill in the missing step discussed above by means of an analogy: claiming that the objects and properties under discussion are analogous to the Lego bricks and their redness.

The most striking thing about this line of argument is that it is clearly unnecessary if there exists a legitimate way to fill in the missing part of the argument. If I understand the way that the specific property under discussion behaves with respect to wholes and parts, I can simply make the argument directly without needing an analogy (except perhaps for illustrative purposes). Resorting to analogy alone is in effect a declaration that I don't understand how the property in question behaves—and this automatically calls into question the validity of the analogy itself.

Iterative obfuscation

A second bad response, specific to the argument from contingency, is to try and justify it by adding logically irrelevant steps. The argument goes like this: given universe U of contingently-existing entities, we can consider removing one entity (since they're all contingent) giving universe U-1, from which we remove another to give U-2, and so on until nothing is left. (A more refined version of the argument allows removing sets of ontologically-linked entities.)

The problem here is that the entire argument as given is an irrelevance, and that the validity of the conclusion turns on an implied final step which is not discussed: the point where the last entity (or set) is removed. The ability to remove all items but the last does not logically imply the ability to remove the last one, so the argument is incomplete.

An excellent demonstration of this is provided by the classic theorem of algebraic topology known as the “hairy ball theorem”. In non-mathematical terms, imagine a ball covered with short hairs which we wish to comb flat without discontinuities or protruding tufts. (The theorem states that this is impossible.) So assuming we start with half a dozen tufts, we can progressively comb them out until one remains—but any attempt to comb that one out fails or leaves another tuft. So clearly we can't claim that the fact that we have no problem going from 6 tufts, to 5, to 4, ... to 1 implies that we must be able to get to 0.


Obviously, these arguments don't demonstrate that the universe is not contingent (assuming “contingent” even means anything useful). All I argue here is that we're entitled to reject contingency arguments that deploy the fallacy of composition to make that point.

(I previously addressed this issue on SN in this comment.)