by Robert C. Koons
rkoons@mail.utexas.edu

ABSTRACT—After sketching the various probabilistic accounts of the design inference, including the Bayesian and Dembskian models, I make a stab at developing, in an admittedly crude form, a non-probabilistic model, based on a measure of ontological complexity, which, I conjecture, may more faithfully represent the design inference as found in such classical texts as Aquinas, Reid and Paley. I discuss the various pluses and minuses of probabilistic and non-probabilistic models, with reference to one important test case: inferring design from anthropic coincidences in the fundamental constants of physics.

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Paper Versions:
-27 November 2001

[ 30 November 2001: Message edited by: Moderator ]

Koons suggests that perhaps this entire process of calculating probability is a "useless shuffle" which may be dispensed with. In its place, Koons proposes the concept of "ontological complexity" based upon "complex causes" and "simple effects." The justification of this idea is clear: one of the defining features of an intelligent agent is that it displays intentionality; the ability to order matter and energy in such a way as to achieve a distant goal. We intuitively infer design when we see many complex parts ("causes") all working toward a single, simple goal ("effect"). Therefore, the design inferrence may be thought of as an Aristotelian diamond which fans out from a single intelligent source to a complex myriad of causes, all of which converge again upon a single, simple effect.

The main weakness of this paper is in its lack of clear definition of "ontological complexity." Nowhere is it clearly and unabiguously stated exactly what this term means. In Dembski's work, complexity is the inverse of probability; it is clearly "nailed down" conceptually. However, ontological complexity must obviously refer to something besides low probability; otherwise, we are back to probabilities which Koons wants to eliminate. Perhaps complexity refers rather to the number of distinct elements working toward the end goal, but then we are justified in asking precisely how many elements are required for a cause to be "complex." Ten? Five? Three? Two? At some point a limit is crossed and it is in attempting to nail down the line that we come back to some sort of arbitrary numbers game that Koons was trying to eliminate in dispensing with probabilities. Furthermore, the very reason for counting the number of elements is that as the number of interacting elements increases, the probability that they will fall together by chance decreases--hence the need for inferring an organizing intelligence. Thus, the very reason for the validity of Koons's design inferrences rests upon an implicit probability calculation.

Here are the sum total of Koons's comments regarding the measurement of ontological complexity:

"All that is required to complete the model is an account of the measure of ontological complexity. This should be a measure that applies to situation types (to types of the internal structures of situations). A simple type should
always be given a non-zero measure, and the measure of the conjunction of two strongly independent types should be the sum of the measures of the conjuncts."

Notice that ontological copmlexity is defined in terms of (1) simple types (in which case we are warranted in asking how we determine what is "simple," and we have to be careful to avoid circularity here) and (2) as the conjunction of independent types. This determination of independence gets us back to the exact same sorts of assumptions that promptied Koons to try to eliminate probabilistic calculations in the first place. Indeed, in earlier critiqing Dembski's method of design inferrence, Koons noted

"We derive a low probability value by multiplying
together some presumed probability of the occurrence of each part of the complex structure, implicitly assuming that the relevant probabilities are mutually independent. As I mentioned above, it is typically very difficult to verify such independence assumptions empirically."

If this is a problem for Dembski, it seems to be just as problemmatic for Koons.

After the brief paragraph outlining the measurement of ontological complexity, Koons comments "If such a measure (mu) can be sufficiently characterized...," suggesting that he is in this paper not attempting to rigorously define how ontological complexity is measured.

This, as I see it, is the pivotal issue upon which Koon's entire paper rests. If ontological complexity can be defined in a non-question-begging way without recourse to probabilities, Koons will have made a significant contribution to our knowledge of design inferrences. I strongly suspect, however, that any attempt to define ontological complexity will always require some sort of probabilistic calculation, even if only intuitively. If this is the case, he will basically have re-discovered Dembski's version of the design inferrence, but from a different angle. Dembski's version of the design inferrence does indeed have a concept of "complex causes" and "simple effects," but they are wedded to actual numbers or probability measures. In Dembski's work, the probability of the cause (or event) in question must be less than 1 in 10^150, while the simplicity of the effect is measured in terms of the algorithmic compressibility of the specification of the event. In essence, then, Dembski's design inferrence plays off of the difference between (1) a very complex event (eg, a radio transmission containing a long string of prime numbers), with (2) a very simple (compressible) specification of that event (eg, the prime numbers, the numbers only divisible by themselves and 1).

A complex cause working toward a simple goal. Intelligent agency working through intentionality. Dembski and Koons both agree in this sense, and both are getting at the same sort of pattern for detecting intelligent agency. The difference is that Dembski uses probabilities to ground his definitions of complex and simple, while Koons does not. Whether Koons can get away with it remains to be seen.

Bracht seems to assume that we know how to apply probability theory to the task of detecting design, and that my proposal in terms of ontological complexity is, at this stage, vague and indeterminate in comparison. I agree to this extent: we have a well-developed mathematical theory of probability, and no counterpart to it yet exists for ontological complexity. In this respect, my paper merely sketches a possibly fruitful research project.

However, when it comes to the detection of design, probability theory alone is not sufficient. We have to figure out how to apply it to putative examples. Here it seems to me that a probabilistic and an ontological approach are both in their very early stages of development. It is not at all clear what probabilities to assign to the anthropic coincidences in cosmology or to any of the instances of "irreducible complexity" in Behe's work. I suspect that any rough and ready estimate of probabilities is based intuitively on a prior rough-and-ready judgment about the degree of ontological complexity.