Phylogeny, induction, and the straight rule of homology

Continuing my “natural classification” series, which I am writing with Dr Malte Ebach of UNSW.

After having experienced the circulation of the blood in human creatures, we make no doubt that it takes place in Titius and Maevius. But from its circulation in frogs and fishes, it is only a presumption, though a strong one, from analogy, that it takes place in men and other animals. The analogical reasoning is much weaker, when we infer the circulation of the sap in vegetables from our experience that the blood circulates in animals; and those, who hastily followed that imperfect analogy, are found, by more accurate experiments, to have been mistaken. [Philo, in David Hume’s Dialogues in Natural Religion, Part II]

Phylogenetic classification is a form of induction. It enables us to infer the properties of an as-yet unobserved member of a clade with a very high degree of likelihood, as was pointed out by Gary Nelson in the 1970s. [1] For inductive inferences to be successful, we have to guard against the grue problem outlined by Nelson Goodman. [2]

While this is very familiar to philosophers, it is less well known to biologists, so a short summary is in order. The grue problem is based on a kind of “broken” predicate or property: ordinarily we might infer from the fact that all prior emeralds have been observed to be green and the future emeralds would also be green – this would be a case of inductive inference. But in the absence of prior certainty about what the rules are, without a “straight rule”, [3] we cannot rule out the existence of another property, which Goodman calls “grue”, in which emeralds are green if observed before some time t and blue thereafter. Hence, every observation of a green emerald strengthens the inference that after t emeralds will be seen to be blue. It must be noted that this is not a claim that emeralds will change color. It is about what we can infer of unseen members of a class. A gruelike predicate is unprojectible, which is to say that it cannot be projected to unobserved entities. What inductive inference promises is projectibility, so that we can say things that are very likely to be true about unobserved members of the class.

This is more than a mere thought experiment. The infamous “black swan” example so beloved of logicians is a simple case. Swans were all observed to be white, until black swans were discovered in West Australia in the late 17th century. Had swans been defined by a white plumage (which was common at the time), then swan plumage would have been a grue property. More generally, consider such classes as Mammalia. Mammals are defined as tetrapodal (four limbed) animals which give live birth, lactate, and have hair. But whales have secondarily lost their hindlegs and hair, not everything that lactates is a mammal, and monotremes lay eggs. More recently it has become clear that lineages of species are not straight but gruesome. What defines a group of organisms may change in a daughter species. Consider sexuality as a trait of a group of lizards. When one species becomes parthenogenic (secondarily asexual) we encounter a grue property for real. This applies to any single property of a group, potentially. Evolution leads to grue problems.

And yet, biology is not deeply troubled by grue problems, even though it is precisely the science that should be. While the colour of the swan’s plumage turned out not to be projectible, the new black swan was not placed in a new order or class. It was recognised to be a swan nevertheless, and placed into the existing genus, hitherto a monotypic genus. Although philosophers, who anyway tended then as now to rely upon folk taxonomic categories for their examples, were shocked in the manner of Captain Renault, biologists simply shrugged, reported the new species, and added it to the existing taxonomy. The reason is quite obvious by now: the swan was not defined, but classified upon the overall affinities it exhibited, and the fact that one homolog differed in character state from the rest was not crucial, any more than if it had a different shaped beak from the rest of the genus.

The issue here is with what Peter Godfrey-Smith calls the “dependence relations”:

We should not make a projection from a sample if there seem to be the wrong kind of dependence relations between properties of the sampled objects. [4]

It is our claim here that homological affinity does act to provide the “right” kind of dependence relations between properties of taxa. A single failure of a homolog to project properties is insufficient to make the taxon natural (that is, in philosophical terms, a projectible class), since the class (the taxon) is formed from the overall suite of homological relations (which my coauthor and I are calling the affinity, following early 19th century taxonomic use). Affinity acts to set up taxonomic kinds, and these act as a “straight rule”, as they do tend to converge upon projectible properties.

In taking inference from homology to be a kind of “straight rule”, the question is why it works. If the universe were such that properties correlated by chance, it would not work, but in the cases of the special/paletiological sciences, properties correlate due to a shared productive cause. If the universe lacked appreciable structure of this kind, then no search method would deliver knowledge (consider Wolpert’s and Macready’s “No Free Lunch” theorem [5]). Assuming that properties can be correlated, the epistemic question is how to identify those that are and to distinguish them from those that aren’t, which in biological systematics is the distinction between homology and homoplasy. If there’s knowledge to be had, then one way to acquire it is to iteratively refine one’s classifications in an attempt to maximize the homological relations on which they are based.

Such inferences are, of course, quite defeasible. It should not be thought we are supposing that natural classifications are in any way certain, or that any given homolog will exemplify the same states in each taxon or object classified. Of course this will not apply. On the one hand this is probabilistic [6] inference, in the sense that there is some likelihood or confidence that the projection will succeed for each property, and a high confidence that it will succeed for most properties. [This is akin to selection on a smooth landscape versus on a rugged landscape; selection can act on traits in a highly correlated “smooth” landscape (where adjacent coordinates are not too different in value from each other), but it fails on an uncorrelated, or “rugged” one. [7] The progress of science has been compared to an adaptive walk, [8] and similar considerations apply to inference in science as apply to selective searching of the adaptive landscape; both are special cases of a search procedure of the kind Wolpert and Macready discuss.]

Systematics in biology, and classification in science generally, resolves much of the practical issues of gruesome induction by, as Godfrey-Smith says, ensuring that the right class is sampled by finding the right dependence relations through a process of iterative refinement. These are what we are generally calling homologies.

Notes

¹ Nelson 1978.

² Goodman 1954. See Godfrey-Smith 2003 for a discussion of the classical problem.

³ Hans Reichenbach proposed a “straight rule” for induction in his The theory of probability (Reichenbach 1949), in which induction was justified when increasing observations converged upon an asymptote. See also Salmon 1991. Here we are using it in a more general sense, as a way of ensuring that gruelike properties are eliminated.

⁴ Godfrey-Smith 2003: 579.

⁵ The No Free Lunch Theorem states that no single algorithm outperforms chance when amortized over all possible search spaces or functions (Wolpert and Macready 1997, Wolpert and Macready 1995).

⁶ Here we mean something like a likelihood probability. This may be Bayesian or some other statistical confidence; it doesn’t materially affect the argument which philosophical stance towards probability one adopts here, and we leave it to the reader to convert the argument to their favorite method or position on the matter.

⁷ Kauffman 1993, Gavrilets 2004.

⁸ Hull 1988, Wilkins 2008.

References

Gavrilets, Sergey. 2004. Fitness landscapes and the origin of species, Monographs in population biology; v. 41. Princeton, N.J.; Oxford, England: Princeton University Press.

Godfrey-Smith, Peter. 2003. Goodman’s Problem and Scientific Methodology. The Journal of Philosophy 100 (11):573-590.

Goodman, Nelson. 1954. Fact, fiction and forecast. London: University of London, The Athlone Press.

Hull, David L. 1988. Science as a process: an evolutionary account of the social and conceptual development of science. Chicago: University of Chicago Press.

Kauffman, Stuart A. 1993. The origins of order: self-organization and selection in evolution. New York: Oxford University Press.

Nelson G (1978) Classification and Prediction: A Reply to Kitts. Systematic Zoology 27: 216-218.

Reichenbach, Hans. 1949. The theory of probability, an inquiry into the logical and mathematical foundations of the calculus of probability. 2nd ed. Berkeley: University of California Press.

Salmon WC (1991) Hans Reichenbach’s vindication of induction. Erkenntnis 35: 99-122.

Wolpert, David H. , and William G. Macready. 1995. No free lunch theorems for search. Sante Fe, NM: Santa Fe Institute.

Wolpert, David H., and William G. Macready. 1997. No free lunch theorems for search. IEEE Transactions on Evolutionary Computation 1 (1):67-82.

Filed under: Epistemology, Logic and philosophy, Natural Classification, Philosophy, Science, Systematics Tagged: Natural Classification, Philosophy

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