Many people dismiss evolution as “survival of the fittest is a tautology — the fittest are the ones who survive.”

This is wrong for many reasons, but one of the problems with that is something I have yet to see among the writings of evolution. As is standard in defenses of evolution, I will begin my thesis with analogy to gravity. But before that, I would like to analyze what we mean by “tautology”. A “tautology” is something that is true by definition, or cannot be logically anything other than true. An example is “x=x”. X must always be equal to itself.

Now, open a math journal. Any math journal. Choose a paper. Any paper. I will do it, now, by choosing a paper from arxiv.org (it’s not strictly a math journal, but close enough for what I have in mind): I tried to be “random” about it by going to “new” and choosing the first one that I could half-way understand: All automorphisms of all Calkin algebras. As an aside, much like most readers of this, I’m not really qualified to judge it. But just reading the abstract, the author claims: “The Proper Forcing Axiom implies all automorphisms of every Calkin algebra associated with an infinite-dimensional complex Hilbert space and the ideal of compact operators are inner.” Assuming his proof is correct, this means that this thing that is fairly non-trivial to understand is a *tautology. *I am willing to bet that even if you specialize in the field, the above was not obvious to you. In fact, this is true of any math paper: it is completely filled with tautologies, and is completely and utterly non-obvious.

Let me give you another example of a tautology: given that the gravitational force is GMm/r**2, a “solar system” (one very heavy body and a bunch of significantly lighter bodies) will move in close approximations to ellipses (that is not an exact phrasing, but a proper estimate of the approximation is outside the real of this post). That is a tautology, and is also fairly non-trivial.

Now, here is another: assuming that genes are passed in a mostly-faithful (small number of mutations) to the next generation, and that genes correlate to reproductive success, we expect to see “evolution”. This is a *mathematical *theorem, in that the axiom can be modeled mathematically and “evolution” (meaning many of the phenomena under “evolutionary biology” such as exaptation, adaptation, complexity and variety) be proven. Note that the initial axiom is not a tautology: there is no a-priory logical reason to assume changes in an individual’s life-style won’t change their genetic code. However, the initial axiom, despite not being a tautology, meaning *logically true*, is factually true: many experiments have been done on this. By the way, it’s as true as GMm/r**2: it’s a useful approximation, not the complete truth: there are epigenetic pressures on heredity. Just like in gravitation theory, we use a simple model to derive predictions, and the correlation of the predictions with the model gives us evidence that the model is true.

Summary: a significant part of evolutionary biology *is *a tautology. But tautology is not a bad word — it means that a significant part of biology is mathematics. This is good. Mathematical modeling is the best modeling.

This fits perfectly with the Kuhnian perspective that at the basis of every scientific theory is a set of tautologies. Those tautologies cannot be proven or refuted within the theory; they serve as the framework for discussion, like axioms do in a mathematical system.

What makes a scientific theory useful is that it gives a good foundation for finding models that fit observations and provide insight. And that certainly applies to the theory of evolution.