- We have to have (at least) two of something
- The two somethings have to be material somethings; they must be independently determinable aspects of the physical world
- The two somethings have to be fundamentally irreconcilable; they can't just be two ways of talking about the same thing
*I mean 'materialism' in the looser, more general sense, technically philosophical physicalism.
In evolution, the two "somethings" are heritable variation and natural selection. They are material somethings: variation is physically inherited, mostly by DNA, plus some epigenetic factors (also material, mostly methylation and acetylation*). In other words, there's nothing outside evolution, no intelligence, no "absolute ideal", no grand scheme; everything in evolution can be reduced to material causes of genes (and other heritable information) and the natural selection of the material environment. (These material causes appear to be local as well, but locality might no longer be a strict requirement for materialism.)
They are fundamentally irreconcilable because all the elements of heritable variation are fundamentally uncorrelated with selection. There are mechanisms of heritable variation that are correlated with selection, as Comrade PhysioProf notes. But these mechanisms themselves are material elements, and the mechanisms themselves evolved by heritable variations that were uncorrelated with selection.
Suppose there's some epigenetic mechanism that is correlated with selection. For example, when food is scarce, an animal might "turn off" heritable genes that promote the growth of its offspring. It's a variation, it's heritable, but the variation is correlated with selection: the parent correctly "knows" that its offspring will have better selective fitness when food is scarce if they're smaller. This specific mechanism of heritable variation, then, is not in dialectical contradiction with natural selection. However, this specific method evolved by uncorrelated variation: ancestor organisms turned genes on or off at "random" (i.e. uncorrelated with selection), and only the progeny of those ancestors that turned on or off the "correct" genes survived selection pressures.
The principle of irreconcilability or non-correlation does not mean that there's no teleology at all. Human beings are teleological — we can anticipate and plan for the future — and are still subject to dialectical materialistic evolution at many different levels. Even genetic information* is "teleological"; the genetic information "knows" a lot about the future adult organism. The principle of irreconcilability means only that there's if there's any teleology, it's part of the dialectical elements in contraction; there's no teleology outside the elements. (More precisely, at higher levels of abstraction like human social evolution, if there is teleology outside the system, there is something about the elements that is not subject to the outside teleology.) And there's no teleology at all outside the material, physical universe: no God, no Hegelian Absolute Ideal, no Platonic Ideal plane, no abstract truths that cannot ultimately be reduced to truths about the properties of material objects.
*DNA, heritable patterns of gene activation, the biochemical machinery of the blastocyst, the larger environment of the uterus or egg, etc.