Lamarck is representative of the tradition of science that preceded Positivism with its emphasis on elemental matter and its exclusion from consideration of mind and volition. Lamarck would therefore be a useful starting point, along with his contemporary Erasmus Darwin, Charles Darwin's grandfather, for a Post Positivist tradition of evolutionary theory.
To account for how the invertebrate species he studied appeared to generate one another in succession, while becoming better adapted to their environments, Lamarck proposed two processes. One was a complexifying process leading to new capabilities, due he supposed to a "subtle fluid" in creatures' bodies, employing a catch phrase of 18th century science. The other process was adaptation to the environment through the use and disuse by individual creatures of those capabilities. The changes wrought in creatures' bodies by that use and disuse Lamarck supposed got inherited in progeny.
"Subtle fluid'" didn't cut any ice with Positivists like Charles Darwin, who replaced both of Lamarck's processes with the implacable grinding mill of natural selection. Turned out, though, that natural selection couldn't generate complexifying variation as efficiently as Lamarck's "subtle fluid," whatever that really was.
Unfortunately for us today, Erasmus Darwin's fame died with the 19th century and Lamarck is notorious for his obscurity. Fortunately Samuel Butler in "Life and Habit" came up with a more accessible summary of their views that we can use as our jumping off point.
Butler opted for Erasmus Darwin's "living filament "over Lamarck's "subtle fluid," fortuitously pointing forward to the genome. We may therefore begin a Post Positivist theory of evolution by supposing the genome to be Lamarck's complexifying agent, magically generating new capabilities with potential for new uses while not presumably being the drag on development that mere mutation of genes is likely to be.
We must then ask of the genome two talents. One is intelligently-applied trial and error, demanding of the genome some degree of intelligence. The other is an ability to read success in the application of that intelligence into corresponding properties in genes. No problem. As I have suggested elsewhere, if the genes act as the genome's brain then just by wishing it so the genome could think the necessary changes into the appropriate genes. We see a similar command of brain activation by an intelligence when a dancer effortlessly translates a concept of movement into a massive program of brain cell firings resulting in precisely coordinated contractions of hundreds of muscles.
Hey Presto, a new theory of evolution. Now our work begins. What can we do with such a theory? How can we use it to enrich our experience of the world and of ourselves? That's a task worthy of the humanities.