Lyell's 4 Assumptions

For this they willingly are ignorant of,
that by the word of God the heavens 

were of old,
and the earth standing 

out of the water and in the water:
2 Peter 3:5

"Lyell's concept of uniformity had four components.
Lyell, Darwin's geology sidekick,
who led the charge against a Biblical Flood
--First, he quite reasonably assumed that the natural laws are constant. Scientific inquiry of any kind is impossible if we cannot assume that, for example, the laws holding the planets in orbit or the laws of chemical affinity have not been constant.
Implicit in this assumption is the belief that God has never at any time violated those laws by intervention.

--Second, Lyell assumed that the earth's geological features were caused entirely by processes we see taking place today.
Again, this is reasonable but excludes the possibility of large-scale catastrophic events, whether or not they were divinely originated.

--Third, he assumed that the geological changes are always slow, gradual, and steady; modern geology, however, has conceded that this assumption is too rigid and that some catastrophes have occurred but have been relatively small, local events.

--Fourth, although Lyell could not accept until quite late in life that species could gradually change from one to another, he proposed that the fossil record represented but one part of a "great year" or grand cycle, where the ichthyosaur and pterodactyl might return once more to inhabit the earth."
MindsAndMen