First, that the non-teleological and timeless laws of physics--those governing the ultimate elements of the physical universe, whatever they are--are not fully deterministic. Given the physical state of the universe at any moment, the laws of physics would have to leave open a range of alternative successor states, presumably with a probability distribution over them. Second, among those possible futures there will be some that are more eligible than others as possible steps on the way to the formation of more complex systems, and ultimately of the kinds of replicating systems characteristic of life. The existence of teleology requires that successor states in this subset have a significantly higher probability than is entailed by the laws of physics alone--simply because they are on the path toward a certain outcome. Teleological laws would assign higher probability to steps on paths in state space that have a higher "velocity" toward certain outcomes. They would be laws of the self-organization of matter, essentially--or of whatever is more basic than matter. (pp. 92-3)This is a good summary of Nagel's attempts to reintroduce teleology into the natural universe. Nagel realizes that neo-Darwinism is a fatally flawed theory. The gist of the argument is that naturalism has to reintroduce final causes. Blind chance and mechanistic evolution don't get it. Mixed up in the argument is the typical atheist reliance on chance and probability. The motions of matter are not deterministic.
Okay, for the sake of argument, let's grant that. As theists we deny that the source of "probability" is what the atheist claims it to be -- an ultimate irrational residue of lawlessness. A world in which things happen for "no reason!" But back to the technical issues.
The probability distributions of quantum field theory can be computed with some very precise results for things like scattering amplitudes,half-lives, branching ratios and the like. These probability "amplitudes" are all functions of the basic properties of the physical systems being modeled. And, here's the point: the amplitudes have no teleological aspect. All of physics exhibits non-teleology. The future state(s) of the universe are solely determined by the present state, past and future are irrelevant. This principle falls out rather neatly from the principle of least action -- a very general principle from which all equations of motion can be derived given a Hamiltonian (think, "energy") or Lagrangian function that depends on the constituents of the system and their configurations. Moreover Nagel's plan is to require "... that successor states in this subset [those favoring replicating life] have a significantly higher probability than is entailed by the laws of physics alone--simply because they are on the path toward a certain outcome."
The nail in this coffin is that Nagel imagines some non-physical laws that must alter half-lives, branching ratios and so on, along the way. After all, according to the atheist myth of macro evolution, the journey to replicating life is via small steps with compounded probabilities. We ought to be able to see such evidence in pre-biotic chemical reactions.
Embracing such non-physical laws is to accept a new dualism and to abandon the pillar of monism in the atheist's philosophy. Paradoxically, the positing of extra-physical (should we say supernatural!) properties seems not to worry Nagel's new born "naturalism."