It is remarkable how closely Lucretius intuited ideas that would in the fullness of time become foundational to modern science. Greenblatt lists them in detail; I will summarize more succinctly here.
Everything that exists, on earth or in the sky, is composed of invisible particles -- atoms. The forms of things change; the atoms are eternal. They are infinite in number, but limited in shape and size. Their limited characteristics determine how they attract, repel, and hook up with others.
There is no predetermined design to the universe. There is, in fact, a random "swerve" to things. Nature ceaselessly experiments. Some forms are well adapted to survive and endure. Others pass away. Humans are not unique; they are part of a universal material process that links them to all other forms, organic and inorganic. We are made of the same stuff as stars, "a small part of a vast process of world-making that Lucretius celebrated as essentially erotic" (Greenblatt).
The soul is a manifestation of the body. It dies when he body dies. There is no afterlife.
We are curious by nature. Understanding the nature of things is a well of deep wonder, and ultimately a source of happiness and freedom from fear.
These are ideas that have become foundations of modern life, says Greenblatt, at least for those who are likely to be reading his book. They are certainly ideas that are foundational to modern physics, chemistry and biology, and therefore their acceptance -- at least tacitly -- was essential to the development of modern technology and medicine.
And here we reach the great cognitive dissonance of modern times.
Almost everyone embraces the technological and medical gifts of science, the longer life spans, the economic affluence. But only a minority will follow Lucretius to his naturalistic conclusion. The great majority of people in the "modern" world choose to live their lives in thrall to the pre-modern gods.
Of course, the majority -- including some of my closest friends -- may be right. Maybe the gods do watch and listen, and consign immortal souls to eternal reward or punishment. Who am I to say?
(Tomorrow: Lucretius and religious naturalism.)