Final answer:
Lucretius' philosophy is characterized as Epicurean, focusing on atomism and ethical ideas that reject religious explanations for the workings of the universe, which he believed was governed by chance and natural laws.
Step-by-step explanation:
The philosophy of Lucretius is best characterized as Epicurean. Lucretius, a disciple of Epicurus, developed his ideas in the poem 'De Rerum Natura' (On the Nature of Things), which largely covers ethics grounded in atomism and the rejection of divine intervention in favor of chance events and the motion of atoms. While Lucretius and his mentor Epicurus responded to Greek thought leaders like Plato and Aristotle, they showed continuity with Presocratic thinkers, specifically in their skeptical view of religion and their belief in atomic theory.
In the broader context of philosophy at the time, Roman philosophy was influenced by earlier Greek traditions, and Romans often looked to Plato and Aristotle as reference points. However, they developed their ideas within a Roman cultural context that went from a republic to an empire. Lucretius and other Roman philosophers, while grounded in Greek thought, conveyed their philosophies in works that reflected the social and political landscapes of Rome.