David Hume begins by dividing all philosophy into the easy and obvious, which appeals to sentiment and action, and the accurate and abstruse, which examines the principles of the understanding. He argues that all perceptions divide into strong impressions and faint ideas, and that every simple idea is a copy of a preceding impression. The association of ideas operates through three principles: resemblance, contiguity in time or place, and cause and effect. All reasonings concerning matters of fact rest upon the relation of cause and effect, yet our knowledge of this relation is derived entirely from experience rather than a priori reasoning.
Even after observing constant conjunction, no process of the understanding bridges the gap to conclude that the future will resemble the past. Instead, custom or habit is the great guide of life, determining us to expect similar effects from similar causes based on past repetition. Probability and chance operate through the same mechanism of the mind meeting concurring views.
When we search for the idea of necessary connexion, we find no impression in a single instance of cause and effect; the idea arises solely from the internal sentiment of the mind accustomed to transition from one object to its usual attendant. This insight resolves the long-standing controversy surrounding liberty and necessity, showing that human actions exhibit the same regular conjunction as material causes, making necessity essential to morality and human accountability. Animals learn from experience through the identical instinct of custom, rather than complex ratiocination. Examining miracles, Hume argues that no testimony is sufficient to establish a violation of the laws of nature unless its falsehood would be even more miraculous, making popular religions dependent on faith rather than reason. He concludes with a critique of teleological arguments for a particular providence, asserting that we cannot infer attributes in a cause beyond what are strictly displayed in its effects. Finally, he advocates for a mitigated scepticism that restricts our enquiries to common life and the demonstrable sciences of quantity and number, casting all abstract metaphysics and theology aside.