Principle of Proportionality
Proposed by Hume and summarised in his famous quote 'A wise man proportions his belief to the evidence', The Principle of Proportionality is a ontological and epistemological principle generally considered central to all forms of inductive reasoning- i.e., science, theology, philosophy, and logic. It holds that the act of valuing, trusting, or believing in something is not a discrete state- we can value, trust, or believe in some things more than others. For instance, a person might believe in both the existence of aliens and existence of tables, based on a body of evidence he is presented with. However, it is clear that there is far more evidence for the existence of tables than the existence of aliens- so, the person should recognise that their belief in tables has a stronger foundation, and is hence a stronger belief, than their belief in aliens.
The Principle of Proportionality is particularly useful when the agent is attempting to integrate a discordant belief into their mental framework. For example, suppose a person is a materialist based on past evidence and experience, and is then suddenly confronted with a substantial body of evidence supporting the existence of immaterial ghosts. Although this new evidence may appear persuasive, Hume argues that in order for this new, contradictory belief to be rationally accepted, it must 'overthrow' the entire incumbent weight of evidence showing the existence of ghosts to be impossible. Ie, so many of our day-to-day, implicit beliefs (such as the existence of tables) rely on an empirical framework to be effective, that each effectively adds weight to the bulk of evidence supporting empiricism. He goes on to implicitly argue that, as empiricism has such a large, richly interconnected pattern of theories, that the likelihood of anything thus far undiscovered overthrowing of this incumbent body of evidence is exceedingly remote.