Arbitrary Reference

Two fundamental rules of reasoning are Universal Generalisation (UG) and Existential Instantiation (EI). The former is the rule that allows us, given that we stipulate that ABC is an arbitrary triangle and prove that ABC has a property p, to conclude that all triangles have p. The latter is the rule that allows us, given that there exists a continuous function, to stipulate that f is an (arbitrary) continuous function. Reasoning according to these rules (or, as Kit Fine calls it, ‘instantial reasoning’) is ubiquitous in both formal and informal contexts.