General propositions in Modern logic — universal and existential propositions

“All trespassers will be prosecuted” does not promise that any trespasser actually exists to be caught. “Some officer is on duty” does promise at least one officer actually exists. Modern logic captures that exact difference with two symbols — ∀ and ∃ — and a variable that has no meaning at all until you attach one of them to it.

In two minutes

Modern logic symbolises general propositions using a propositional function (an expression like ‘x is P’ that becomes a proposition only once its variable is bound) together with one of two quantifiers: the universal quantifier (∀x, ‘for all x’), which does not assert that anything exists, and the existential quantifier (∃x, ‘there exists an x such that’), which does.

The rest of this chapter

The full explanation, the cheat sheet, every previous-year question at every mark weight, the quiz and the answer skeletons are part of Logic – I on LexBlox Semester. Sign in to unlock the subject, or read Module 1 of Legal Language and Writing free.