Editing Finitary (section)

== Finitary argument ==
A '''finitary argument''' is one which can be translated into a [[finite set]] of symbolic propositions starting from a finite<ref>The number of axioms ''referenced'' in the argument will necessarily be finite since the proof is finite, but the number of axioms from which these are ''chosen'' is infinite when the system has [[axiom scheme]]s, e.g. the axiom schemes of [[propositional calculus]].</ref> set of [[axiom]]s. In other words, it is a [[Mathematical proof|proof]] (including all assumptions) that can be written on a large enough sheet of paper.

By contrast, '''[[infinitary logic]]''' studies logics that allow infinitely long [[statement (logic)|statements]] and [[Mathematical proof|proofs]]. In such a logic, one can regard the [[existential quantifier]], for instance, as derived from an infinitary [[disjunction]].