Existential proposition
Existential proposition
Traditionally, a proposition which directly asserts the existence of its subject, as, e.g., Descartes’s “ergo sum” or the Christian’s “Good exists.” Expressed in symbolic notation, such a proposition has a form like (Ex)M.
By an extension of this, a proposition expressible in the functional calculus of first order may be called existential if the prenex normal form has a prefix containing an existential quantifier (see Logic, formal, 3).
Brentano (Psychologie, 1874) takes an existential proposition (Existentialsatz) to be one that directly affirms or denies existence, and shows that each of the four traditional kinds of categorical propositions is reducible (i.e., equivalent) to an existential proposition in this sense; thus, e.g., “all men are mortal” becomes “immortal men do not exist.” This definition of an existential proposition and the reduction of categorical propositions to existential appears also in Keynes’s Formal Logic, 4th edn. (1906). — A.C.