Barcan formula

The Barcan Formula states:

In English, the statement reads, "'For all x, it is necessary that A', implies, 'It is necessary that for all x, A'". The formula tells us that if everything is quantifiable in all other worlds then it would have to be necessary that everything is quantifiable in our world as well.

The Barcan formula is used in S5 modal logic of the Kripke System.

The Barcan formula has generated some controversy because some philosophers believe the formula violates the structure of the Kripke System. It implies that all objects which exist in this world (which the first is quantified over) must also exist in the sucessor states to this world (which the second is quantified over), so one interpretation is that no new objects can ever be created.

The formula was first proposed by Ruth Barcan Marcus.

Related formulas include the Converse Barcan formula, Buridian formula, and the Converse Buridian formula.