Barcan Formula - The Barcan Formula

The Barcan Formula

The Barcan formula is:

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In English, the schema reads: If everything is necessarily F, then it is necessary that everything is F. It is equivalent to

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The Barcan formula has generated some controversy because - in terms of possible world semantics - it implies that all objects which exist in any possible world (accessible to the actual world) exist in the actual world, i.e. that domains cannot grow when one moves to accessible worlds. This thesis is sometimes known as actualism--i.e. that there are no merely possible individuals. There is some debate as to the informal interpretation of the Barcan formula and its converse.