Buridan formula

In quantified modal logic, the Buridan formula and the converse Buridan formula (more accurately, schemata rather than formulas) (i) syntactically state principles of interchange between quantifiers and modalities; (ii) semantically state a relation between domains of possible worlds. The formulas are named in honor of the medieval philosopher Jean Buridan by analogy with the Barcan formula and the converse Barcan formula introduced as axioms by Ruth Barcan Marcus.

The Buridan formula is:

In English, the schema reads: If possibly everything is F, then everything is possibly F. It is equivalent in a classical modal logic (but not necessarily in other formulations of modal logic) to

The converse Buridan formula is:

${\displaystyle \forall x\Diamond Fx\rightarrow \Diamond \forall xFx}$.

... As well as providing running commentaries on Aristotle's texts, Buridan wrote particularly influential question-commentaries, a typical genre of the medieval scholastic output, in which authors systematically discussed the most problematic issues raised by the text on which they were lecturing. The question-format allowed Buridan, using the conceptual tools he developed in his works on logic, to work out in detail his characteristically nominalist take on practically all aspects of Aristotelian philosophy. Among his logical works (which also comprise a number of important question-commentaries on Aristotle's logical writings), two stand out for their originality and significance: the short Treatise on Consequences, which provides a systematic account of Buridan's theory of inferences, and the much larger Summulae de Dialectica, Buridan's monumental work covering all aspects of his logical theory.

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