In quantified
modal logic
Modal logic is a collection of formal systems developed to represent statements about necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and natural language semantics. Modal logics extend other ...
, 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
Jean Buridan (; Latin: ''Johannes Buridanus''; – ) was an influential 14th-century French people, French Philosophy, philosopher.
Buridan was a teacher in the Faculty (division)#Faculty of Art, faculty of arts at the University of Paris for hi ...
by analogy with the
Barcan formula In quantified modal logic, the Barcan formula and the converse Barcan formula (more accurately, schemata rather than formulas) (i) syntactically state principles of interchange between quantifiers and modalities; (ii) semantically state a relation b ...
and the
converse Barcan formula introduced as axioms by
Ruth Barcan Marcus
Ruth Barcan Marcus (; born Ruth Charlotte Barcan; 2 August 1921 – 19 February 2012) was an American academic philosopher and logician best known for her work in modal and philosophical logic. She developed the first formal systems of quant ...
.
The Buridan formula
The Buridan formula is:
:
.
In
English
English usually refers to:
* English language
* English people
English may also refer to:
Peoples, culture, and language
* ''English'', an adjective for something of, from, or related to England
** English national ide ...
, the schema reads: If possibly everything is F, then everything is possibly F. It is equivalent in a
classical modal logic
In modal logic, a classical modal logic L is any modal logic containing (as axiom or theorem) the duality of the modal operators
\Diamond A \leftrightarrow \lnot\Box\lnot A
that is also closed under the rule
\frac.
Alternatively, one can gi ...
(but not necessarily in other formulations of modal logic) to
:
.
The converse Buridan formula
The converse Buridan formula is:
.
Buridan's logic
In medieval scholasticism, nominalists held that universals exist only subsequent to particular things or pragmatic circumstances, while
realists followed Plato in asserting that universals exist independently of, and superior to, particular things.
References
*
*
* {{cite book, chapter-url=https://books.google.com/books?id=9kMqQTs3ITcC&pg=PA190, author=Besnard, P., author2=Guinnebault, J. M., author3=Mayer, E., year=1997, chapter=Propositional quantification for conditional logic, title=''In'' Qualitative and Quantitative Practical Reasoning, pages=183–197, publisher= Springer Berlin Heidelberg See page 190.
Modal logic