In quantified
modal logic
Modal logic is a kind of logic used to represent statements about Modality (natural language), necessity and possibility. In philosophy and related fields
it is used as a tool for understanding concepts such as knowledge, obligation, and causality ...
, 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 14thcentury French scholastic philosopher.
Buridan taught in the faculty of arts at the University of Paris for his entire career and focused in particular on logic and ...
by analogy with the
Barcan formula 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, 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 g ...
(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, isbn=978-3-540-63095-1 See page 190.
Modal logic