
related topics 
{theory, work, human} 
{game, team, player} 
{math, number, function} 
{township, household, population} 
{water, park, boat} 

Boolean logic is a system of syllogistic logic invented by 19thcentury British mathematician George Boole, which attempts to incorporate the "empty set", that is, a class of nonexistent entities, such as round squares, without resorting to uncertain truth values.
In Boolean logic, the universal statements "all S is P" and "no S is P" (contraries in the traditional Aristotelian schema) are compossible provided that the set of "S" is the empty set. "All S is P" is construed to mean that "there is nothing that is both S and notP"; "no S is P", that "there is nothing that is both S and P". For example, since there is nothing that is a round square, it is true both that nothing is a round square and purple, and that nothing is a round square and notpurple. Therefore, both universal statements, that "all round squares are purple" and "no round squares are purple" are true.
Similarly, the subcontrary relationship is dissolved between the existential statements "some S is P" and "some S is not P". The former is interpreted as "there is some S such that S is P" and the latter, "there is some S such that S is not P", both of which are clearly false where S is nonexistent.
Thus, the subaltern relationship between universal and existential also does not hold, since for a nonexistent S, "All S is P" is true but does not entail "Some S is P", which is false. Of the Aristotelian square of opposition, only the contradictory relationships remain intact.
See also
Full article ▸


related documents 
Emergent organisation 
Political economy 
Navigation research 
Aristoxenus 
ELIZA effect 
Invariance 
List of agnostics 
Biosecurity protocol 
Vere Gordon Childe 
Anaximenes of Miletus 
Retreat (spiritual) 
Linus's Law 
The Memory of Whiteness 
Georg Henrik von Wright 
Argumentum ad baculum 
Homesteading the Noosphere 
Entity 
Alexandrists 
Trivium (education) 
Reverse speech 
Truth condition 
Strategy 
Declarative memory 
Safe, sane and consensual 
Ewald Hering 
Biological anthropology 
Specialization 
Physical science 
Ken MacLeod 
Gerald Schroeder 
