Changes

*'''[[Paraconsistent logic|Paraconsistency]]''': paraconsistent logic and mathematics rejects the principle that every proposition must be either true or false, but not both—it posits that there are propositions that are both true and false simultaneously. Thus, for example, there may be some set, which both does and does not contain a given element. (This is proposed as an alternative solution to paradoxes such as [[Russell's paradox]] and the [[liar paradox]].)

*'''[[Paraconsistent logic|Paraconsistency]]''': paraconsistent logic and mathematics rejects the principle that every proposition must be either true or false, but not both—it posits that there are propositions that are both true and false simultaneously. Thus, for example, there may be some set, which both does and does not contain a given element. (This is proposed as an alternative solution to paradoxes such as [[Russell's paradox]] and the [[liar paradox]].)

Constructivism, finitism and ultrafinitism generally entail a rejection of much of classical mathematics; so, they tend not to be popular with practicising mathematicians. However, there are alternative systems of mathematics which have been worked out based on their assumptions—in particular, constructivist or intuitionistic mathematics, is a significant and continuing area of mathematical research. Some of its formulations (e.g. intuitionistic logics) have been found useful by those who don't necessarily agree with the philosophical theories which motivated their development.

Constructivism, finitism and ultrafinitism generally entail a rejection of much of classical mathematics; so, they tend not to be popular with practicising mathematicians. However, there are alternative systems of mathematics which have been worked out based on their assumptions—in particular, constructivist or intuitionistic mathematics, is a significant and continuing area of mathematical research. Some of its formulations (e.g. intuitionistic logics) have been found useful by those who don't necessarily agree with the philosophical theories which motivated their development.

[[Category:Philosophy]][[Category:Mathematics]]

[[Category:Philosophy]][[Category:Mathematics]]