|
Postmodern mathematics
|
|
Postmodern mathematics is a thought developed as a result of postmodernism. The theory asserts that there is no such thing as ‘absolutism’ or ultimate truth in mathematics. It also declares that the term ‘mathematics’ can't be used to define a specific object. However, mathematics, in its plural form, describes the multiplicity and flexibility of this term based upon context. All these various definitions are not necessarily true or false and can be right or wrong based on the context in which they are defined. This view sees mathematics as: imbued with moral and social values which play a significant role in the development and applications of mathematics. This theory was first proposed by Lakatos in his book "Proofs and Refutation". It also constitutes the hypothetical-deductive system of mathematics which declares that the discipline of mathematics is fallible and corrigible, the development of theorems require the falsification of “falsifiers” and transmission to hypothetical knowledge. In other words, in order to develop theorems, one must first falsify the premises under which the theorem would be falsified. For modernists, knowledge is the use of empirical methodologies in order to discover the ‘ultimate truth’. Postmodernism counters that knowledge isn't as empirical and logical as modernism persists, rather it is subjective and is open to change. For postmodernists, knowledge is a construct of the society and is subject to change over time and place. Logicism (the view that perceives mathematics as a part of Logic) Modernism, on the other hand, propose no question for the nature of mathematics or education as they contend that the two entities are not related to one another. Karl Popper Karl Popper (1902-1994) introduced the notion of falsification and asserted that to prove theories in sciences, researchers should strive to disprove them. Wilkinson He introduced the idea of 'fuzzy logic'. This idea rejects the Aristotelian Law of Truth and fallibility of an object (the notion that an object is either true or false). He instead proposed the existence of 'degrees of truth', the idea that an object is characterised into various degrees of truth. According to Kuhn, education and knowledge strives to interpret and represent rather than provide an objective explanation. However, it doesn't mean that the notion can be used based on any ‘personal situation’ rather it is relative to the mathematical context and situation it is used in such that 2 +2 1 is true in mod (3) arithmetic but it would never be true in any other mathematical context. He also claims that to prove the ‘reality’ or the ‘truth’ of a description of an entity, which in this context would be mathematics, the negation of another description is needed. See Also
|
| < Prev | Next > |
|---|
Main Menu
| Home |
| Articles |
| Search |
| Submit Article |
| Contact Us |
| Donate to Wikibin |
