User:Cyan/kidnapped/Platonist

Plato's influence on Western culture was so profound that several different concepts are linked by being called "platonic" or Platonist, for accepting some assumptions of Platonism, but which do not imply acceptance of that philosophy as a whole:
 * In civics or politics, a Platonist is someone who advocates a system resembling Plato's Republic. These are really quite rare.
 * Neoclassical economics is sometimes described as Platonist in some sense, probably because of neoliberal assumptions about pure capitalism as an ideal system which actual economies must attempt but never really achieve.
 * A platonic relationship is one that does not involve sex.

By far the most common use of the word is among mathematicians, where a Platonist is one who believes that mathematics is not created by man but discovered in some undescribed realm. This leads to some serious confusion:

The absence in this thesis of clear distinction between mathematical and nonmathematical "creation" leaves open the inference that it applies to allegedly creative endeavors in art, music, and literature, including articles in Wikipedia, itself. In other words, Wikipedia articles approach some kind of truth that they cannot, in the end, fully express.

In the philosophy of mathematics proper, a Platonist is one who accepts mathematical concepts as real and discovered, period. The "other realm" is rarely discussed. But yet a Platonist must accept an ontology resembling Plato's ontology in order to deal with the tension between real and ideal objects. That is, he (and almost all mathematicians are male) must accept that there is, first and foremost, a "real" and "ideal" realm, and some means to peer between them.

There are theories of realism in mathematics which carefully earmark the assumptions they make to deal with this tension, e.g. the cognitive science of mathematics. Most Platonists do not and are thus accepting Plato's ontology by default as a foundation ontology. A lucid statement of this is found in the autobiography of British mathematician G. H. Hardy.

Hilary Putnam rejected the label Platonist because of this implication, but was otherwise a "realist" in the sense of believing mathematics to be discovered. He proposed that quasi-empirical methods and quasi-empiricism in mathematics were a more useful way to explore the ontology of proofs, via mathematical practice. Today other realist theories explore Where Mathematics Comes From, some of whose ontology is founded on empirical methods. All of this moves towards a single "discovered" realm - away from Platonism.