and the platonic world, i.e. the mathematical universe hypothesis (a variety of mathematicism). In that case, a mathematician's knowledge of mathematics is one mathematical object making contact with another. Semantic anti-realism The term "anti-realism" was introduced by Michael Dummett in his 1982 paper "Realism" in order to re-examine a number of classical philosophical disputes, involving such doctrines as nominalism, Platonic realism, idealism and phenomenalism. The novelty of Dummett's approach consisted in portraying these disputes as analogous to the dispute between intuitionism and Platonism in the philosophy of mathematics. According to intuitionists (anti-realists with respect to mathematical objects), the truth of a mathematical statement consists in our ability to prove it. According to Platonic realists, the truth of a statement is proven in its correspondence to objective reality. Thus, intuitionists are ready to accept a statement of the form "P or Q" as true only if we can prove P or if we can prove Q. In particular, we cannot in general claim that "P or not P" is true (the law of excluded middle), since in some cases we may not be able to prove the statement "P" nor prove the statement "not P". Similarly, intuitionists object to the existence property for classical logic, where one can prove , without being able to produce any term of which holds. Dummett argues that this notion of truth lies at the bottom of various classical forms of anti-realism, and uses it to re-interpret phenomenalism, claiming that it need not take the form of reductionism. Dummett's writings on anti-realism draw heavily on the later writings of Ludwig Wittgenstein, concerning meaning and rule following, and can be seen as an attempt to integrate central ideas from the Philosophical Investigations into the constructive tradition of analytic philosophy deriving from Gottlob Frege. Scientific anti-realism In philosophy of science, anti-realism applies chiefly to claims about the non-reality of "unobservable" entities such as electrons or genes, which are not detectable with human senses. One prominent variety of scientific anti-realism is instrumentalism, which takes a purely agnostic view towards the existence of unobservable entities, in which the unobservable entity X serves as an instrument to aid in the success of theory Y and does not require proof for the existence or non-existence of X. Moral anti-realism In the philosophy of ethics, moral anti-realism (or moral irrealism) is a meta-ethical doctrine that there are no objective moral values or normative