Antiphilosophy has been used as a denigrating word but recently it has acquired more positive connotations as an opposition to more traditional philosophy. The views of Ludwig Wittgenstein, specifically his metaphilosophy, could be said to be antiphilosophy.
Antiphilosophy and Wittgenstein's metaphilosophy
In  Paul Horwich points to Wittgenstein's rejection of philosophy as traditionally and currently practiced and his "insistence that it can't give us the kind of knowledge generally regarded as its raison d'être".
Horwich goes on to argue that:
Wittgenstein claims that there are no realms of phenomena whose study is the special business of a philosopher, and about which he or she should devise profound a priori theories and sophisticated supporting arguments. There are no startling discoveries to be made of facts, not open to the methods of science, yet accessible "from the armchair" through some blend of intuition, pure reason and conceptual analysis. Indeed the whole idea of a subject that could yield such results is based on confusion and wishful thinking.
Horwich concludes that, according to Wittgenstein, philosophy "must avoid theory-construction and instead be merely 'therapeutic,' confined to exposing the irrational assumptions on which theory-oriented investigations are based and the irrational conclusions to which they lead".
Moreover, these antiphilosophical views are central to Wittgenstein, Horwich argues.
Examples of antiphilosophical positions
The antiphilosopher could argue that, with regard to ethics, there is only practical, ordinary reasoning. Therefore, it is wrong to a priori superimpose overarching ideas of what is good for philosophical reasons. For example, it is wrong to blanketly assume that only happiness matters, as in utilitarianism. This is not to say though that some utilitarian-like argument can't be valid when it comes to what is right in some particular case.
Consider the continuum hypothesis, stating that there is no set with size strictly between the size of the natural numbers and the size of the real numbers. One idea is that the set universe ought to be rich, with many sets, which leads to the continuum hypothesis being false. This richness argument, the antiphilosopher might argue, is purely philosophical, and groundless, and therefore should be dismissed; maintaining that the continuum hypothesis should be settled by mathematical arguments. In particular it could be the case that the question isn't mathematically meaningful or useful, that the hypothesis is neither true, nor false. It is then wrong to stipulate, a priori and for philosophical reasons, that the continuum hypothesis is true or false.[i]
- Church's thesis as a definition is an example of a problem where misconceptions may be dissolved, by viewing the thesis as nothing but a normal mathematical definition.
- Quietism also takes a therapeutic approach to philosophy.
- Cf. and Wittgenstein's view on "pure mathematics".
- Bruno Bosteels, "Radical Antiphilosophy," Filozofski vestnik (2008)1, 55-87
- Penelope Maddy, "Wittgenstein's Anti-Philosophy of Mathematics", Johannes Czermak and Klaus Paul, eds., Wittgenstein's Philosophy of Mathematics, 1993, http://www.socsci.uci.edu/~pjmaddy/bio/wittgenstein%27s%20anti-philosophy.pdf
- Jan Riis Flor, "Den senere Wittgenstein", Poul Lübcke, ed., Vor tids filosofi: Videnskab og sprog, Politikens forlag, 1982
- http://opinionator.blogs.nytimes.com/2013/03/03/was-wittgenstein-right/, Paul Horwich, "Was Wittgenstein Right?", The New York Times, 2013-03-03
- Continuum hypothesis#Arguments for and against CH
- Penelope Maddy, June 1988, "Believing the Axioms, I", Journal of Symbolic Logic 53 (2): 481–511, http://www.socsci.uci.edu/~pjmaddy/bio/Believing%20the%20Axioms%20(with%20corrections).pdf
- Paul Horwich, Wittgenstein's Metaphilosophy, Oxford University Press, 2012.
- Ludwig Wittgenstein, Philosophical Investigations, 1953.