Infinite regress arguments show up in many philosophical debates. But what actually is a regress argument? This article reviews two theories: the Paradox Theory and the Failure Theory. According to the Paradox Theory, regress arguments can be used to refute an existentially or universally quantified statement (e.g. to refute the statement that at least one discussion is settled, or the statement that discussions are settled only if there is an agreed-upon criterion to settle them). According to the Failure Theory, regress arguments can be used to demonstrate that a certain solution fails to solve an existentially or universally quantified problem (e.g. to demonstrate that a certain solution fails to settle all discussions, or that it fails to settle even one discussion). In the literature, the Paradox Theory is fairly well-developed, and this article shows that the Failure Theory can be supplied with similar tools.

%B Algemeen Nederlands Tijdschrift voor Wijsbegeerte %V 105 %P 1–14 %G eng %R http://dx.doi.org/10.5117/ANTW2013.1.WIEL