Abstract:
The central thesis of this paper is that the modus ponens reductio argument does not clearly favour impure versions of infinitism. The nub of the modus ponens reduction argument is as follows: an infinite series of justified reasons by itself is vulnerable to the modus ponens reduction in the sense that one can construct an infinite chain of reasons supporting both an affirmative and denial of proposition, say p. The problem here is that, as Aikin urges, pure versions of infinitism do not possess the requisite resource to eliminate one of these chains of infinite reasons. The upshot is that pure versions of infinitism are not able to differentiate between an infinite series that is truth conducive and the ones that are not. Accordingly, Aikin promotes an impure infinitism over pure infinitism because, as he opines, impure infinitism has the requisite resources to eliminate one of the infinite chains of justified reasons and rids itself of the threat of the modus ponens reductio. In the following discussion, I submit that although Aikin seems quite successful in this venture, his version of impure infinitism faces a similar setback, in the form of the new evil demon problem, which is equally fatal to it as that which the modus ponens reductio wrecks on pure versions of infinitism
