Infinite Regress Arguments
In: Johanssonian Investigations. Christer Svennerlind, Jan Almäng, and Röngvaldur Ingthorsson, eds., Heusenstamm: Ontos Verlag, pp. 421-438.
Abstract: According to Johansson (2009: 22) an infinite regress is vicious just in case “what comes first [in the regress-order] is for its definition dependent on what comes afterwards.” Given a few qualifications (to be spelled out below (section 3)), I agree. Again according to Johansson (ibid.), one of the consequences of accepting this way of distinguishing vicious from benign regresses is that the so-called Russellian Resemblance Regress (RRR), if generated in a one-category trope-theoretical framework, is vicious and that, therefore, the existence of tropes only makes sense if trope-theory is understood (minimally) as a two-category theory which accepts, besides the existence of tropes, also the existence of at least one universal: resemblance. I disagree. But how can that be? How can Johansson and I agree about what distinguishes a vicious from a benign regress, yet disagree about which regresses are vicious and which are benign? In this paper I attempt to answer that question by first setting out and defending the sense of viciousness which both Johansson and I accept, only to then argue that to be able to determine if a particular regress is vicious in this sense, more than features intrinsic to the regress itself must be taken into account. This is why, although the RRR as originally set out by Russell is vicious, the seemingly identical resemblance regress which ensues in a one-category (standard) trope-theoretical context is not (provided, that is, that we accept certain views about how the nature of tropes relates to the resemblance between tropes, and given that we set our theory in a truthmaker theoretical framework – all of which are standard assumptions for proponents of (the standard-version of) the trope-theory).
Link to preprint here.