Abstract
This paper presents a uniform general account of regress problems in the form of a pentalemma—i.e., a set of five mutually inconsistent claims. Specific regress problems can be analyzed as instances of such a general schema, and this Regress Pentalemma Schema can be employed to generate deductively valid arguments from the truth of a subset of four claims to the falsity of the fifth. Thus, a uniform account of the nature of regress problems allows for an improved understanding of specific regress objections or arguments, and, correspondingly, of the general logical geography of the debate about infinite regresses. This uniform approach is illustrated by a treatment of the classical epistemological problem of justification, but it encompasses a whole variety of cases including explanation and ontological grounding. Furthermore, this general account is compared and contrasted with the existing literature discussing argument schemata for regress objections, particularly with the work of Jan Willem Wieland. It is shown how such other schemata can be incorporated and superseded by the general Regress Pentalemma Schema.
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Notes
This way of setting up philosophical problems or puzzles as inconsistent sets of claims is not new, of course. One explicit proponent of this methodology is Nicholas Rescher (cf., e.g., Rescher (1987)). But even if many, or all, philosophical problems can be set up in this way, this does not mean that the distinctiveness of regress problems is lost. Instead, what makes a problem a regress problem are the specific forms of the five claims.
Among other things, it also allows for an account of the distinction between vicious and benign regresses, as shown in Section 4.2.
I shall also leave open the possibility, recently defended by Jessica Wilson (2014), that there is no general uniform ‘in-virtue-of’ relation which is applicaple to all relevant cases in which philosophers use this locution. Instead, different cases may rely on different concepts, which merely share some general properties such as those of being transitive, irreflexive and asymmetrical. This, however, is entirely sufficient for the purpose of this paper.
Likewise, one may also hold Non-Circularity without any appeal to proper grounding and explanation, but simply by asserting that there is no such thing as a circle of justified beliefs. This option, however, is less common, and anyway less plausible than the corresponding view about Finity.
In fact, if Trigger is false, there are three options next to (a) and (b) – namely, (c) some Ps are Ps, but not in virtue of anything, (d) some Ps are Ps in virtue of themselves, and (e) some Ps are Ps in virtue of something which is not a further P. However, since Trigger excludes all of (c), (d) and (e), I have stated Alternatives in a simplified form.
By the same token, one may create a total of ten deductively valid arguments, each accepting a subset of three of the claims in the Regress Pentalemma as premises and inferring the conclusion that the remaining two claims cannot both be true – or that one is false if the other is true. Likewise for arguments assuming subsets of two claims.
I have deliberately avoided naming particular philosophers as endorsing the views sketched here. Even if I should have failed to correctly characterize certain specific accounts, I still hope to have provided a rough sketch of the general terrain of the debate.
It should be noted that the inference from (1) and (2) to (3) is invalid as it stands. I come back to this on page 16.
In a slightly improved variant of his Paradox Schema, Wieland has rectified this and formulated this schema in such a way that it can only be analyzed as a refutation of Ground, assuming Recurrence (cf. Wieland (2014), 11-13). While this is clearly an improvement in clarity, it is also a loss in scope since the possibility to reject Recurrence rather than Ground is left out.
Problematically, both inferences in this schema are invalid. I will come back to the first inference from (1), (2) and (3) to (4) on page 21. And I shall discuss the second inference from (4) to (C), where Wieland deliberately suppresses an additional premise, on page 21.
For the purposes of my discussion, I will bracket two complications. First, I shall ignore the markers “Problem” and “Solution” behind (1) and (2), since the succeeding sentences are clearly used as premises despite of these, as explicitly stated by the notation of the derivations of (3) and (4). Also, Wieland has meanwhile published a pair of slightly altered versions of his Failure Schema (cf. Wieland (2014), 21-24), which do not contain these markers anymore. But these new schemata are the second thing which I will bracket here. For Wieland’s new “Failure Schema B” is exactly the one I discuss here and his new “Failure Schema A” differs from it only in that (3) is replaced by two claims which jointly entail (3) and add the requirement that not only those reasons which support a justified belief must be justified themselves, but that all reasons whatsoever must be justified. Now, this much more general claim may well be problematic. But I shall leave this problem aside.
In Section 4, I will expand on these points and respond to Wieland’s further arguments for structural differences between his two schemata.
I have made the same point with respect to the Paradox Schema on page 16.
And maybe it is even intended as stating that Phenomenon is false if both Ground and Recurrence are true. All of these variations are perfectly possible on the Regress Pentalemma Schema (cf. footnote 8 on page 9).
For many helpful comments and suggestions on various earlier drafts of this paper, I am very grateful to an anonymous reviewer at Acta Analytica, as well as to Alexander Dinges, Ansgar Seide, Christian Nimtz, Emanuel Viebahn, Eva-Maria Jung, Fabian Hundertmark, Georg Brun, Gregor Betz, Holm Tetens, Insa Lawler, Julia Zakkou, Julian Husmann, Michael Webermann, Oliver Scholz, Paul Näger, Peter Rohs, Steven Kindley, Ulrich Krohs, and Wolfgang Barz.
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Löwenstein, D. A Uniform Account of Regress Problems. Acta Anal 32, 333–354 (2017). https://doi.org/10.1007/s12136-016-0310-3
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DOI: https://doi.org/10.1007/s12136-016-0310-3