Disjunction and the Logic of Grounding


Many philosophers have been attracted to the idea of using the logical form of a true sentence as a guide to the metaphysical grounds of the fact stated by that sentence. This paper looks at a particular instance of that idea: the widely accepted principle that disjunctions are grounded in their true disjuncts. I will argue that an unrestricted version of this principle has several problematic consequences and that it’s not obvious how the principle might be restricted in order to avoid them. My suggestion is that, instead of trying to restrict the principle, we should distinguish between metaphysical and conceptual grounds and take the principle to apply exclusively to the latter. This suggestion, if correct, carries over to other prominent attempts at using logical form as a guide to ground.

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  1. 1.

    Here and in the rest of this paper, I use sentences in quotes to refer to semantically individuated sentence types and take the relevant notion of ground to be that of full ground. These specifications will be implicit hereafter. For the distinction between partial and full grounds, see Fine (2012, 50). Since my target in this paper is the view that logical form is a guide to ground, I will work on the assumption that grounding claims are intelligible and truth-evaluable. For scepticism about grounding, see Daly (2012) and Wilson (2014).

  2. 2.

    There is a debate as to whether grounding claims are best expressed in terms of a relational predicate flanked by referring expressions (as in “The fact that p grounds the fact that q”) or rather in terms of some operator flanked by sentences (as in “p because q”) (see Correia and Schnieder 2012b and Bliss and Trogdon 2016). Though I will later on adopt a sententialist regimentation, nothing crucial hinges on this choice and I will switch back and forth freely between sententialist and predicationalist locutions.

  3. 3.

    See Leuenberger (2014) and Skiles (2015) for reasons to doubt that grounds necessitate the facts they ground.

  4. 4.

    On some accounts, 'p v ~ p' can be true even if neither of its disjuncts is, for example if 'p' is a future contingent or a sentence involving the ascription of a vague predicate to a borderline case. The parenthetic proviso is meant to exclude such cases from our focus and will be left implicit hereafter.

  5. 5.

    One should not be distracted by reference to truth here. As Fine says elsewhere, “what matters is not so much that the truth of p should help ground the truth of p & q but that p should help ground p & q” (Fine 2010, 106). The same applies to the case of disjunction.

  6. 6.

    Philosophers who agree with Audi that grounding is a relation between facts and that there are no disjunctive facts can identify the Disjunction Principle precisely with this conditional thesis. In the rest of the paper, I will be working on the simplifying assumption that there are disjunctive facts.

  7. 7.

    Some philosophers deny that grounding is ever expressed in ordinary language (Hofweber 2009; Daly 2012). The kind of examples discussed by Witmer et al. (2005, 335–338) seem to me to suggest that this extreme position is misguided. See also (Audi 2012b) and (Krämer and Roski 2015, 60) for discussion.

  8. 8.

    For other examples, see Tsohatzidis (2015, 47–48).

  9. 9.

    See Schnieder (2016).

  10. 10.

    According to some, ‘either…or' admits of an ‘exclusive' reading on which ‘either p or q' is false if both p and q are true. For discussion of the relationship between ‘either…or' and logical disjunction, see Jennings (1994). For discussion of the distinction between metaphysical, causal and evidential readings of ‘because', see Schnieder (2011).

  11. 11.

    Rosen (2010, 131) offers a closely analogous argument, based on the ‘essence’ of disjunction. I will focus on the argument from truth-conditions because I find the invocation of ‘essence’ problematic in this context (see McSweeney (forthcoming a) for discussion). Schnieder (2016) suggests that denying the logicist principles leads to results that are implausible or theoretically costly—I will discuss these claims in Sect. 4.

  12. 12.

    An alternative argument would proceed by comparing the property of being an H-electron with the property of being either an H- or a T-electron: given some suitable principles connecting property-naturalness with fact-naturalness, one could plausibly show that, since the first property is less natural than the second, the fact that Sparky is an H-electron is less natural than the fact that it is either an H- or a T-electron.

  13. 13.

    For a different but related principle connecting naturalness (hence, fundamentality) with grounding, see Bricker (2006, 271). Bennett argues that “naturalness is not obviously a unified phenomenon, and it is also a poor fit for our pretheoretic relative fundamentality concepts” (Bennett 2017, 140). However, her worries can be at least partly assuaged by taking the criteria mentioned above to provide only sufficient and other-things-being-equal conditions for greater/lesser naturalness.

  14. 14.

    Instances of this reply can be found in the work of Correia (2010), Krämer and Roski (2015) and Correia and Schnieder (2012b, 18).

  15. 15.

    I note in passing that Fine himself (Fine 2005, 324) is not entirely unsympathetic to the idea of treating facts of the form ‘ϕ v ~ ϕ’ as fundamental. His only reason to resist this idea is that it conflicts with the Disjunction Principle.

  16. 16.

    See (Lewis 1986, 61, 1999, 66).

  17. 17.

    Cf. Chalmers (2012, 452–458); Correia (2013, 2), Dodd (2007), Correia and Schnieder (2012b, 21), Poggiolesi (2016) and McSweeney (forthcoming b). For discussion of conceptual grounding and conceptual explanation, see also Schnieder (2006, 32–33) and Liggins (2012, 260–262). For some ways of understanding conceptual priority here, see Chalmers (2012, 307–308).

  18. 18.

    Richardson's (2018) notion of ‘how-grounding’ might provide the basis for an alternative treatment of (one or more of) these cases. I won’t explore this strategy here.

  19. 19.

    For a defence of (B), see Künne (2003, 154–155) and Dodd (2007, 399–400). For additional reasons to regard the kind of grounding involved in logical cases as different from the kind of grounding involved in metaphysical cases, see Koslicki (2015, 317–318) and McSweeney (forthcoming b).

  20. 20.

    See McSweeney  (forthcoming a) for discussion of these cases.


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Some of the research for this study was conducted as part of my work for the project ‘Knowledge Beyond Natural Science’ (KBNS), which was funded by the John Templeton Foundation at the University of Stirling from March 2017 to November 2019. A first version of this paper was presented at the philosophy Institutskolloquium of the University of Hamburg on 13 April 2016 and at the ‘Metaphysics of Grounding' workshop held at TU Dresden on 29-30 April 2016—thanks to the participants in these events for their comments and criticisms. I am very grateful to Philipp Blum, Michael Clark, Fabrice Correia, Ryan Cox, Yannic Kappes, Martin Lipman, Stefan Roski, Benjamin Schnieder, Moritz Schulz, Nathan Wildman, and two anonymous referees for their feedback on subsequent versions.

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Correspondence to Giovanni Merlo.

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Merlo, G. Disjunction and the Logic of Grounding. Erkenn (2020). https://doi.org/10.1007/s10670-019-00208-0

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