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The logic of relative fundamentality

  • S.I.: Ground, Essence, Modality
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Abstract

I introduce a proof system for the logic of relative fundamentality, as well as a natural semantics with respect to which the system is both sound and complete. I then “modalise” the logic, and finally I discuss the properties of grounding given a suggested account of this notion in terms of necessity and relative fundamentality.

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Notes

  1. Sider (2011) is a book-length study on fundamentality which defends a particular account of the notion inspired by David Lewis’ (1983) notion of perfect naturalness. More recent discussions on fundamentality include Bennett (2017) (chs. 5 and 6), deRosset 2017, Koslicki (2015); Wilson (2012, 2016) and Zylstra (2014). Fine (2001, 2012a), Rosen (2010) and Schaffer (2009) are landmarks in the current debate. The current discussions focus on both absolute and relative fundamentality, and on the conception of (absolute and relative) fundamentality understood as qualifying or relating facts as well as on other conceptions of fundamentality. I will be exclusively concerned with relative fundamentality understood as a relation between facts. Discussions specifically about relative fundamentality can be found in §7.11 of Sider (2011), ch. 6 of Bennett (2017), and in all the articles cited in the second sentence of this footnote.

  2. See e.g. Correia (2010, 2014, 2015, 2017), deRosset (2014, 2015), Fine (2012a, b), Krämer and Roski (2015), Litland (2016, 2017), Poggiolesi (2016) and Schnieder (2011).

  3. See e.g. Bennett (2011, p. 1; 2017, p. 40), Koslicki (2015, p. 306), Rosen (2010, p. 116) and Wilson (2012, p. 1).

  4. Skiles (2015) argues against this “grounding necessitarianism” and contains numerous references both to friends and to foes of the view.

  5. Thanks to a referee for pressing me to address this objection.

  6. See Bennett (2011), fn. 2.

  7. Bennett (2017, §6.5), proposes a sophisticated account of relative fundamentality indexed to “building” relations. Given that grounding is one of Bennett’s building relations, this yields an account of relative fundamentality of the kind that is relevant to this paper. For each building relation R, the proposed account of relative fundamentality\(_R\) is highly disjunctive, and for that reason “begs to be counterexampled”, as Bennett herself puts it (p. 161). She is confident that her characterisation points in the right direction, but it is not clear to me why we should follow her on that point.

  8. See e.g. deRosset (2017) and Rosen (2010).

  9. See for instance Bennett (2017, pp. 236–237), for a discussion.

  10. This example is from a referee. I am grateful to this referee for pressing me to discuss this issue, as well as the issue about density I discuss below. See Bennett (2017, pp. 172–173), for a discussion on incomparability.

  11. This example is from the same referee.

  12. See Correia (2005, pp. 63–64), for an argument to the effect that grounding may fail to be well-founded in this sense.

  13. Correia (2017) introduces a variant of the main system it puts forward, but the difference between the two systems will not be relevant.

  14. Given that conjunction is a binary operator, the notation \(\bigwedge \nolimits _{i=1}^n\) should in principle be properly spelled out. All the ways of doing it, of course, yield equivalent definientia. Note that whatever formally impeccable version of (RV) is adopted, the order of the formulas \(\phi _1,\ldots ,\phi _n\) in the definiendum will not matter, since any permutation will yield an equivalent definiens. Thus, in practice, one can treat the ordered sequence \(\phi _1,\phi _2, \ldots \) as a plurality or even as a set.

  15. The labels are borrowed from Fine (2012a).

  16. For more on this distinction, see Correia (2010, pp. 256–259, 264, 266–267; 2017, p. 508), Correia and Schnieder (2012, §3.3) and Fine (2017, §6). In the 2010 paper, I argued against conceptual notions of grounding, but I now think there is room for both kinds of notions (see Correia 2011).

  17. It is also in conflict with C1. For a suitable choice of A and B (take e.g. ‘Socrates is human’ for the former and ‘\(2+2=4\)’ for the latter) one will have both \(A < A \vee (A\wedge B)\) and \(B < B \vee (A\wedge B)\). But in the system, \(A \wedge B\) and \((A \vee (A\wedge B))\wedge (B \vee (A\wedge B))\) are always ground-theoretically equivalent, and hence none can strictly ground the other. (The same is true in the system \(\mathbf C ^*\) mentioned below.)

  18. See Fine (2012a, pp. 51–53) on weak grounding, and pp. 47–48 on zero-grounding. The conception of weak grounding at work in C2 is quite different from Fine’s, see Correia (2017, pp. 515–516).

  19. Thanks to Kit Fine for steering me towards this option.

  20. I am grateful to the audience of the Humboldt Workshop on the History of Ground (Helsinki, June 2016) for useful comments on an earlier version of this paper. This work was carried out while I was in charge of the SNF projects Grounding – Metaphysics, Science, and Logic (CRSII1_147685), The Metaphysics of Time and its Occupants (BSCGI0_157792), The Nature of Existence: Neglected Questions at the Foundations of Ontology (100012_150289) and Essences, Identities and Individuals (100012_159472), and of the University of Neuchâtel’s module of the European Commission’s HORIZON 2020 Marie Skłodowska-Curie European Training Network DIAPHORA (H2020-MSCA-ITN-2015-675415).

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Acknowledgements

Funding was provided by Swiss National Science Foundation (Grant Nos. CRSII1_147685, 100012_159472, BSCGI0_157792 and 100012_150289).

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  1. University of Geneva, Geneva, Switzerland

    Fabrice Correia

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Correia, F. The logic of relative fundamentality. Synthese 198 (Suppl 6), 1279–1301 (2021). https://doi.org/10.1007/s11229-018-1709-8

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