How to properly lose direction


One of the central puzzles in ontology concerns the relation between apparently innocent sentences and their ontologically loaded counterparts. In recent work, Agustín Rayo has developed the insight that such cases can be usefully described with the help of the ‘just is’ operator: plausibly, for there to be a table just is for there to be some things arranged tablewise; and for the number of dinosaurs to be Zero just is for there to be no dinosaurs. How does the operator relate to another prominent notion that is frequently put to similar use: metaphysical grounding? In this paper I show that despite what has been argued in the literature the ‘just is’ operator can be spelled out in terms of grounding: roughly, as having the same ultimate grounds. This is good news for Rayo, for it broadens his target audience. It is even better news for the friends of ground. For it exemplifies the immense fruitfulness of the notion of grounding in its ability to incorporate philosophically highly significant subtheories.

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  1. 1.

    Cp., e.g. Hofweber (2007).

  2. 2.

    Fine (2012) is an incredibly useful introduction to the notion of grounding. I will freely use the results compounded there in what follows. The distinctions between forms of grounding that are relevant for the present paper are discussed in §1.5.

  3. 3.

    See, e.g., Rosen (2010) and Schwartzkopff (2011) for the view that the fact that there are no dinosaurs grounds the fact that the number of dinosaurs is Zero. Cp. also Schaffer (2009) for a more general plea for existential permissivism backed by grounding claims.

  4. 4.

    The paper is, thus, a partial mirror image of Correia and Skiles (2017) who propose to account for grounding and essence in terms of ‘just is’-statements (what they call generalized identity). I am not prepared to enter into a discussion about what the right direction of analysis is here—partly because I suspect that this might be a matter of preference or at the very least of subtle overall theory comparison that cannot be decided here. Let me just note that ideological parsimony, appealed to by Correia and Skiles, seems unable to decide between the two approaches. For, while they have generalized identity as their only fundamental notion, in terms of which they propose to account for essence and grounding, the account proposed here recognizes grounding as its only fundamental notion, in terms of which it accounts for generalized identity, which, if Correia and Skiles are right, can in turn be used to account for essence. Though it cannot be shown here, all axioms and rules of the system GI (cp. Correia and Skiles 2017: §1) turn out to be correct on our account, given plausible principles about grounding.

  5. 5.

    The correspondence should be at least as strong as follows: \(\forall p\, q \left( p \equiv q \leftrightarrow [p] R [q]\right) \), where ‘[p]’ denotes the sentence-like entity correlated with p. Presumably, Rayo would be happy to say that for it to be the case that \(p \equiv q\) just is for it to be the case that [p]R[q], from which the correspondence follows. In the informal discussions to follow I will sometimes talk in this relational way for presentational purposes, since I agree with Rayo that it is unproblematic. Official formulations will be framed in terms of the sentential operator, however. A similar distinction in framing grounding claims relationally vs. with the help of a sentence-operator is discussed, e.g., in Fine (2012: §1.4).

  6. 6.

    These are examples 6 and 7 on Rayo’s list. See Rayo (2013: p. 3).

  7. 7.

    Cf. Rayo (2013: p. 49 & p. 52).

  8. 8.

    Cf. Rayo (2013: p. 49 & p. 55). I have chosen a straightforwardly equivalent reformulation of the connection with possible scenarios for presentational reasons.

  9. 9.

    Given the symmetry of ‘just is’ the reasonable response would seem to be to claim that the truth of the ‘just is’-statement opens the door for a theoretical reduction, but that further (partially epistemic) facts determine the direction of the reduction. The very same thing could then be said about the proposed definiens. Moreover, the assumed connection with reduction is glaringly absent from Rayo’s own discussion of the connections ‘just is’-statements have that was summarized above. Cf. Rayo (2013: §2.2).

  10. 10.

    Since Cameron does not seem to be aware of it, while there are various straightforward moves one could make to fix it, I will ignore the factivity problem for the time being.

  11. 11.

    Cameron’s own reason for being dissatisfied with the proposal is a special case of the problem stated in the main text having to do with fundamental facts. As the consideration in the main text shows, fundamentality is inessential to the problem.

  12. 12.

    Cf. Cameron on the claim (Set) ‘For a set to exist just is for its members to exist’: ‘[...] my first inclination is [...] to hear (Set) as saying that it is the existence of some individuals that explains the existence of a set containing them; that the individal-facts are metaphysically prior to the set-facts’.

  13. 13.

    Here is a pertinent quotation: ‘[...] as far as grounding goes, [(10)] is structurally identical to the Tony example. [...] So [sic.] the grounding structure is the same, but whether the associated just is statement is acceptable is different’ (Cameron 2014: p. 434).

  14. 14.

    This is not quite Cameron’s own count. But the ‘third’ proposal he proposes on p. 434 (\(p\equiv q :\leftrightarrow \exists f (f = [p] \wedge f \text { grounds }[q] \vee f = [q] \wedge f \text { grounds }[p]\)) seems to differ from his first proposal only by the (not clearly motivated) introduction of factual assent. Consequently, the former shares the latter’s shortcomings and need not be discussed separately.

  15. 15.

    This is an instance of Fine (2012: p. 55)’s first subsumption rule. It can also be proved in a one liner using the definition of weak ground and a Cut-rule for strict ground (a generalisation of transitivity). Proof. Suppose \(\Delta <q\) and \(q,\Gamma <r\). By Cut these strict grounding claims may be chained and we get: \(\Delta , \Gamma <r\). Thus, by definition, \(\Delta \le q\).

  16. 16.

    Though Cameron does not explicitly appeal to it, this might be his reason for the switch from strict to weak grounding.

  17. 17.

    I myself am not quite convinced. Standard logics of ground yield that the fact that Tiger Tony is a tiger strictly grounds the fact that there are tigers, but that is not quite what Cameron claims. If we change the example accordingly, it is not clearly correct that for there to be an even prime just is for the number Two to be an even prime. I ignore this difficulty in the main text.

  18. 18.

    Note that the modal aspect of the proposal was not appealed to in order to show that these cases are distinguishable. It would, however, have some work to do in distinguishing between cases that concern existential quantifications both of which have only one true instance, e.g. the even prime case and the pair consisting of the fact that there is a first US president and the fact that George Washington was the first US president. Note also that, since weak ground is definable in terms of strict ground, Cameron’s original pairs were not strict ground-indistinguishable to begin with.

  19. 19.

    (R1) conforms to the spirit if not the letter of the proposal that is rendered as follows in Rayo (2014: p. 520):

    where \({\bar{r}} = r\) if r is true, and [if r] is false.

    On this formulation, the proposal would make ‘\(p\equiv q\)’ equivalent to ‘\(p\equiv \lnot q\)’, which is clearly not intended. Consequently, I opted for the formulation in the main text. Note also that the difficulty arises because Rayo, without mentioning it, attempts to deal with the factivity problem that plague Cameron’s proposals.

  20. 20.

    The key claim here is, of course, that no fact grounds itself.

  21. 21.

    Thanks to Peter Fritz, Jon Litland and Agustín Rayo whose comments convinced me that I need to be more explicit on this point. It is spelled out further in the next section.

  22. 22.

    The assumption is only made for simplicity and will eventually be dropped in what follows.

  23. 23.

    Note that ‘\([\_]\)’ gets temporarily reappropriated as well, to denote states which, contrary to facts, may exist without obtaining. In fact, in the main text I use the bracket notation to denote whatever sentence-like entities are at issue, since we will soon have occasion to talk about facts again. Note also that, just as before, talk of states is just a presentational tool. Cf. fn. 5 above.

  24. 24.

    Rayo (2013: p. 53) disagrees, so this reason carries no weight for him. But then, his views on the matter are shaped by his belief that there is a particularly tight connection between true ‘just is’-statements and strict implications, which the current proposal cannot sustain in full generality in any case. This topic will be discussed in Sect. 4 below.

  25. 25.

    Proof. [ ] Suppose \(p\equiv q\). Then, by our definition, (a) the G-state that p has the same fundamental grounds as the G-state that q. Let s be an element of the R-state that p. By construction, s has the same fundamental grounds as the G-state that p. By (a), s has the same fundamental grounds as the G-state that q. Thus, by construction, s is an element of the R-state that q. The same holds, mutatis mutandis, in the reverse direction. Consequently, (b) the R-state that p = the R-state that q. By (a) and our assumption that the Fundamental Grounds of Negations Principle holds, we get that the G-state that \(\lnot p\) has the same fundamental grounds as the G-state that \(\lnot q\). An analogous argument yields that (c) the R-state that \(\lnot p\) = the R-state that \(\lnot q\). Now, either it is true that p or it is true that \(\lnot p\). [Note that this is a non-trivial step. It assumes that if a ‘just is’-statement is true, its subclauses are either true or false. But this is an assumption on which the plausibility of (R1) itself relies. For, suppose it fails for ‘\(p\equiv q\)’. Then, presumably, there will neither be an R-fact that p nor an R-fact that q, and, thus, the left-hand side of (R1) will be true, while the right-hand side is not.] If the former, then all states obtain that have the same fundamental grounds as the G-state that p. Thus, the R-state that p obtains, and, by (b), the R-fact that p = the R-fact that q. [I’m assuming here that an R-state obtains just in case all of its elements do.] If the latter, all states obtain that have the same fundamental grounds as the G-state that \(\lnot p\). Thus, the R-state that \(\lnot p\) obtains, and, by (c), the R-fact that \(\lnot p\) = the R-fact that \(\lnot q\). [\(\Leftarrow \)] Suppose now that the R-fact that p = the R-fact that q or the R-fact that \(\lnot p\) = the R-fact that \(\lnot q\). By the assumption that the Fundamental Grounds of Negations Principle holds, it follows that the R-state that p = the R-state that q. Thus, by (R2), \(p\equiv q\).

  26. 26.

    Cf., e.g.: ‘the fundamental facts are those cast in terms that carve at the joints’ (Sider 2011: p. 6).

  27. 27.

    Sider could, of course, retreat to the position that every fact is fundamental. But then the proposal boils down to Rayo’s unsatisfactory (R1).

  28. 28.

    Cp. also Dasgupta (2014) who argues that we should add an irreducibly plural notion of ground to our repertoire. Thanks to Jon Litland for suggesting to simplify the formulation of the explication proposal by appeal to Fine’s notion of distributive grounds.

  29. 29.

    It is worth noting that prior commitments on grounding will force one’s hand on which ‘just is’-statements to accept on our proposal. In particular, unorthdox views on what grounds what will result in unorthodox views on which ‘just is’-statements are true. For instance, a proponent of what we may call grounding monism—mimicking Schaffer’s (2010) priority monism—holds that every fact is ultimately grounded in the Maximal Fact. The grounding monist should consequently accept that \(p\equiv q\) whenever it is true that p and it is true that q. She will thus be committed to infinitely many wildly implausible ‘just is’-statements. However, this is a direct result of the infinitely many wildly implausible grounding claims she is also committed to, and I don’t see any convincing reason to think that unorthodoxy in the latter area must be combinable with orthodoxy in the former. Thanks to a reviewer for this journal for urging me to address this issue.

  30. 30.

    In fact, in a companion paper I argue that the developed notion is a very good fit for a notion of content with which we can make sense of Gottlob Frege’s talk in Grundlagen about certain sentences’ (e.g., about whether two lines are parallel) carving up the content of some other sentences (e.g., about the identity of directions) in a different way. See Frege (1884) and cp. Hale (2001) for an alternative attempt.

  31. 31.

    This disagreement is mirrored by the fact that the set of R-states is a coarsening of the set of unit sets of G-states.

  32. 32.

    Cf., e.g. Rayo (2013: p. 36).

  33. 33.

    Cp., e.g. Rayo (2013: p. 56).

  34. 34.

    This was pointed out to me by Øystein Linnebo in personal communication.

  35. 35.

    For a sketch of the ‘impure’ logic of ground see, e.g. Fine (2012: §1.7 & 1.8). Cp. also Schnieder (2011) for a corresponding logic of ‘because’-statements.

  36. 36.

    There is a more general point that underlies the difficulty. ‘Because’-statements backed by grounding explanations are plausibly taken to be hyper-intensional: that ‘\(p\text { because }q\)’ and ‘’ are true does not ensure that ‘\(r\text { because }q\)’ is true as well. The same holds, mutatis mutandis, for the explanans clause of the ‘because’-statement. This observation strongly suggests that there is no straightforward connection between the truth of strict biconditionals and why-closure. Given that Rayo takes there to be an extremely tight connection between true ‘just is’-statements and strict biconditionals, there will be no straightforward connection between true ‘just is’-statements and why-closure either.

  37. 37.

    See Rayo (2014: §II.ii) for the moves he does make concerning Linnebo’s original complaint.


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I’d like to thank Oslo’s ConceptLab for hosting me on an equally as productive as pleasant research stay during which the bulk of this paper came into existence as well as Peter Fritz for inviting me to present at a mini workshop on Rayo’s work which sparked my interest in the main question of this paper. Thanks are also due to audiences at the mini workshop, particularly Katharina Felka, Jon Litland, Øystein Linnebo and Agustín Rayo as well as at research colloquia at the universities of Essen, Bielefeld and Zurich. I gratefully acknowledge financial support from the University of Zurich’s Forschungskredit (grant no. FK-16-078). Funding was provided by Universität Zürich (Grant No. FK-16-078).

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Steinberg, A. How to properly lose direction. Synthese (2019).

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  • Just is
  • Grounding
  • Agustín Rayo