Abstract
The paper deals with the notions of grounding and of existential dependence. It is shown that cases of existential dependence seem to be systematically correlated to cases of grounding and hence the question is raised what sort of tie might hold the two notions together so as to account for the observed correlation. The paper focusses on three possible ties between grounding and existential dependence: identity (as suggested in Jonathan Schaffer’s works), definition (as suggested by Fabrice Correia and Benjamin Schnieder), and grounding (as suggested by Kathrin Koslicki and Francesco Orilia). A case for the definitional tie is made.
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Notes
By way of example, Fine’s (1995) account of dependence in terms of essence and ground-theoretical notions of existential dependence (Correia 2005; Schnieder 2006a) satisfy the Priority Constraint, as does a primitive notion of dependence understood as a form of posteriority (as postulated, e.g., in Cameron 2008). Lowe’s (1998: ch. 6) idea of identity-dependence may also do it, although Lowe himself (2012) argues that it only yields a weak priority relation, which is only anti-symmetrical but not irreflexive, since it allows for special cases of self-dependent entities.
For an influential take on existential dependence in modal terms, see Simons (1987: ch. 8).
Note that some authors in the debates about grounding and existential dependence work with notions which they take to behave asymmetrically in typical cases, while arguing that they allow for violations of asymmetry in special cases. As it stands, the discussion that follows has no direct bearing on such proposals because it presupposes the Priority Constraint. However, depending on the details of such proposals, the discussion may nevertheless apply to them mutatis mutandis: It does so if the alleged violations of the asymmetry of one sort of dependence are either (i) irrelevant to the other sort of dependence, or are (ii) always accompanied by parallel violations of the asymmetry of the other sort of dependence. Let me illustrate these remarks by way of example (but note that the following remarks are mainly for illustration; for a full appreciation, one would have to discuss them and others in more detail than can be done within the word limitations of this paper): Re (i): Rodriguez-Pereyra (2015) holds that the truth-teller (i.e. the proposition that claims itself to be true) violates the irreflexivity and hence the asymmetry of factual dependence (for a similar case, see Correia 2014: p. 54f.). This point, if admitted, would seem to have no bearing on any cases of existential dependence. Hence, someone who endorses Rodriguez-Pereyra’s example, but who acknowledges no further types of violations of asymmetry, could still make sense of the remainder of the paper by appropriately restricting the Priority Constraint. Re (ii): Barnes (forthcoming) defends a non-modal, primitive notion of dependence that allows for mutual cases of dependence. At least some of her examples, e.g., the case of nodes in mathematical structures, would seem to arise for factual and for existential dependence alike.
E.g., Correia (2010) argues that the individuation of facts heavily bears on the logic of ground.
Here is another exemplary quotation: ‘This is an intuition about dependence (or grounding, or ontological priority)’ (Schaffer 2008: p. 308).
See, e.g., Trogdon (2013a) where the issue explicitly comes up. Also in other recent survey articles (as well as in many research papers), Schaffer is discussed along with ground-theorists such as Fine, Rosen, or Correia, which indicates that the authors do not take him to speak about a different phenomenon; see, e.g., Clark and Liggins (2012).
This is further supported by other passages; see, e.g., Schaffer’s (2010: p. 70) remarks on James.
The locus classicus for the idea is Lewis (1983).
See Frege (1918: p. 74).
But note that talk about equivalence must be taken cum grano salis here, unless one wants to accept disjunctions of more than set-sized length.
For those who prefer a more formal presentation, let us first state the three pertinent principles in a semi-formal version:
- CF (Conflation):
\(\forall x \forall y\): x and y are facts \(\rightarrow \) (y grounds x iff x existentially depends on y)
- CR (Corr):
\(\forall x\forall y\): \((\Box (\hbox {E}!x \rightarrow \exists \hbox {F} {<}\hbox {F}y{>} \hbox { grounds } {<}\hbox {E}!x{>}))\)\(\rightarrow x\) existentially depends on y
- EP (Exist \(\Rightarrow \) Pred):
\(\Box \forall x \quad \forall \hbox {F}\, (\hbox {F} x \rightarrow {<}\hbox {E}!x{>} \hbox { grounds } {<}Fx {>})\)
EP implies the following corollary (apply universal instantiation and substitute ‘F’ with ‘E!’):
- \(\hbox {EP}_{\mathrm{C}}\) :
\(\Box \forall x\) (\(\hbox {E}! x \rightarrow {<}\hbox {E}!x{>}\) grounds \({<}\hbox {E}!x{>}\))
So, every existence fact grounds itself. We furthermore get (by existential generalization):
- \(\textsc {EP}_{\mathrm{C2}}\qquad \):
\(\Box \forall x (\hbox {E}! x \rightarrow \exists \hbox {F } {<}\hbox {F}x{>}\) grounds \({<}\hbox {E}!x{>})\)
The following derivation then shows how CF, Cr, and EP entail that every fact grounds itself (for reasons of space, I do not spell out all trivial logical steps):
See Correia (2005: p. 66) and Schnieder (2006a: p. 412). Note that in our expositions, we vary between using ‘grounds’, ‘because’, ‘in virtue of’, or variants of ‘explanation’. But we invariantly aim at grounding. Correia (2008: p. 1020f.) explicitly stresses that the idioms are treated as interchangeable in the context at hand. Note also that there is a minor difference between the above definition and that in Schnieder (2006a), where the quantifier ‘\(\exists F\)’ has a wider scope so that the definiens reads ‘\(\exists F\)\(\Box \) (x exists \(\rightarrow \) (\({<}y\) is \(F{>}\) grounds \({<}x\) exists\({>}\)))’. This might result in an extensional difference between the proposals; but arguably they are in fact extensionally equivalent. Be this as it may, though, in any case both placements of the quantifier yield workable definitions; in the present paper, I want to focus on the version above.
For instance, Koslicki (2013) argues that the proposal is only compatible with some, but not with all trope theories. Presumably that is correct, so Correia and I would have to reject those particular trope theories. Our proposal would therefore not be neutral with respect to all controversial questions of existential dependence. But it is unlikely that any definition of existential dependence can be completely neutral (compare Lowe 2013: p. 202f.), and we do argue that the definition is compatible with a huge range of existing views. Another potential problem of the proposal is that it quantifies into the apparently opaque context of ‘because’/‘grounds’/ (as noted, e.g., by Lowe 1998: p. 146); but I know of no detailed criticism that builds on this observation.
For instance, Lowe (2013: p. 203f.) is worried about the notion of grounding being treated as an unanalysedprimitive. A fair response seems to be that even if grounding is treated as an unanalysed primitive, much progress has been made in systematizing our understanding of the notion by developing non-reductive theories of ground both with respect to its rationale and with respect to its logical properties (as, e.g., in Rosen 2010; Correia 2010, Fine 2012a).
Orilia (2009: p. 334, footnote).
Koslicki (2013: p. 47).
As a referee pointed out, Koslicki takes on a more general critical stance towards the notion of grounding itself in a more recent paper (see Koslicki 2015). As far as Koslicki’s overall view is concerned, the criticisms in that recent paper may well supersede the earlier criticism discussed above. But whether it reflects Koslicki’s current views or not, the discussed criticism is of interest in its own right and deserves to be put under scrutiny. (How exactly Koslicki’s recent views relate to the discussion in the main text would require a longer investigation, in particular because she does not explicitly discuss our proposal in her 2015 paper. For reasons of space I must put this issue aside here.)
A referee found a semi-formal explication of my talk about systematic links desirable. Here it is: A systematic link of the sort envisaged above obtains between facts of kinds Kand \(K^{*}\) if for every fact f of kind K there is a fact \(f^{*}\) of kind \(K^{*}\) which grounds f.
For references, see fn. 23.
Note, firstly, that this view even seems forced upon those philosophers who, unlike Correia and me, take quantification into non-nominal position just to be first-order quantification in disguise. Note, secondly, that the principle that non-nominal existential quantifications are grounded in their instances may have to be restricted somehow (for instance to non-impredicative cases; see Krämer 2013), due to the threat of semantic paradoxes. For present purposes, such complications can be safely ignored.
The rule that embodies the idea says that if something is a ground of a disjunction, then it is a weak ground of one of the two disjuncts, or a distributive weak ground of both of them. (loc. cit.) For a complete appreciation of how the rule works, the notions of weak and distributive grounding would have to be explained; but for current purposes, we can skip over those details and focus on Fine’s informal statement of the rule.
Again, let me skip over the details of the rule which is formulated in terms of weak and distributive grounds (see Fine 2012a: p. 65). Moreover, Fine also argues that a full ground of an existential quantification must, in addition to weakly grounding at least one instance, involve a weak ground for the totality fact that states what things there are at all; for current purposes, the issue of the totality fact can be set aside.
I took the liberty to modify the quoted passage; originally, Fine talks about conjunctions, not quantifications. But his point directly carries over to quantifications.
For illustration, compare the following case that a referee suggested as a potential counter-example to the claim that the only immediate grounds of existential truths are their instances: According to a widespread view, singular existential statements can be analyzed in terms of the existential quantifier and the identity predicate. For instance, the analysis of ‘Ralf exists’ would read ‘\(\exists x\) (x = Ralf)’. But now consider ‘Singleton Ralf exists’. This would get analyzed as ‘\(\exists x\) (x = {Ralf})’; the fact that {Ralf} exists would therefore be an existential quantification and hence be grounded in its pertinent true instance, i.e., the fact that {Ralf}={Ralf}. But independently of the analysis, one may have the strong intuition that the fact that {Ralf} exists is immediately grounded in the fact that Ralf exists; for, the existence of an entity directly brings about the existence of its singleton. This could motivate to allow, in this particular case, an immediate ground of the fact that \(\exists x\) (x = {Ralf}) apart from its true instance.
Here is a twofold reply: Firstly, the example hinges on a particular analysis of singular existential statements. Even though the analysis is commonly taken to be extensionally correct, it is controversial whether it succeeds as a reductive analysis of the concept of existence. In particular, it has been argued that its failure as an analysis becomes apparent once it is evaluated in the theory of grounding (see Fine 2012a: p. 59f.). Secondly, however, assume the analysis is accepted so that singular existential statements are quantifications of the said form. That the fact <{Ralf} exists\({>}\), now analysed as \({<}\exists x\) (x = {Ralf})>, should have additional immediate grounds, apart from their instances, would then strongly be supported by the intuition that the existence of the member brings about the existence of the set (while, at least to my ears, the claim that F\(_{3}\) grounds F\(_{2}\)—see above—sounds less intuitive). Moreover, the instance that grounds a fact of the form \({<}\exists x (x = \{a\}){>}\) would be systematically related to the additional ground postulated for it: the latter would be of the form \({<}\exists x (x=a){>}\) while the corresponding instance would be of the form \({<}\{a\}=\{a\}{>}\). So, the problem described for Dep\({\Rightarrow }\)Grounds would not arise, namely that instances that immediately ground the existential statements relevant for Dep\({\Rightarrow }\)Grounds significantly vary from case to case; if every existential statement of the sort in question has an additional, independent immediate ground (namely a fact about existential dependence) it is fair to ask for an account of how that ground is related to the variable true instances of the existential statements. But there is no relevant variation in which instances ground statements such as \({<}\exists x (x = \{{ Ralf}\}){>}\) that would be in need of an explanation.
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Acknowledgements
I am grateful for valuable input that I received from Fabrice Correia, Frazer MacBride, Stefan Roski, Moritz Schulz, Alex Steinberg, Tuoamas Tahko, Nathan Wildman, and other members of the audiences when I presented earlier versions of the paper in Bamberg, Glasgow, Groningen, Helsinki, Milano, Paris, and at the Phlox research colloquium in Hamburg. I would also like to thank two anonymous referees for their helpful comments. Finally, I’d like to thank Singa Behrens, Florian Fuchs, and Nina Scheller for their help with the manuscript. Work on this paper was part of research projects funded by the BWF (project: Welt der Gründe), the DFG (project: Nominalizations, SCHN 1137/2–1; project: Maimonides Centre for Advanced Studies, FOR 2311), and the SNF (project: Grounding Metaphysics, Science, and Logic, CRSII1 147685/1).
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Schnieder, B. Grounding and dependence. Synthese 197, 95–124 (2020). https://doi.org/10.1007/s11229-017-1378-z
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DOI: https://doi.org/10.1007/s11229-017-1378-z