Abstract
Gideon Rosen has recently sketched an argument which aims to establish that the notion of metaphysical modality is systematically ambiguous. His argument contains a crucial sub-argument which has been used to argue for Metaphysical Contingentism, the view that some claims of fundamental metaphysics are metaphysically contingent rather than necessary. In this paper, Rosen’s argument is explicated in detail and it is argued that the most straight-forward reconstruction fails to support its intended conclusion. Two possible ways to save the argument are rebutted and it is furthermore argued that the crucial sub-argument only supports a rather particular variant of Metaphysical Contingentism.
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Notes
See Rosen (2006, Sect. 2, pp. 15–16).
This matches the definition of absoluteness of Hale (1996).
Note that the two claims together imply that logical and conceptual modality are not real modalities.
Further examples of propositions in the differential class are the principle of universal mereological composition, the claim that God exists, and Armstrong’s claim that resemblance between particulars is a matter of the sharing of immanent universals. See Rosen (2006, pp. 19, 26).
‘Feature’ is here used as a an ontologically neutral term for whatever predicates stand for (e.g. properties and relations, universals, tropes, ...).
See Rosen (2006, p. 23).
David Mark Kovacs has made the interesting suggestion that the AAA might be read as requiring that essential truths do not introduce further ontological or ideological commitments. This proposal is however not pertinent in the context of a discussion of Rosen’s argument, since the argument is aimed at a minimal version of the Non-Standard conception which does not come with a particular stock of posterior ontological or ideological commitments.
It focuses only on one of three cases regarding the nature of the relevant entity, namely the case in which the relevant proposition (e.g. Pairing) expresses an essential truth about the relevant feature (e.g. that of being a set). The more detailed reconstruction of the next section will show that the second case, in which the proposition expresses an essential falsehood is perfectly analogous. Rosen’s third case, in which the truth or falsity of the proposition is not settled by the relevant essences trivially supports the conclusion of the Contingentist Argument.
The label ‘GO’ indicates that the definition takes into account both generic and objectual essence, i.e. the essences of objects and features. In the following, I will abbreviate the phrase ‘objects, features of objects, or objects and features of objects’ to ‘objects or features’.
For the sake of ease of expression, I will not always use Fine’s notion to express essentialist claims. Any such claim is straightforwardly translatable into a claim involving it.
Note that I here slightly deviate from Fine (1995) in how I draw the distinction between consequential and constitutive essentiality, since one may read Fine as defining the distinction as exclusive. My inclusive reading of consequential essence simplifies the discussion and is harmless in this context.
See Oliver and Smiley (2013), Sect. 12.7 for a definition.
Note that it is also equivalent to a modified version of Correia (2012)’s definition which in addition to the basic natures/constitutive essences of objects also takes the basic natures of features (and objects and features) into account, for parallel reasons.
See Rosen (2006, p. 24, footnote 10). Note that this footnote already appears to hint at the equivalence for which I am now going to provide an argument.
That \(\varGamma\,\vDash\, p\) either means that \(p \in \varGamma\) or that \(p \not \in \varGamma \wedge \varGamma\,\vDash\, p\), i.e. that p is either a trivial or a non-trivial logical consequence of the propositions in \(\varGamma\). Given the assumed inclusive reading of ‘true in virtue of the nature of’, both of these sentences have the same Finean translation, the one stated above.
Note that this characterization of the two versions of the AAA presupposes that the AAA is applied to an already existing stock of constitutive or consequential essential truths. The AAA can accordingly be thought of as an algorithm which operates on a class of propositions which express essential truths as its input. In a first step, it checks whether these propositions conform to the constraint it places on their form and content. The second step is sensitive to whether the input propositions already conform to the AAA: If a proposition does conform to the constraint, it is directly put into the output class of AAA-conform propositions. If it does not conform to the condition, it is translated into a proposition which does by turning the proposition into the consequent of a conditional proposition and adding a suitable existential claim in the antecedent. (This of course leaves some room for what ‘suitable’ means, since the existential claim can be about different objects or features.) The two versions of the AAA result from different inputs, the first taking only the propositions which express constitutively essential truths as input, the second also those which express purely consequential essential truths. This understanding of the AAA can be called the a posteriori view, since according to it, the AAA is applied to an a priori existing stock of essential truths. There is a second, wholly different way of thinking about the AAA. According to it, the AAA should not be thought of as an algorithm which is applied to an existing stock of essential truths, but rather as expressing a precondition for what it takes for a proposition to express such a truth. For the constitutive reading of the AAA, this does not make a substantive difference, since both the a posteriori view and the precondition-view will deliver the same class of AAA-conform propositions if the essences are the same. It does however make a substantial difference for the consequential reading of the AAA. Given the a posteriori-view, to generate the AAA-conform propositions which express constitutively essential truths, we take those propositions which follow from the propositions which capture the essences of objects and features before the AAA is applied to them and then apply the AAA to them. Assume for example that it is constitutively essential to being a proper class that sets exist. The corresponding proposition \(\langle\)Sets exist\(\rangle\) is, like any proposition, trivially a logical consequence of itself. This means that without the AAA, it would both capture an aspect of the constitutive and the consequential essence of being a proper class. According to the a posteriori-view, the constitutive reading of the AAA disqualifies this proposition from expressing a constitutively essential truth, but at the same time leaves it in the class of propositions which express consequential essential truths. The consequential reading of the AAA furthermore disqualifies it from belonging to that class. Contrast this with the precondition-view: According to it, the proposition \(\langle\)Sets exist\(\rangle\) and its logical consequences are completely irrelevant when it comes to which propositions belong to the class of the consequentially essential truths. This is because the class of constitutive essential truths which generate the logical consequences which in turn make up the consequentially essential truths consist exclusively of AAA-conform propositions, i.e. propositions which have the logical forms of material conditionals with existence claim in the antecedent. So instead of \(\langle\)Sets exist\(\rangle\), only propositions such as e.g. \(\langle\)If proper classes exist, sets exist\(\rangle\) matter for determining the consequential essential truths. This means that the class of these truths is very limited compared to the a posteriori-view, since the class of the logical consequences of a class of material conditionals with existential claims in the antecedent is very limited. To give an example of the sort of propositions which can end up expressing a consequential essential truth, consider e.g. the conditional proposition just mentioned and assume that it and e.g. \(\langle\)If sets exist, the empty set exists\(\rangle\) express constitutively essential truths. The two proposition together logically entail \(\langle\)If proper classes exist, the empty set exists\(\rangle\) which would accordingly express a consequentially essential truth. It should be clear from this that the a posteriori-view gives us a more charitable interpretation of the Non-Standard Conception. Note that the following first schematic version of the Contingentist Argument presupposes this view. The relevant version of the argument given the the precondition-view is the Abbreviated Argument introduced at the end of this subsection.
I will again follow Rosen (2006, p. 24f) in assuming that if the essences are silent on whether p is true, then p is trivially Non-Standardly contingent, but will, for the sake of generality, explicitly include the case that the essential truths entail that \(\lnot p\).
Note that if the argument is run for a proposition which either makes a simple existential claim (i.e. has the logical form \(\exists xx F xx\) or \(\exists xx (xx = aa)\), where aa is a constant assigned to one or more objects) or expresses the negation of such a claim, things get more complicated. Rosen’s statement of the argument focuses on a case in which we have an AAA-conform conditional proposition and the proposition expressing its antecedent which together entail the proposition expressing its consequent (i.e. on the two cases 2.i and 2.ii). I.e. the focus is on cases in which the rule of inference Modus Ponens is applied to establish the essential truth of the consequent of a conditional proposition based on the essential truth of the conditional proposition and its antecedent. If p expressed a simple existence claim, a claim of the sort which can occur as the antecedent of an AAA-conform proposition, it would also be possible to derive \(\lnot p\) by an application of Modus Tollens instead. This would give us two further cases to consider in step 2:
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2.iii
There are some objects or features such that it is true in virtue of their consequential nature that if p, then q and is true in virtue of their own consequential nature or that of some other objects or features.
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2.iv
There are some objects or features such that it is true in virtue of their consequential nature that if \(\lnot p\), then q and \(\lnot q\) is true in virtue of their own consequential nature or that of some other objects or features.
To successfully run the argument, a proponent of the Non-Standard Conception would therefore also have to establish that no matter what q stands for, its negation does not express an essential truth. Since my aim here is not to defend Rosen’s argument and since this complication does not affect my point that the consequential rather than the constitutive reading of the AAA is needed in order to run the argument, I will not discuss this complication any further.
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2.iii
Note that premise 3 is entailed by premise 4 given the inclusive reading of the constitutive/consequential essence-distinction which I presuppose and is therefore not really needed. It is included for illustrative purposes as will become clear shortly.
Recall that we are working with the inclusive reading of ‘consequential’ which includes the constitutively essential truths.
Note that the negation of Pairing does express a complex existence claim, but that all textual evidence points towards reading the AAA as requiring the antecedent of essentially true propositions to express (on their own) simple existence claims, i.e. propositions of the logical form \(\exists xx Fxx\), where F is a logically simple predicate or of the form \(\exists { xx} ({ aa}={ xx})\), where aa is a constant. Without this very plausible reading of the AAA, the instance of the argument for Pairing would have to go through step 2.iv mentioned in footnote 20. It is likely that further modifications of the AAA or other assumptions would be needed to get a sound instance of the argument.
The condition is plausibly not sufficient, since not all AAA-conform proposition are such that they or their negation express an essential truth about some objects or features. Consider e.g. \(\langle\)If the Louvre exists, someone will run through it in record time\(\rangle\).
Note that Kripke’s famous proof for the necessity of identity statements, does not undermine this claim. As Burgess (2013) points out, Kripke assumes that the necessity-operator \(\Box\) expresses a weak notion of necessity, so that ‘[w]e can count statements as necessary if whenever the objects mentioned therein exist, the statement would be true’ (Kripke 1971; cited from Burgess 2013, p. 1567). This assumption is not satisfied if one interprets \(\Box\) as the Non-Standard necessity-operator, since e.g. all existence claims (including in particular mathematical existence claims such as the claim that sets exists) are weakly necessary in this sense, but are supposed to be Non-Standardly contingent according to the Non-Standard Conception. See also Rosen (2006, p. 24, footnote 10).
In developing the arguments of this section, I have greatly benefited from exchanges with Pierre Saint-Germier.
One might be tempted to object that the Non-Standard Definition could also be adjusted to take only the essences of features into account, since the feature-only-version of the AAA would support the resulting feature-only-version of premise 1a. This objection falls flat, since a feature-only-version of the Non-Standard Definition would partly re-introduce the overgeneration problem through the back door. According to this version of the definition, no proposition which expresses an essential truth about objects, but not about features can be Non-Standardly necessary. This plausibly includes both the essential predications and the true identities involving rigid designators.
As an exegetical sidenote, Fine does not explicitly endorses the idea of identifying analyticity with truth in virtue of the nature of concepts, even though he at length discusses the analogy between analyticity and essential truth in his informal papers on essence (Fine 1994, 1995). He strictly treats analyticity as a property of sentences and identifies it with truth in virtue of the meaning of terms, not concepts. This does of course not rule out that someone working within his framework, might accept this identification and one might even argue that Fine himself at least comes close to accepting it. In his discussion of the parallel between analyticity and essence, Fine introduces the distinction between thin and thick words, where a thick word is a word (presumably a word-type) plus its meaning. Analytic truths generally involve words which one might assume to have concepts as their meanings. Given this assumption and Fine’s claim that ‘in giving a definition we are giving an essence–though not now of the word itself, but of its meaning’ (Fine 1994, p. 13), one might read Fine’s definition of analyticity as defining the notion in terms of truth in virtue of the nature of thick words. This interpretation at least strongly suggests the identification. Note also that independently of this interpretation of Fine (1994), Russell (2011, p. 13 and footnote 9, p. 150) reads Fine as accepting the identification.
The principle captures the idea that concepts essentially represent something, echoing the very common view that concepts are mental representations. See Margolis and Laurence (2014), Sect. 1.1 for an overview and references.
Note that one might still object that the divergence, while in principle problematic, is not substantial enough to pose a real problem. The idea underlying this objection is that PairingAA, which per assumption expresses an essential truth about the feature, only trivially differs from Pairing, which characterizes the concept/captures its essence. The two problems with this objection are that, first, the difference between Pairing and PairingAA is actually non-trivial in the context of the Non-Standard Conception, since the antecedent of PairingAA (‘sets exist’) is a Non-Standard contingency, and second, that the divergence matters regarding substantial questions about sets: The claim that there are identical sets which differ regarding their elements is inconsistent with what the concept tells us about sets, but consistent with what the feature tells us about them.
Note that Rosen himself appears to assume that there is no different regarding the essences of the concept and the feature of being a set when he introduces the AAA-conform version of Pairing by stating that ‘[y]ou can know full well what set membership is supposed to be–what it is to be a set, what the word “set” means–without knowing whether any sets exist, and hence without knowing whether Pairing is true’ (Rosen 2006, p. 18; my emphasis). Given any of the two modifications, what it is to be a set (i.e. the essence of the feature of being a set) and what the word ‘set’ means (i.e. how the concept of being a set as either captured by its essence or its negative characterization in terms of conceptual absurdities represents sets) come apart and, contrary to what Rosen says in the quoted passage, only the latter, but not the former is subject to the AAA.
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Acknowledgements
I would like to thank Martina Botti, Fabrice Correia, Peter Fritz, Ghislain Guigon, David Mark Kovacs, Matteo Morganti, Kevin Mulligan, Benjamin Neeser, Jan Plate, Magali Roques, Gideon Rosen, Alexander Skiles, Pierre Saint-Germier, Alexander Steinberg, Nathan Wildman and audiences at Issues on the (Im)Possible IV in Bratislava, the Contingentism workshop at the Fifth Italian Conference in Analytic Ontology in Padua and the participants of a session of the eidos-seminar at the University of Neuchâtel. Special thanks to Nathan Wildman for his commentary at Issues on the (Im)Possible IV and to Pierre Saint-Germier for discussion and written comments. I gratefully acknowledge financial support of the Swiss National Science Foundation (Project ‘Indeterminacy and Formal Concepts’, Grant-No. 156554, University of Geneva, principal investigator: Kevin Mulligan).
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Michels, R. The limits of non-standard contingency. Philos Stud 176, 533–558 (2019). https://doi.org/10.1007/s11098-017-1027-x
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DOI: https://doi.org/10.1007/s11098-017-1027-x