Abstract
The aim of this paper is to provide a systematic account of the metaphysically important distinction between haecceitistic properties, such as being David Lewis or being acquainted with David Lewis, and qualitative properties, such as being red or being acquainted with a famous philosopher. I first argue that this distinction is hyperintensional, that is, that cointensional properties can differ in whether they are qualitative. Then I develop an analysis of the qualitative/haecceitistic distinction according to which haecceitistic properties are relational in a certain sense. I argue that this analysis can capture the hyperintensionality of the qualitative/haecceitistic distinction and is generally in accordance with the use of the notion of a qualitative property in philosophical debates.
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Notes
The conclusion that Q and being a duplicate of David Lewis@ are distinct properties falling on different sides of the qualitative/haecceitistic divide could be avoided if being a duplicate of David Lewis@ was either identical to Q or did not count as a genuine property at all. It is not clear, however, why being a duplicate of David Lewis@ should be disqualified from being genuine if properties such as being acquainted with David Lewis or being David Lewis’s mother qualify as genuine, which seems to be an implicit assumption of the debate on the qualitative/haecceitistic distinction. Moreover, being a duplicate of David Lewis@ seems to be intuitively distinct from being a duplicate of Jimmyw1 (that is, having the intrinsic qualitative properties that Jimmy has at w1), even if Jimmy has Q at w1. But this implies that neither of these properties should be identified with Q.
An account that relies on linguistic considerations to define the metaphysical distinction between qualitative and haecceitistic properties has been proposed by Adams. According to Adams, a property is haecceitistic iff it cannot be expressed without the use of terms typically referring to concrete individuals, such as proper names or indexical expressions (Adams 1979, 7). Adams himself points out, however, that such a definition ‘may be suspected of circularity, on the ground that the distinction between qualitative and nonqualitative might be prior to’ the notion of a linguistic expression typically referring to concrete individuals and that considering haecceitistic properties a particular type of relational property (the approach defended in the present paper) might be the ‘more illuminating approach’ (Adams 1979, 7–8). I therefore assume that Adams’s criterion should be understood as a useful intuitive elucidation of the qualitative/haecceitistic distinction, rather than as a strict definition. It should be noted, however, that Adams’s account is widely accepted as a working definition of qualitative properties, particularly in the debate on haecceitism (Legenhausen 1989, 625–626; Diekemper 2009; Fara 2009, 286).
An immediate objection to this criterion is that it involves non-standard logical notions, that is, relations holding between individuals inhabiting distinct possible worlds and quantifiers whose domains contain actual and non-actual individuals. However, this is rather common for definitions of metaphysical notions and does not per se render them inadequate. One example is the following definition of strong supervenience frequently employed in the debate on the mind–body relation: A-properties supervene on B-properties iff for any individuals x and y inhabiting the same or different possible worlds, if x and y have the same B-properties, they have the same A-properties (see, e.g., Kim 1987, 317). Another pertinent example is the definition of an intrinsic property as one that cannot differ between duplicates, that is, between actual or non-actual individuals standing in the duplication relation to each other (see, e.g., Langton and Lewis 1998, 337).
According to Francescotti, the consists-in relation can be accounted for in terms of event identity. x’s having P consists in x’s standing in R to y iff x’s having P is the same event as x’s standing in R to y (Francescotti 1999, 599). The difficulty with this approach is to provide a criterion of event individuation which is sensitive to hyperintensional differences without having to presuppose the qualitative/haecceitistic distinction itself (see, however, Francescotti 2014, 190–191, for discussion). An alternative option might be to account for the consists-in relation in terms of the grounding relation. A more detailed discussion of both options would go beyond the scope of the present paper and will have to be postponed to a different occasion.
The account originally proposed by Lange refers to sentences rather than propositions. However, since it can be argued that necessity is primarily a property of propositions (McGrath 2014) and since considering propositions instead of sentences does not change the general structure of Lange’s account, this modification does not seem to be problematic.
There are always three possibilities to form the existential derivative of a two-place relation R: the existential derivative of R is either the property which x has iff ∃yRxy or the property instantiated by x iff ∃yRyx or the property instantiated by x iff ∃y∃zRyz. In what follows, the term ‘the existential derivative of R’ always refers to the first property.
This way of blocking counterexamples to (RC)1 is structurally similar to the procedure of ‘generalizing out’ non-essential individuals which Fine employs when defining the notion of consequentialist essence (Fine 1995, 277–278).
More specifically, if P is a haecceitistic property and Q is some (qualitative or haecceitistic) property, then ¬P, (P & Q), (P ∨ Q), (P → Q), (P ↔ Q), being such that ∃xPx, being such that ∀xPx, being possibly P and being necessarily P are haecceitistic properties. (This is, of course, analogous to Rosenkrantz's approach, see Rosenkrantz 1979, 522–523.).
A fundamental objection to all attempts to define the qualitative/haecceitistic distinction has been raised by Marshall, who provides a proof according to which the intrinsic/extrinsic distinction cannot be defined in terms of broadly logical notions and claims that it could be shown along analogous lines that the same holds for the qualitative/haecceitistic distinction (Marshall 2009, particularly 669). Whether or not Marshall’s argument applies to (RC)3 depends on whether or not (RC)3 is a definition in terms of broadly logical notions. According to Marshall, broadly logical notions are those notions that can be expressed using the following vocabulary: the logical vocabulary of first order predicate logic; the predicates ‘is a possible world’, ‘is a set’, ‘exists’, ‘=’; ‘∈’, ‘is a proper part of’, ‘instantiates’ and ‘is a property’; and the modal operators ‘possibly’, ‘necessarily’ and ‘at’ (Marshall 2009, 647).
However, the notion of invariance under all counterfactual perturbations used to define the concept of logical equivalence figuring in (RC)3 is not a broadly logical notion in Marshall’s sense, nor can it be reduced to such notions. It follows that Marshall’s argument does not apply to (RC)3.
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Acknowledgements
A first version of this paper was submitted to a journal in March 2010. I would like to thank several anonymous referees for their helpful feedback on previous versions of the manuscript. My work on this topic was supported by the Deutsche Forschungsgemeinschaft (research unit FOR 2495) and by the German-Israeli Foundation for Scientific Research and Development (grant number G-1257-116.4/2014).
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Hoffmann-Kolss, V. Defining Qualitative Properties. Erkenn 84, 995–1010 (2019). https://doi.org/10.1007/s10670-018-9991-x
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DOI: https://doi.org/10.1007/s10670-018-9991-x