Cartesian Minds
Cartesian Minds


In this paper I propose a new argument against the Cartesian conception of the mind. I start by showing that if this conception assumes either of the two main versions of nominalism – extreme nominalism and trope theory – it is inconsistent. I then show that if it assumes either extreme nominalism or realism it is unintelligible. However, the Cartesian conception must assume either nominalism or realism, since these views are jointly exhaustive and mutually exclusive. I conclude therefore that this conception is either inconsistent, or unintelligible or both.

Table of contents

    1 According to a basic dualistic conception that originated in Descartes, minds are immaterial, non-spatial and simple thinking particulars that are independent of anything material. Call this view the Cartesian conception, and minds thus conceived, Cartesian minds. In what follows I propose a new version of an argument against the Cartesian conception that can be traced back to Descartes’ days (Garber and Ayers 1998, 232). The inspiration behind my version is an argument suggested by Strawson’s seminal discussion of the concept of a person (1959, Chaps. 3-4). However, in both form and substance my argument takes its own course.

    2 Simplicity in the sense assumed by the Cartesian conception means absolute indivisibility. As Leibniz insisted simplicity in this sense is compatible with complexity of internal structure (Rutherford 1995, 159): A complex whole may be such that it cannot exist except in its entirety. Indeed, on the Cartesian conception the properties of minds relate to them as constituents relate to wholes, and here is my starting point.

    Properties of concrete particulars are respects in which these entities may be alike or differ – e.g., the similar shape but different colour of two objects. Similarly with relations, or properties of ordered n-tuples of concrete particulars – e.g., the parent-child relation in which I stand to each of my children but in which none of them stands to me (Mellor and Oliver 1997, 1). In itself this characterization is not controversial. Nevertheless, it has given rise to an age-old debate concerning the question of how the similarities and differences embodied in properties should be accounted for. One basic answer to this question, which goes back to Plato, is what has traditionally been called realism (Loux 1998, Chap. 1). On this view properties are a special type of entities, universals, that differ from particulars in that they are repeatable – i.e. while no particular can have distinct occurences at the same time, numerically one and the same property can, realists maintain, be wholly and completely exhibited or, as they typically put it, exemplified simultaneously by several distinct particulars, or n-tuples of particulars, or even by other properties. According to realism then, particulars are similar or agree in attribute if and only if there is some one thing, a universal, which they literally share or have in common. And similarly with properties, and properties of properties, and so on without end.

    Realism’s traditional rival account, nominalism, denies the existence of universals, and acknowledges only the existence of particulars. Going back to Abelard, Ockham and perhaps even Aristotle, this account has two main variants. According to the first, extreme nominalism, concrete particulars exhaust the things that exist (Loux 1978, 6-7; Loux 1998, 58-60). Therefore, the similarities and differences between them must be irreducibly primitive features of the world that cannot be explained in more basic terms. Likewise, talk about properties of properties should be construed in ways that do not presuppose anything above and beyond concrete particulars (Loux 1998, 62-79).

    On the second main variant of nominalism, trope theory, properties, as well as properties of properties, should be accounted for in terms of a special type of particulars, tropes: Where concrete particulars agree in attribute, trope theorists maintain, it is because they have similar tropes (Loux 1998, 79-82). As particulars tropes are supposed to be nonrepeatable. But unlike their concrete kin, they are taken to be abstract in some sense (Mellor and Oliver 1997, 121-3 and 126), and the similarities and differences between them are considered irreducibly primitive features of the world (ibid. 169-70).

    3 Extreme nominalism conflicts with the Cartesian conception. For it implies that concrete particulars have no constituents of a more basic ontological status. But Cartesian minds are supposed to be ontologically structured in the sense of having such constituents. As will become clear below this difficulty may be relieved by slightly modifying the Cartesian conception. But as we shall also see, extreme nominalism raises another problem for the Cartesian conception, which resists this modification.

    Trope theory too clashes with the Cartesian conception. For it considers the particularity of tropes to be acquired through location (Mellor and Oliver 1997, 136), which implies that attribute agreement should be accounted for in terms of spatial things. But Cartesian minds are supposed to be completely non-spatial.

    Finally, realism does not sit very well with the notion of simplicity that the Cartesian conception assumes. For even on an Aristotelian version of realism that denies the possibility of there being uninstantiated universals (Loux 1998, 45-8), a property of a given Cartesian mind can exist independently of all other constituents of this mind – viz. as a property of a different mind. It may perhaps be possible to get around this problem by modifying the said notion of simplicity. But as I shall now show, realism raises another, insurmountable problem for the Cartesian conception.

    4 According to the principle of the identity of indiscernibles it is impossible for numerically different concrete particulars to share all their properties. Although this principle is trivially true under trope theory (Loux 1998, 108), there are very strong reasons to consider it false under realism (Armstrong 1989, 64-70). This is therefore the majority view today as well as what I shall assume.

    Call the question of what it takes for concrete particulars of the same sort to be numerically identical or distinct, the individuation problem. My assumption concerning the falsity under realism of the principle of the identity of indiscernibles immediately entails that, given realism, numerical diversity cannot consist of the having of at least some different properties, nor can numerical identity consist of the having of exactly the same properties. Thus, this assumption entails that, given realism, an account of the ontological structure or constitution of concrete particulars cannot solve the individuation problem if it involves only properties. Are there then any accounts of this structure that involve more than properties, and can they solve the individuation problem?

    5 Of the three accounts of the ontological constitution of concrete particulars that contemporary metaphysicians hold to be exhaustive, one, bundle theory, involves only properties (Loux 1978, 112-115; Loux 1998, 98-100). However, the two other accounts – bare substratum and characterized particulars - are less spartan. A basic idea of bare substratum theory is that the properties of concrete particulars must be supported by an entity, substratum, which is completely independent from them. Another basic idea is that the relation between a substratum and its properties – if there are such - must be the same as the relation between concrete particulars and their properties. This means that if a substratum has properties of its own, there must be another substratum that supports them, which will immediately set us off on an infinite regress. So yet another basic idea of this theory is that a substratum must be devoid of any properties of its own (Loux 1970, 235-44; Loux 1998, 93-8).

    The basic idea of a representative and particularly elaborated version of characterized particulars theory, namely substance theory, is that concrete particulars are instantiations of a special type of universals, kinds, that represent irreducibly unified ways of being (Loux 1970, 193-195; Loux 1978, 158-166; Loux 1998, 117-127). This means, first, that a concrete particular’s belonging to a kind cannot be analyzed in terms of its possessing given properties. But secondly, it also means that a concrete particular can be construed as a genuine subject of the properties associated with it. Thirdly, it means that a subset of these properties that are determined by the kind to which the concrete particular belongs, expresses its core being or essence thereby enabling it to function as the possessor of all its other properties.

    6 Both bare substratum theory and substance theory hold that the bare substrata and kinds which they postulate respectively, make it possible to solve the individuation problem. Thus, according to bare substratum theory bare substrata are what endow concrete particulars with individuality, thereby rendering them distinct (Loux 1970, 192 and 242). Similarly, substance theory takes the irreducible unity represented by kinds to be reflected in concrete particulars, qua instantiations of kinds, thereby rendering these instantiations distinct (Loux 1998, 121-123). However, merely to postulate a sort of individuating entities is not yet to explain what it means for the things individuated by these entities to be identical or distinct. Ontological generosity, as Strawson most aptly put it, is no substitute for elucidation (1997, 38). Apart from this problem substance theory’s approach to the individuation problem entails that instantiations of kinds must be considered numerically diverse (Loux 1978, 161), which does not seem to cohere with the fact that qua universals kinds must have numerically identical instantiations. Moreover, other versions of characterized particulars theory (Loux 1998, 129), are not better off than substance theory with respect to the individuation problem. It follows that, given realism, a proper solution to the individuation problem requires some other ontological machinery. But what can this other machinery be?

    7 Going back to Avicenna and Duns Scotus, the first of what seems to be the only two possible answers to this question, is haecceity or thisness – i.e. a primitive feature of a particular, which that particular alone possesses and which nothing else could have had either instead of or as well as it. Obviously this solution to the individuation problem does not advance us beyond the solutions offered by bare substratum theory and bundle theory. For like the latter two the “thisness” solution does not specify in an informative way what it takes for concrete particulars to be the same or different. Indeed, all it says concerning this question is tantamount to the claim that there is some feature of concrete particulars in virtue of which such entities are identical or distinct. But then, short of explaining - as a proper solution to the individuation problem should - what it means for concrete particulars to be identical or distinct, the “thisness” account presupposes an understanding of what this means.

    The second possible answer to our question is, of course, a spatio-temporal position. A widely accepted view is that it is impossible for two distinct particulars to occupy precisely the same region of space at a given time. Consider, however, the possibility of, e.g., two objects that consist of distinct parts or particles, which mingle so that the parts/particles constituting the one fill the gaps between those constituting the other. Examples of this type show, I take it, that although the said view is not very wide of the mark, it requires some refinement or perhaps even reformulation in terms of spatio-temporal history (Hamlyn 1984, 72-75). Nevertheless I will keep to the original formulation since it will simplify my discussion without significantly affecting its main points.

    If distinct particulars cannot occupy the same spatio-temporal position, then any such position is nonrepeatable – i.e. it cannot characterize more than one thing. Given realism, this means that spatio-temporal positions are not properties. But it also means that the spatio-temporal positions that particulars occupy can be considered as that which individuates them. This suggestion may be objected to on the grounds that given the widely accepted relational conception of space and time it is viciously circular: If spatio-temporal positions are determined by relations between distinct particulars they must apparently presuppose rather than explain numerical difference. However, this objection would be justified only if the relational conception of space and time requires that the individuation of spatio-temporal positions be separate from and posterior to the individuation of particulars. But insofar as the relational conception is concerned the individuation of spatio-temporal positions and that of concrete particulars may be intimately linked in much the same way as, e.g., the justification of specific deductive inferences and that of general logical rules are interrelated (Goodman 1983, 63-64) – i.e. each may require the other and be inseparable from it (Strawson 1959, 36-38). So the circularity objection is unsound. This rejoinder requires of course further elaboration. But even in its present, very sketchy form it is sufficient to block the main objection to the spatio-temporal account of individuation.

    8 Since incorporeal things like Cartesian minds are supposed to be non-spatial, it is impossible to apply to them directly the spatio-temporal account of individuation. However, this does not preclude the possibility of applying this account to Cartesian minds indirectly by way of some non-spatial relation in which they stand to corporeal objects like human bodies. As examples of such relations one can bring (1) a relation of uniform regularity between mental and bodily events, (2) a nomic (or lawful) connection between such events, (3) natural supervenience (Chalmers 1995, 34-38) of Cartesian minds on bodies. However, for reasons we already saw, it is – given realism - logically possible for there to be numerically distinct Cartesian minds that are qualitatively indistinguishable. This being the case, whatever the non-spatial relation between a given Cartesian mind and a given body, it is logically possible that there are other Cartesian minds that stand in exactly the same relation to this very same body. In Strawson’s apt formulation “uniqueness of the body does not guarantee uniqueness of the Cartesian soul” (1959, 101). It follows that, given realism, it is impossible to apply the spatio-temporal account of individuation to Cartesian minds even indirectly. This being the case realism entails that no answer can be given to the question wherein the identity or diversity of Cartesian minds consists. But without an answer to this question the idea of Cartesian minds would not not really make sense. For such an answer is partially constitutive of the meaning of sortals like this idea (Lowe 1989, 24-5). Thus, realism renders the idea of Cartesian minds unintelligible.

    9 Unlike the supposed non-spatiality of Cartesian minds the fact that such minds are supposed to be ontologically structured is not a very central feature of the Cartesian conception. Thus, unlike the conflict between this conception and trope theory, which is due to the former feature, its clash with extreme nominalism, which is due to the latter feature, may be resolved by simply forgoing this very feature. However, such a course will not remedy the Cartesian conception. For extreme nominalism must allow for the possibility of there being distinct yet absolutely alike Cartesian minds. Otherwise it will have extremely implausible consequences – e.g., that distinct yet very similar minds, which it certainly must allow, merge into one mind when becoming, as they certainly can, absolutely alike. But then, problems analogous to those that realism faces with respect to the individuation of Cartesian minds, will also inflict extreme nominalism. And this means that this view as well renders the notion of Cartesian minds unintelligible.

    10 To sum up, then, the Cartesian conception must assume either nominalism or realism, since these ontological views are jointly exhaustive and mutually exclusive. However, if it assumes either extreme nominalism or trope theory it is incoherent. And if it assumes either extreme nominalism or realism it is unintelligible. Thus, the Cartesian conception is either incoherent or unintelligible or both.1


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    8. Lowe, E.J. 1989 Kinds of Being, Oxford: Blackwell.
    9. Mellor, D.H. and Oliver, A. (eds.) 1997 Properties, Oxford: OUP.
    10. Rutherford, D. 1995 Leibniz and the Rational Order of Nature, New York: Cambridge UP.
    11. Strawson, P. 1959 Individuals, London: Methuen.
    12. Strawson, P. 1997 Entity and Identity, Oxford: Clarendon.
    13. Garber, D. and Ayers, M. (eds.) 1998 The Cambridge History of Seventeenth Century Philosophy Vol. I, Cambridge: Cambridge UP.
    Many thanks to Dalia Drai, Jerome Gellman and Hami Verbin for thei helpful comments.
    Yakir Levin. Date: XML TEI markup by WAB (Rune J. Falch, Heinz W. Krüger, Alois Pichler, Deirdre C.P. Smith) 2011-13. Last change 18.12.2013.
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