Leibnizian Rejection of Standard Thought Experiments against Identity of Indiscernibles

Abstract

It is argued that from a genuine Leibnizian point of view the well-known thought experiment, BTE, involving a possible world with only two exactly similar objects, cannot be used to refute Leibniz's Principle of the Identity of Indiscernibles (LIdI). If the claim that there are two objects in BTE is based on primitive thisnesses, the Leibnizian objection is that there are no such things; and even if there were, then, quite generally, something true of one object – that it has its primitive thisness – would not be true of the other. Secondly, if the duality claim is based on a primitive, irreducible relation of distinctness, the Leibnizian objection is that there are no irreducible relations. Finally, if it is said that the (putatively) two objects in BTE cannot be separately individuated, then BTE is not a counter-example to LIdI, because if there is no individuation, there are no individuals either, while LIdI presupposes that there are individuals.

Keywords: Leibniz, indiscernibility, identity, thisness, individuation

0. Introduction

Immanuel Kant (A 263-64, 272 / B 319, 328), C. D. Broad (1933, 173-76), Max Black (1952), and others have provided us with thought experiments aimed at the refutation of Leibniz's Principle of the Identity of Indiscernibles (LIdI) or the principle that “it is not true that two substances can resemble each other completely and differ only in number [solo numero]” (Leibniz 1686, 9); “For it certainly must be possible to explain why they are different, and that explanation must derive from some difference they contain” (Leibniz 1999, 1645 / Leibniz 1989, 32; emphasis removed).

In his version Black gives a thought experiment – let’s call it BTE – in which we have “nothing but two exactly similar spheres”, being located at a distance of one sphere-diameter from each other. “Then every quality and relational characteristic of the one would also be a property of the other” (Black 1952, 156). While Baruch Brody (1980, 19-20), for instance, has questioned the usability of BTE, suggesting that the supposition of its consistency is question-begging, a much commoner, even standard, view is that thought experiments of this sort are consistent and thus do refute LIdI. The purpose of this paper is to argue that from an orthodox Leibnizian point of view, BTE cannot be used against LIdI.

1. Primitive thisnesses

One way to articulate the claim that there are in BTE two objects, b and c, is to posit primitive thisnesses (haecceities), i.e., primitive b-ity B* and primitive c-ity C*, which cannot be accounted for by means of purely descriptive constructions.1
Leibniz rejects primitive thisnesses (see, for instance, Adams 1979 and Cover & O'Leary-Hawthorne 1999, Ch. 4), which means that within Leibniz’s system they cannot be appealed to in an attempted refutation of LIdI. However, Leibniz’s reasons for his rejection need not concern us here because if primitive thisnesses are posited, they themselves constitute, obviously, a further factor, distinct from the mere difference in number, which separates b and c: If in BTE we have the primitive thisnesses B* of b and C* of c, BTE cannot be used to repudiate LIdI, because something that is true of one sphere, viz., that it has its primitive thisness, is not true of the other. In short, posited primitive thisnesses constitute something more than just solo numero difference, for we then have distinctness based on distinct primitive thisnesses – accordingly, BTE with primitive thisnesses does not threaten LIdI because in this case we do have a difference between individuals.2

2. Primitive distinctness

Another way to regard BTE as a counter-example to LIdI is to say that in BTE we have two objects – let’s still call them b and c – standing in the relation of primitive, irreducible distinctness, without there being between them any separating property or relation (other than the primitive distinctness itself). However, from Leibniz’s point of view this is not cogent: Whereas individual accidents inhere in substances, such inherence in two substances does not make sense and thus relations cannot be real (in the way accidents are) and, parallelly,3 there are no purely extrinsic denominations, or extrinsic denominations not founded on intrinsic ones.

Elaborating, a statement such as “Caius is wise” is according to Leibniz true only if the modification of being wise belongs to Caius, or, more precisely, only if the individual accident Caius's wisdom inheres in Caius, this accident being a real entity dependent on (the substance) Caius. If “Paris loves Helen”, or “The relation of loving holds between Paris and Helen (in that order)”, were treated exactly analogously, it would be taken to be true only if the modification of loving belongs to both Paris and Helen (or to the ordered pair <Paris, Helen>), or only if the accident loving inheres in both Paris and Helen, "having, so to speak, one foot in one and one foot in the other" (Leibniz 1879, 517 / Leibniz 1989, 203). Leibniz, however, being committed to the doctrine of individual accidents, cannot accept such an account, for it "is contrary to the notion of accidents" (Leibniz 1716, 47). Thus, a relation, "being neither a substance nor an accident, must be a mere ideal thing" (ibid.) ─ that is, Leibniz holds that relations are not real, but are merely mental, ideal, phenomenal.4

Again, for Leibniz substances are self-sufficient and independent from each other.5 An intrinsic denomination of a substance, such as the one expressed by 'is wise' in “Caius is wise”, is exclusively about that substance (Caius) in the sense of involving no other substances, or representing that particular substance in a manner that does not make it appear as dependent on others, or as not self-sufficient. In contrast, an extrinsic denomination of a substance, say, Paris's denomination expressed in 'loves Helen', does not represent Paris as he is on his own but only in relation to Helen. Leibniz's explicit view, arising from his commitment to internal individuation and self-sufficiency of substances, is that extrinsic denominations of a substance are founded or grounded in, or result or arise from, its intrinsic denominations.6

3. No individuation

Those proponents of BTE who accept that positing either primitive thisnesses or primitive distinctness won't do may hold that these strategies presuppose separate individuatability of the two spheres, and claim that there is no such thing in BTE and that it is for this reason improper to try to pick out either of the spheres. Indeed, this seems to be Black's opinion of what the opponent of LIdI should say: when the defender, A, of LIdI in Black's (1952) article tries to get the opponent, B, to consider one of the spheres by calling it a, the opponent B protests that “there is no way of telling them [i.e., the two spheres] apart”, that we “don't know how to identify one of two spheres”, and that the defender has “no right to talk about a” (Black 1952, 156-57). 

However, the adherents of LIdI are now warranted to claim that if lack of individuation is appealed to, it, surely, cuts both ways: those opponents of LIdI who think that there is no individuation in BTE, have no right to hold that there are individuals in BTE and thus claim that there are two of them. This is what Leibniz may be interpreted to suggest in his New Essays (Leibniz 1704) 2.27.3:

If two individuals were perfectly similar and equal and, in short, indistinguishable in themselves, there would be no principle of individuation. I would even venture to say that in such a case there would be no individual distinctness, no separate individuals.

According to this line of defence of LIdI, the very concept of an individual presupposes individuatability, which means, of course, that it is a prerequisite in LIdI that there are individuatable individuals to begin with. Supplementing the passage from Discourse on Metaphysics (Leibniz 1686), given above, Leibniz's view is that “it is not true that two individuatables can resemble each other completely and differ only in number” ─ and no thought experiment without individuatables can refute this claim. In short, LIdI is, more explicitly, the principle that if there are individuals at all, no two of them are perfectly similar (i.e., appropriately symmetrical). Thus, the defender of LIdI is in a position to hold that even if cases like BTE were consistent (despite the lack of individuation), LIdI holds unrestrictedly, because it contains, implicitly, the requirement of individuatability; and, accordingly, BTE with non-individuatables does not work against LIdI.

4. Conclusion

(i) BTE with primitive thisnesses does not threaten LIdI because in this case we do have a difference between individuals (Section 1).

(ii) For Leibniz, there are no irreducible relations, which means that (within Leibniz’s system) primitive distinctness cannot be appealed to in representing BTE as a reason for rejecting LIdI (Section 2).

(iii) If there is no individuation, there are no individuals either, and thus BTE-with-nonindividuation is not a counter-example LIdI because this principle presupposes that there are individuals (Section 3).

References

Author’s Paper.

Adams, R. M. (1979), “Primitive Thisness and Primitive Identity”, Journal of Philosophy 76, 5-26.

Black, M. (1952), “The Identity of Indiscernibles”, Mind 61, 153-64.

Broad, C. D. (1933), Examination of McTaggart's Philosophy, Volume I, London: Cambridge University Press.

Brody, B. (1980), Identity and Essence, Princeton: Princeton University Press.

Cover, J. A. & O'Leary-Hawthorne, J. (1999), Substance and Individuation in Leibniz: An Essay in Metaphysics, Cambridge: Cambridge University Press.

Kant, I. (1996), Critique of Pure Reason, trans. W. S. Pluhar, Indianapolis: Hackett.

Leibniz, G. W. (1686), Discours de métaphysique, in Leibniz 1999, 1529-88. English translation in Leibniz 1989, 35-68. Cited by section number.

Leibniz, G. W. (1704), Nouveaux essais sur l'entendement humain, in his Sämtliche Schriften und Briefe, Series 6, Volume 6, ed. Leibniz-Forschungstelle der Universität Münster, Berlin: Akademie-Verlag, 1962, 43-527. English translation in New Essays on Human Understanding, ed. & trans. P. Remnant & J. Bennett, Cambridge: Cambridge University Press, 1981. Cited by section number.

Leibniz, G. W. (1716), The Leibniz-Clarke Correspondence: Letter 5, in his Die philosophischen Schriften von Gottfried Wilhelm Leibniz (Band 7), ed. C. I. Gerhardt, Berlin: Weidmann, 1890, 389-440. Partial English translation in Leibniz 1989, 333-346. Cited by section number.

Leibniz, G. W. (1879), Die philosophischen Schriften von Gottfried Wilhelm Leibniz (Band 2), ed. C. I. Gerhardt, Berlin: Weidmann. 

Leibniz, G. W. (1989), Philosophical Essays, ed. & trans. R. Ariew & D. Garber, Indianapolis: Hackett.

Leibniz, G. W. (1999), Sämtliche Schriften und Briefe, Series 6, Volume 4, ed. Leibniz-Forschungstelle der Universität Münster, Berlin: Akademie Verlag.