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{\field{\*\fldinst {\lang4105  SEQ CHAPTER \\h \\r 1}}{\fldrslt }}\pard \fs24\sl480\slmult1 
Leibnizian Rejection of Standard Thought Experiments against Identity of Indiscernibles\par
\par
\par
Abstract\par
\par
It is argued that from a genuine Leibnizian point of view the well-known thought experiment, \softline
BTE, involving a possible world with only two exactly similar objects, cannot be used to \softline
refute Leibniz's Principle of the Identity of Indiscernibles (LIdI). If the claim that there are two \softline
objects in BTE is based on primitive thisnesses, the Leibnizian objection is that there are no \softline
such things; and even if there were, then, quite generally, something true of one object {\u8211\'96} that it \softline
has {\plain \fs24 \i\lang2057 its}{\plain \fs24 \lang2057  primitive thisness {\u8211\'96} would not be true of the other. Secondly, if the duality claim is \softline
based on a primitive, irreducible relation of distinctness, the Leibnizian objection is that there \softline
are no irreducible relations. Finally, if it is said that the (putatively) two objects in BTE cannot \softline
be separately individuated, then BTE is not a counter-example to LIdI, because if there is no \softline
individuation, there are no individuals either, while LIdI presupposes that there are \softline
individuals.\par
}{\plain \fs24 \lang2057 \par
}{\plain \fs24 \lang2057 Keywords: Leibniz, indiscernibility, identity, thisness, individuation\par
}{\plain \fs24 \lang2057 \par
}{\plain \fs24 \lang2057 \par
}{\plain \fs24 \lang2057 0. Introduction\par
}{\plain \fs24 \lang2057 \par
}{\plain \fs24 \lang2057 Immanuel Kant (A 263-64, 272 / B 319, 328), C. D. Broad (1933, 173-76), Max Black (1952), \softline
and others have provided us with thought experiments aimed at the refutation of Leibniz's \softline
Principle of the Identity of Indiscernibles (LIdI) or the principle that {\u8220\'93}it is not true that two 
substances can resemble each other completely and differ only in number [}{\plain \fs24 \i\lang2057 solo numero}{\plain \fs24 \lang2057 ]{\u8221\'94} \softline
(Leibniz 1686, 9); {\u8220\'93}For it certainly must be possible to explain why they are different, and that \softline
explanation must derive from some difference they contain{\u8221\'94} (Leibniz 1999, 1645 / Leibniz \softline
1989, 32; emphasis removed).\par
}{\plain \fs24 \lang2057 \par
}{\plain \fs24 \lang2057 In his version Black gives a thought experiment {\u8211\'96} let{\u8217\'92}s call it BTE {\u8211\'96} in which we have \softline
{\u8220\'93}nothing but two exactly similar spheres{\u8221\'94}, being located at a distance of one sphere-diameter \softline
from each other. {\u8220\'93}Then every quality and relational characteristic of the one would also be a \softline
property of the other{\u8221\'94} (Black 1952, 156). While Baruch Brody (1980, 19-20), for instance, has \softline
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 \softline
consistent and thus do refute LIdI. The purpose of this paper is to argue that from an orthodox \softline
Leibnizian point of view, BTE cannot be used against LIdI.\par
}{\plain \fs24 \lang2057 \par
}{\plain \fs24 \lang2057 \par
}{\plain \fs24 \lang2057 1. Primitive thisnesses\par
}{\plain \fs24 \lang2057 \par
}{\plain \fs24 \lang2057 One way to articulate the claim that there are in BTE two objects, }{\plain \fs24 \i\lang2057 b}{\plain \fs24 \lang2057  and }{\plain \fs24 \i\lang2057 c}{\plain \fs24 \lang2057 , is to posit }{\plain \fs24 \i\lang2057 primitive \softline
thisnesses}{\plain \fs24 \lang2057  (}{\plain \fs24 \i\lang2057 haecceities}{\plain \fs24 \lang2057 ), i.e., primitive }{\plain \fs24 \i\lang2057 b}{\plain \fs24 \lang2057 -ity }{\plain \fs24 \i\lang2057 B*}{\plain \fs24 \lang2057  and primitive }{\plain \fs24 \i\lang2057 c}{\plain \fs24 \lang2057 -ity }{\plain \fs24 \i\lang2057 C*}{\plain \fs24 \lang2057 , which cannot be \softline
accounted for by means of purely descriptive constructions.{}{\plain \fs24 \super\lang2057 1{\footnote \pard \fs24\sa453\sl480\slmult1 
{\plain \fs24 \super\lang2057 1}{}{\plain \fs24 \lang2057  Following Robert M. Adams (1979), I use the term 'primitive thisness' for a thisness that is \softline
not explicable by suchnesses; here a {\u8220\'93}thisness is the property of being identical with a certain \softline
particular individual{\u8221\'94} (Adams 1979, 6), and a property is a suchness, if its expression is purely 
descriptional, without involving any particular individuals, or, more precisely, {\u8220\'93}if and only if \softline
it could be expressed, in a language sufficiently rich, without the aid of such referential \softline
devices as proper names, proper adjectives and verbs (such as 'Leibnizian' and 'pegasizes'), \softline
indexical expressions, and referential uses of definite descriptions{\u8221\'94} (Adams 1979, 7).}}}
}{\plain \fs24 \lang2057 \par
}{\plain \fs24 \lang2057 Leibniz rejects primitive thisnesses (see, for instance, Adams 1979 and Cover & O'Leary-Hawthorne 1999, Ch. 4), which means that within Leibniz{\u8217\'92}s system they cannot be appealed \softline
to in an attempted refutation of LIdI. However, Leibniz{\u8217\'92}s reasons for his rejection need not \softline
concern us here because if primitive thisnesses are posited, they themselves constitute, \softline
obviously, a further factor, distinct from the mere difference in number, which separates }{\plain \fs24 \i\lang2057 b}{\plain \fs24 \lang2057  and \softline
}{\plain \fs24 \i\lang2057 c}{\plain \fs24 \lang2057 : If in BTE we have the primitive thisnesses }{\plain \fs24 \i\lang2057 B*}{\plain \fs24 \lang2057  of }{\plain \fs24 \i\lang2057 b}{\plain \fs24 \lang2057  and }{\plain \fs24 \i\lang2057 C*}{\plain \fs24 \lang2057  of }{\plain \fs24 \i\lang2057 c}{\plain \fs24 \lang2057 , BTE cannot be used to \softline
repudiate LIdI, because something that is true of one sphere, viz., that it has }{\plain \fs24 \i\lang2057 its}{\plain \fs24 \lang2057  primitive \softline
thisness, is not true of the other. In short, posited primitive thisnesses constitute something \softline
more than just }{\plain \fs24 \i\lang2057 solo numero}{\plain \fs24 \lang2057  difference, for we then have distinctness based on distinct \softline
primitive thisnesses {\u8211\'96} accordingly, BTE with primitive thisnesses does not threaten LIdI \softline
because in this case we do have a difference between individuals.{}{\plain \fs24 \super\lang2057 2{\footnote \pard \fs24
{\plain \fs24 \super\lang2057 2}{\par
}\pard \fs24\sa453\sl480\slmult1 
{\plain \fs24 \lang2057  Cf. Leibniz 1999, 554: {\u8220\'93}it cannot be said that there exist two singular things similar in all \softline
respects, e.g., two eggs, for it is necessary that something can be said of one which cannot be \softline
said of the other{\u8221\'94}. If two eggs have their respective primitive thisnesses, then something can \softline
be said of one {\u9472\'20} namely, that it has }{\plain \fs24 \i\lang2057 its}{\plain \fs24 \lang2057  primitive thisness {\u9472\'20} which cannot be said of the other.}}}
}{\plain \fs24 \lang2057 \par
}{\plain \fs24 \lang2057 \par
}{\plain \fs24 \lang2057 \par
}\pard \fs24\sl480\slmult1\keep\keepn 
{\plain \fs24 \lang2057 2. Primitive distinctness\par
}{\plain \fs24 \lang2057 \par
}\pard \fs24\sl480\slmult1 
{\plain \fs24 \lang2057 Another way to regard BTE as a counter-example to LIdI is to say that in BTE we have two \softline
objects {\u8211\'96} let{\u8217\'92}s still call them }{\plain \fs24 \i\lang2057 b}{\plain \fs24 \lang2057  and }{\plain \fs24 \i\lang2057 c}{\plain \fs24 \lang2057  {\u8211\'96} standing in the relation of }{\plain \fs24 \i\lang2057 primitive, irreducible \softline
distinctness}{\plain \fs24 \lang2057 , without there being between them any separating property or relation (other than \softline
the primitive distinctness itself). However, from Leibniz{\u8217\'92}s point of view this is not cogent: \softline
Whereas }{\plain \fs24 \i\lang2057 individual accidents}{\plain \fs24 \lang2057  }{\plain \fs24 \i\lang2057 inhere}{\plain \fs24 \lang2057  in substances, such inherence in two substances does not \softline
make sense and thus relations cannot be }{\plain \fs24 \i\lang2057 real}{\plain \fs24 \lang2057  (in the way accidents are) and, parallelly,{}{\plain \fs24 \super\lang2057 3{\footnote \pard \fs24\sa453\sl480\slmult1 
{\plain \fs24 \super\lang2057 3}{}{\plain \fs24 \lang2057  I say {\u8220\'93}parallelly{\u8221\'94} because I do not want to commit myself to the view that individual \softline
accidents }{\plain \fs24 \i\lang2057 are}{\plain \fs24 \lang2057  intrinsic denominations and relations }{\plain \fs24 \i\lang2057 are}{\plain \fs24 \lang2057  extrinsic denominations. See Author{\u8217\'92}s \softline
Paper, 146-47.}}}
}{\plain \fs24 \lang2057  there \softline
are no }{\plain \fs24 \i\lang2057 purely extrinsic denominations}{\plain \fs24 \lang2057 , or extrinsic denominations not founded on intrinsic \softline
ones.\par
}\pard \fs24\sl480\slmult1 
{\plain \fs24 \lang2057 \par
}{\plain \fs24 \lang2057 Elaborating, a statement such as {\u8220\'93}Caius is wise{\u8221\'94} is according to Leibniz true only if the \softline
modification of being wise belongs to Caius, or, more precisely, only if the individual \softline
accident }{\plain \fs24 \i\lang2057 Caius's wisdom}{\plain \fs24 \lang2057  inheres in Caius, this accident being a real entity dependent on (the \softline
substance) Caius. If {\u8220\'93}Paris loves Helen{\u8221\'94}, or {\u8220\'93}The }{\plain \fs24 \i\lang2057 relation}{\plain \fs24 \lang2057  of loving holds between Paris and \softline
Helen (in that order){\u8221\'94}, were treated exactly analogously, it would be taken to be true only if \softline
the modification of loving belongs to both Paris and Helen (or to the ordered pair <Paris, \softline
Helen>), or only if the accident }{\plain \fs24 \i\lang2057 loving}{\plain \fs24 \lang2057  inheres in both Paris and Helen, "having, so to speak, \softline
one foot in one and one foot in the other" (Leibniz 1879, 517 / Leibniz 1989, 203). Leibniz, \softline
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, \softline
"being neither a substance nor an accident, must be a mere ideal thing" (}{\plain \fs24 \i\lang2057 ibid.}{\plain \fs24 \lang2057 ) {\u9472\'20} that is, \softline
Leibniz holds that relations are not real, but are merely mental, ideal, phenomenal.{}{\plain \fs24 \super\lang2057 4{\footnote \pard \fs24\sa453\sl480\slmult1 
{\plain \fs24 \super\lang2057 4}{}{\plain \fs24 \lang2057  See also, for instance, Leibniz 1704, 2.12.3-5, 2.25.1, 2.30.4; Leibniz 1789, 486, 517 / \softline
Leibniz 1989, 203.}}}
}{\plain \fs24 \lang2057 \par
}{\plain \fs24 \lang2057 \par
}{\plain \fs24 \lang2057 Again, for Leibniz substances are }{\plain \fs24 \i\lang2057 self-sufficient}{\plain \fs24 \lang2057  and }{\plain \fs24 \i\lang2057 independent}{\plain \fs24 \lang2057  from each other.{}{\plain \fs24 \super\lang2057 5{\footnote \pard \fs24\sa453\sl480\slmult1 
{\plain \fs24 \super\lang2057 5}{}{\plain \fs24 \lang2057  See, for instance, Leibniz 1686, 14; Leibniz 1879, 517-19 / Leibniz 1989, 203-4.}}}
}{\plain \fs24 \lang2057  An \softline
}{\plain \fs24 \i\lang2057 intrinsic denomination}{\plain \fs24 \lang2057  of a substance, such as the one expressed by 'is wise' in {\u8220\'93}Caius is \softline
wise{\u8221\'94}, is exclusively }{\plain \fs24 \i\lang2057 about}{\plain \fs24 \lang2057  that substance (Caius) in the sense of involving no other \softline
substances, or representing that particular substance in a manner that does not make it appear \softline
as dependent on others, or as not self-sufficient. In contrast, an }{\plain \fs24 \i\lang2057 extrinsic denomination}{\plain \fs24 \lang2057  of a \softline
substance, say, Paris's denomination expressed in 'loves Helen', does not represent Paris as he \softline
is on his own but only in relation to Helen. Leibniz's explicit view, arising from his \softline
commitment to internal individuation and self-sufficiency of substances, is that extrinsic \softline
denominations of a substance are founded or grounded in, or result or arise from, its intrinsic \softline
denominations.{}{\plain \fs24 \super\lang2057 6{\footnote \pard \fs24\sa453\sl480\slmult1 
{\plain \fs24 \super\lang2057 6}{}{\plain \fs24 \lang2057  See, for instance, DM 8; Leibniz 1999, 308, 996, 1458, 1503, 1618, 1645-46 / Leibniz 1989, \softline
32; Leibniz 1879, 240, 249-50 / Leibniz 1989, 174-75; Leibniz 1704, 2.25.5, 2.27.3.}}}
}{\plain \fs24 \lang2057 \par
}{\plain \fs24 \lang2057 \par
}{\plain \fs24 \lang2057 \par
}\pard \fs24\sl480\slmult1\keep\keepn 
{\plain \fs24 \lang2057 3. No individuation\par
}{\plain \fs24 \lang2057 \par
}\pard \fs24\sl480\slmult1 
{\plain \fs24 \lang2057 Those proponents of BTE who accept that positing either primitive thisnesses or primitive \softline
distinctness won't do may hold that these strategies presuppose separate }{\plain \fs24 \i\lang2057 individuatability}{\plain \fs24 \lang2057  of \softline
the two spheres, and claim that there is no such thing in BTE and that it is for this reason \softline
improper to try to pick out either of the spheres. Indeed, this seems to be Black's opinion of \softline
what the opponent of LIdI should say: when the defender, A, of LIdI in Black's (1952) article \softline
tries to get the opponent, B, to consider one of the spheres by calling it }{\plain \fs24 \i\lang2057 a}{\plain \fs24 \lang2057 , the opponent B \softline
protests that {\u8220\'93}there is no way of telling them [i.e., the two spheres] apart{\u8221\'94}, that we {\u8220\'93}don't know \softline
how to identify one of two spheres{\u8221\'94}, and that the defender has {\u8220\'93}no right to talk about }{\plain \fs24 \i\lang2057 a}{\plain \fs24 \lang2057 {\u8221\'94} \softline
(Black 1952, 156-57). \par
}\pard \fs24\sl480\slmult1 
{\plain \fs24 \lang2057 \par
}{\plain \fs24 \lang2057 However, the adherents of LIdI are now warranted to claim that if lack of individuation is \softline
appealed to, it, surely, cuts both ways: those opponents of LIdI who think that there is no \softline
individuation in BTE, have no right to hold that there are individuals in BTE and thus claim \softline
that there are two of them. This is what Leibniz may be interpreted to suggest in his }{\plain \fs24 \i\lang2057 New \softline
Essays}{\plain \fs24 \lang2057  (Leibniz 1704) 2.27.3:\par
}{\plain \fs24 \lang2057 \par
}\pard \fs24\li720\sl480\slmult1 
{\plain \fs24 \lang2057 If two individuals were perfectly similar and equal and, in short, }{\plain \fs24 \i\lang2057 indistinguishable}{\plain \fs24 \lang2057  in \softline
themselves, there would be no principle of individuation. I would even venture to say \softline
that in such a case there would be no individual distinctness, no separate individuals.\par
}\pard \fs24\sl480\slmult1 
{\plain \fs24 \lang2057 \par
}{\plain \fs24 \lang2057 According to this line of defence of LIdI, the very concept of an individual presupposes \softline
individuatability, which means, of course, that it is a prerequisite in LIdI that there are 
individuatable individuals to begin with. Supplementing the passage from }{\plain \fs24 \i\lang2057 Discourse on \softline
Metaphysics}{\plain \fs24 \lang2057  (Leibniz 1686), given above, Leibniz's view is that {\u8220\'93}it is not true that two \softline
}{\plain \fs24 \i\lang2057 individuatables}{\plain \fs24 \lang2057  can resemble each other completely and differ only in number{\u8221\'94} {\u9472\'20} and no \softline
thought experiment without individuatables can refute this claim. In short, LIdI is, more \softline
explicitly, the principle that if there are individuals at all, no two of them are perfectly similar \softline
(i.e., appropriately symmetrical). Thus, the defender of LIdI is in a position to hold that even if \softline
cases like BTE were consistent (despite the lack of individuation), LIdI holds unrestrictedly, \softline
because it contains, implicitly, the requirement of individuatability; and, accordingly, BTE \softline
with non-individuatables does not work against LIdI.\par
}{\plain \fs24 \lang2057 \par
}{\plain \fs24 \lang2057 \par
}{\plain \fs24 \lang2057 4. Conclusion\par
}{\plain \fs24 \lang2057 \par
}{\plain \fs24 \lang2057 (i) BTE with primitive thisnesses does not threaten LIdI because in this case we do have a \softline
difference between individuals (Section 1).\par
}{\plain \fs24 \lang2057 \par
}{\plain \fs24 \lang2057 (ii) For Leibniz, there are no irreducible relations, which means that (within Leibniz{\u8217\'92}s system) \softline
primitive distinctness cannot be appealed to in representing BTE as a reason for rejecting LIdI \softline
(Section 2).\par
}{\plain \fs24 \lang2057 \par
}{\plain \fs24 \lang2057 (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 \softline
are individuals (Section 3).\par
}{\plain \fs24 \lang2057 \par
}{\plain \fs24 \lang2057 References\par
}{\plain \fs24 \lang2057 \par
}{\plain \fs24 \lang2057 Author{\u8217\'92}s Paper.\par
}{\plain \fs24 \lang2057 \par
}{\plain \fs24 \lang2057 Adams, R. M. (1979), {\u8220\'93}Primitive Thisness and Primitive Identity{\u8221\'94}, }{\plain \fs24 \i\lang2057 Journal of Philosophy}{\plain \fs24 \lang2057  76, \softline
5-26.\par
}{\plain \fs24 \lang2057 \par
}{\plain \fs24 \lang2057 Black, M. (1952), {\u8220\'93}The Identity of Indiscernibles{\u8221\'94}, }{\plain \fs24 \i\lang2057 Mind}{\plain \fs24 \lang2057  61, 153-64.\par
}{\plain \fs24 \lang2057 \par
}{\plain \fs24 \lang2057 Broad, C. D. (1933), }{\plain \fs24 \i\lang2057 Examination of McTaggart's Philosophy, Volume I}{\plain \fs24 \lang2057 , London: Cambridge \softline
University Press.\par
}{\plain \fs24 \lang2057 \par
}{\plain \fs24 \lang2057 Brody, B. (1980), }{\plain \fs24 \i\lang2057 Identity and Essence}{\plain \fs24 \lang2057 , Princeton: Princeton University Press.\par
}{\plain \fs24 \lang2057 \par
}{\plain \fs24 \lang2057 Cover, J. A. & O'Leary-Hawthorne, J. (1999), }{\plain \fs24 \i\lang2057 Substance and Individuation in Leibniz: An \softline
Essay in Metaphysics}{\plain \fs24 \lang2057 , Cambridge: Cambridge University Press.\par
}{\plain \fs24 \lang2057 \par
}{\plain \fs24 \lang2057 Kant, I. (1996), }{\plain \fs24 \i\lang2057 Critique of Pure Reason}{\plain \fs24 \lang2057 , trans. W. S. Pluhar, Indianapolis: Hackett.\par
}{\plain \fs24 \lang2057 \par
}{\plain \fs24 \lang2057 Leibniz, G. W. (1686), }{\plain \fs24 \i\lang2057 Discours de m{\u233\'e9}taphysique}{\plain \fs24 \lang2057 , in Leibniz 1999, 1529-88. English \softline
translation in Leibniz 1989, 35-68. Cited by section number.\par
}{\plain \fs24 \lang2057 \par
}{\plain \fs24 \lang2057 Leibniz, G. W. (1704), }{\plain \fs24 \i\lang2057 Nouveaux essais sur l'entendement humain}{\plain \fs24 \lang2057 , in his }{\plain \fs24 \i\lang2057 S{\u228\'e4}mtliche Schriften \softline
und Briefe}{\plain \fs24 \lang2057 , Series 6, Volume 6, ed. Leibniz-Forschungstelle der Universit{\u228\'e4}t M{\u252\'fc}nster, Berlin: 
Akademie-Verlag, 1962, 43-527. English translation in }{\plain \fs24 \i\lang2057 New Essays on Human \softline
Understanding}{\plain \fs24 \lang2057 , ed. & trans. P. Remnant & J. Bennett, Cambridge: Cambridge University \softline
Press, 1981. Cited by section number.\par
}{\plain \fs24 \lang2057 \par
}{\plain \fs24 \lang2057 Leibniz, G. W. (1716), The Leibniz-Clarke Correspondence: Letter 5, in his }{\plain \fs24 \i\lang2057 Die \softline
philosophischen Schriften von Gottfried Wilhelm Leibniz}{\plain \fs24 \lang2057  (Band 7), ed. C. I. Gerhardt, Berlin: \softline
Weidmann, 1890, 389-440. Partial English translation in Leibniz 1989, 333-346. Cited by \softline
section number.\par
}{\plain \fs24 \lang2057 \par
}{\plain \fs24 \lang2057 Leibniz, G. W. (1879), }{\plain \fs24 \i\lang2057 Die philosophischen Schriften von Gottfried Wilhelm Leibniz}{\plain \fs24 \lang2057  (Band \softline
2), ed. C. I. Gerhardt, Berlin: Weidmann. \par
}{\plain \fs24 \lang2057 \par
}{\plain \fs24 \lang2057 Leibniz, G. W. (1989), }{\plain \fs24 \i\lang2057 Philosophical Essays}{\plain \fs24 \lang2057 , ed. & trans. R. Ariew & D. Garber, \softline
Indianapolis: Hackett.\par
}{\plain \fs24 \lang2057 \par
}{\plain \fs24 \lang2057 Leibniz, G. W. (1999), }{\plain \fs24 \i\lang2057 S{\u228\'e4}mtliche Schriften und Briefe}{\plain \fs24 \lang2057 , Series 6, Volume 4, ed. Leibniz-Forschungstelle der Universit{\u228\'e4}t M{\u252\'fc}nster, Berlin: Akademie Verlag.\par
}}