A Response: Leibniz’s Principle of (Sufficient) Reason and Principle of Identity of Indiscernibles
Valérie Debuiche
With his chapter, Martin Lin means to demonstrate that Spinoza’s rationalism is not as broad as some commentators, himself included but a few years ago, and, paradigmatically, Michael Della Rocca, are inclined to believe. His main argument rests upon the fact that the so-called Principle of Sufficient Reason is not the basis of the entirety of Spinoza’s metaphysical doctrine. It only is used with regard to establishing the existence and the nonexistence of substances (in fact, of God) and cannot entail anything else, such as the metaphysical Principle of Identity of Indiscernibles, for instance, or Spinoza’s necessitarianism. As a Leibnizian scholar, I do not intend to discuss Lin’s statements on the subject of rationalistic interpretations of Spinoza. Rather, I would like to consider the way Lin appeals to Leibniz’s own rationalism in order to deflate Spinoza’s.
According to Lin, Spinoza’s rationalism, based on the Principle of Sufficient Reason, must not be considered the strongest variant of Early Modern rationalism, because there is at least one variant of Early Modern rationalism which is stronger than Spinoza’s, namely Leibniz’s. Specifically, Lin claims that Leibniz puts the Principle of Sufficient Reason to a broader use than Spinoza and that, moreover, Leibniz’s Principle of Sufficient Reason entails the Principle of Identity of Indiscernibles. In a way, Lin is right: Spinoza’s Principle of Sufficient Reason does only concern “facts about existence and non-existence,” whereas, on the contrary, Leibniz seems to apply the Principle of Sufficient Reason to “every truth, every fact, and every event.” Furthermore, in several texts, Leibniz argues that the Principle of Identity of Indiscernibles derives from the Principle of Sufficient Reason. But, if we examine these two theses more carefully, we have to admit that it is not obvious that Leibniz’s Principle of Sufficient Reason applies to “facts about non-existence” or to “negative existentials,” or that the Principle of Identity of Indiscernibles can be reduced to the Principle of Sufficient Reason. In some ways, Leibniz might not be Spinoza’s super-rationalist alter-ego.
A first remark can be made about the name given to Spinoza’s claim at E1p11d2 that “if something exists, there is a cause or reason why it exists, and if it doesn’t, there is an explanation of its non-existence,” which is called the “Principle of Sufficient Reason” by many commentators. The expression is originally Leibnizian and the term “sufficient” contains something more than “there is an explanation” or even “there is a cause or reason why something exists or not”: it asserts that such a cause or reason is also all that is sufficient for such an explanation. It is not only about giving a reason for the existence of things, but also about giving the ultimate reason why something exists in the way it does. In Spinoza’s Ethics, the so-called Principle of Sufficient Reason is used in the demonstration for the necessary existence of God [E1p11d2] and, as such, it deals not only with a cause or reason, but indeed with a sufficient cause, in that it has its own reason to exist in itself. Such a use of the terminology of sufficiency is totally consistent with Leibniz’s one.
The issue now is to verify whether Leibniz’s Principle of Sufficient Reason does apply to non-existential facts, as Lin suggests in order to prove that it entails Spinoza’s Principle of Sufficient Reason and goes beyond it. For that purpose, we need to carefully read Leibniz’s references to the Principle of Sufficient Reason. Doing so, some subtle but meaningful nuances appear in Leibniz’s explanations of what a principle of reason is. First, such a principle means that nihil est sine causa. In the 1680s, Leibniz details what he has in mind by claiming that nothing is without a cause. Among many other references, we can quote this passage from a letter Leibniz wrote to Arnauld in June 1686:
Et c’est ce qu’Aristote et l’École veulent signifier en disant: Praedicatum inest subjecto. C’est aussi à quoi revient cet axiome, nihil est sine causa, ou plutôt, nihil est cujus non possit reddi ratio, c’est-à-dire toute vérité de droit ou de fait, peut être prouvée a priori en faisant voir la liaison du prédicat et du sujet. Quoique le plus souvent il n’appartienne qu’à Dieu de connaître distinctement cette connexion, surtout en matières de fait, que les esprits finis ne connaissent qu’a posteriori et par expérience. Or ce que je viens de dire est à mon avis la nature de la vérité en général, ou bien je ne connais pas ce qu’est vérité. [A II.2.56]1
In another text from the same period, De arte characteristica ad perficiendas scientias ratione nitentes (1688), Leibniz writes:
Duobus utor in demonstrando principiis, quorum unum est: falsum esse quod implicat contradictionem, alterum est, omnis Veritatis (quae immediata sive identica non est) reddi posse rationem, hoc est notionem praedicati semper notioni sui subjecti vel expresse vel implicite inesse; idque non minus in denominationibus extrinsecis quam intrinsecis, nec minus in veritatibus contingentibus quam necessariis locum habere. [A VI.4.912]2
The important point here is that the principle is not called the principle of “sufficient reason” but is presented as the principle “of the reason to be given” [Principium Reddendae Rationis]. The Principium Reddendae Rationis refers to a principle of knowledge and reasoning. It is closely related to another principle according to which, in any true proposition, the notion of predicate is contained in the notion of subject [praedicatum inest subjecto].3 The Principle Praedicatum Inest Subjecto is also the mere definition of truth. With regard to any true proposition, it is possible to give the reason for why it is true, since it suffices to show that the predicate inheres in the subject—which it always does.4
Let me briefly discuss the relation between the two principles of knowledge in Leibniz: the Principle of Contradiction and the Principium Reddendae Rationis. It is worth noting that the Principle of Contradiction postulates that (a proposition containing a) contradiction is always false or, equivalently, that a proposition cannot be true and false at the same time, or that, if two propositions are contradictory, one is true and the other is false. This principle is obviously valid for both necessary truths as well as for contingent ones: if one contingent proposition is true, the contradictory proposition is false. But with respect to a necessary proposition, the appeal to the Principle of Contradiction is sufficient to prove its truth, since the contradictory proposition of a necessary truth is impossible or, what is the same, contains a contradiction such as Anon-A. In other words, to prove a necessary truth, and to know it as such, it suffices to demonstrate the impossibility of its contradictory proposition by means of a finite number of steps of reasoning (in fact, by means of notional resolutions or definitions). This is not the case for contingent truths, since the contradictory proposition of a contingent truth is possible and does not contain any contradiction in itself. The analysis of such propositions must be infinite. Nonetheless, thanks to the Principle Praedicatum Inest Subjecto, it is always theoretically possible to show how a contingently true proposition is true by means of the analysis of its notions. This cannot fail to reveal the inherence of the predicate within the subject, even if only to God. Hence, if there is undoubtedly a reason which can be given why a necessary proposition is true, and if the Principle of Contradiction is not invalidated by any contingent truths, contingent truths can only be known in virtue of the Principium Reddendae Rationis, which is based on the Principle Praedicatum Inest Subjecto:
Or c’est la même raison, qui me fait douter s’il est convenable de dire qu’un autre principe qui n’a gueres moins d’usage, que celuy de la contradiction, sçavoir que rien n’arrive sans qu’il y ait quelque raison que celuy qui sçauroit tout, pourroit rendre, pourquoy il soit plustost arrivé que non, cesse à l’egard de la liberté. D’autant plus qu’il paroist à moy que ce principe nous sert exprés dans les matieres contingentes comme celuy de la contradiction nous sert dans les matieres necessaires. Et c’est pour cela que les loix du mouvement en dependent, parce [qu’elles] ne sont pas d’une necessité geometrique, leur source estant la volonté de Dieu reglée par la sagesse. Or comme le principe de contradiction est celuy de la necessité, et le principe de la raison à rendre est celuy de la contingence. [To Alberti, c. 1689, A II.2.300–301]5
We come now to our point. For Leibniz, the Principium Reddendae Rationis is also the principle of contingency or of existence: nothing happens without a reason for it happening the way it happens. This principle (of the reason to be given) becomes the principle of “sufficient” reason as soon as the issue is metaphysical and consists not in proving the truth of any contingent proposition, nor only in giving the cause of one existing or contingent thing, but in determining the reason why the existing things do exist in the way they exist and not in another possible way. Lin refers to Leibniz’s Monadologie when arguing that Leibniz “thinks that all facts require a cause or reason”:
§31. Our reasonings are based upon two great principles: the first the principle of contradiction, by virtue of which we judge that false which involves a contradiction and that true which is opposed or contradictory to the false;
§32. And the second the principle of sufficient reason, by virtue of which we observe that there can be found no fact that is true or existent, or any true proposition, without there being a sufficient reason for its being so and not otherwise, although we cannot know these reasons in most cases. [GP VI 612/L 646]
The following passages are required to determine what Leibniz could think such a sufficient reason to be:
§33. There are also two kinds of truths, truths of reasoning and truths of fact. […]
§36. But a sufficient reason must also be found in contingent truths or truths of fact, that is to say, in the sequence of things distributed through the universe of creatures, whose analysis into particular reasons could proceed into unlimited detail because of the immense variety of things in nature and the division of bodies into the infinite. […]
§37. As all this detail includes other earlier or more detailed contingent factors, each of which in turn needs a similar analysis to give its reason, one makes no progress, and the sufficient or final reason will have to be outside the sequence or series of these detailed contingent factors, however infinite they may be.
§38. Thus the final reason of things must be in a necessary substance in which the detail of the changes can be contained only eminently, as in their source. It is the substance that we call God. [GP VI 612–613/L 646]
We see that, if the sufficient reason of necessary truths may be found with use of the mere Principle of Contradiction (by the possibility of reducing the proposition to logical identity, A is A or A is not non-A or AB is B, with a finite number of resolutions or definitions, or by the possibility of reducing its contradictory to antilogy, A is not A, A is non-A, AB is not B, AB is non-B), the sufficient reason of the truth of contingent propositions can only be found in an ultimate thing outside the series of contingent things and necessary in itself, that is to say in God. In that text, as in many others,6 the Principle of Sufficient Reason is devoted to the demonstration of the existence of God as the only necessary being, cause of itself and of every contingent thing, which makes it a “sufficient” cause.
Accordingly, it is correct to refer here to both Spinoza’s principle as well as to the Leibnizian Principle of Sufficient Reason, since both are related to the demonstration of the existence of God as a necessary being. Nevertheless, this does not mean that, while referring to the Principium Reddendae Rationis, Leibniz always identifies this reason (to be given) as the sufficient one. The “reason to be given” is not necessarily God as the ultimate cause of every real effect, of any existing thing. It can also be a proximate cause, for instance the preceding state that explains the following one,7 just like in mechanics one physical effect such as the change of the direction of a motion of a ball is explained through the motion of another ball striking it in a certain way. The Principium Reddendae Rationis states that any truth can be proven but a proof might sometimes not arrive at the sufficient and divine reason, when for instance it is based on the analysis of propositions (and not of notions).8 For example, it can be established that if A is B, then A is C, without giving the final reason why A exists or why A is the way it is.
To further explain the difference between the Principium Reddendae Rationis and the Principle of Sufficient Reason, we may also look at Lin’s considerations with regard to the equivalence by means of which he proves that Leibniz’s Principle of Sufficient Reason also bears on non-existential facts. He notes that “every universal generalization [is] logically equivalent to a negative existential”: all ravens are black is logically equivalent to there does not exist a nonblack raven. As a consequence, Lin states that Leibniz’s Principle of Sufficient Reason applies to “negative existentials as well.” This reasoning calls for some remarks. The first one concerns the identification of a generalized fact with a universal fact. This does not seem to be right, because of the nature of statistical truth, which only tells us that, as far as we know, ravens are always black but not that they are all black. Even if we ignore this point, a second remark leads us to notice that a statistical truth, such as ravens are always black, is not sufficient to claim that ravens are essentially or necessarily black. In other words, that all ravens are always black does not mean that it is impossible for a raven to be nonblack. Fortunately, Lin does not talk about possibility or impossibility, but about existence and nonexistence. But instead of resolving the difficulty, this may make it only stronger.
According to the logical expression of a universal affirmative in Leibniz’s rational calculus, if all ravens are black, it is then necessary that any nonblack raven is impossible9: (all R is B) ⇔ (RB≡R) ⇔ (R≡RB) ⇔ (RnonB≡RBnonB) ⇔ (RnonB≡AnonA)—since BnonB is equivalent to any contradiction, it can be generally expressed as AnonA. Consequently, if (it is true that) all ravens are black, then it is impossible for a raven to be nonblack and, therefore, there does not exist any nonblack raven. In fact, all we might say regarding the relation between the universal affirmative proposition and the corresponding negative existential proposition depends on such a conditional statement whose reciprocal statement is problematic. Indeed, if there does not exist any nonblack raven, then (it is true that) all ravens are black, on the condition that the existence of a nonblack raven is impossible in itself. It must be that RnonB, or at least RnonBexisting, are equivalent to AnonA. Let me now clarify this last point.
It is quite obvious that RnonB cannot be impossible in itself: a nonblack raven is totally conceivable. For instance, we can easily imagine an albino raven. What can we say about RnonBexisting? Does the possibility or the impossibility of such a notion depend on the analysis of its notion? In other words, is its truth or falsity knowable by means of the Principium Reddendae Rationis? Is “existing” a predicate contained in the subject which exists? One of the most important points of Leibniz’s logic concerns the precise notations he uses and the fact that he clearly distinguishes between “being” [ens] and “existing” [existens]. Ens is defined as a being which is possible, which means it contains no contradiction. In that sense, RnonB is an ens, a being. Existens is defined as “what is compatible with more things than other things are incompatible with it” [quod cum pluribus compatibile est, quam quodlibet aliud incompatiblile cum ipso] [A VI.4.744].
Leibniz will tackle the delicate issue of the predicative status of existens in Generales Inquisitiones de Analysi Notionum et Veritatum (1686), §§71–74, which are devoted to this question [A VI.4.762–763]. Leibniz there examines the conjunction A is B and A exists (or A is existing), asking whether it is equivalent to AB is existing, that is to say whether AB is said to contain existing, or Aexisting is said to contain B, or A is said to contain both B and existing. His solution is that, in fact, we should say A is B existing (for instance, Pierre is renouncing existing, meaning Pierre is actually renouncing) each time A is a concrete individual. The main theoretical element of Leibniz’s doctrine at play here is the distinction between ens and existens:
§73. non video quid aliud in Existente concipiatur, quam aliquis Entis gradus, quoniam variis Entibus applicari potest. Quanquam nolim dicere aliquid existere esse possibile seu Existentiam possibilem, haec enim nihil aliud est quam ipsa Essentia; nos autem Existentiam intelligimus actualem seu aliquid superadditum possibilitati sive Essentiae […]. [A VI.4.762]10
In other words, even if “existing” can be predicated of a subject, it is only in the case of an individual being endowed with what Leibniz calls a “complete notion.” It does not depend on possibility, since any ens is as possible as any other. Rather, it requires the additional idea of “degree of being” which can be determined only through a comparison, not between possible beings, but between the degrees of their compatibility. “Existing” is the being which is compatible with the largest number of other possible beings. The complete notion, which defines Leibnizian individuals, is the one containing anything which can be truly said about the thing the notion is applied to. The notion Caesar contains anything that can be said about the subject it is applied to: that he was a human being, an emperor, was murdered, and so on. On the contrary, the notion emperor does not contain anything that can be said about the subject, Caesar, to whom it can be truly applied. Emperor is an incomplete notion, just like raven or black is, and it has no relation to existence. Still, the completeness of the notion of an individual does not even contain the existence predicate unless this individual pertains to the set of compatible things which is the largest one. And the determination of this kind of optimality (among compatible beings) is ultimately grounded in the powerful and omniscient mind pleased with such an optimality of beings. This is, of course, connected to the Principle of Sufficient Reason: the reason for the truth of contingent propositions has to be found in the proper nature of a mind endowed with all specifically divine qualities: power, intelligence, and perfection.
Nonetheless, there is no logical equivalence between “all ravens are black” and “there does not exist a nonblack raven,” because the falsity of RnonBexisting does not depend on any logical reasons and its falsity is no impossibility—even if blackness were essential to ravenness. This is why it is very problematic to claim that, applying to general propositions, Leibniz’s Principle of Sufficient Reason consequently applies to non-existential facts. Besides, the Principle of Sufficient Reason founds existential propositions, but in a totally positive way: there is nothing like a choice of avoiding certain existences, such as the one of a nonblack raven. Divine choice is the choice of the greatest good or of the largest number of existing things. All that could be said about this is that this choice of the best renders impossible the actualization of other possible sets of compatible things, including the ones in which ravens were not black or Caesar would not have been murdered. But such sets remain possible in themselves and do exist in the “area of eternal truths,” that is in God’s understanding.
To conclude, even if the Principium Reddendae Rationis can be applied to general propositions thanks to the Principle Praedicatum Inest Subjecto, this does not mean that such propositions are true in virtue of the Principle of Sufficient Reason. The Principle of Sufficient Reason goes further: it calls for the ultimate reason, that is for God, and it supposes another fundamental principle: the Principle of Perfection. The ultimate reason for God to choose this possible set of compatible things instead of any other one depends on the fact that this set is the best one, the most perfect, the one endowed with the highest degree of being. All the truths concerning existence are finally based on this idea that, whereas any possible thing tends to exist, it exists only if it is a part of the best, richest, most perfect whole. This leads me to the last remark I wanted to make about Lin’s claim that the Principle of Identity of Indiscernibles derives from the Principle of Sufficient Reason in Leibniz’s doctrine.
This claim is based on a text from around 1689, Principia logico-metaphysica [A VI.4.1645]. In this text, Leibniz derives the Principle of Sufficient Reason and the Principle of Identity of Indiscernibles from the Principle Praedicatum Inest Subjecto. Nonetheless, although it is also true that Leibniz sometimes derives the Principle of Identity of Indiscernibles from the Principle of Sufficient Reason, sometimes he also derives it from the Principle of Perfection, and some other times, he considers them to be two fundamental and non-equivalent principles.11 My last remark only deals with the way Lin presents Leibniz’s reasoning in Principia logico-metaphysica. I am not sure I perfectly understand what “an identity” and a “qualitative truth” should correspond to in Leibniz’s text. According to Leibniz, “identity” is not something depending on identity predicates such as is identical to B. Leibniz refers to identity as the fundamental logical principle which states that A is A and A is not non-A, and if A is B, then A is not non-B, or if it is true that A is B, then it is false that A is not B (which corresponds to the Principle of Contradiction). As far as I understand it, a qualitative truth would be a proposition like Caesar is emperor. Martin Lin states that “the only thing that can explain an identity is a qualitative truth,” but in my opinion, it would be the contrary: “the only thing that can explain a qualitative truth is (the principle of) identity,” that is, the fact that a thing is what it is and is not what it is not, as soon as we also have the Principle Praedicatum Inest Subjecto.
Furthermore, the Principle of Identity of Indiscernibles postulates that two things which are not different are one and the same thing. Such an identity is both numerical and ontological (or essential and relative to their being). The main point of this principle is that it only applies to concrete beings endowed with a complete notion: incomplete and abstract notions are not concerned by it.12 In short, it is possible for two distinct incomplete objects to have the same “qualitative” predicates, just as do two similar triangles or two points. Yet this is impossible for concrete individual beings, since they cannot be distinguished in one way or another without having in their own notion the reason for that difference in virtue of the completeness of their notions. Thus, as soon as two things have exactly the same properties (are indiscernible), they may differ by names, but they are identical, not only logically, but ontologically: they are one thing, A is A. Conversely, if apparently indiscernible concrete things are distinguished as two things, like two leaves or two drops of water, this can only be according to an intrinsic difference we are simply incapable of perceiving, knowing, or determining.
In conclusion, even if we consider Leibniz to be the philosopher of the Principle of Sufficient Reason, it does not seem to me that his principle contains Spinoza’s idea for the “explanation” of nonexistences, since Leibniz is keen to maintain a strong distinction between possible and real, contingency and necessity, tendency to exist and actuality of existence. His means for grounding the passages of possible ens to existens in the idea of the highest degree of being, which is both best and most perfect, crystallizes the peculiarity of Leibniz’s approach to existential considerations. In this context, the Principle of Sufficient Reason, leading to God, is something more metaphysical than the Principium Reddendae Rationis, which is the specific principle for explanations (this is Spinoza’s so-called Principle of Sufficient Reason), even if in some ways they are equivalent, mostly when the Principle Praedicatum Inest Subjecto is used. Besides, the relation of the Principle of Sufficient Reason to the Principle of Perfection also allows us to better understand how Leibniz can sometimes also consider the Principle of Identity of Indiscernibles as an independent principle.
1 “And this is what Aristotle and the School means by saying: Praedicatum inest subjecto. This is the same thing meant by this axiom, nihil est sine causa, or, more exactly, nihil est cujus non possit reddit ratio, that is to say, any truth of reason or any truth of fact can be proven a priori by showing the relation of the predicate and the subject. Though most often it only belongs to God to distinctly know this connection, especially with regards to matters of fact, which finite minds only know a posteriori and by experience, nevertheless, what I have just said, in my opinion, is either the nature of truth in general, or I do not know what truth is” (our translation).
2 “For demonstrations, I use two principles, one being: is false what involves a contradiction; and the other being: it is possible to give a reason for every truth (which is not immediate or identical), that is, the notion of the predicate is always in the notion of the subject, either expressly or implicitly. This holds no less in case of the extrinsic denominations than in the case of intrinsic ones, no less in the case of contingent truths than in the case of the necessary ones” (our translation).
3 In contemporary Anglo-American Leibniz literature, PPIS (Principle Praedicatum Inest Subjecto) is often known as PIN (Predicate-In-Notion principle). PIN might lead us to believe that, in the case of true propositions, the predicate is in the notion without qualification. But this is odd: according to the terms of the principle, in the case of true propositions, the notion of the predicate is in the notion of the subject—praedicatum inest subjecto.
4 I want to thank Arnaud Lalanne for the many references he gave on this topic during his talk: “Les deux grands principes de raisonnement” (Université d’Aix-Marseille, January 13, 2018).
5 “Indeed, it is the same reason that makes me wonder whether it is right to say that another principle which has hardly any less usage than the one of contradiction, namely that nothing happens without there being some reason, which whoever knew everything could render, why what happened did happen rather than not, ceases with regard to freedom. Insofar as it seems to me that this principle especially serves us in contingent matters in the same way that the principle of contradiction serves us in necessary matters. And this is why the laws of movement depend on it, because they are not of a geometrical necessity, their source being the will of God regulated by his wisdom. The principle of contradiction is the one of necessity, the principle of the reason to be given is the one of contingency” (our translation).
6 For instance, from Confessio philosophi from 1673 [A VI.3.115–149] or De arte characteristica ad perficiendas scientias ratione nitentes from 1688 [A VI.4.912] to Essais de Théodicée from 1710 [GP VI 127, §44], Principes de la nature et de la grâce fondés en raison from 1714 [GP VI 602, §§7–8], and the letter to Clarke from November 1715 [GP VII 355–356].
7 See again De arte characteristica ad perficiendas scientias ratione nitentes [A VI.4.912].
8 The idea that the analysis of propositions, by which some truth is demonstrated, is easier to carry out than the analysis of notions is frequent and can already be found in 1679, in Introductio ad Encyclopaediam arcanam [A VI.4.530–531]. On such matters, see the major text for Leibniz’s rational calculus and logic in the 1680s: Generales inquisitiones de analysi notionum et veritatum from 1686 [A VI.4.739–788].
9 “≡” is the sign for logical coincidence.
10 “I do not see what else can be conceived by existing [existens] other than a certain degree of being [ens], since it can be applied to different beings. Nonetheless, by saying that something exists, I do not want to say that this is possible, i.e. a possible existence, for this [a possible existence] is nothing other than Essence itself. In effect, we conceive actual existence as something which is added to possibility or essence” (our translation).
11 For a very recent discussion on that topic in its locus classicus, the correspondence between Clarke and Leibniz, see Christian Leduc, “Indiscernables et raison suffisante dans la correspondance Leibniz-Clarke,” in Lumières no. 29: Principia rationis: Les principes de la raison dans la pensée de Leibniz, ed. Arnaud Lalanne (Bordeaux: Presses Universitaires de Bordeaux, 2017), 135–150.
12 This is why, in his very interesting paper devoted to Leibniz’s conception of space, Lin should not have applied the Principle of Identity of Indiscernibles to points, which are abstract and incomplete beings. See Martin Lin, “Leibniz on the Modal Status of Absolute Space and Time,” Noûs 50, no. 3 (2015): 447–464, here 457. From another point of view, it also seems problematic to me to imagine two individuals with the same intrinsic properties but with different extrinsic properties, just as Lin does in “The Principle of Sufficient Reason in Spinoza,” in The Oxford Handbook of Spinoza, ed. Michael Della Rocca (New York: Oxford, 2017). Indeed, extrinsic properties are only the phenomenal or material expressions of intrinsic properties, that is of the perceptive states of substances which are always conceived and created together in harmony. It is not that God “would have no reason to create the actual world rather than a world in which two indiscernible individuals were switched with respect to their extrinsic relations”; rather, the fact is that there is no reason to have different extrinsic properties without having different intrinsic properties, since intrinsic properties metaphysically ground the extrinsic ones.