| 489 | Each thing must be in some way unique [Diogenes of Apollonia] |
| Full Idea: No one thing among things subject to change can possibly be exactly like any other thing, without becoming the same thing. | |
| From: Diogenes (Apoll) (fragments/reports [c.440 BCE], B05), quoted by Simplicius - On Aristotle's 'Physics' 153.8 | |
| A reaction: This is said to be the first ever formulation of the principle of identity of indiscernible. |
| 13788 | If we made a perfect duplicate of Cratylus, there would be two Cratyluses [Plato] |
| Full Idea: Soc: Suppose we made a duplicate of everything you have and put it beside you; would there then be two Cratyluses, or Cratylus and an image of Cratylus? Crat: It seems to me, Socrates, that there would be two Cratyluses. | |
| From: Plato (Cratylus [c.377 BCE], 432c) | |
| A reaction: Don't think that science fiction examples are a modern development in philosophy. Plato has just invented the Startrek transporter. The two Cratyluses are the two spheres in Max Black's famous example. |
| 17175 | There cannot be two substances with the same attributes [Spinoza] |
| Full Idea: In nature there cannot be two or more substances of the same nature or attribute. | |
| From: Baruch de Spinoza (The Ethics [1675], I Pr 05) | |
| A reaction: This is the Identity of Indiscernibles. |
| 17554 | There must be some internal difference between any two beings in nature [Leibniz] |
| Full Idea: There are never two beings in nature that are perfectly alike, two beings in which it is not possible to discover an internal difference, that is, one founded on an intrinsic denomination. | |
| From: Gottfried Leibniz (Monadology [1716], §09) | |
| A reaction: From this it follows that if two things really are indiscernible, then we must say that they are one thing. He says monads all differ from one another. People certainly do. Leibniz must say this of electrons. How can he know this? |
| 5055 | No two things are totally identical [Leibniz] |
| Full Idea: By virtue of insensible variations, two individual things can never be perfectly alike. | |
| From: Gottfried Leibniz (New Essays on Human Understanding [1704], Pref) | |
| A reaction: This sounds a bit like the 'discernibility of non-identicals', except that he says that the differences may not be 'sensible'. He has to be talking of physical things, since I presume that, say, the symmetry of two circles is perfectly identical. |
| 13178 | Things in different locations are different because they 'express' those locations [Leibniz] |
| Full Idea: Things that differ in place must express their place, that is, they must express the things surrounding, and thus they must be distinguished not only by place, that is, not by an extrinsic denomination alone, as is commonly thought. | |
| From: Gottfried Leibniz (Letters to Burcher De Volder [1706], 1703.06.20) | |
| A reaction: This is an unusual view, which has some attractions, as it enables the relations of a thing to individuate it, while maintaining that this is a real difference in character. |
| 19412 | If two bodies only seem to differ in their position, those different environments will matter [Leibniz] |
| Full Idea: If two bodies differ only in their position, their individual relations to the environment must be taken into account, so that more is involved in their distinguishability than just position. | |
| From: Gottfried Leibniz (Letters to Burcher De Volder [1706], 1703.06.20) | |
| A reaction: This seems to allow that two bodies could be intrinsically type-identical (though differing in extrinsic features), which is contrary to his normal view. I suppose a different location in the gravitational field will make an intrinsic difference. |
| 19411 | In nature there aren't even two identical straight lines, so no two bodies are alike [Leibniz] |
| Full Idea: In nature any straight line you may take is individually different from any other straight line you may find. Accordingly, it cannot come about that two bodies are perfectly equal and alike. | |
| From: Gottfried Leibniz (Letters to Burcher De Volder [1706], 1703.06.20) | |
| A reaction: Leibniz was very good at persuasive examples! It remains unclear, though, why he takes the Identity of Indiscernibles to be a necessary truth, when he seems to have only observed it from experience. This is counter to his other principles. |
| 16504 | Two eggs can't be identical, because the same truths can't apply to both of them [Leibniz] |
| Full Idea: It isn't possible to have two particulars that are similar in all respects - for example two eggs - for it is necessary that some things can be said about one of them that cannot be said about the other, else they could be substituted for one another. | |
| From: Gottfried Leibniz (works [1690]), quoted by David Wiggins - Sameness and Substance 2.2 | |
| A reaction: [from a 'fragment' for which Wiggins gives a reference] This quotation doesn't rest the distinctness of the eggs on some intrinsic difference, but on the fact that we can say different things about the two eggs. |
| 7576 | The Identity of Indiscernibles is true of concepts with identical properties, but not of particulars [Kant, by Jolley] |
| Full Idea: Kant said that the principle of the Identity of Indiscernibles is true only at the level of concepts; two concepts having identical properties are the same concept; the principle is not true at the level of particulars given in sensory experience. | |
| From: report of Immanuel Kant (Critique of Pure Reason [1781]) by Nicholas Jolley - Leibniz Ch.8 | |
| A reaction: Good. I would think that should be the last word on that particular subject. ...Suppose, though, that two people had identical concepts with identical properties, but believed that the extensions (application to particulars) were different? |
| 14509 | If we ignore differences between water drops, we still distinguish them by their location [Kant] |
| Full Idea: In the case of two drops of water one can completely abstract from all inner difference (of quality and quantity), and it is enough that they be intuited in different places at the same time in order for them to be held to be numerically different. | |
| From: Immanuel Kant (Critique of Pure Reason [1781], B319/A263) | |
| A reaction: Adams points out that this is the same idea as Max Black's famous two spheres thought experiment. We assume that all the water drops are distinct from one another, even if we are unable to perceive the fact. Best explanation. |
| 12033 | An object is identical with itself, and no different indiscernible object can share that [Russell/Whitehead, by Adams,RM] |
| Full Idea: Trivially, the Identity of Indiscernibles says that two individuals, Castor and Pollux, cannot have all properties in common. For Castor must have the properties of being identical with Castor and not being identical with Pollux, which Pollux can't share. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913], I p.57) by Robert Merrihew Adams - Primitive Thisness and Primitive Identity 2 | |
| A reaction: I suspect that either the property of being identical with itself is quite vacuous, or it is parasytic on primitive identity, or it is the criterion which is actually used to define identity. Either way, I don't find this claim very illuminating. |
| 11849 | It at least makes sense to say two objects have all their properties in common [Wittgenstein on Russell] |
| Full Idea: Russell's definition of '=' is inadequate, because according to it we cannot say that two objects have all their properties in common. (Even if this proposition is never correct, it still has a sense). | |
| From: comment on Bertrand Russell (The Principles of Mathematics [1903]) by Ludwig Wittgenstein - Tractatus Logico-Philosophicus 5.5302 | |
| A reaction: This is what now seems to be a standard denial of the bizarre Leibniz claim that there never could be two things with identical properties, even, it seems, in principle. What would Leibniz made of two electrons? |
| 14107 | Terms are identical if they belong to all the same classes [Russell] |
| Full Idea: Two terms are identical when the second belongs to every class to which the first belongs. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §026) |
| 11095 | We should just identify any items which are indiscernible within a given discourse [Quine] |
| Full Idea: We might propound the maxim of the 'identification of indiscernibles': Objects indistinguishable from one another within the terms of a given discourse should be construed as identical for that discourse. | |
| From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 2) | |
| A reaction: This increasingly strikes me as the correct way to discuss such things. Identity is largely contextual, and two things can be viewed as type-identical for practical purposes (e.g. teaspoons), but distinguished if it is necessary. |
| 10195 | If the universe just held two indiscernibles spheres, that refutes the Identity of Indiscernibles [Black] |
| Full Idea: Isn't it logically possible that the universe should have contained nothing but two exactly similar spheres? ...So two things would have all their properties in common, and this would refute the Principle of the Identity of Indiscernibles. | |
| From: Max Black (The Identity of Indiscernibles [1952], p.67) | |
| A reaction: [Black is the originator of this famous example] It also appears to be naturally possible. An observer at an instant of viewing will discern a relational difference relative to themselves. Most people take Black's objection to be decisive. |
| 5477 | One thing can look like something else, without being the something else [Ellis] |
| Full Idea: In considering questions of real possibility, it is important to keep the distinction between what a thing is and what it looks like clearly in mind. There is a possible world containing a horse that could then look like a cow, but it wouldn't BE a horse. | |
| From: Brian Ellis (The Philosophy of Nature: new essentialism [2002], Ch.6) | |
| A reaction: This is an interesting test assertion of the notion that there are essences (although Ellis does not allow that animals actually have essences - how could you, given evolution?). His point is a good one. |
| 12034 | If the universe was cyclical, totally indiscernible events might occur from time to time [Adams,RM] |
| Full Idea: There is a temporal argument for the possibility of non-identical indiscernibles, if there could be a cyclical universe, in which each event was preceded and followed by infinitely many other events qualitatively indiscernible from itself. | |
| From: Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979], 3) | |
| A reaction: The argument is a parallel to Max Black's indiscernible spheres in space. Adams offers the reply that time might be tightly 'curved', so that the repetition was indeed the same event again. |
| 14510 | Two events might be indiscernible yet distinct, if there was a universe cyclical in time [Adams,RM] |
| Full Idea: Similar to the argument from spatial dispersal, we can argue against the Identity of Indiscernibles from temporal dispersal. It seems there could be a cyclic universe, ..and thus there could be distinct but indiscernible events, separated temporally. | |
| From: Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979], 3) | |
| A reaction: See Idea 14509 for spatial dispersal. If cosmologists decided that a cyclical universe was incoherent, would that ruin the argument? Presumably there might even be indistinguishable events in the one universe (in principle!). |
| 16455 | Black's two globes might be one globe in highly curved space [Adams,RM] |
| Full Idea: If God creates a globe reached by travelling two diameters in a straight line from another globe, this can be described as two globes in Euclidean space, or a single globe in a tightly curved non-Euclidean space. | |
| From: Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979], 3) | |
| A reaction: [my compression of Adams's version of Hacking's response to Black, as spotted by Stalnaker] Hence we save the identity of indiscernibles, by saying we can't be sure that two indiscernibles are not one thing, unusually described. |
| 12130 | a and b share all properties; so they share being-identical-with-a; so a = b [Brody] |
| Full Idea: Suppose that a and b have all of their properties in common. a certainly has the property of-being-identical-with-a. So, by supposition, does b. Then a = b. | |
| From: Baruch Brody (Identity and Essence [1980], 1.2) | |
| A reaction: Brody defends this argument, and seems to think that it proves the identity of indiscernibles. As far as I can see it totally begs the question, since we can only assume that both have the property of being-identical-with-a if we have assumed a = b. |
| 16453 | The bundle theory makes the identity of indiscernibles a necessity, since the thing is the properties [Stalnaker] |
| Full Idea: On the bundle theory, the identity of indiscernibles (for 'individuals') is a necessary truth, since an individual is just the co-instantiation of all the properties represented by a point in the space of properties. | |
| From: Robert C. Stalnaker (Mere Possibilities [2012], 3.6) | |
| A reaction: So much the worse for the bundle theory, I presume. Leibniz did not, I think, hold a bundle theory, but his belief in the identity of indiscernibles seems to have had a theologicial underpinning. |
| 16505 | By the principle of Indiscernibility, a symmetrical object could only be half of itself! [Wiggins] |
| Full Idea: The full Identity of Indiscernibles excludes the existence in this world of a symmetrical object, which is reduced to half of itself by the principle. If symmetrical about all planes that bisect it, it is precluded altogether from existence. | |
| From: David Wiggins (Sameness and Substance [1980], 2.2) | |
| A reaction: A really nice objection. Do the parts even need to be symmetrical? My eyeballs can't be identical to one another, presumably. Electrons already gave the principle big trouble. |
| 7566 | The Identity of Indiscernibles is really the same as the verification principle [Jolley] |
| Full Idea: Various writers have noted that the Identity of Indiscernibles is really tantamount to the verification principle. | |
| From: Nicholas Jolley (Leibniz [2005], Ch.3) | |
| A reaction: Both principles are false, because they are the classic confusion of epistemology and ontology. The fact that you cannot 'discern' a difference between two things doesn't mean that there is no difference. Things beyond verification can still be discussed. |
| 4033 | Two pure spheres in non-absolute space are identical but indiscernible [Campbell,K] |
| Full Idea: The Identity of Indiscernibles is not a necessary truth. It fails in possible worlds where there are two identical spheres in a non-absolute space, or worlds without beginning or end where events are exactly cyclically repeated. | |
| From: Keith Campbell (The Metaphysic of Abstract Particulars [1981], §5) | |
| A reaction: The principle was always very suspect, and these seem nice counterexamples. As so often, epistemology and ontology had become muddled. |
| 3145 | The Indiscernibility of Identicals is a truism; but the Identity of Indiscernibles depends on possible identical worlds [Rey] |
| Full Idea: Leibniz's Law, the indiscernibility of identicals, is a truism which should not be confused with the more controversial identity of indiscernibles, which depends on the possibility of perfectly replicated universes. | |
| From: Georges Rey (Contemporary Philosophy of Mind [1997], 2.4) |
| 13379 | If two objects are indiscernible across spacetime, how could we decide whether or not they are the same? [Jubien] |
| Full Idea: If a bit of matter has a qualitatively indistinguishable object located at a later time, with a path of spacetime connecting them, how could we determine they are identical? Neither identity nor diversity follows from qualitative indiscernibility. | |
| From: Michael Jubien (Possibility [2009], 1.3) | |
| A reaction: All these principles expounded by Leibniz were assumed to be timeless, but for identity over time the whole notion of things retaining identity despite changing has to be rethought. Essentialism to the rescue. |
| 13730 | The Indiscernibility of Identicals has been a big problem for modal logic [Fitting/Mendelsohn] |
| Full Idea: Equality has caused much grief for modal logic. Many of the problems, which have struck at the heart of the coherence of modal logic, stem from the apparent violations of the Indiscernibility of Identicals. | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 7.1) | |
| A reaction: Thus when I say 'I might have been three inches taller', presumably I am referring to someone who is 'identical' to me, but who lacks one of my properties. A simple solution is to say that the person is 'essentially' identical. |
| 4203 | Identity of Indiscernibles (same properties, same thing) ) is not Leibniz's Law (same thing, same properties) [Lowe] |
| Full Idea: The Identity of Indiscernibles (no two objects can possess exactly the same properties) is not the same as Leibniz's Law (what is true of a thing is true of what is identical with that thing). | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.62) | |
| A reaction: Two things can't be the same because we can't discern the difference, which may be our inadequacy. But if they actually have identical properties, it is hard to see how they could be different. A universe with just two perfect spheres is couterexample. |
| 13702 | The identity of indiscernibles is necessarily true, if being a member of some set counts as a property [Sider] |
| Full Idea: The identity of indiscernibles (∀x∀y(∀X(Xx↔Xy)→x=y) is necessarily true, provided that we construe 'property' very broadly, so that 'being a member of such-and-such set' counts as a property. | |
| From: Theodore Sider (Logic for Philosophy [2010], 5.4.3) | |
| A reaction: Sider's example is that if the two objects are the same they must both have the property of being a member of the same singleton set, which they couldn't have if they were different. |
| 4476 | Most philosophers think that the identity of indiscernibles is false [Moreland] |
| Full Idea: Most philosophers think that the identity of indiscernibles is false. | |
| From: J.P. Moreland (Universals [2001], Ch.7) | |
| A reaction: This is as opposed to the generally accepted 'indiscernibility of identicals'. 'Discernment' is an epistemological concept, and 'identity' is an ontological concept. |
| 10198 | If only two indiscernible electrons exist, future differences must still be possible [Zimmerman,DW] |
| Full Idea: If nothing existed except two electrons, which are indiscernible, it remains possible that differences will emerge later. Even if this universe has eternal symmetry, such differences are still logically, metaphysically, physically and causally possible. | |
| From: Dean W. Zimmerman (Distinct Indiscernibles and the Bundle Theory [1997], p.306) | |
| A reaction: The question then is whether the two electrons have hidden properties that make differences possible. Zimmerman assumes that 'laws' of an indeterministic kind will do the job. I doubt that. Can differences be discerned after the event? |
| 10199 | Discernible differences at different times may just be in counterparts [Zimmerman,DW] |
| Full Idea: Possible differences which may later become discernible could be treated as differences in a counterpart, which is similar to, but not identical with, the original object. | |
| From: Dean W. Zimmerman (Distinct Indiscernibles and the Bundle Theory [1997], p.307) | |
| A reaction: [compressed] This is a reply to Idea 10198, which implies that two things could never be indiscernible over time, because of their different possibilities. One must then decide issues about rigid designation and counterparts. |
| 5746 | The Identity of Indiscernibles is contentious for qualities, and trivial for non-qualities [Melia] |
| Full Idea: If the Identity of Indiscernibles is referring to qualitative properties, such as 'being red' or 'having mass', it is contentious; if it is referring to non-qualitative properties, such as 'member of set s' or 'brother of a', it is true but trivial. | |
| From: Joseph Melia (Modality [2003], Ch.3 n 11) | |
| A reaction: I would say 'false' rather than 'contentious'. No one has ever offered a way of distinguishing two electrons, but that doesn't mean there is just one (very busy) electron. The problem is that 'indiscernible' is only an epistemological concept. |
| 4639 | Leibniz's Law is about the properties of objects; the Identity of Indiscernibles is about perception of objects [Baggini /Fosl] |
| Full Idea: Leibniz's Law ('if identical, must have same properties') defines identity according to the properties possessed by the object itself, but the Identity of Indiscernibles defines identity in terms of how things are conceived or grasped by the mind. | |
| From: J Baggini / PS Fosl (The Philosopher's Toolkit [2003], §3.16) | |
| A reaction: This is the heart of the problem of identity. We realists must fight for Leibniz's Law, and escort the Identity of Indiscernibles to the door. |
| 7927 | At different times Leibniz articulated three different versions of his so-called Law [Macdonald,C] |
| Full Idea: There are three distinct versions of Leibniz's Law, all traced to remarks made by Leibniz: the Identity of Indiscernibles (same properties, same thing), the Indiscernibility of Identicals (same thing, same properties), and the Substitution Principle. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.2) | |
| A reaction: The best view seems to be to treat the second one as Leibniz's Law (and uncontroversially true), and the first one as being an interesting but dubious claim. |
| 7928 | The Identity of Indiscernibles is false, because it is not necessarily true [Macdonald,C] |
| Full Idea: One common argument to the conclusion that the Principle of the Identity of Indiscernibles is false is that it is not necessarily true. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.2 n32) | |
| A reaction: This sounds like a good argument. If you test the Principle with an example ('this butler is the murderer') then total identity does not seem to necessitate identity, though it strongly implies it (the butler may have a twin etc). |
| 18764 | The notion of 'property' is unclear for a logical version of the Identity of Indiscernibles [Anderson,CA] |
| Full Idea: In the Identity of Indiscernibles, one speaks about properties, and the notion of a property is by no means clearly fixed and formalized in modern symbolic logic. | |
| From: C. Anthony Anderson (Identity and Existence in Logic [2014], 1.5) | |
| A reaction: The unclarity of 'property' is a bee in my philosophical bonnet, in speech, and in metaphysics, as well as in logic. It may well be the central problem in our attempts to understand the world in general terms. He cites intensional logic as promising. |