Defending the Principle of Identity of Indiscernibles - Essay Example

of Defending the Principle of Identity of Indiscernibles The principle of identityof indiscernibles (PII) is stated as follows: “It states that no two distinct things exactly resemble each other. This is often referred to as ‘Leibniz's Law’ and is typically understood to mean that no two objects have exactly the same properties” (Forrest, “The Identity of”). Thus, if, for every property F, object x has F if and only if object y has F, then x is identical to y, which can be symbolized in the following manner: (x)(y)[(f)( fx > fy ) > x=y]. Max Black, in his work The Identity of Indiscernibles, attempts to refute this principle by means of a thought experiment. He claims to prove that it is possible to show that there could be two distinct objects with exactly the same properties. If so, then the PII must be false. Dean Zimmerman, also provides a similar take on the said matter. In this paper, I shall argue that Black and Zimmerman fail to refute the PII. In arguing against them, I shall divide this paper into four main parts. The fist part will discuss Black’s thought experiment, which serves as his refutation of the PII. The second part will discuss Zimmerman’s take on Black’s thought experiment, as well as his defense of the bundle theory, which will also serve as his basis to refute the PII. The third part will deal with the failure of Black and Zimmerman’s arguments in refuting the PII. And finally, the fourth part will be devoted to my defense of the PII. Black’s Two-Sphere World and His Refutation of the PII Black offers a refutation of the principle of identity of indiscernibles (PII) through the use of a thought experiment concerning two spheres. Black’s thought experiment goes as follows, we are asked to imagine a world where there are two and only two symmetrical spheres: Isn’t it logically possible that the universe should have contained nothing but two exactly similar spheres? We might suppose that each was made of chemically pure iron… and that nothing else existed. Then every quality and relational characteristic of the one would also be a property of the other. Now if what I am describing is logically possible, it is not impossible for two things to have all their properties in common. This seems to me to refute the principle (156). Here, A and B are essentially the same with respect to their properties. Thus, distinguishing between accidental and essential properties is irrelevant. Moreover, distinguishing between numerical identity and qualitative similarity is also irrelevant, since what is important are the qualities or properties that both A and B have in common, and not their numerical relation. The latter merely leads us to trivializing the issue. In addition, distinguishing between intrinsic and extrinsic properties also become irrelevant, since this possible world only contains these two spheres. Thus, the extrinsic properties of the spheres turn out to be the same; change in a sphere’s intrinsic property would correspond to a symmetrical change in the other sphere’s intrinsic property as well. Furthermore, the existence of a third party is ruled out from the picture, such as when a possible observer was put to question. This was maintained so as to emphasize that this possible world has only two spheres in it, and nothing more. So it seems that Black was successful in describing a possible world that seemed to refute the PII. Or was he unsuccessful in his attempt? It is in my contention that given the aforementioned thought experiment, Black fails to refute the PII. However, I shall suspend any judgments for the time being. I shall first introduce Zimmerman’s take on the said problem. Zimmerman’s Distinct Indiscernibles and The Bundle Theory Zimmerman agrees with Black insofar that a two-sphere-world where both spheres exist symmetrically towards each other, but are nevertheless two separate spheres altogether, is a possible world. He claims that the situation that Black describes is possible, “but it is a world in which a single bundle of universals—the universals of solidity, mass, shape, color, etc. collocated in one of the spheres— is at some distance from itself” (Zimmerman 306). Here, Zimmerman shows that the “bundle theory” is compatible with Black’s two-sphere world. Generally, the bundle theory posits that particulars can be reduced to universals, i.e. bundle of universals. It is formulated as follows: “Necessarily, for every particular x and every particular y, y constitutes x if and only if y is a universal and x instantiates y” (Rodriguez-Pereyra 72). Zimmerman defends the compatibility of the bundle theory by claiming that a single bundle of universals is at some distance from itself, that is to say, just like universals, it can be multiply located in more than one location at a time. So Black’s two-sphere world does not really contain two indiscernible particulars, but rather, one bundle of universals. This bundle is merely located in two different places, i.e. sphere A and B. Zimmerman provides a redescription of Black’s two-sphere world, which tells us: Suppose that nothing exists save two electrons – or if you like, that the same bundle of electronish properties appears on opposite sides of a symmetrical universe. Suppose further that electrons obey indeterministic laws. In that case, even though the electron on the one side is now indiscernible from the one on the other, it remains possible that differences will emerge later on – in other words, it is possible that this one should have a future differing from that one. And even in the case of an eternally symmetrical, two-electron universe in which differences never change, such differences were nonetheless possible… (306). Here, we see that Zimmerman’s example is quite similar to Black’s thought experiment, except that Zimmerman, accounts for “future” possibilities as opposed to Black. Nevertheless the significant point herein is that both philosophers aim to refute the PII, and to prove that it is false. In the next section, I shall show how Black and Zimmerman’s arguments fail when attempting to refute the PII of its necessity and significance. Failure of Black and Zimmerman: Refuting The Possibility of A Two-Sphere World As we can see now, Black begins by creating a thought experiment of a logically possible world, in order to prove the PII false. However, He does not mention anything about the nomological possibility of this two-sphere world. For as speaker-A argues, none of the characteristics of this possible world is verifiable, hence it must altogether be meaningless as a basis for refuting the PII. Moreover, we are given a scenario wherein two spheres share the exact same properties, wherein a change in one sphere corresponds to a symmetrical change in the other sphere. In fact, we are even restricted to describe these worlds for they are indistinguishable. Hence, it is impossible to come up with either a name for them, or a definite description. We are prohibited by a lot of factors in order to describe this world – even the mere fact of naming these worlds were not permitted due to its symmetrical nature. However, does this prove the PII false? “The impossibility of having definite descriptions for the objects in question does not prove the PII as false” (Foster 30). A major fallback in Black and Zimmerman’s arguments is its restriction in the involvement of a third agent, i.e. an outside observer. Black’s two-sphere world does not admit an observer to enter the scenario. However, that would miss the entire point altogether for the PII, the principle that Black and Zimmerman are refuting, is nonetheless dependent on an observer, otherwise, it is impossible for any judgments about similarity and/or difference to arise. An observer must necessarily be present in order to claim that these two spheres are identical or not. In fact, the threat of an observer destroying the symmetry of Black’s possible world is not so much of a threat if we imagine that there exists an observer inside each sphere. That way, we would have a description of each sphere, based on the observer’s description. Given that Black restricts any involvement of an observer, our understanding of his thought experiment is limited to what we cannot name or describe at all, which is our main tool for understanding to take place in this actual world. This barrier is a significant factor, and a pretty god tactic for Black, if I must say. Hence, even if we grant that this two-sphere world is indeed possible, it seems irrelevant as a basis for refuting the PII. For, the PII cannot apply in situations like this. It’s as if saying that if I wanted to refute the proposition “pigs float”, it wouldn’t be much use if I go to a place where there are no pigs and no water. Moreover, Black only discusses the possibility of a two-sphere symmetrical world, given that these two spheres exist independently from each other. That is to say, these two indistinguishable spheres are not mutually dependent for their existence. But what if one of the spheres dissolves? Would it make any difference with the existence of the remaining sphere? So it seems that it is also possible that only one, not two spheres existed after all, which thus explains the perfect symmetry between these two spheres. Perhaps, what appears to us, as a “two-sphere world” is merely a single-sphered world that has two distinct modes of presentation, yet is nevertheless the same sphere. One may want to consider Zimmerman’s bundle theory and his redescription of Black’s two-sphere world herein. For, he claims that “the situation Black describes is surely possible; but it is a world in which a single bundle of universals… is at some distance from itself” (Zimmerman 306). Here, he reduces the same properties that Black refers to, to that of immanent universals, which is always at some distance from itself, i.e. multiply located. Thus, not only does Zimmerman’s bundle theory compliment Black’s two-sphere world, but also, it further refutes the PII. But is Zimmerman successful? I believe not, for the bundle theory does not quite compliment Black’s two-sphere world, but rather, it compliments the PII. Thus, supposing that the possibility of Black’s two-sphere world proves the PII to be false, then “this means that the bundle theory is false as well, for the spheres of Black’s world instantiate exactly the same universals. So the possibility of Black’s world is taken to show that particulars are not bundles of universals” (Rodriguez-Pereyra 72-73). In other words, if the bundle theory is true, then the PII is a necessary truth. If the PII is a necessary truth, then there cannot be two distinct objects with exactly the same properties. The example of the two-sphere world proves to show that there could be two distinct objects with exactly the same properties. Therefore, the bundle theory is false. But why bother defending the PII in the first place, given all these counter-examples? Defending The Principle of Identity of Indiscernibles “The principle of the Identity of Indiscernibles seems to me obviously true. And I don’t see how we are going to define identity or establish the connection between mathematics and logic without using it” (Black 11). Indeed, speaker-A does have a point in claiming that the PII has its own fundamental value. In this section, I shall defend the PII against a Black and Zimmerman’s argument. We begin our defense from the alleged thought experiment by laying down its strongest premise, i.e. that each of the two spheres is at a distance from something, for it is in this manner that they are the same. But since these spheres have no names, Black argues that there are no particular properties that belong to these spheres. Rather, they share all their properties insofar that when one changes, the other changes as well. However, if the spheres have the all the same properties, and are at a distance from something, then it also implies that each sphere will also be a distance from the same thing. That is to say, that each sphere is at a distance from something is actually at a distance from the same thing. If so, then the relation of distance seems to be that nothing is at a distance from itself. But it cannot be that nothing is at a distance from itself, for that would lead to a contradiction, i.e. that two spheres are at a distance from itself and that nothing is at a distance from itself. Thus, we would have to revaluate the premise by which Black and Zimmerman shares in their refutation of the PII. For, in assuming that Black and Zimmerman were right in assuming that these two spheres are at distance from something or itself, we are thus led to a contradiction. Therefore, it is in my contention that although Black and Zimmerman created a thought experiment that aimed to refute the PII, such an experiment does not prove the PII false. Conclusion Take note that I am not saying that the PII is correct, but as far as Black and Zimmerman is concerned, their defense of a two-sphere world as a viable refutation against the PII is unfounded, and therefore invalid. Regardless of the possible weaknesses of the PII, it is a fact that it has proven its own merits, and has contributed to our present knowledge, such as its significance within the field of logic and mathematics. I believe that the question regarding the falsity of the PII is not what is of significance to us, but rather, its purpose and role in our metaphysical discourse. Michael Della Rocca (2005), for instance, argues that if we reject the PII, it would thus lead to an absurdity. Della Rocca argues that if PII is false, then the two spheres can differ with respect to numerical identity without differing in qualitative identity. And if the two spheres can differ in their numerical identity without differing in qualitative identity, then we can have two, or three, or a hundred spheres in exactly the same place all at once. That is to say, they can be primitively distinct. However, such a scenario is absurd. Therefore, the PII must be true. Nevertheless, the aforementioned argument is only one among the many arguments that defend the PII, not because it is correct, but it plays a significant role in our discourse. It is in this regard that by showing where Black and Zimmerman fails, I would have shown the significance of the principle in question. Perhaps it deserves another chance after all. Works Cited Black, Max. “The Identity of Indiscernibles.” Mind, New Series 61.242 (Apr., 1952) : 153-164. Print. Della Rocca, Michael. “Two Spheres, Twenty Spheres, and The Identity of Indiscernibles.” Pacific Philosophical Quarterly 86 (2005) : 480–92. Print. Forest, Peter. “The Identity of Indiscenibles.” The Stanford Encyclopedia of Philosophy (Spring, 2011). Ed. Edward N. Zalta. Web. 31 Mar. 2011. Foster, Thomas R. “The Identity of Indiscernibles.” Journal of Comprehensive Research 9 (2011) : 21-39. Web. 1 Apr. 2011. Rodriguez-Pereyra, Gonzalo. “The Bundle Theory is Compatible with Distinct but Indiscernible Particulars.” Analysis 64.1 (Jan., 2004) : 72-81. Print. Zimmerman, Dean W. “Distinct Indiscernibles and The Bundle Theory.” Mind, New Series 106.422 (Apr., 1997) : 305-309. Print. Read More