Identity Of Indiscernibles Research Articles

Omnidesire as the Ending of Desire: Zarathustra, Mahāyāna Buddhism, Tiantai

ABSTRACT Nietzsche's Thus Spoke Zarathustra is a work that bears comparison to Mahāyāna Buddhist literature in more ways than one. Nietzsche was turning against the Schopenhauerian doctrine of the denial of the will, which he read as symptomatic of a larger nihilistic trend swallowing up almost all existing spiritual culture, while the Mahāyāna was turning against the world-denying implications of the doctrine of Nirvana as the ending of desire and samsara that was so central to early Buddhism. In this article, I explore one move made in both of these cases: the move from total negation to total affirmation seen as a convergence of these two apparently opposed extremes. Of central interest here is the “identity of indiscernibles” that applies structurally to these two opposite extremes, “willing nothing” and “willing everything,” with the latter effected only through “willing one thing intensely,” at once excluding and including all other things, and its liberative potential.

The Identity of Indiscernibles

AbstractA number of distinctions are needed to assess The Identity of Indiscernibles. The first concerns its purported status as true or, more strongly, necessarily true. The second concerns the nature of the properties the principle ranges over. One way to divide up properties is in terms of those that entail the existence of a particular object, those that entail the existence of an object but no particular object, and those that don't entail the existence of an object at all. A second way is divide up properties is in terms of ‘indicative’ and ‘counterfactual’ properties. Combining these three distinctions yields twelve different versions of the Identity of Indiscernibles. In the long run, however, four more are needed to do the principle justice. Sixteen different versions of the principle, then, need to be, and in this paper are, assessed. Particular attention is paid to methodology and to constraints on the generation of properties needed to support various versions of the principle. Bottom-up reasoning is found sufficient to vindicate the great majority of them, but there does not appear to be a good bottom-up or top-down argument for the two most interesting and important versions of the Identity of Indiscernibles, and there is some reason to think both false. An open mind needs to be kept, however, for definitively establishing or refuting them probably requires a relatively complete and plausible metaphysics.

Back to Black

AbstractThis is a brief sequel to Max Black's classic dialogue on the Identity of Indiscernibles. Interlocutor A defends the bundle theory by endorsing the (by now popular) view according to which Black's world does not contain two indiscernible spheres but rather a single, bi‐located sphere. His opponent, B, objects that A cannot distinguish such a world from a world with a single, uniquely located sphere, hence that the view in question adds nothing to A's original response to Black's challenge. A is simply denying that there can be worlds with two or more indiscernible entities.

Similarity-Preserving Binary Signature for Linear Subspaces

Linear subspace is an important representation for many kinds of real-world data in computer vision and pattern recognition, e.g. faces, motion videos, speeches. In this paper, first we define pairwise angular similarity and angular distance for linear subspaces. The angular distance satisfies non-negativity, identity of indiscernibles, symmetry and triangle inequality, and thus it is a metric. Then we propose a method to compress linear subspaces into compact similarity-preserving binary signatures, between which the normalized Hamming distance is an unbiased estimator of the angular distance. We provide a lower bound on the length of the binary signatures which suffices to guarantee uniform distance-preservation within a set of subspaces. Experiments on face recognition demonstrate the effectiveness of the binary signature in terms of recognition accuracy, speed and storage requirement. The results show that, compared with the exact method, the approximation with the binary signatures achieves an order of magnitude speed-up, while requiring significantly smaller amount of storage space, yet it still accurately preserves the similarity, and achieves high recognition accuracy comparable to the exact method in face recognition.

Indiscernibles and Plato’s Forms vs. Parmenides

In Parmenides, the young Socrates defends several candidate forms against Parmenides, who makes five objections: the objection of forms of common things, the question of the part vs. the whole, the third man argument, infinite regress, and the greatest difficulty problem. I define forms in terms of Leibniz’s Principle of the Identity of Indiscernibles (PII) in an attempt to overcome Parmenides’ opposition. I show that the main force in Parmenides’ objections consists of absurdities that emerge in relations between forms and particulars: absurdities that are avoided if the form and its instantiation in the particular are identical.

On Bauckham’s Bargain

Richard Bauckham argues that every book in the New Testament contains a “christology of divine identity,” according to which Jesus is “included in the divine identity.” He also argues that traditional Christians may avoid or dissolve a large number of theoretical problems by embracing this thesis. Here I clarify the concepts of personal identity, numerical identity, and identifying features, and critically examine Bauckham’s thesis and his arguments for it in light of these analyses. Of central importance is the self-evident truth that a thing cannot at one time differ from itself (the indiscernibility of identicals). It is argued that Bauckham’s thesis is unclear, and that on one interpretation it is manifestly self-inconsistent, while on the other it is too thin in content to do the work Bauckham assigns it, which is expressing “the highest possible christology.” I thus argue that the theoretical costs of Bauckham’s theory outweigh its theoretical benefits. Section I summarizes the touted benefits. Section II clarifies the aforementioned concepts. Section III applies these analyses to Bauckham’s work. In Section IV I weigh some reasons for thinking that the interpretation of Section III is mistaken. Section V continues the interpretive struggle, and VI draws a negative conclusion.

An Explanation of Complete Colocation of Indiscernibles

The Principle of the Identity of Indiscernibles (PII) claims that objects that share all of the same properties are the same object. If this claim is denied, then, as is commonly believed, the denier must accept the possibility of objects completely overlapping in space. Michael Della Rocca argues that this possibility is absurd, and therefore PII should be accepted. He claims that the problem with colocated objects lies in the inexplicability of the distinctness of the objects. This inexplicability, he argues, is contrary to the brute fact method of demonstrating the distinctness of objects in counterexamples to PII. Without any other method for demonstrating distinctness of qualitatively indiscernible objects deniers of PII are simply begging the question when they posit the possibility of distinct indiscernibles. I argue in this paper that a clear understanding of the different ways that objects can be colocated removes the counterintuitiveness of colocation, and thereby supports the denial of PII.

The Rumble in the Bundle

In 1952, two well-known characters called 'A' and 'B' met for the first time to argue about the Identity of Indiscernibles (Black, 1952). A argued that the principle is true, and B that it is false. By all accounts A took a bit of a beating and came out worst-off. Forty-three years later John O’Leary-Hawthorne offered a response on behalf of A that looked as if it would work so long as A was willing to accept the universal-bundle theory of substance (Hawthorne, 1995). In 1997, A and B met again (Zimmerman, 1997). A took Hawthorne's advice and revealed himself as a universal-bundle theorist. But B was well-prepared, and once more A took a beating. Since then Gonzalo Rodriguez-Pereyra (2004) has put the boot in, offering further criticism of A's position. In recent years A has been rather quiet, leaving B to reign as the undisputed champion. However, it turns out that A is down, but not out. And now it's time for A's revenge.

Weak Discernibility in Quantum Mechanics: Does It Save PII?

The Weak Principle of the Identity of Indiscernibles (weak PII), states that numerically distinct items must be discernible by a symmetrical and irreflexive relation. Recently, some authors have proposed that weak PII holds in non relativistic quantum mechanics, contradicting a long tradition claiming PII to be simply false in that theory. The question that arises then is: are relations allowed in the scope of PII? In this paper, we propose that quantum mechanics does not help us in deciding matters concerning that problem, since that is a metaphysical problem rather than a quantum mechanical one. We argue further that weak PII is unmotivated on metaphysical grounds. We examine three metaphysical theses (bundle theory, counting, empiricism) that may provide reasons for one to sustain PII, and we conclude that weak PII gets no independent motivation from them.

Leibniz’s Argument for the Identity of Indiscernibles in his Letter to Casati (with Transcription and Translation)

Leibniz’s Argument for the Identity of Indiscernibles in his Letter to Casati (with Transcription and Translation)

The Relationist and Substantivalist Theories of Time: Foes or Friends?

Abstract: There are two traditionally rival views about the nature of time: substantivalism that takes time to be a substance that exists independently of events located in it, and relationism that takes time to be constructed out of events. In this paper, first, I want to make some progress with respect to the debate between these two views, and I do this mainly by examining the strategies they use to face the possibilities of ‘empty time’ and ‘time without change’. As we shall see, the two allegedly very different rival views are much less different than has been thought: their structure is extremely similar, their strategies are extremely similar, and they can both face the possibilities of ‘empty time’ and ‘time without change’ in the same way. Thus, I argue in favour of a certain kind of equivalence between the two views; I discuss a Strong and a Weak version of this claim; and I provide reasons for endorsing the former. I also discuss the parallel between this pair of views about the nature of time and another analogous pair of views: the bundle theory and the substratum theory about the nature of material objects, with respect to the problem with Identity of Indiscernibles.

Modal Objection to Naive Leibnizian Identity

This essay examines an argument of perennial importance against naive Leibnizian absolute identity theory, originating with Ruth Barcan in 1947 (Barcan, R. 1947. ‘The identity of individuals in a strict functional 3 calculus of second order’, Journal of Symbolic Logic, 12, 12–15), and developed by Arthur Prior in 1962 (Prior, A.N. 1962. Formal Logic. Oxford: The Clarendon Press), presented here in the form offered by Nicholas Griffin in his 1977 book, Relative Identity (Griffin, N. 1977. Relative Identity. Oxford: The Clarendon Press). The objection considers the property of being necessarily identical to a specific object a as a counterexample to Leibnizian identity conditions, and more particularly to the indiscernibility of identicals, when it is only contingently true that a=b. The inquiry eliminates necessity and reference to a specifically designated object as responsible for the counterexample, leaving only identity. The requirements for an exact reinterpretation of Leibniz's Law in light of counterexamples involving converse intentional properties and the family of properties suggested by the property of being necessarily identical to a where a=b (or an equivalent definite descriptor variation) is only logically contingently true, are formalized in a more powerful, counterexample-resistant version of Leibniz's Law that does not succumb to relative identity as a necessary alternative motivated by desperation over the failure of the absolute identity principle.

Ontic Structural Realism and the Principle of the Identity of Indiscernibles

Recently, there has been a debate as to whether or not the principle of the identity of indiscernibles (the PII) is compatible with quantum physics. It is also sometimes argued that the answer to this question has implications for the debate over the tenability of ontic structural realism (OSR). The central aim of this paper is to establish what relationship there is (if any) between the PII and OSR. It is argued that one common interpretation of OSR is undermined if the PII turns out to be false, since it is committed to a version of the bundle theory of objects, which implies the PII. However, if OSR is understood as the physical analogue of (sophisticated) mathematical structuralism then OSR does not imply the PII. It is further noted that it is (arguably) a virtue of OSR that it is compatible with a version of the PII for possible worlds.

Teaching & Learning Guide for: Essentialism

Teaching & Learning Guide for: Essentialism

BRUTE FACTS, THE NECESSITY OF IDENTITY, AND THE IDENTITY OF INDISCERNIBLES

AbstractIn ‘Two Spheres, Twenty Spheres, and the Identity of Indiscernibles,’ Della Rocca argues that any counterexample to the PII would involve ‘a brute fact of non‐identity [. . .] not grounded in any qualitative difference.’ I respond that Adams's so‐called Continuity Argument against the PII does not postulate qualitatively inexplicable brute facts of identity or non‐identity if understood in the context of Kripkean modality. One upshot is that if the PII is understood to quantify over modal as well as non‐modal properties, the qualitative explicability of numerical distinctness requires not the PII but a principle of the identity of necessary indiscernibles.

On some putative graph-theoretic counterexamples to the Principle of the Identity of Indiscernibles

Recently, several authors have claimed to have found graph-theoretic counterexamples to the Principle of the Identity of Indiscernibles (PII). In this paper, I argue that their counterexamples presuppose a certain view of what unlabeled graphs are, and that this view is optional at best.

Alternative splicing variability: exactly how similar are two identical cells?

Alternative splicing variability: exactly how similar are two identical cells?

Individuation in Quantum Mechanics and Space-Time

Two physical approaches—as distinct, under the classification of Mittelstaedt, from formal approaches—to the problem of individuation of quantum objects are considered, one formulated in spatiotemporal terms and one in quantum mechanical terms. The spatiotemporal approach itself has two forms: one attributed to Einstein and based on the ontology of space-time points, and the other proposed by Howard and based on intersections of world lines. The quantum mechanical approach is also provided here in two forms, one based on interference and another based on a new Quantum Principle of Individuation (QPI). It is argued that the space-time approach to individuation fails and that the quantum approach offers several advantages over it, including consistency with Leibniz’s Principle of Identity of Indiscernibles.

Individuation in Quantum Mechanics

It has been claimed that the Principle of the Identity of Indiscernibles (PII) is incompatible with quantum mechanics, considered as a complete theory. Van Fraassen has argued specifically that a conflict between the two arises due to the requirements of Bose-Einstein statistics when imposed on two-particle quantum states. It is shown here that this apparent contradiction of the PII with quantum mechanics can be removed by the introduction of a natural criterion of individuality.

God Interrupted: Heresy and the European Imagination between the World Wars. By Benjamin Lazier

God Interrupted: Heresy and the European Imagination between the World Wars. By Benjamin Lazier