Gonzalo Rodriguez-Pereyra presents an original study of the place and role of the Identity of Indiscernibles in Leibniz's philosophy. The Principle of the Identity of Indiscernibles rules out numerically distinct but perfectly similar things; Leibniz derived it from more basic principles and used it to establish important philosophical theses. Rodriguez-Pereyra aims to establish what Leibniz meant by the Principle of Identity of Indiscernibles, what his arguments for and from it were, and to assess those arguments (...) and Leibniz's claims about the Principle of Identity of Indiscernibles. He argues that Leibniz had a very strong version of the principle, according to which no possibilia are intrinsically perfectly similar, where this excludes things that differ in magnitude alone. The book discusses Leibniz's arguments for the Identity of Indiscernibles in the Meditation on the Principle of the Individual, the Discourse on Metaphysics, Notationes Generales, Primary Truths, the letter to Casati of 1689, the correspondence with Clarke, as well as the use of the Identity of Indiscernibles in Leibniz's arguments against the Cartesian conception of the material world, atoms, absolute space and time, the Lockean conception of the mind as a tabula rasa, and freedom of indifference. Rodriguez-Pereyra argues that the Identity of Indiscernibles was a central but inessential principle of Leibniz's philosophy. (shrink)

This article discusses Heidegger’s interpretation of Parmenides given in his last public lecture ‘The Principle of Identity’ in 1957. The aim of the piece is to illustrate just how original and significant Heidegger’s reading of Parmenides and the principle of identity is, within the history of Philosophy. Thus the article will examine the traditional metaphysical interpretation of Parmenides and consider G.W.F. Hegel and William James’ account of the principle of identity in light of this. (...) It will then consider Heidegger’s contribution, his return to and re-interpretation of Parmenides in his last lecture. Heidegger will, through the Parmenidean claim that ‘Thinking and Being are one’ deconstruct the traditional metaphysical understanding of the principle of identity, and in its place offer a radically different conception of how our relationship, our ‘belonging together’ with Being can be understood. (shrink)

The aim of this paper is to render a detailed analysis of the correspondence with Clarke in order to shed some light in the relationship between the Principle of Identity of Indiscernibles and the Principle of Sufficient Reason. Most of the secondary literature takes for granted that Leibniz derives the Principle of Identity of Indiscernible from the Principle of Sufficient Reason in at least some parts of the correspondence. This would render the Principle (...) of Identity of Indiscernibles a merely contingent truth and not a necessary principle. I will argue that this interpretation is misleading, and that Leibniz never abandoned the idea that the Principle of Identity of Indiscernibles is a necessary truth. Although he is continuously using the Principle of Sufficient Reason in his argumentation, he keeps in parallel a strong argumentation that entails the necessity of the Principle of Identity of Indiscernibles. To achieve this goal, it will be necessary to point out first some contextual facts that may determine a correct understanding of the correspondence. It will be also necessary to frame the discussion about the principles into the broader debate on the possibility of Newtonian space. Finally, it will be shown that the mentioned hypothesis is supported by textual evidence throughout the entire correspondence. (shrink)

La plupart des commentateurs interprète le principe de l'identité des indiscernables comme principe purement logique, mais avec des implications métaphysiques, et donc, selon l'interprétation commune, comme fausseté ou vérité contingente ou triviale. Je soutiens, au contraire, que le principe, selon Leibniz, est vrai, mais que cette vérité n'est triviale ni contingente, mais nécessaire dans un sens métaphysique. Leibniz tent à démontrer la nécessité du principe dans deux manières : une manière logique et une manière métaphysique . Je soutiens que seule (...) la manière métaphysique peut réussir, et que la négligeance de cette manière aboutit au malentendu de ce principe. (shrink)

Leibniz was a philosopher of principles: the principles of Contradiction, of Sufficient Reason, of Identity of Indiscernibles, of Plenitude, of the Best, and of Continuity are among the most famous Leibnizian principles. In this article I shall focus on the first three principles; I shall discuss various formulations of the principles (sect. 1), what it means for these theses to have the status of principles or axioms in Leibniz’s philosophy (sect. 2), the fundamental character of the Principles of Contradiction (...) and Sufficient Reason (sect. 3), some attempts to demonstrate the Principles of Contradiction and Sufficient Reason (sect. 4), and one attempt to demonstrate the Principle of Identity of Indiscernibles (sect. 5). The main results of the chapter are summarized in a short conclusion (sect. 6). (shrink)

본 연구는 논리학 및 수리논리학의 토대 개념인 동일성 원리에 대한 역사적인 논쟁들의 교육학적 함의를 도출하는 것이다. 이때 필자가 사용할 중심 방법은 구조-구성주의 인식론이다. 따라서 필자는 구조-구성주의 인식론의 관점에서 동일성 원리에 대한 핵심 논쟁들을 역사-비판적으로 재구성함으로써, 필자가 지속적으로 논변해 온 구조-구성주의 교수학습이론의 확고한 토대를 제공하고자 한다. 이를 위해 본고는 동일성 원리에 대한 역사발생학적 탐구와 정신발생학적 탐구를 종합한다. 구체적인 내용은 피아제의 발생학적 인식론의 관점에서 논리적 개념들 및 공리화에 대한 프레게-러셀의 선험주의적 논리주의와 비트겐슈타인의 회의론적 유명론을 동시에 비판하면서, 구조-구성주의 인식론 및 이것의 교육학적 함의를 (...) 도출하는 것이다. 본고의 최종 결론은 이것이다. 논리적 법칙 또는 공리들은 초인적인 논리학자의 선험적인 직관에 의해서 구성된 것도 아니고, 유명론적 입장의 순수 기호게임으로 환원되는 것도 아니라, 정신 발달과 함께 발달되는 주체와 대상의 상호작용의 결과물, 즉 조작적 구조들의 형식화에 근거한다. 따라서 논리학적 개념들뿐만 아니라, 모든 일반적인 개념을 교육할 때, 교사는 실체와 술어, 개념과 판단, 판단과 추론 사이에 성립되는 미시적 상호의존성과 순환성뿐만 아니라, 이들 전체들 사이에 성립하는 거시적 상호의 존성과 순환성을 동시에 고려해야 한다. (shrink)

We discuss some logico-mathematical systems which deviate from classical logic and mathematics with respect to the concept of identity. In the first part of the paper we present very general formulations of the principle of identity and show how they can be ‘relativized’ to objects and to properties. Then, as an application, we study the particular cases of physics and logic . In the last part of the paper, we discuss the alphabar logics, that is, those logical (...) systems which violate a formulation of one of the most fundamental versions of the principle of identity; in these logics, there are formulas which are not deducible from themselves. (shrink)

It is argued that recent discussion of the principle of the identity of indiscernibles (PII) and quantum mechanics has lost sight of the broader philosophical motivation and significance of PII and that the `received view' of the status of PII in the light of quantum mechanics survives recent criticisms of it by Muller, Saunders, and Seevinck.

In Propositional Attitudes, Mark Richard claims that some natural and formal language sentences of the form(∀ x)(∀ y)(x = y → α → α [y/x])are false. He suggests a substitution for α that is sensitive to certain ancillary features of the variable letter as well as the assignment, and then argues that this substitution generates a false instance of the above-mentioned schema. I reject Richard's argument and argue further that the sentence is not an instance of that schema. I then (...) argue that his putative natural language example fails as well. Finally, I suggest that although Richard's mistake here does not present any technical problem for his semantics for attitude ascriptions, it undermines his claim that his semantic theory is better able to respect the surface form of attitude ascriptions in natural languages than competing theories. (shrink)

Most analysts agree that democratic theorists have not offered a persuasive answer to the question of how the boundaries of a demos, a democratic people, should legitimately be defined. Some contend that boundaries should be maintained in ways that preserve sufficient sense of common identity to sustain support for redistributive policies. Many others endorse the “principle of all affected interests,” but it has been widely criticized as unrealistically destructive of too many existing community boundaries. This essay argues for (...) an alternative “principle of constituted identities.” It holds that, subject to certain important qualifications, modern constitutional democracies, at least, are morally obligated to extend the option of full membership to all those whose identities have been substantially constituted through such regimes’ coercive policies. Keywords : civic boundaries; principle of affected interests; constitutional democracy; stories of peoplehood; cultural identity (Published online: 25 August, 2008) Citation: Ethics & Global Politics 2008. DOI: 10.3402/egp.v1i3.1860. (shrink)

I argue that, despite van Inwagen’s pessimism about the task, it is worth looking for answers to his General Composition Question. Such answers or ‘principles of composition’ tell us about the relationship between an object and its parts. I compare principles of composition with criteria of identity, arguing that, just as different sorts of thing satisfy different criteria of identity, they may satisfy different principles of composition. Variety in criteria of identity is not taken to reflect ontological (...) variety in the identity relation; I discuss whether variety in principles of composition should be taken to reflect ontological variety in the composition relation. (shrink)

There is a certain argument against the principle of the indiscernibility of identicals, or the thesis that whatever is true of a thing is true of anything identical with that thing. In this argument, PInI is used together with the self-evident principle of the necessity of self-identity to reach the conclusion, which is held to be paradoxical and, thus, fatal to PInI. My purpose is to show that the argument in question does not have this consequence. Further, (...) I argue that PInI is a universally valid principle which can be used to prove the necessity of identity. (shrink)

In 1907 Einstein had the insight that bodies in free fall do not “feel” their own weight. This has been formalized in what is called “the principle of equivalence.” The principle motivated a critical analysis of the Newtonian and special-relativistic concepts of inertia, and it was indispensable to Einstein’s development of his theory of gravitation. A great deal has been written about the principle. Nearly all of this work has focused on the content of the principle (...) and whether it has any content in Einsteinian gravitation, but more remains to be said about its methodological role in the development of the theory. I argue that the principle should be understood as a kind of foundational principle known as a criterion of identity. This work extends and substantiates a recent account of the notion of a criterion of identity by William Demopoulos. Demopoulos argues that the notion can be employed more widely than in the foundations of arithmetic and that we see this in the development of physical theories, in particular space–time theories. This new account forms the basis of a general framework for applying a number of mathematical theories and for distinguishing between applied mathematical theories that are and are not empirically constrained. (shrink)

The first principle of Fichte’s philosophy, the Wissenschaftslehre, is “I am,” whereas the logical principle of identity is “A is A.” The relationship of Fichte’s philosophy to logic helps us understand the relation between the principles of these two disciplines. The first principle of the Wissenschaftslehre as an Act (Thathandlung) is the ground of consciousness and therefore renders logic possible as a science. Even though logic is grounded on the Wissenschaftslehre, the form of logic is used (...) by the latter to comprehend itself. The difference between logic and the Wissenschaftslehre consists in the fact that the former merely supplies a form and the latter contains both the form and the content. Logic arises from the Wissenschaftslehre through the free acts termed “abstraction” and “reflection.” In the Wissenschaftslehre, the form of logical propositions as equality, affirmation and substitution, are derived from the primordial act of the self-positing of the I. (shrink)

James cornman and r routley and v macrae have argued that the principle of identity (alias leibniz's law) is inconsistent with certain plausible and widely accepted identity statements; e.G., "the temperature of a gas is identical with the mean kinetic energy of the molecules of the gas." they argue on this ground that the principle of identity should be modified to remove this appearance of inconsistency. The requisite modification however, Removes whatever "metaphysical teeth" the unmodified (...) version might have had. I argue in this paper that such attacks on the principle of identity are utterly unwarranted. (shrink)

The Principle of the Identity of Indiscernibles —the principle that no two numerically distinct things are perfectly similar—features prominently in Leibniz’s metaphysics. Despite its centrality to his philosophical system, it is surprisingly difficult to determine what modal status Leibniz ascribes to the PII. On many occasions Leibniz appears to endorse the necessity of the PII. There are a number of passages,however, where Leibniz seems to imply that numerically distinct indiscernibles are possible, which suggests that he subscribes to (...) a merely contingent version of the PII. In this paper I attempt to resolve this apparent inconsistency. I argue that Leibniz consistently takes the PII to be necessary and that this view of his shines through even in his correspondence with Clarke. I also show that competing interpretations, on which Leibniz’s PII is contingent, misread a number of crucial passages from this correspondence. (shrink)

Faced with strong arguments to the effect that Leibniz''sPrinciple of the Identity of Indiscernibles (PII) is not a necessary truth, many supporters of the Principle have staged a strategic retreat to the claim that it is contingently true in this, the actual, world. The purpose of this paper is to examine the status of the various forms of PII in both classical and quantum physics, and it is concluded that this latter view is at best doubtful, at worst, (...) simply wrong. (shrink)

One of the key questions in the contemporary analytic ontology concerns the relation between the Principle of Identity of Indiscernibles (PII) and the Bundle Theory (BT). The majority of authors believe that BT implies PII. Therefore, it is widely believed that the world violating PII presented by Max Black (1952. “The Identity of Indiscernibles.” Mind 61 (242): 153–64) is also devastating for BT. However, this has been questioned by Rodriguez-Pereyra (2004. “The Bundle Theory is Compatible with Distinct (...) but Indiscernible Particulars.” Analysis 64 (1): 72–81), who formulated an interpretation of BT with instances. Recently Robert (2019. “Can the Realist Bundle Theory Account for the Numerical Difference between Qualitavely Non-discernible Concrete Particulars?” Theorema 38 (1): 25–39) argued that this version of BT is not a constituent ontology and, therefore, Rodriguez-Pereyra’s solution comes at a price of excluding bundle theory from the domain of constituent ontologies, and, in this sense, it fails. I question Robert’s point by claiming that his account of constituent ontologies is too demanding. In particular, I show that the instance version of BT is compatible with the constrains defining constituent ontologies in general, and therefore Rodriguez-Pereyra’s argument is correct. (shrink)

In considering the possibility that the fundamental particles of matter might violate Leibniz's Principle, one is confronted with logical proofs that the Principle is a Theorem of Logic. This paper shows that the proof of that theorem is not universal enough to encompass entities that might not be unique, and also strongly suggests that photons, for example, do violate Leibniz's Principle. It also shows that the existence of non-individuals would imply the breakdown of Quine's criterion of ontological (...) commitment. (shrink)

This book brings together the debate concerning personal identity and central topics in biomedical ethics. Based on a metaphysical account of personal identity in the sense of persistence and conditions for human beings, conceptions for beginning of life, and death are developed. Based on a biographical account of personality, normative questions concerning autonomy, euthanasia, living wills and medical paternalism are dealt with. By these means the book shows that “personal identity” has different meanings which have to be (...) distinguished so that human persistence and personality can be used to deal with central questions in biomedical ethics. (shrink)

Klimuk I. M. The methodological principles of the study of religious identity.The article deals with the problem of religious identity, which become more intense in the world and needs to determine the principles of the study of this phenomenon.

Can the persistence of a human being's soul at death and prior to the bodily resurrection be sufficient to guarantee that the resurrected human being is numerically identical to the human being who died? According to Thomas Aquinas, it can. Yet, given that Aquinas holds that the human being is identical to the composite of soul and body and ceases to exist at death, it's difficult to see how he can maintain this view. In this paper, I address Aquinas's response (...) to this objection . After making a crucial clarification concerning the nature of the non-repeatability principle on which the objection relies, I argue that the contemporary notion of immanent causal relations provides us with a way of understanding Aquinas's defence that renders it both highly interesting and philosophically plausible. (shrink)

First published in 1903, _Principles of Mathematics_ was Bertrand Russell’s first major work in print. It was this title which saw him begin his ascent towards eminence. In this groundbreaking and important work, Bertrand Russell argues that mathematics and logic are, in fact, identical and what is commonly called mathematics is simply later deductions from logical premises. Highly influential and engaging, this important work led to Russell’s dominance of analytical logic on western philosophy in the twentieth century.

First published in 1903, _Principles of Mathematics_ was Bertrand Russell’s first major work in print. It was this title which saw him begin his ascent towards eminence. In this groundbreaking and important work, Bertrand Russell argues that mathematics and logic are, in fact, identical and what is commonly called mathematics is simply later deductions from logical premises. Highly influential and engaging, this important work led to Russell’s dominance of analytical logic on western philosophy in the twentieth century.

In discussions about whether the Principle of the Identity of Indiscernibles is compatible with structuralist ontologies of mathematics, it is usually assumed that individual objects are subject to criteria of identity which somehow account for the identity of the individuals. Much of this debate concerns structures that admit of non-trivial automorphisms. We consider cases from graph theory that violate even weak formulations of PII. We argue that (i) the identity or difference of places in a (...) structure is not to be accounted for by anything other than the structure itself and that (ii) mathematical practice provides evidence for this view. We want to thank Leon Horsten, Jeff Ketland, Øystein Linnebo, John Mayberry, Richard Pettigrew, and Philip Welch for valuable comments on drafts of this paper. We are especially grateful to Fraser MacBride for correcting our interpretation of two of his papers and for other helpful comments. CiteULike Connotea Del.icio.us What's this? (shrink)

The relationship of the identity of indiscernibles principle to other major metaphysical principles (e.g., relational doctrine of space and time, elimination of singular terms) is discussed, the aim being to outline the necessary requirements of a systematic metaphysics incorporating the former principle. the conclusion is that no adequate systematic metaphysics of this sort is defensible. throughout special attention is paid to modern logical formulation of the principle and to its role in quine's philosophy.

Published in 1903, this book was the first comprehensive treatise on the logical foundations of mathematics written in English. It sets forth, as far as possible without mathematical and logical symbolism, the grounds in favour of the view that mathematics and logic are identical. It proposes simply that what is commonly called mathematics are merely later deductions from logical premises. It provided the thesis for which _Principia Mathematica_ provided the detailed proof, and introduced the work of Frege to a wider (...) audience. In addition to the new introduction by John Slater, this edition contains Russell's introduction to the 1937 edition in which he defends his position against his formalist and intuitionist critics. (shrink)

we propose a revised version of Black's original argument against the principle of identity of indiscernibles. Our aim is to examine a puzzle regarding the intuitiveness of arguments, by showing that the revised version is clearly less intuitive than Black's original one, and appears to be unjustified by our ordinary means of assessment of intuitions.

The Principle of Sufficient Reason is very seldom, if ever, referred to in the works of whom we might think of as the eminent Asian metaphysicians. In spite of this, the big picture metaphysical views available in the thought of philosophers such as Nāgārjuna, Fazang and Nishida appear to share certain structural features with views more familiar to us from our own tradition; views that explicitly accept or reject the Principle of Sufficient Reason. Nāgārjuna looks to develop a (...) kind of metaphysical infinitism, Fazang an extreme form of coherentism, and Nishida a species of foundationalism. These three positions - infinitism, coherentism and foundationalism - are typically thought to exhaust the spread of possibilities by those working within the Western tradition. -/- In spite of their similarities to positions advanced within our own tradition, the cosmologies of many of the giants of Asian philosophy are characterised by their rather striking conclusions. Amongst such conclusions for Nāgārjuna is that everything is empty; for Fazang that everything is identical to everything else; and for Nishida that everything depends on absolute nothingness. If the Principle of Sufficient Reason is playing a role in the derivation of such striking conclusions, then it looks that there are more options regarding the metaphysical structure of the world available to us than our own tradition typically courts. If, on the other hand, these striking cosmological conclusions are arrived at without any consideration of sufficient reason, then there may well be ways of reasoning about the overarching structure of reality that are powerful but unfamiliar to Western thinking. In this contribution, I explore what, if any, role the PSR might be playing in the thought of Nāgārjuna , Fazang and Nishida, and what we might be able to learn from it. (shrink)

This article attempts to bring some questions proposed by Hegel on the philosophy of Leibniz, in view of the considerations of this with respect to Principles of Philosophy or Monadology. Specifically, the question to be addressed is about reading proposed by Hegel around the whole notion of Monad in order to clarify some thoughts on this concept and how this comes within the second part of the Science of Logic, namely, the Doctrine of the Concept. The question posed is affiliated (...) with two separate issues: the principle of sufficient reason and principle of identity. We should consider ultimately the thought of Leibniz proposes a philosophy for the reasoning of the individual, and the experience of identity and difference are still, albeit insufficient author Monadology. (shrink)

이 논문은 아도르노 철학의 핵심 문제 중 하나인 정신과 자연의 화해가능성을 해명하기 위하여 정신을 동일성 및 친화성 원칙 속에서 규정한다. 이를 위한 근거가 되는 것은 정신의 자연사적 기원에 관한 아도르노의 두 가지 테제(“정신은 자기보존에서 발생했다”와 “미메시스는 정신의 생리학적 전형식이다”)이며, 이에 따라 정신은 각각 동일성 그리고 친화성 원칙 속에서 파악될 수 있다. 상세한 고찰 속에서 밝혀질 바는 이 개념들의 양의성 및 상호지시성이다. 아도르노에게 있어 동일성은 자기보존 및 자연지배의 수단이지만 동시에 화해적 잠재력의 담지자라는 이중의 사실을 의미한다. 그러나 동일성의 틀 안에 갇혀 있는 (...) 한 정신은 자신과 타자의 근원적 관계를 충분히 자각할 수 없다는 한계에 노출된다. 마찬가지로 친화성 개념 또한 이중적인데, 한편으로 그것은 합리성의 타자로서 퇴행을 의미하지만 다른 한편 동일성 정신을 질적으로 변화시킴으로써 그것을 타락에서 구제해줄 해방의 계기이기 때문이다. 그러나 친화성, 미메시스적 태도는 특유의 맹목성으로 인하여 혼자서는 결코 화해와 해방을 보증할 수 없다. 이러한 양의성은 따라서 동일성 정신의 자기 반성과 타자에로의 개방은 함께 이루어져야만 함을 암시한다. 즉 아도르노는 저 두 가지의 과제가 하나의 정신이 수행하는 하나의 행위임을 보고 있는 것이다. 오직 이속에서만 자연과의 화해를 통한 정신의 자기 해방이 가능해진다. (shrink)