What is the relation between some things and the set of these things? Mathematical practice does not provide a univocal answer. On the one hand, it relies on ordinary plural talk, which is implicitly committed to a traditional form of plural logic. On the other hand, mathematical practice favors a liberal view of definitions which entails that traditional plural logic must be restricted. We explore this predicament and develop a “critical” alternative to traditional (...) class='Hi'>plural logic. (shrink)

In this Critical Notice on Oliver and Smiley's Plural Logic, I defend the dominant paradigm in the semantics of plurals among linguists against several objections Oliver and Smiley raise, focusing especially on the proper treatment of plural definite descriptions, the threat posed by Russell's paradox, and the notion of objecthood.

Plural expressions found in natural languages allow us to talk about many objects simultaneously. Plural logic — a logical system that takes plurals at face value — has seen a surge of interest in recent years. This book explores its broader significance for philosophy, logic, and linguistics. What can plural logic do for us? Are the bold claims made on its behalf correct? After introducing plural logic and its main applications, the book (...) provides a systematic analysis of the relation between this logic and other theoretical frameworks such as set theory, mereology, higher-order logic, and modal logic. The applications of plural logic rely on two assumptions, namely that this logic is ontologically innocent and has great expressive power. These assumptions are shown to be problematic. The result is a more nuanced picture of plural logic's applications than has been given thus far. Questions about the correct logic of plurals play a central role in the final chapters, where traditional plural logic is rejected in favor of a "critical" alternative. The most striking feature of this alternative is that there is no universal plurality. This leads to a novel approach to the relation between the many and the one. In particular, critical plural logic paves the way for an account of sets capable of solving the set-theoretic paradoxes. (shrink)

This chapter provides an overview of the philosophical and linguistic debate about the logic of plurals. We present the most prominent singularizing analyses of plurals as well as the main criticisms that such analyses have received. We then introduce an alternative approach to plurals known as plural logic, focusing on the question whether plural logic can count as pure logic.

I first show that most authors who developed Plural Quantification Logic (PQL) argued it could capture various features of natural language better than can other logic systems. I then show that it fails to do so: it radically departs from natural language in two of its essential features; namely, in distinguishing plural from singular quantification and in its use of an relation. Next, I sketch a different approach that is more adequate than PQL for capturing (...) class='Hi'>plural aspects of natural language semantics and logic. I conclude with a criticism of the claim that PQL should replace natural language for specific philosophical or scientific purposes. (shrink)

1960년대에 집중적으로 제기된 논리경험주의에 대한 대다수의 철학적 공격은 이른바 논리경험주의의 ‘수용된 견해’를 향한 것이었고, 이후 과학철학자들이 공공연히 ‘논리경험주의는 죽었다’라는 표현을 쓸 정도로까지 논리경험주의 과학철학의 위상은 낮아졌다. 문제는 이와 같은 논리경험주의의 ‘수용된 견해’가 대부분 비엔나 학파를 대표하는 카르납의 철학적 관점을 반영하고 있다는 데 있다. 최근의 논리경험주의에 대한 역사철학적 탐구가 보여주듯, 논리경험주의 내에 다양성이 존재했고 특히 카르납으로 대표되는 비엔나 학파와 라이헨바흐로 대표되는 베를린 학파 사이에는 중요한 철학적 입장의 차이가 있었다. 만약 우리가 라이헨바흐의 과학철학적 입장을 카르납과 비견될 만한 논리경험주의의 중요한 인식론적 입장이라고 간주한다면, (...) 과연 그의 입장이 이후 논리경험주의에 대해 제시된 각종 비판을 견딜 수 있는지 다시 점검해 볼 필요가 있다. 이를 위해 우선 나는 논리경험주의의 입장과 이에 대한 비판을 체계적으로 정리하는 과학철학자 수피(Suppe)의 논의를 검토한 후, 논리경험주의에 대한 후대 철학자들의 비판이 결정적이지는 않았음을 보인다. 다음으로 나는 ‘과학적 철학’ 개념, ‘발견의 맥락’과 ‘정당화의 맥락’ 구분, ‘과학 이론의 합리적 재구성’, ‘과학자와 철학자의 노동 분업’ 등 논리경험주의의 주요 인식론적 논제에 관한 라이헨바흐의 입장을 재구성한다. 이러한 재구성을 통해 나는, 라이헨바흐의 인식론적 입장이 구체적인 과학 이론의 인식론적 의의와 함축을 도출해내는데 있어 여전히 유효한 입장이라는 것을 보일 것이다. 실제로 라이헨바흐가 주장한 ‘이론 구체적인 인식론적 분석’은 오늘날에도 여전히 유용하고 필요한 철학적 방법론이며, 이 방법론은 논리경험주의에 반대하면서 얻어진 것이 아니라 논리경험주의가 오늘날의 과학철학에 남긴 소중한 유산이라고 보아야 한다. (shrink)

This paper criticizes George Boolos's famous use of plural quantification to argue that monadic second-order logic is pure logic. I deny that plural quantification qualifies as pure logic and express serious misgivings about its alleged ontological innocence. My argument is based on an examination of what is involved in our understanding of the impredicative plural comprehension schema.

Plural logic is widely assumed to have two important virtues: ontological innocence and determinacy. It is claimed to be innocent in the sense that it incurs no ontological commitments beyond those already incurred by the first-order quantifiers. It is claimed to be determinate in the sense that it is immune to the threat of non-standard interpretations that confronts higher-order logics on their more traditional, set-based semantics. We challenge both claims. Our challenge is based on a Henkin-style semantics for (...) plural logic that does not resort to sets or set-like objects to interpret plural variables, but adopts the view that a plural variable has many objects as its values. Using this semantics, we also articulate a generalized notion of ontological commitment which enables us to develop some ideas of earlier critics of the alleged ontological innocence of plural logic. (shrink)

In linguistics, the dominant approach to the semantics of plurals appeals to mereology. However, this approach has received strong criticisms from philosophical logicians who subscribe to an alternative framework based on plural logic. In the first part of the article, we offer a precise characterization of the mereological approach and the semantic background in which the debate can be meaningfully reconstructed. In the second part, we deal with the criticisms and assess their logical, linguistic, and philosophical significance. We (...) identify four main objections and show how each can be addressed. Finally, we compare the strengths and shortcomings of the mereological approach and plural logic. Our conclusion is that the former remains a viable and well-motivated framework for the analysis of plurals. (shrink)

The article covers such issues as the relevance of the theory of perception as a multi-level information processing, the methodological role of the concept of representation and the relation of neurodynamic structures to subjective experience. The author critically reviews the philosophical presumptions underlying the various concepts of “local rationality,” the core of which is constituted by the belief that large ethnic cultures generate or are based on their own rationality and their own logic. Three statements are successively considered: thinking (...) is based on the inherent rules of rationality, logic is an extract of rationality, and types of rationality are geographically consistent with large ethnocultural communities. Empirical arguments are presented that demonstrate equivocality of the first two theses. In particular, firstly, it is shown that the genuine rationality of thinking lies not in following the rules that are immanent to it, but in the development of thinking and, more broadly, cognitive operations towards optimization of certain indicators of the cognitive or motor system that are important for survival and adaptation. In addition, this rationality is multivariate, and the choice between variants is often weakly determined or even random. Thus, the first statement turns out to be refuted. Secondly, by reference to the well-known experiments, it is shown that most people do not explicitly follow some declared logical rules in solving even logical or mathematical problems, and yet there is reason to consider their behavior rational. The third thesis, as shown with some limited empirical material, appears to be partially confirmed. Nevertheless, the demonstration of the doubtfulness of the first two theses makes the conclusion that different nations have different logics insufficiently substantiated. (shrink)

A plurality or plural object is a single object that is also many, and pluralitism is the thesis that there is such an object. This paper argues that pluralitism and closely related theses (e.g., the many-one identity thesis and the composition as identity thesis) violate logic. To do so, it formulates an approach to the logic and semantics of plural constructions that results in plural logic and relates treatments of plural constructions to accounts (...) of natural number. And it gives a critical examination of Frege’s views of numbers and plural constructions, and sketches the view of plural constructions as devices for talking about the many (as such), and an account of natural numbers as properties of a special kind, plural properties. (shrink)

Mereological universalists and nihilists disagree on the conditions for composition. In this paper, we show how this debate is a function of one’s chosen semantics for plural quantifiers. Debating mereologists have failed to appreciate this point because of the complexity of the debate and extraneous theoretical commitments. We eliminate this by framing the debate between universalists and nihilists in a formal model where these two theses about composition are contradictory. The examination of the two theories in the model brings (...) clarity to a debate in which opponents frequently talk past one another. With the two views stated precisely, our investigation reveals the dependence of the mereologists’ ontological commitments on the semantics of plural quantifiers. Though we discuss the debate with respect to a simplified and idealized model, the insights provided will make more complex debates on composition more productive and deflationist criticisms of the debate less substantial. (shrink)

Responding to the increasingly influential role of Hannah Arendt's political philosophy in recent years, Hannah Arendt and the Limits of Total Domination: The Holocaust, Plurality, and Resistance, critically engages with Arendt's understanding of totalitarianism. According to Arendt, the main goal of totalitarianism was total domination; namely, the virtual eradication of human legality, morality, individuality, and plurality. This attempt, in her view, was most fully realized in the concentration camps, which served as the major "laboratories" for the regime. While Arendt focused (...) on the perpetrators' logic and drive, Michal Aharony examines the perspectives and experiences of the victims and their ability to resist such an experiment. The first book-length study to juxtapose Arendt's concept of total domination with actual testimonies of Holocaust survivors, this book calls for methodological pluralism and the integration of the voices and narratives of the actors in the construction of political concepts and theoretical systems. To achieve this, Aharony engages with both well-known and non-canonical intellectuals and writers who survived Auschwitz and Buchenwald concentration camps. Additionally, she analyzes the oral testimonies of survivors who are largely unknown, drawing from interviews conducted in Israel and in the U.S., as well as from videotaped interviews from archives around the world. Revealing various manifestations of unarmed resistance in the camps, this study demonstrates the persistence of morality and free agency even under the most extreme and de-humanizing conditions, while cautiously suggesting that absolute domination is never as absolute as it claims or wishes to be. Scholars of political philosophy, political science, history, and Holocaust studies will find this an original and compelling book. (shrink)

According to the logical pluralism of Beall and Restall, there are several distinct relations of logical consequence. Some critics argue that logical pluralism suffers from what I call the collapse problem: that despite its intention to articulate a radically pluralistic doctrine about logic, the view unintentionally collapses into logical monism. In this paper, I propose a contextualist resolution of the collapse problem. This clarifies the mechanism responsible for a plurality of logics and handles the motivating data better than the (...) original view. It is a major improvement that should be embraced by all logical pluralists. (shrink)

To commemorate the centenary of Ernst Cassirer's Philosophy of Symbolic Forms this essay focuses on how Cassirer in the development of a distinctive philosophical method analyzed the newest development within philosophy and science. Discussing Einstein's theory of relativity and Russell's formal logic Cassirer found tools to expand the critique of reason into a critique of culture. The course of argumentation is as follows. At the outset Cassirer's outline of the idea of The Philosophy of Symbolic Forms in the 1920 (...) book Einstein's Theory of Relativity is presented as a reaction to the increasing distance between theoretical physics and ordinary experience. The Philosophy of Symbolic Forms can be read as an answer to an inner methodological demand within critical idealism. I encircle this motif in Cassirer's comment that Plato's idealism, understood as the dianoia of thought, is reiterated in Kant's transcendental philosophy and Herman Cohen's reception of Kant. This leads to a discussion of how Cassirer breaks away from Cohen by the positive reception of Russell's symbolic logic. Finally, I present the theory of functional concepts developed by Cassirer (1910) in the book Substance and Function as a prerequisite for the conception of a plural but systematic philosophy of symbolic forms. (shrink)

Composition as Identity is the view that an object is identical to its parts taken collectively. I elaborate and defend a theory based on this idea: composition is a kind of identity. Since this claim is best presented within a plural logic, I develop a formal system of plural logic. The principles of this system differ from the standard views on plural logic because one of my central claims is that identity is a relation (...) which comes in a variety of forms and only one of them obeys substitution unrestrictedly. I justify this departure from orthodoxy by showing some problems which result from attempts to avoid inconsistencies within plural logic by means of postulating other non-singular terms besides plural terms. Thereby, some of the main criticisms raised against Composition as Identity can be addressed. Further, I argue that the way objects are arranged is relevant with respect to the question which object they compose, i.e. to which object they are identical to. This helps to meet a second group of arguments against Composition as Identity. These arguments aim to show that identifying composite objects on the basis of the identity of their parts entails, contrary to our common sense view, that rearranging the parts of a composite object does not leave us with a different object. Moreover, it allows us to carve out the intensional aspects of Composition as Identity and to defend mereological universalism, the claim that any objects compose some object. Much of the pressure put on the latter view can be avoided by distinguishing the question whether some objects compose an object from the question what object they compose. Eventually, I conclude that Composition as Identity is a coherent and plausible position, as long as we take identity to be a more complex relation than commonly assumed. (shrink)

In the opinion of the art critic Julius Meier-Graefe (1867-1935), pictures have a specific logic which is impossible to translate into spoken language. Given this premise, Meier-Graefe develops a specific theory of how art history constructs itself as an interpictorial, self-regulated reference system. Furthermore, in order to convey works of art, he operates with pictures and images in a remarkable way: on the one hand, he makes specific use of reproductions, on the other hand, he communicates via body language (...) that parallels the iconic deixis: By describing and presenting himself in his texts in the physical act of perception and/or reception, he turns himself into a tableau and makes the effect as well as the potential of the artwork visible. The basis of these ideas and methods seems to be the modern experience of museum presentation and reception. Meier-Graefe develops a kind of “practical aesthetic” which can enrich the current debates on interpictoriality. (shrink)

The relationship between reason and faith is one of the most important topics in the philosophy of religion. This issue has been investigated from several aspects. One of these aspects is the relationship between action and religious belief. John Cottingham, a contemporary analytical philosopher, emphasizes the primacy of religious practice over belief, as well as the involuntary nature of belief. In his opinion, the factor that causes people to become religious is not intellectual discussions about God but the internal aspects (...) of religion itself and the transforming power of religious practices in human life and experiences. In the present work, a critique has been made of his point of view with an explanatory-critical method. Criticisms that his point of view includes: First, the belief resulting from the course of action is only psychological certainty and such certainty is beyond the logic of verification. Secondly, knowledge of God and the practical system is a condition for entering it and precedes it. The third criticism is the problem of the plurality of religions and practical systems which causes people to mistrust reasons of the heart. The fourth criticism is that entering into a practical system is a confirmation of its benefits and anyone who does not believe this would have no reason to enter such a system. Introduction John Cottingham is a contemporary English philosopher, and one of the contemporary theorists in the field of the relationship between reason and faith. The relationship between reason and religious faith can be examined from four aspects: 1) The relationship between reason and the epistemological area of faith, 2) the relationship between reason and the practical area of faith, 3) the relationship between reason and the commitment area of faith, and 4) the relationship between reason and the area of faith. Explanation of Cottingham’s view Cottingham’s view can be presented in seven steps: -/- Criticism of the current situation in analytical philosophy; Changing the topic of discussion from the religious field to the spiritual field in order to expand the topic of discussion to non-religious spiritual fields; Comparison of spiritual practice with devotional orders in the past philosophical tradition; Understanding religion is based on practical participation in it; -/- This introduction is expressed according to Pascal’s point of view. According to Pascal, faith should be acquired in the atmosphere of a living tradition of practical religious worship, not through discussion and analysis in a seminar room. The basis of this view is that issues related to the nature and existence of God are beyond the reach of reason. -/- The role of emotions in human understanding; -/- Using Nussbaum’s point of view, Cottingham says: There are types of truth that the intellectual effort to obtain is equivalent to not reaching them. Religious truth is also a part of these truths. Because religious truths are beyond the direct understanding of humans and trying to understand them through logical analysis is moving away from them. -/- Involuntary belief; -/- Human belief, whether religious or otherwise, is not optional and there is a kind of passivity in all human perceptions. According to Cottingham, this point is shared by philosophers such as Hume and Descartes. Cottingham is also influenced by Pascal in this introduction. According to Pascal, although belief in God is not optional, there are indirect ways such as participating in religious activities to realize it, which are available to humans. The role of these ways in the formation of belief is a preliminary role and creating the ability to accept. -/- The necessity of trusting the witnesses of the heart; -/- According to Cottingham, such a thing is necessary for the human condition, and this issue exists in all fields of human knowledge, as well as in human daily life. For example, to go to work, a person must believe that when he turns the switch on the car, the car will not explode, even if such a belief is not the result of checking the car’s electrical system, you still have to trust this article or you will lose your job. Cottingham’s conclusion from the seven premises is that the factor that causes people to become religious is not intellectual discussions about God but the internal aspects of religion itself and the transformative power of religious practices in human life and experiences. Accordingly, faith in God is a product of trust and participation in a living community of faith. When the truth of religion is obtained through faith, and faith depends on a practical religious tradition, then there will be no other choice but to enter into the practical system of religion. Of course, he emphasizes that entering the life of faith does not mean abandoning the critical method in content analysis, and the previous reasons resulting from religious practice must be supplemented or regularized by subsequent intellectual reflections. According to Cottingham, worship precedes rational theory in four ways: 1) temporally; 2) heuristically; 3) psychologically; 4) morally Critical Review In the following, I will do a critical review of Cottingham’s view. His view on the priority of action over religious belief and that the understanding of religion is based on practical participation faces criticisms: First, the belief resulting from participation in religious actions is only psychological certainty and such certainty is beyond the logic of confirmation. Secondly, knowing God and the practical system is a condition for entering this system and has precedence over it. The third criticism is the problem of the plurality of religions and practical systems which causes people to mistrust reasons of the heart. The fourth criticism is that entry into a practical system is a confirmation of its benefits and anyone who does not believe this would have no reason to enter such a system. Therefore, at this stage as well, it is necessary to have a rational way to confirm the usefulness of this path. His view on Doxastic voluntarism is also under the involuntary approach of indirect belief, which is Pascal’s view. This component is also present in the opinions of Allamah Tabatabai. The difference between Cottingham and Allameh’s points of view is that Cottingham and Pascal consider rational arguments to be inefficient in the realization of belief and scientific verification, and they consider a practical commitment to be necessary for the realization of such verification, but Allameh Tabatabai considers scientific premises and rational proof to be the necessary conditions for faith. Conclusion Although the theory of the precedence of action over belief is faced with numerous criticisms, it is an undeniable matter. Paying attention to different levels of religious faith makes the value of theoretical discussions as well as paying attention to practical refinement and participation in spiritual actions be considered together. (shrink)

This article critiques Homi Bhabha's proposal that mimicry, as a transgressive performance of ambivalence, disrupts the colonial violence of the stereotype, and as such, generates emancipatory conditions for postcolonial subjects. I am critical of this naming of mimicry as enabling a possible liberation from colonial violence not only because it fails to address the loss of belonging that significantly marks the experience of being so violated, but also because it seems to intensify this loss in the hybridity and fragmentation (...) that it celebrates. Through the work of María Lugones and Mariana Ortega, I propose a reimagined sense of Sartrean bad faith as one that corrects for this failure. This account of bad faith—as subversive, anticolonial practice—legitimizes my longing for a stability made impossible by the violent ambivalence that pervades both the colonial and postcolonial condition. Lugones's accounts of multiplicity and ontological plurality, as well as Ortega's conception of hometactics, help me argue that this reimagined conception of bad faith ought to be considered productive when it comes to existential strategies that pursue the possibility of free black life. (shrink)

It is almost unanimously acknowledged that the formation of Hegel’s philosophy was largely determined by the appropriation and further development of some fundamental achievements of Kant’s transcendental idealism - first of all his polemic against the “old metaphysics” or, as Hegel also said, the “empty metaphysics of the understanding”. The most decisive assumption of this metaphysics consisted, indeed, in the belief that the totality of our universe could be exhaustively resolved into a plurality of isolated entities, devoid of any “internal,” (...) essential, mutual relations. Each entity was, as a consequence, considered to be only abstractly self-identical and so different from any other. In such a perspective, the absolute, the infinite, the divine, could not but be conceived as being substantially alien to the human mind’s innermost life and essence, as a merely motionless object, absolutely transcendent to the self-creative process in which our rational subjectivity essentially consists. Kant’s critique - especially by virtue of his conception of knowledge as an “a priori synthesis” of intuition and category, of experience and concept, which finds the ultimate condition of its possibility not in its conformity to a presupposed objectivity, but precisely in the original unity of self-consciousness, the “I-think-in general” - has certainly by now rendered unsustainable the strict dualism typical of such a metaphysics, and in particular its pretension of rationally “demonstrating” the existence and the most general properties of the alleged merely transcendent absolute. Whereas Kant’s idealism seems nevertheless to limit itself to the statement and foundation of this simply critical and negative outcome of the transcendental analysis of our knowledge, the ultimate aim of Hegel’s whole philosophy consists rather in the attempt explicitly and systematically to develop a conception of the universe, according to which the universe, far from dividing into a plurality of absolutely different and exclusive entities, instead constitutes itself as a unique, absolute, organic totality, in which any immediate difference and opposition tends to merge, to “reconcile” itself in a superior and deeper “dialectical” unity, which is both divine and human, infinite and finite, identical and different, ideal and real, eternal and in a process of becoming, transcendent and immanent. Every one of its determinate aspects and grades of development, every element into which it differentiates itself, thus turns out to be intimately immanent in, and connected with, every other, and finally in and with the absolute totality itself. Totum in toto et in qualibet parte. “Outside” of such unique, concrete totality, there appear to be but empty, irrational, unreal abstractions: first of all the A = A of formal logic and the absolutely transcendent God of the “old metaphysics.”. (shrink)

The first book of the Aristotelian Physics may be considered as a sort of general introduction to the whole work. In particular, chapters 2 and 3 result very interesting for the foundation of the science of nature according to Aristotle; indeed, in these two chapters, the Stagirite criticizes the position of the Eleates Parmenides and Melissus. These two philosophers are considered as those who claim that change does not exist because the existence of the not-being is impossible to suppose. For (...) this reason, since the Eleates deny that motion and change really exist, the refutation of their thesis results essential for the logical and ontological foundation of the Aristotelian science of nature. This paper wants to make light on the argumentations that Aristotle uses against Parmenides and Melissus. Indeed, since the Stagirite makes often use of his philosophical categories, it seems that his critics sound a little bit anachronistic. In many passages of the text is seems that Aristotle “simply” replace the presupposition of the Eleatic philosophy with the thesis of the evidence of moving and plurality, in general. The aim of this contribution is to reflect on the critics present in Ph. I 2–3 in order to underline the importance of the Eleatic philosophy for the Aristotelian science of nature. (shrink)

In constructional ontology, entities emerge by construction, that is, from the application of constructors to objects. We explore this approach to ontology, focusing on three modules: the constructors, the inputs to the constructors, and the constructional process. Our aim is to identify and assess some key theoretical choices arising in an ontology of this kind.

Sentences that exhibit sensitivity to order (e.g. 'John and Mary arrived at school in that order' and 'Mary and John arrived at school in that order') present a challenge for the standard formulation of plural logic. In response, some authors have advocated new versions of plural logic based on fine-grained notions of plural reference, such as serial reference (Hewitt 2012) and articulated reference (Ben-Yami 2013). The aim of this article is to show that sensitivity to (...) order should be accounted for without altering the standard formulation of plural logic. In particular, sensitivity to order does not call for a fine-grained notion of plural reference. We point out that the phenomenon in question is quite broad and that current proposals are not equipped to deal with the full range of cases in which order plays a role. Then we develop an alternative and unified account, which locates the phenomenon not in the way in which plural terms can refer, but in the meaning of special expressions such as 'in that order' and 'respectively'. (shrink)

Alex Oliver and Timothy Smiley provide a new account of plural logic. They argue that there is such a thing as genuinely plural denotation in logic, and expound a framework of ideas that includes the distinction between distributive and collective predicates, the theory of plural descriptions, multivalued functions, and lists.

This article deals with Kant’s intentions in adding § 12 of the second edition of the Critique of Pure Reason. Here, Kant remarks on the so-called transcendentals (unum, verum, bonum) in the metaphysical or ontological tradition. This article focuses on their trans-categorial character to clarify their role in the system formation of Kant’s three critiques. In order to clarify Kant’s difficult terminology in § 12, fragments from his reflections and transcripts of his lectures are analyzed. Furthermore, an examination of Kant’s (...) references to qualitative unity, plurality, and perfection reveals that these logical criteria of cognition in general help him to organize the content of the three critiques. (shrink)

It is a high merit of this book to emphasize that "philosophy properly speaking is characterized by the kind of logic it employs, for what it employs it assumes, however silently; and what it assumes it presupposes. The logic stands behind the ontology and is, so to speak, metaphysically prior." By "logic" here is meant a species of philosophical logic, concerned in part with "systematic metaphysics" and with "critical ontology." The term "Grand Logic" is (...) due to Peirce, but has been given a more modern reading by George Berry and Hao Wang. Feibleman uses the phrase in the plural to seek out the "common assumptions of the leading western logicians from Aristotle to Quine." However, the only logicians whose work is discussed at any depth are Aristotle, Frege, Whitehead, Russell, and Quine, with only the most casual reference to Ockham, Duns Scotus, Leibniz, De Morgan, Boole, Schröder, Peirce himself, Lesniewski, Carnap, Tarski, and Gödel, all "leading" logicians surely in any suitable list. Also there is total neglect of all recent work in systematic semantics and pragmatics of the very kind that is of the greatest metaphysical relevance. To determine with precision the assumptions common to the work of all of these writers would be a formidable historical as well as analytic task. Nonetheless, the use of modern logic in the detailed formulation of specific metaphysical systems has great promise for the future, as does the criticism of alternative "logics" within the context of specific metaphysical assumptions.--R.M.M. (shrink)

Alex Oliver and Timothy Smiley provide a new account of plural logic. They argue that there is such a thing as genuinely plural denotation in logic, and expound a framework of ideas that includes the distinction between distributive and collective predicates, the theory of plural descriptions, multivalued functions, and lists.

Unlike him who said: “Man is something that must be gone beyond,” I shall have the temerity to say: “Man is something that must be opened out.” But this opening out presupposes a statutory plurality of the person, society and the world. It is because it ignored this plurality and broke away from it that the industrial era is experiencing what have been called contradictions.

Moderate composition as identity holds that there is a generalized identity relation, “being the same portion of reality,” of which composition and numerical identity are distinct species. Composition is a genuine kind of identity; but unlike numerical identity, it fails to satisfy Leibniz’s Law. A composite whole and its parts differ with respect to their numerical properties: the whole is one; the parts (collectively) are many. Moderate composition as identity faces the challenge: how, in the absence of Leibniz’s Law, can (...) one characterize what counts as a genuine kind of identity? This paper explores a promising answer: a genuine kind of identity must satisfy a version of Leibniz’s Law restricted to properties that ascribe qualitative character. Strong composition as identity holds that there is only one identity relation, that it satisfies Leibniz’s Law, and that the parts are identical with the whole that they compose. Strong composition as identity faces the challenge of showing that numerical properties do not provide counterexamples to Leibniz’s Law, and doing so in a way that is compatible with the framework of plural logic that is needed to formulate the theory. The most promising way to do this is to hold that plural logic is fundamental at the level of our representations, but not fundamental at the level of being. At the level of being, portions of reality cannot be characterized as either singular or plural. It turns out that the proposed moderate theory and the proposed strong theory are one and the same. In spite of its many attractions, I reject it. The main issue has to do with whether slice-sensitive emergent properties are possible. I argue that they are, making use both of specific examples and general principles of modal plenitude. I do not claim that my arguments are irresistible. But they cannot be evaded as easily as a related argument against strong composition as identity given by Kris McDaniel. I critically examine McDaniel’s argument to pave the way for my own. (shrink)

Alex Oliver and Timothy Smiley provide a new account of plural logic. They argue that there is such a thing as genuinely plural denotation in logic, and expound a framework of ideas that includes the distinction between distributive and collective predicates, the theory of plural descriptions, multivalued functions, and lists.

Unity and Plurality. Logic, Philosophy, and Linguistics. Edited by Carrara Massimiliano, Arapinis Alexandra, Moltmann Friederike.

A new axiomatization of set theory, to be called Bernays-Boolos set theory, is introduced. Its background logic is the plural logic of Boolos, and its only positive set-theoretic existence axiom is a reflection principle of Bernays. It is a very simple system of axioms sufficient to obtain the usual axioms of ZFC, plus some large cardinals, and to reduce every question of plural logic to a question of set theory.

Plural Logic is an extension of First-Order Logic which has, as well as singular terms and quantifiers, their plural counterparts. Analogously, Higher-Level Plural Logic is an extension of Plural Logic which has, as well as plural terms and quantifiers, higher-level plural ones. Roughly speaking, higher-level plurals stand to plurals like plurals stand to singulars; they are pluralised plurals. Allegedly, Higher-Level Plural Logic enjoys the expressive power of a simple (...) type theory while committing us to nothing more than the austere ontology of First-Order Logic. Were this true, Higher-Level Plural Logic would be a useful tool, with various applications in philosophy and linguistics. However, while the notions of plural reference and quantification enjoy widespread acceptance today, their higher-level counterparts have been received with a lot of scepticism. In this paper, I argue for the legitimacy of Higher-Level Plural Logic by providing evidence to the effect that natural languages contain higher-level plural expressions and showing that it is likely that they do so in an indispensable manner. Since the arguments I put forward are of the same sort advocates of Plural Logic have employed to defend their position, I conclude that the commonly held view that Plural Logic is legitimate, but not so its higher-level plural extensions is untenable. (shrink)

In this paper I argue that we need to take irreducibly plural logic more seriously in metaphysical debates due to the fact that the verdict of many metaphysical debates hangs on it. I give two examples. The main example I focus on is the debate recently revived by Jonathan Schaffer over the fundamental cardinality of the world. I show how the three main arguments provided by Schaffer are unsound in virtue of an employment of plural logic. (...) The second example I give is a more general issue about the possibility of emergent properties of mereological wholes. Employing plural logic there is a new way to understand such cases. The upshot is that plural logic greatly matters to metaphysics and hence can no longer be ignored the way it has in this area. (shrink)

A dilemma put forward by Schein (1993) and Rayo (2002) suggests that, in order to characterize the semantics of plurals, we should not use predicate logic, but plural logic, a formal language whose terms may refer to several things at once. We show that a similar dilemma applies to mass nouns. If we use predicate logic and sets when characterizing their semantics, we arrive at a Russellian paradox. And if we use predicate logic and mereoogical (...) ums, the semantics turns out to be too weak. We then develop an account where mass nouns are treated as non-singular terms. This semantics is faithful to the intuition that, if there are eight pieces of silverware on a table, the speaker refers to eight things at once when he says: "The silverware that is on the table comes from Italy." We show that this account provides a satisfactory semantics for a wide range of sentences. (shrink)

In recent decades, plural logic has established itself as a well-respected member of the extensions of first-order classical logic. In the present paper, I draw attention to the fact that among the examples that are commonly given in order to motivate the need for this new logical system, there are some in which the elements of the plurality in question are internally singularized (e.g. ‘Whitehead and Russell wrote Principia Mathematica’), while in others they are not (e.g. ‘Some (...) philosophers wrote Principia Mathematica’). Then, building on previous work, I point to a subsystem of plural logic in which inferences concerning examples of the first type can be adequately dealt with. I notice that such a subsystem (here called ‘discrete plural logic’) is in reality a mere variant of first-order logic as standardly formulated, and highlight the fact that it is axiomatizable while full plural logic is not. Finally, I urge that greater attention be paid to discrete plural logic and that discrete plurals are not used in order to motivate the introduction of full-fledged plural logic—or, at least, not without remarking that they can also be adequately dealt with in a considerably simpler system. (shrink)

In this paper, I ask whether we should see different logical systems as appropriate for different domains (or perhaps in different contexts) and whether this would amount to a form of logical pluralism. One, though not the only, route to this type of position, is via pluralism about truth. Given that truth is central to validity, the commitment the typical truth pluralist has to different notions of truth for different domains may suggest differences regarding validity in those different domains. Indeed, (...) as we’ll see, the differences between the proposed multiple notions of truth are often of a type that is clearly significant in relation to logical features, such as whether or not a constructive notion of truth is at issue. I criticise domain-based logical pluralism. Having done so I introduce a context-based framework that operates with a context-relative notion of validity. I show that this context-based framework can be employed by the domain-specific logical pluralist, but that framework also allows for logical pluralism that does not involve several domains. Different contexts may demand rules of classical logic, where others only justify intuitionistic rules, even when the same domain (e.g. mathematics) is at issue. (shrink)

A distinction is introduced between itemized and non-itemized plural predication. It is argued that a full-fledged system of plural logic is not necessary in order to account for the validity of inferences concerning itemized collective predication. Instead, it is shown how this type of inferences can be adequately dealt with in a first-order logic system, after small modifications on the standard treatment. The proposed system, unlike plural logic, has the advantage of preserving completeness. And (...) as a result, inferences such as ‘Dick and Tony emptied the bottle, hence Tony and Dick emptied the bottle’ are shown to be first-order. (shrink)

We note that a plural version of logicism about arithmetic is suggested by the standard reading of Hume's Principle in terms of `the number of Fs/Gs'. We lay out the resources needed to prove a version of Frege's principle in plural, rather than second-order, logic. We sketch a proof of the theorem and comment philosophically on the result, which sits well with a metaphysics of natural numbers as plural properties.

John Burgess in a 2004 paper combined plural logic and a new version of the idea of limitation of size to give an elegant motivation of the axioms of ZFC set theory. His proposal is meant to improve on earlier work by Paul Bernays in two ways. I argue that both attempted improvements fail. I am grateful to Philip Welch, two anonymous referees, and especially Ignacio Jané for written comments on earlier versions of this paper, which have led (...) to substantial improvements. Thanks also to the participants in a discussion group at the University of Bristol, where an earlier version was presented. (shrink)

This is a critique of Michael P. Lynch’s functional pluralism with respect to truth. The paper is sympathetic to Lynch’s overall approach to truth, but is critical of (i) his platitudinous characterization of the general principles of truth, (ii) his excessive pluralism with respect to the “realizers” of truth, (iii) his treatment of atomic truth, and (iv) his analysis of “mixed” logical inferences. The paper concludes with a proposal for a functional pluralism that puts greater emphasis on the unity (...) of truth. For example: while Lynch regards truth as based on correspondence principles in some domains and on coherence principles in others, the current proposal regards truth as based on correspondence principles in all domains, restricting the plurality of truth to a plurality of correspondence principles. (shrink)

It is often assumed that pluralities are rigid, in the sense of having all and only their actual members necessarily. This assumption is operative in standard approaches to modal plural logic. I argue that a sceptical approach towards the assumption is warranted.

In this paper, I fill out the received view of logical positivism within professional philosophy against which Thomas Kuhn’s Structure appeared. To do this, I look at the methodological dimensions of ordinary language criticisms of logical positivist analysis from P.F. Strawson and J.L. Austin. While no one would confuse Strawson and Austin for philosophers of science, I look to their criticisms given the general porousness of sub-disciplinary boundaries in mid-20th century philosophy, the prominence of ordinary language philosophy in the 1950s, (...) and also because Kuhn was likely aware of their criticisms via Stanley Cavell. Their main charge is that the positivists base their ideal language analysis on an impoverished, yet overreaching account of meaning because they ignore ordinary linguistic practices. I then show how these methodological criticisms run parallel to points Kuhn makes against logical positivist approaches to the study of scientific knowledge. The parallels I draw emphasize methodological, rather than doctrinal dissatisfaction in mid-20th century philosophy with logical positivism’s perceived neglect of linguistic and scientific practices. An insight shared by these parallel criticisms is that logical positivists cannot declare linguistic and scientific practices irrelevant to their philosophical aims without an antecedent investigation of the practices under question. (shrink)

There is a sense in which pluralism needs no advocate. It is enough to take a quick look at contemporary science to realise that pluralism is common currency. It is a ‘fact’ that scientific disciplines entail a plurality of approaches, methods, styles of inquiry. It is equally easy to acknowledge how the referents of scientific investigation require a concert of disciplines and a variety of explanatory strategies. So pluralism seems to have both an epistemological and an ontological backing.1 Nor is (...) pluralism properly a new topic in philosophy of science. To some extent it is as old as its contending topic, the unity of science – that is at least as old as logical positivism, though back in those days, more than a properly well defined alternative perspective, it ranked as a critical reaction of the few against the many to the excesses of unification, and of reduction. One voice among the few was that of Patrick Suppes who, in a rather memorable PSA Presidential address in 1978, forcefully argued that neither the languages nor the subject matters of scientific disciplines were reducible to one. (shrink)

In this sequel to "The logic and meaning of plurals. Part I", I continue to present an account of logic and language that acknowledges limitations of singular constructions of natural languages and recognizes plural constructions as their peers. To this end, I present a non-reductive account of plural constructions that results from the conception of plurals as devices for talking about the many. In this paper, I give an informal semantics of plurals, formulate a formal characterization (...) of truth for the regimented languages that results from augmenting elementary languages with refinements of basic plural constructions of natural languages, and account for the logic of plural constructions by characterizing the logic of those regimented languages. (shrink)

“Science does not rest on a rockbed. Its towering edifice, an amazingly bold structure of theories, rises over a swamp,” wrote Karl Popper in the fall of 1932. “The foundations are piers going down into the swamp from above. They do not reach a natural base, but ... one resolves to be satisfied with their firmness, hoping they will carry the structure. ... The objectivity of science can be bought only at the cost of relativity.1 The tower over the swamp (...) represented the end of foundationist philosophy. Objectivity no longer rested on a rockbed but on the turns of scientific experimentation and criticism, as much a matter of vagary and luck as of talent and method. Surely, historians should have written Popper into the hall of fame of nonfoundationist philosophers. They did not. In fact, recent scholarship on the Vienna Circle, especially on Otto Neurath, represents Popper as the foundationist philosopher par-excellence. Some of his followers seem to miss his nonfoundationism, too. A House Built on Sand is the title Popperian philosopher Noretta Koertge chose for a spirited collection of essays that takes aim at the follies of science studies.2 Alas, Popper describes science itself as built on sand . But, then, why should historians and philosophers care about misreadings of Popper? Because they create a distorted picture of interwar Viennese philosophy that obscures, rather than reveals its contemporary relevance. This essay, focusing on the Neurath-Popper debate, attempts to redraw the picture and set the record straight. (shrink)