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)

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.

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 plural (...) logic. (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.

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)

A version of Frege's theorem can be proved in a plural logic with pair abstraction. We talk through this and discuss the philosophical implications of the result.

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.

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 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)

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.

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 non-singular 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, we arrive at a Russellian paradox when characterizing the semantics of mass nouns. Likewise, a semantics of mass nouns based (...) upon predicate logic and mereological sums is too weak, since it cannot characterize the “intermediary” construals that sentences containing mass nouns may receive. We then develop an account where mass nouns are treated as non-singular terms, which may refer to several things at once. 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, including cases often seen as difficult, like “The gold on the table weighs seven ounces” (Bunt 1985) and “All phosphorus is either red or black” (Roeper 1983). (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)

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)

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)

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)

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.

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.

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

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)

Equality and identity. Bulletin of Symbolic Logic. 19 (2013) 255-6. (Coauthor: Anthony Ramnauth) Also see https://www.academia.edu/s/a6bf02aaab This article uses ‘equals’ [‘is equal to’] and ‘is’ [‘is identical to’, ‘is one and the same as’] as they are used in ordinary exact English. In a logically perfect language the oxymoron ‘the numbers 3 and 2+1 are the same number’ could not be said. Likewise, ‘the number 3 and the number 2+1 are one number’ is just as bad from a logical (...) point of view. In normal English these two sentences are idiomatically taken to express the true proposition that ‘the number 3 is the number 2+1’. Another idiomatic convention that interferes with clarity about equality and identity occurs in discussion of numbers: it is usual to write ‘3 equals 2+1’ when “3 is 2+1” is meant. When ‘3 equals 2+1’ is written there is a suggestion that 3 is not exactly the same number as 2+1 but that they merely have the same value. This becomes clear when we say that two of the sides of a triangle are equal if the two angles they subtend are equal or have the same measure. -/- Acknowledgements: Robert Barnes, Mark Brown, Jack Foran, Ivor Grattan-Guinness, Forest Hansen, David Hitchcock, Spaulding Hoffman, Calvin Jongsma, Justin Legault, Joaquin Miller, Tania Miller, and Wyman Park. -/- ► JOHN CORCORAN AND ANTHONY RAMNAUTH, Equality and identity. Philosophy, University at Buffalo, Buffalo, NY 14260-4150, USA E-mail: [email protected] The two halves of one line are equal but not identical [one and the same]. Otherwise the line would have only one half! Every line equals infinitely many other lines, but no line is [identical to] any other line—taking ‘identical’ strictly here and below. Knowing that two lines equaling a third are equal is useful; the condition “two lines equaling a third” often holds. In fact any two sides of an equilateral triangle is equal to the remaining side! But could knowing that two lines being [identical to] a third are identical be useful? The antecedent condition “two things identical to a third” never holds, nor does the consequent condition “two things being identical”. If two things were identical to a third, they would be the third and thus not be two things but only one. The plural predicate ‘are equal’ as in ‘All diameters of a given circle are equal’ is useful and natural. ‘Are identical’ as in ‘All centers of a given circle are identical’ is awkward or worse; it suggests that a circle has multiple centers. Substituting equals for equals [replacing one of two equals by the other] makes sense. Substituting identicals for identicals is empty—a thing is identical only to itself; substituting one thing for itself leaves that thing alone, does nothing. There are as many types of equality as magnitudes: angles, lines, planes, solids, times, etc. Each admits unit magnitudes. And each such equality analyzes as identity of magnitude: two lines are equal [in length] if the one’s length is identical to the other’s. Tarski [1] hardly mentioned equality-identity distinctions (pp. 54-63). His discussion begins: -/- Among the logical concepts […], the concept of IDENTITY or EQUALITY […] has the greatest importance. -/- Not until page 62 is there an equality-identity distinction. His only “notion of equality”, if such it is, is geometrical congruence—having the same size and shape—an equivalence relation not admitting any unit. Does anyone but Tarski ever say ‘this triangle is equal to that’ to mean that the first is congruent to that? What would motivate him to say such a thing? This lecture treats the history and philosophy of equality-identity distinctions. [1] ALFRED TARSKI, Introduction to Logic, Dover, New York, 1995. [This is expanded from the printed abstract.] . (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.

We present a plural logic that is as expressively strong as it can be without sacrificing axiomatisability, axiomatise it, and use it to chart the expressive limits set by axiomatisability. To the standard apparatus of quantification using singular variables our object-language adds plural variables, a predicate expressing inclusion (is/are/is one of/are among), and a plural definite description operator. Axiomatisability demands that plural variables only occur free, but they have a surprisingly important role. Plural description (...) is not eliminable in favour of quantification; on the contrary, quantification is definable in terms of it. Predicates and functors (function signs) can take plural as well as singular terms as arguments, and both many-valued and single-valued functions are expressible. The system accommodates collective as well as distributive predicates, and the condition for a predicate to be distributive is definable within it; similarly for functors. An essential part of the project is to demonstrate the soundness and completeness of the calculus with respect to a semantics that does without set-theoretic domains and in which the use of settheoretic extensions of predicates and functors is replaced by the sui generis relations and functions for which the extensions were at best artificial surrogates. Our metalanguage is designed to solve the difficulties involved in talking plurally about individuals and about the semantic values of plural items. (shrink)

Contemporary accounts of logic and language cannot give proper treatments of plural constructions of natural languages. They assume that plural constructions are redundant devices used to abbreviate singular constructions. This paper and its sequel, "The logic and meaning of plurals, II", aim to develop an account of logic and language that acknowledges limitations of singular constructions and recognizes plural constructions as their peers. To do so, the papers present natural accounts of the logic (...) and meaning of plural constructions that result from the view that plural constructions are, by and large, devices for talking about many things (as such). The account of logic presented in the papers surpasses contemporary Fregean accounts in its scope. This extension of the scope of logic results from extending the range of languages that logic can directly relate to. Underlying the view of language that makes room for this is a perspective on reality that locates in the world what plural constructions can relate to. The papers suggest that reflections on plural constructions point to a broader framework for understanding logic, language, and reality that can replace the contemporary Fregean framework as this has replaced its Aristotelian ancestor. (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)

Modal sentences of the form "every F might be G" and "some F must be G" have a threefold ambiguity. in addition to the familiar readings "de dicto" and "de re", there is a third reading on which they are examples of the "plural de re": they attribute a modal property to the F's plurally in a way that cannot in general be reduced to an attribution of modal properties to the individual F's. The plural "de re" readings (...) of modal sentences cannot be captured within standard quantified modal logic. I consider various strategies for extending standard quantified modal logic so as to provide analyses of the readings in question. I argue that the ambiguity in question is associated with the scope of the general term 'F'; and that plural quantifiers can be introduced for purposes of representing the scope of a general term. Moreover, plural quantifiers provide the only fully adequate solution that keeps within the framework of quantified modal logic. (shrink)

This paper proposes a formalization of the class of sentences quantified by most, which is also interpreted as proportion of or majority of depending on the domain of discourse. We consider sentences of the form “Most A are B”, where A and B are plural nouns and the interpretations of A and B are infinite subsets of \. There are two widely used semantics for Most A are B: \ > C \) and \ > \dfrac{C}{2} \), where C (...) denotes the cardinality of a given finite set X. Although is more descriptive than, it also produces a considerable amount of insensitivity for certain sets. Since the quantifier most has a solid cardinal behaviour under the interpretation majority and has a slightly more statistical behaviour under the interpretation proportional of, we consider an alternative approach in deciding quantity-related statements regarding infinite sets. For this we introduce a new semantics using natural density for sentences in which interpretations of their nouns are infinite subsets of \, along with a list of the axiomatization of the concept of natural density. In other words, we take the standard definition of the semantics of most but define it as applying to finite approximations of infinite sets computed to the limit. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:BOOK REVIEWS 741 pointedly, what he is asking for is " the ' planned dissolution ' of the Latin Church into a considerable number of distinct, autonomous ' patriarchates ' " (p. 132). These suggestions, although not original, are intriguing. They deserve, however, more than three pages. What is needed is a detailed presentation of these changes, indicating their historical context, their advantages and disadvantages, and their practical implementation. (...) Despite the criticisms given above, there is much good material to be found in this crisply written book. I agree in general with Hill's judgment that Church authority should embody a collegial rather than a monarchical ecclesiology. He shows that the MC ecclesiology has a solid foundation in scripture and tradition and its cornerstone is the theology of the local Church. Furthermore, he is correct in insisting that the doctrines of collegiality and the priesthood of the faithful are urgent questions in contemporary ecclesiology and that they have broad ecumenical ramifications. He speaks convincingly of greater lay participation, local autonomy, consultation, and accountability. At the same time, his partisanship leads him to caricature the MP view. He will not persuade many MP supporters by criticizing their "highhanded authoritarianism and paternalism " (p. 53) and " ecclesiastical dishonesty " (p. 127) or by claiming that the Roman Curia " is neuro· tically obsessed with the matter of papal authority" (p. 114). Hill makes many valid and important points, but, on occasion, he weakens them by exaggeration. At times his partisan style overcomes his theo· logical substance. The Catholic University of America Washington, D.C. pATRICK GRANFIELD Many Paths: A Catholic Approach to Religious Pluralism. By EUGENE HILLMAN. Maryknoll, New York: Orbis Books, 1989. Pp. 95. A Christian theology of religions raises fundamental epistemological and methodological questions. Hillman comes to the debate from what Lindbeck has called an " experiential expressivist " background, that is, there is a tacit assumption that reality is experienced and then expressed, that reality precedes language rather than being disclosed and shaped through language. When such an outlook is applied to the theology of religions, the outcome is often the " discovery " of a common experience underlying all religions, despite their different expressions. The latter can be seen to vary according to climate, history, temperament, and so on. Such expressions are loose symbols for a 742 BOOK REVIEWS greater reality, which takes on an increasingly vague shape with the demise of the signifier. History can offer very little resistance to such a model, and the conflicts, differences, intractabilities, and real problems of religious plurality are slowly silenced, almost numbed into a drowsy calm. That history refuses to play this role, while theologies of religion are often demanding it, is indicative of the difficulties with such a model. Hillman's first book on this topic (The Wider Ecumenism, 1968) showed him to be a follower of Rahner. He stressed the universality of grace and its mediation through the historical and particular; he thereby argued for a wider ecumenism with regard to the world religions, in a model analogous to intra-Christian ecumenism. In this book, Hillman advances the same position, but now infused with a strong dose of Wilfred Cantwell Smith. He does not confront the theological criticisms made against either of his mentors. The book is divided into four lucid chapters. The first considers the meaning and role of religion, and much of Hillman's discussion is helpful. However, as the chapter proceeds, one finds that the definition of religion is not controlled by the particularities and intractable dif. ferences presented by the subject matter but rather by an experiential essentialism. Hillman uses Smith's distinction between "faith" and " belief " to two ends, one descriptive, the other evaluative. However he, like Cantwell Smith, conflates description with evaluation. Furthermore, he is untroubled that the subject matter under inspection does not easily yield to such distinctions. Descriptively, " belief " or the " cumulative tradition " involves the " myriad historico-cultural par· ticularizations " that go to make up a religion such as liturgies, doc· trines, ethical systems, practices, histories, and so on {20). Faith is basically an experience of " the tr,anscendent, which is presumably the same for every person," and can be distinguished from the "cumulative tradition, which is different for each people, nation or... (shrink)

IntroductionIn May 2006, the small group of doctoral students working on ecophilosophy at the Higher Institute of Philosophy at K.U.Leuven invited the Dutch environmental philosopher Martin Drenthen to a workshop to discuss his writings on the concept of wilderness, its metaphysical and moral meaning, and the challenge social constructivism poses for ecophilosophy and environmental protection. Drenthen’s publications on these topics had already been the subject of intense discussions in the months preceding the workshop. His presentation on the workshop and the (...) three critical responses by Wim Bollen, Glenn Deliège, and Richard Kover are published here in a thoroughly revised form on the basis of further and ongoing discussions about the issues involved. Three further contributions to the discussion are added: one by Nathan Edward Kowalski, a young Canadian philosopher who studied in Leuven and wrote his as yet unpublished dissertation on “Evil in Nature,” a second one by Kingsley Goodwin who is currently writing a dissertation on deep ecology at University College in Dublin and, finally, my own unsystematic thoughts inspired by Martin Drenthen’s provocative and stimulating hermeneutics of our postmodern understanding of nature and wilderness, as well as the diverse critical responses to Drenthen’s views by the other contributors. I owe gratitude to all of them for enriching my own ecophilosophical thought and enlarging its horizon although as my fragmentary reflections show at the cost of yet greater uncertainty and more questions about the possibilities of arguing for a radical environmentalist position. Such a position would somehow connect or ground our moral obligation to preserve genuine non-human otherness, wild and free nature, in the non-human meaning of such nature and in our essential need to be in direct and concrete contact with that field of wild non-human meaning because we ourselves belong to nature, because we are not only and purely civilized but are also and most fundamentally wild and free. Three fundamental questions need to be distinguished: the question about our moral obligations regarding nature and its preservation, the metaphysical question about the nature of nature or the meaning of nature, and the question of the metaphysical grounding of our morals in general, and of our moral obligation regarding nature in particular, in the nature or meaning of nature. The complex intertwinement between these three questions is at the heart of Martin Drenthen’s reflections.The authors contributing to the present discussion approach the various issues from markedly different philosophical backgrounds and concerns: critical theory, anthropology, analytic philosophy, phenomenology, hermeneutics, and deep ecology are all to some degree or other brought to bear on the question of what wilderness means for us, why we are fascinated by it and what it actually and in the first place is.Another interesting difference between the five respondents to Martin Drenthen’s wilderness-philosophy relates to the place from which they write: while the Canadians Richard Kover and Nathan Edward Kowalski have wilderness of some sort still close at hand, the Belgians Wim Bollen and Glenn Deliège write from a place which has been thoroughly domesticated, cultivated, and industrialised for a long time. Martin Drenthen himself, of course, writes from the same kind of place as these last two, which explains why he only refers to the wilderness that he has read about in novels, seen in movies, or experienced as recreated in the reserves of the Netherlands. The Irish Kingsley Goodwin writes perhaps from a third, intermediate place that is not wild anymore but still much more natural than Belgium or the Netherlands are.The differences in philosophical approach and concern combined with the difference of place generate a rich tapestry of perspectives and voices wrestling with the fundamental questions of our perceived homelessness and alienation from nature, our cultural discontent, our longing for and need for radical alterity, of immanence and transcendence, of who we are and where we belong, and more concretely of whether there is more to ground our efforts to preserve nature than enlightened self-interest and subjective preference. Martin Drenthen deserves praise for inaugurating this fruitful discussion with his intriguing and highly paradoxical effort to hybridize a postmodern deconstruction of the idea and ideal of wilderness as unspoilt and true nature on the one hand with a new metaphysics of wilderness on the other. Arne Naess, who is generally regarded as the founding father of deep ecology, pointed out the positive and stimulating role that vagueness in the expression of ideas can play in political and philosophical debate. Such general and vague but highly suggestive expressions as ‘all life is one’ are not empty at all, as is often claimed; they are rather full of possibilities of ‘precisation’ and differentiation. Drenthen’s wilderness-philosophy is certainly not vague to the degree of ‘all life is one,’ but his expositions are similarly pregnant with a wealth of further questions, precisations, distinctions, and conceptual clarifications. Good examples of different kinds are to be found in the contributions of Nathan Edward Kowalski and Richard Kover. Kowalski points out that Drenthen’s notions of culture and wilderness need to be made more precise by distinguishing them from the notions of civilization and wildness such that wild cultures become a conceptual possibility. Richard Kover takes the lead from Drenthen’s question about the reason for our postmodern fascination for wilderness to confront it with our primordial fascination in terms of the dependence in the evolution of our subjectivity and our consciousness on the focused perceptual attention on wild forms.Glenn Deliège situates Martin Drenthen’s wilderness-philosophy in its original context of the Dutch debate on the preservation of nature, in particular on the new wilderness paradigm. According to this paradigm, the nature to be preserved should be true and pure, truly natural and wild nature, that is nature outside of and free from the cultivating and domesticating influence of humans. In the Netherlands, however, such nature no longer exists; it can only be preserved after it has first been artificially recreated. Deliège gives an informative summary account of the highly charged three-cornered debate between the adepts of this wilderness-paradigm, the proponents of the more traditional form of conservation of remnants of the typical European landscapes created by pre-industrial farming practices and the modern technocratic functionalists. This debate makes obvious that there are quite different views of the nature of nature and its value. Enter social constructivism: the contested nature of nature is nothing more than a social construct, an idea in a collective mind. The contestation itself is a struggle for authority and power between different such social constructs, any claim to scientific objectivity and objective truth for one’s image of nature is an arrogation of a truth which doesn’t exist and is potentially oppressive by silencing other views. Nature then is up for the grabs of politics, political negotiation, and compromise between various interest groups who all want to get some benefit from nature, some use-value.The problem with Drenthen’s effort to articulate a normative concept of nature which cannot be deconstructed in this way is the extreme formality and emptiness of his metaphysical concept of wilderness as that which is always ‘beyond’, always ‘more’ and which can never be exhausted by any image and construction of nature. Any more concrete determination is mere appearance; the thing in itself is a border concept of that which in fact cannot be grasped conceptually. Glenn Deliège is critical of this formality and emptiness from which it will be impossible to derive any concrete guidance for our conservation practices. He then goes on to defend the Arcadian tradition of our appreciation of nature as giving us a historically well-grounded orientation for those practices. Of course that Arcadian tradition is obviously a cultural construction but that doesn’t make it completely arbitrary and contingent since it is itself ultimately grounded in and open to modification by our concrete sensuous experiences of nature.Deliège here raises the very important issue of the relation between our concrete perceptual and bodily experiences in and with nature and our concepts and metaphysical images of nature. Drenthen himself approaches this issue from the hermeneutical perspective of our need to make sense of our experiences and to articulate their meaning. His confrontation with social constructivism and his effort to salvage something from its relativizing acid lead him, however, into the direction of a highly abstract and empty concept of wilderness.Richard Kover shows that perception is, indeed, the key to a radical critique of social constructivism. He does this with the help of the ecological anthropology of Paul Shepard, the structuralist anthropology of Claude Levi-Strauss and the phenomenology of Maurice Merleau-Ponty. It needs to be said here that Kover takes his leave from an unpublished paper by Martin Drenthen with the title “How to appropriate wilderness appropriately?” – the paper is accessible though on Drenthen’s web-site - in which Drenthen comments and reflects upon three contemporary wilderness-tales, one of them being Werner Herzog’s much-discussed documentary on Timothy Treadwell, an American environmentalist drop-out who lived thirteen summers among wild grizzlies in the Alaskan wilderness before being killed together with his girlfriend by a grizzly bear.Kover tries to show that we are not imprisoned in the mirror-cabinet of our mind or of our human sociality. To make his case, he starts from Paul Shepard’s thoughtful observation that the evolutionary emergence of the mind did not remove us from the natural world but actually connected us deeper with it. Through our mind we evolved more fully into it because our mind is primordially in our senses and in the ability to articulate a perceptual world. The natural world in the form of the system of natural species and their relations is the primary model for perceptual discriminations, for the fundamental discovery of order with its twin-aspects of distinction and discontinuity on the one side and relations and continuity on the other side. Our cognition is essentially perceptually based, our subjectivity is primordially informed by our inherence in the sensible world. Perceptual cognition is inherently intentional and relational, it is not an autonomous mental construction, it is rather in the world and informed by that which is perceived. The other is always intertwined with the subject. We are always already hooked up with the world, with the others, before we start reflecting, thinking, and conceptualizing. This is one of the major themes in Shepard’s work: what this insight means with regard to our relations to non-human otherness, in particular to our perceptual encounter with wild animals. In our encounter with non-human otherness, we are confronted with an essentially ambiguous sense of both affinity and disjuncture. Wild animals demonstrate to us that we are not homeless or alien to this world, that we fundamentally belong to it and are part of it. Their difference, however, shows us that there are different perspectives and ways of being in the world. “Thus the encounter with non-human others inform humans that we are both of the world and simultaneously not the world and there are horizons of significance beyond our own perspective.”Nathan Edward Kowalski comes to a similar conclusion when he situates our morality in the larger moral order of wild nature. According to Kowalski it is indeed a moral order though not our own, an Other to our morality but not simply a negative one. It is, as Drenthen says, a highly paradoxical amoral morality. But what can it mean to speak of morality here? For Kowalski it means that the issue is not merely the theoretical recognition and acknowledgment of axiological transcendence, of non-human values out there, but whether we will appropriately conform to and comport ourselves towards that axiological transcendence so that we can find a human homeland in wild nature instead of turning it into a wasteland. The question then is, how to fit our own human morality into this larger order and greater reality, to subordinate it to that greater reality as a part of it and encompassed but not denied by it so that we can be moral and natural at the same time, tender carnivores hunting the sacred game. Indigenous people follow a moral protocol in their relationship with non-human others which acknowledge and respects their autonomy, their alterity, and the sacred mystery of their different ways of being. They are not befriended but some of them are hunted and eaten – as an exchange in the gift-economy of nature.The problem of the homelessness and alienation from nature is discussed by Wim Bollen from the radically different vantage point of critical theory. In Adorno’s and Horkheimer’s Dialectic of Enlightenment the human story unfolds as a tragic effort to liberate ourselves from nature and to become fully human through rational control when in the end this effort turns against ourselves and instead of liberation and human flourishing we get social domination and repression of our natural needs. The frustrations and mutilations imposed upon us by a repressive civilization give rise to the regressive desire for a return to a natural existence. Referring to the myth of Odysseus and Circe as interpreted by Adorno and Horkheimer, Wim Bollen equates such a natural existence with animal life. In the light of contemporary knowledge about primitive existence, however, this equation is highly problematic. Palaeolithic foragers were already fully human in all respects. A life without civilization need not be an animal-existence.According to Adorno/Horkheimer, our subjectivity and autonomy have to be wrested from animal-nature through an exertive struggle that cannot but proceed by a threefold strategy of domination: the domination of non-human otherness, of human others, and of our own inner nature. The siren song of nature consists in the temptation to give up that struggle for the promise of an unreflective, non-alienated natural existence without toil.When Odysseus’ men give in to Circe’s seduction they are, however, not transformed into wild animals but into swine. According to Bollen this signifies that we cannot re-wild ourselves, that we remain imprisoned in civilization, either as master-subjects or as domesticated animals. Bollen, by the way, like Drenthen, does not distinguish conceptually between civilization and culture. Since re-wilding for Bollen means the impossibility of returning to animal-existence, which is actually the impossibility of becoming another species since biologically we are animals already, to be imprisoned in civilisation means nothing else than to be imprisoned in our humanity. The fact that we cannot become wild animals again – according to Paul Shepard, however, we are still wild animals – is indeed, as Bollen stresses, a trivial form of alienation. A more meaningful concept of alienation which can be put to critical use must refer to a culturally and historically determined frustration and deficit inside the cultural order that is to be overcome not by an impossible regression but by progressive politics leading beyond the three intertwined forms of domination. Not back to nature but forward towards a reconciliation of culture with nature! Such a reconciliation would neither collapse culture into the immanence of nature nor submerge nature into the transcendence of culture. According with the three forms of domination it would be a three-dimensional form of reconciliation.Odysseus’ men did not got what they thought were promised them: the complete liberation from the burden of being autonomous subjects, of being civilized, but they got something worthwhile, namely a certain from of pleasure, a limited and provisional relief and escape. Bollen sees a critical potential in these piggish pleasures after all and consequently even in the siren song of nature since these pleasures were only experienced because Odysseus’ men gave in to it. But one has to give in to this siren song critically if it is to unfold its liberating potential. The problem with pleasure though in bourgeois society is that it is necessarily betrayed, instrumentalized and sold.Kingsley Goodwin’s paper starts by defending deep ecology against the charge of asserting a naïve and dogmatic metaphysics of nature. For convenience sake, but not quite unproblematically, he identifies deep ecology with the environmental thought of Arne Naess. A metaphysics of nature for Naess is always part of a personal worldview. Worldviews which are partly inspired by ecology Naess calls ecosophies. Naess always stresses the personal character of such a worldview and the irreducible plurality of them. It used to be a common misunderstanding of the platform of deep ecology which Naess conceived together with George Sessions that it expressed in a condensed form the metaphysical beliefs of deep ecology. Naess’ intention, however, was to try to articulate in a general fashion the basic viewpoints on which the supporters of the deep ecology movement agreed. It would be possible then to derive these viewpoints from quite different worldviews. In light of this, I think, that Goodwin’s characterisation of the platform as “pragmatic and activist” is not quite appropriate.Goodwin goes on to compare Drenthen’s conception of wilderness and wildness with the similar position developed by Neil Evernden in his book The Social Creation of Nature. He like Naess in his personal ecosophy stresses the crucial role of perceptual experience of wild otherness to find an antidote to the relativity and contingency of our interpretations of nature. Evernden refers to studies on child development to argue for a non-dualistic and relational conception of the self, similar to Naess’ relational ontology. According to Goodwin, Drenthen, in spite of his hermeneutical approach remains too much indebted to the Western subject/object-dualism. The object, in this case wild nature, is pure otherness.With regard to a compost heap, Goodwin shows that we are not separated from nature by an inseparable gulf, that nature is close at hand, and that we can experience and explore it, appreciate the complex play of identity and difference it consists of, the exchanges and transformations and that we can identify with the organisms involved in these exchanges.*The proceeding remarks only highlight some of the prominent themes and considerations in the various contributions to this topical issue of Ethical Perspectives. Hopefully the reader will feel invited and enticed to read the articles themselves, starting, preferably of course, with the essay by Martin Drenthen, who sparked off this lively discussion on the moral meaning of wild nature. I am honoured and pleased to be able to introduce these rich explorations by such talented young environmental philosophers who are eager to develop environmental philosophy further and lead it into new directions. They all have to wrestle with and find answers to the challenge postmodern deconstruction and social constructivism pose for environmental philosophy. In the face of that challenge, it is even more difficult than it already was to provide solid and convincing arguments for the defence of wild and free nature beyond merely pragmatic arguments in terms of its utilitarian value for us. The reason for that defence is not clear-cut and proves to be just as evasive as the moral meaning of nature itself. But neither that reason nor that meaning are mere phantoms and mirages that vanish when we approach them and try to grasp them. They are more substantial, even if they will never have the solidity of a mathematical proof or a scientific measurement. Their locale is the lifeworld which from the point of view of scientific and logical precision and clarity is a messy place where subject and object, reason and heart, fact and value, experience and thought and, yes, nature and culture cannot be clearly separated. This has important consequences for environmental philosophy and its methodology. Conceptual analysis and logical argumentation have to become sensitive to the richness of experience in the lifeworld and to the diverse efforts of its articulation: i.e., they have to open themselves up and maybe even to subordinate themselves to phenomenological and hermeneutical approaches. For me personally this is one of the most important conclusions I draw from the discussion presented here. (shrink)

Several natural languages such as English contain prima facie different kinds of referential and quantificational expressions. In particular, natural languages.

Ethicists tend to enjoy an extraordinary status in the scientific world, in spite of the fact that their knowledge is not based on empirical facts or logical principles. When they philosophise, they appear to be intervening in a discussion that started long before they existed and will probably continue long after they have disappeared. They are inclined, after all, to base their arguments on convictions. If you point this out, most people will more than likely admit that their ethical principles (...) are indeed based on convictions that have acquired a self-evident character in our actual day-to-day relations although they cannot be solidly founded. It is virtually impossible to strengthen or weaken the capacity of moral convictions by trying to justify them.In our everyday interactions, discussions intended to justify or defend something never start from absolute zero. All sorts of authoritative points of departure established in the course of history inevitably insinuate themselves from the very outset. Empirical scientists often believe that what they introduce into the debate is based on bare, unadulterated facts. But even here questions can be raised. Empirical scientists use language and participate in discussions in which unspoken presuppositions are just about everywhere. The very act of speaking presupposes that we already have a notion of what our addressee understands by the expressions we use. Without a perspective on what the other can be generally presumed to understand, none of us will be able to picture the kind of impression our interventions will have on others or understand their interventions in the way they are expected to be understood. Those who are unable to distinguish the items relevant for discussion from the endless stream of fragmented experiences because they have no idea of the frame of reference within which associations are ultimately established, will likewise have no idea what is going on. Without this frame of reference we are lost.One of the problems that would appear to be confronting the humanities today is the exponential numerical growth of frames of reference, which has resulted in an inevitable decline in the existence of broad-based debate. Modern methods of communication have made it possible to find enough dialogue partners within every specialised frame of reference to maintain group-specific discussions that interest no one in the external forum. This sort of compartmentalisation of academic potential tends to result in a situation in which the theoreticians and those endowed with more practical common sense are no longer on the same wavelength and no longer understand one another. It is clear to one and all that the humanities are in need of interdisciplinary debate, but are there enough scholars willing to dismantle their technical jargon in order to facilitate such debate?Theoretical and methodological plurality would appear to be even greater in the domain of ethics. The debate concerning the relationship between fundamental and applied ethics has a long history. The same discussion will no doubt have to be pursued today within the context of the fragmentation of the humanities and the social sciences, a theme that certainly deserves further reflection. (shrink)

This edited volume brings together 18 state-of-the art essays on pluralism about truth and logic. Parts I and II are dedicated to respectively truth pluralism and logical pluralism, and Part III to their interconnections. Some contributors challenge pluralism, arguing that the nature of truth or logic is uniform. The majority of contributors, however, defend pluralism, articulate novel versions of the view, or contribute to fundamental debates internal to the pluralist camp. The volume will be of interest to truth (...) theorists and philosophers of logic, as well as philosophers interested in relativism, contextualism, metaphysics, philosophy of language, semantics, paradox, epistemology, or normativity. (shrink)

Neo-Fregeanism aims to provide a possible route to knowledge of arithmetic via Hume’s principle, but this is of only limited significance if it cannot account for how the vast majority of arithmetic knowledge, accrued by ordinary people, is obtained. I argue that Hume’s principle does not capture what is ordinarily meant by numerical identity, but that we can do much better by buttressing plural logic with plural versions of the ancestral operator, obtaining natural and plausible characterizations of (...) various key arithmetic concepts, including finiteness, equinumerosity and addition and multiplication of cardinality—revealing these to be logical concepts, and obtaining much of ordinary arithmetic knowledge as logical knowledge. Supplementing this with an abstraction principle and a simple axiom of infinity (known either empirically or modally) we obtain a full interpretation of arithmetic. (shrink)

Noun phrases with overt determiners, such as <i>some apples</i> or <i>a quantity of milk</i>, differ from bare noun phrases like <i>apples</i> or <i>milk</i> in their contribution to aspectual composition. While this has been attributed to syntactic or algebraic properties of these noun phrases, such accounts have explanatory shortcomings. We suggest instead that the relevant property that distinguishes between the two classes of noun phrases derives from two modes of existential quantification, one of which holds the values of a variable fixed (...) throughout a quantificational context while the other allows them to vary. Inspired by Dynamic Plural Logic and Dependence Logic, we propose Plural Predicate Logic as an extension of Predicate Logic to formalize this difference. We suggest that temporal <i>for</i>-adverbials are sensitive to aspect because of the way they manipulate quantificational contexts, and that analogous manipulations occur with spatial <i>for</i>-adverbials, habituals, and the quantifier <i>all</i>. (shrink)

Consider one of several things. Is the one thing necessarily one of the several? This key question in the modal logic of plurals is clarified. Some defenses of an affirmative answer are developed and compared. Various remarks are made about the broader philosophical significance of the question.

Ordinary English contains different forms of quantification over objects. In addition to the usual singular quantification, as in 'There is an apple on the table', there is plural quantification, as in 'There are some apples on the table'. Ever since Frege, formal logic has favored the two singular quantifiers ∀x and ∃x over their plural counterparts ∀xx and ∃xx (to be read as for any things xx and there are some things xx). But in recent decades it (...) has been argued that we have good reason to admit among our primitive logical notions also the plural quantifiers ∀xx and ∃xx. More controversially, it has been argued that the resulting formal system with plural as well as singular quantification qualifies as ‘pure logic’; in particular, that it is universally applicable, ontologically innocent, and perfectly well understood. In addition to being interesting in its own right, this thesis will, if correct, make plural quantification available as an innocent but extremely powerful tool in metaphysics, philosophy of mathematics, and philosophical logic. For instance, George Boolos has used plural quantification to interpret monadic second-order logic and has argued on this basis that monadic second-order logic qualifies as “pure logic.” Plural quantification has also been used in attempts to defend logicist ideas, to account for set theory, and to eliminate ontological commitments to mathematical objects and complex objects. (shrink)

This paper replies to Himmelreich's ‘The Paraphrase Argument Against Collective Actions’ [2017], which presents three putative counterexamples to the multiple agents analysis of plural action sentences. The paper shows that the argument from the first example, the discursive dilemma, fails because it relies crucially on a simplification of the target analysis, and that the others don't bear on the question because they turn out on examination to be about individual rather than group action sentences.

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.

Frege's invention of the predicate calculus has been the most influential event in the history of modern logic. The calculus’ place in logic is so central that many philosophers think, in fact, of it when they think of logic. This book challenges the position in contemporary logic and philosophy of language of the predicate calculus claiming that it is based on mistaken assumptions. Ben-Yami shows that the predicate calculus is different from natural language in its fundamental (...) semantic charac. (shrink)

This volume brings together new work on the logic and ontology of plurality and a range of recent articles exploring novel applications to natural language semantics. The contributions in this volume in particular investigate and extend new perspectives presented by plural logic and non-standard mereology and explore their applications to a range of natural language phenomena. Contributions by P. Aquaviva, A. Arapinis, M. Carrara, P. McKay, F. Moltmann, O. Linnebo, A. Oliver and T. Smiley, T. Scaltsas, P. (...) Simons, and B.-Y. Yi . (shrink)