The logic of ‘being informed’ gives a formal analysis of a cognitive state that does not coincide with either belief, or knowledge. To Floridi, who first proposed the formal analysis, the latter is supported by the fact that unlike knowledge or belief, being informed is a factive, but not a reflective state. This paper takes a closer look at the formal analysis itself, provides a pure and an applied semantics for the logic of being informed, (...) and tries to find out to what extent the formal analysis can contribute to an information-based epistemology. (shrink)

One of the open problems in the philosophy of information is whether there is an information logic (IL), different from epistemic (EL) and doxastic logic (DL), which formalises the relation “a is informed that p” (Iap) satisfactorily. In this paper, the problem is solved by arguing that the axiom schemata of the normal modal logic (NML) KTB (also known as B or Br or Brouwer’s system) are well suited to formalise the relation of “being informed”. After (...) having shown that IL can be constructed as an informational reading of KTB, four consequences of a KTB-based IL are explored: information overload; the veridicality thesis (Iap → p); the relation between IL and EL; and the Kp → Bp principle or entailment property, according to which knowledge implies belief. Although these issues are discussed later in the article, they are the motivations behind the development of IL. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:544 BOOK REVIEWS vide critical editions of the contributions by Richard Rufus and·-even more important-Richard Fishacre to the theology of Oxford and the continent Bayerishe Akademie der Wissenschaften Munich, West Germany RICH.ARD SCHENK, O.P. The Logic of Being: Historical Studies. Edited by SIMO KNUUTTIL.A and J.A.AKKO HINTIKK.A. Synthese Historical Library, 28. Dordrecht: D. Reidel, 1985. Pp. xvi + 300 pp. $54.00 (cloth). Unlike many examples of the (...) genre, this collection of articles on the concept of being from Parmenides to Frege should and will be profitably consulted by philosophers of various stripes. Whether read piecemeal or straight through, these investigations carry on an open-ended dialogue in which historians of philosophy, philosophers of logic, and semanticists can participate equally. The editors are to be commended for presenting eleven articles (about an equal number of previously published and new studies) that are generally complementary to one another. What makes the collection so useful and interesting·, however much one disagrees with the thesis, is its concentrated focus on the difficulties of attributing to philosophers from Plato to Kant the Frege-Russell view that verbs for being are multiply ambiguous. It will perhaps be useful 'to begin with the concluding essay,· L. Haaparanta 's study " On Frege's Concept of Being," where the ambiguity thesis is discussed in greatest detail. She presents Frege's well-known articulation of the meanings of the verb ' to be ' as follows : (1) the is of identity (2) the is of predication (3) the is of existence, expressed by means either (i) of the existential quantifier and the symbol for identity or (ii) of the existential quantifier and the symbol for predication (4) the is of class-inclusion or generic implication Two points are worth noting. First, most of the contributors explore the ambiguity with reference to the is of identity, predication, and existence. Sceond, while ithe verb has several different meanings for Frege, most of the other philosophers discussed distinguish, at most, different uses. Many of the arguments against applying Frege's ambiguity thesis to earlier philosophers depend on this distinction between meaning and use; I will assess its cogency in specific contexts as they arise. BOOK REVIEWS 545 In Frege's analysis the crucial distinction is between the first-order copulative is and existence, a second-order concept. Since in Frege's view existence is a property of a first-order concept, it must lack all content. Haaparanta sums up the position well: "We presuppose the existence of objects; we do not say that they exist. For Frege, every predication carries with itself the claim of existence" (277). Influenced by Kant's argument that u existence is not predicate of a thing itself," Frege is willing to regard it as a proper concept, but not a first-order concept. This superordination of existence sounds reminiscent of Aristotle 's focus on predication and identity at the expense of existence (here it is better to speak of subordination, as the studies of Dancy and Hintikka on Aristotle indicate), but Frege's sharp distinction between concepts and objects is much closer to the Kantian position that we cannot know the essence of things in themselves. Thus, existence is a conceptual property though applicable to the instantiation of an object's properties; and identity statements, since they concern objects in themselves, are beyond the ken of reason. Certainly, Frege's thesis is " epistemologically motivated", as Haaparanta observes, but one is tempted to adopt a stronger conclusion: that the shift from an Aristotelian, or even Thomistic, ontology to Kantian epistemology contributes greatly to the emergence of the ambiguity thesis and renders it inapplicable to ancient and medieval metaphysics, even if, as Hintikka argues ("Kant on Existence and Predication"), Kant does not clearly distinguish different meanings of is·. The first four articles present a multi-faceted assault on the contemporary penchant for reading the Frege-Russell ambiguity thesis into the Greek philosophers. C. H. Kahn's ''Retrospect on the Verb ' To Be' and the Concept of Being " is a useful precis of his indispensable work on the Greek verb for being. His particular concern is to further the "campaign against the uncritically ' existential ' interpretation... (shrink)

In the Logic of Being: Realism, Truth, and Time, the influential philosopher Paul M. Livingston explores and illuminates truth, time, and their relationship by employing methods from both Continental and analytic philosophy.

The last twenty years have seen remarkable developments in our understanding of how the ancient Greek thinkers handled the general concept of being and its several varieties. The most general examination of the meaning of the Greek verb 'esti'/'einai'/'on' both in common usage and in the philosophical literature has been presented by Charles H. Kahn, most extensively in his 1973 book The Verb 'Be' in Ancient Greek. These discussions are summarized in Kahn's contribution to this volume. By and large, (...) they show that conceptual schemes by means of which philosophers have recently approached Greek thought have not been very well suited to the way the concept of being was actually used by the ancients. For one thing, being in the sense of existence played a very small role in Greek thinking according to Kahn. Even more importantly, Kahn has argued that Frege and Russell's thesis that verbs for being, such as 'esti', are multiply ambiguous is ill suited for the purpose of appreciating the actual conceptual assumptions of the Greek thinkers. Frege and Russell claimed that a verb like 'is' or'esti' is ambiguous between the 'is' of identity, the 'is' of existence, the copulative 'is', and the generic 'is' (the 'is' of class-inclusion). At least a couple of generations of scholars have relied on this thesis and fre quently criticized sundry ancients for confusing these different senses of 'esti' with each other. (shrink)

COMMUNICATION 1. Every philosophy presupposes a theory of communication and conversely every theory of communication implies a philosophy. ...

Recently a view of Hegel’s “idealism” which hitherto had seemed unquestionable—the view that it is fundamentally a metaphysical doctrine—has been seriously challenged. Thus yesterday’s metaphysical Hegel, complete with his cosmic megasubject hidden behind the events of nature and history, has been joined by today’s “nonmetaphysical Hegel,” the postkantian categorial “genealogist.” According to the nonmetaphysical Hegelians, a century and a half of misunderstanding has been based on the confusion of two distinct philosophical projects: on the one hand, that originating in the (...) Aristotelian project of “ontology”—the reconstruction of the categorial structure of to on e on, “being qua being”—and on the other, that stemming from the very different Aristotelian project of “theology”—the investigation of to theion, primary being or that which is first in the order of substances. (shrink)

The first volume presents a collection of papers in honor of the fiftieth birthday of Jean-Yves Béziau. These 25 papers have been written by internationally distinguished logicians, mathematicians, computer scientists, linguists and philosophers, including Arnon Avron, John Corcoran, Wilfrid Hodges, Laurence Horn, Lloyd Humbertsone, Dale Jacquette, David Makinson, Stephen Read, and Jan Woleński. It is a state-of-the-art source of cutting-edge studies in the new interdisciplinary field of universal logic. The papers touch upon a wide range of topics including combination (...) of logic, non-classical logic, square and other geometrical figures of opposition, categorical logic, set theory, foundation of logic, philosophy and history of logic (Aristotle, Avicenna, Buridan, Schröder, MacColl). This book offers new perspectives and challenges in the study of logic and will be of interest to all students and researchers interested the nature and future of logic. (shrink)

The square of opposition is a diagram related to a theory of oppositions that goes back to Aristotle. Both the diagram and the theory have been discussed throughout the history of logic. Initially, the diagram was employed to present the Aristotelian theory of quantification, but extensions and criticisms of this theory have resulted in various other diagrams. The strength of the theory is that it is at the same time fairly simple and quite rich. The theory of oppositions has (...) recently become a topic of intense interest due to the development of a general geometry of opposition (polygons and polyhedra) with many applications. A congress on the square with an interdisciplinary character has been organized on a regular basis (Montreux 2007, Corsica 2010, Beirut 2012, Vatican 2014, Rapa Nui 2016). The volume at hand is a sequel to two successful books: The Square of Opposition - A General Framework of Cognition, ed. by J.-Y. Béziau & G. Payette, as well as Around and beyond the Square of Opposition, ed. by J.-Y. Béziau & D. Jacquette, and, like those, a collection of selected peer-reviewed papers. The idea of this new volume is to maintain a good equilibrium between history, technical developments and applications. The volume is likely to attract a wide spectrum of readers, mathematicians, philosophers, linguists, psychologists and computer scientists, who may range from undergraduate students to advanced researchers. (shrink)

Let $ be the restriction of usual order relation to integers which are primes or squares of primes, and let ⊥ denote the coprimeness predicate. The elementary theory of $\langle\mathbb{N};\bot, , is undecidable. Now denote by $ the restriction of order to primary numbers. All arithmetical relations restricted to primary numbers are definable in the structure $\langle\mathbb{N};\bot, . Furthermore, the structures $\langle\mathbb{N};\mid, and $\langle\mathbb{N};=,+,x\rangle$ are interdefinable.

In his major work, the Periphyseon, the ninth century Latin philosopher John Scottus Eriugena gives, with the help of what he calls "dialectic", a rational analysis of reality. According to him, dialectic is a science which pertains both to language and reality. Eriugena grounds this position in a realist ontological exegesis of the Aristotelian categories, which are conceived as categories of being. His interpretation tends to transform logical patterns, such as Porphyry's Tree or the doctrine of the categories, into (...) a structure which is both ontological and logical, and to use them as tools for the analysis of the sensible world. The combination of dialectic interpreted as a science of being, capable of expressing truths about the sensible world as well as about discourse, with an ontological interpretation of logical concepts allows Eriugena to develop his metaphysical theory, a strong realism. Eriugena not only supports a theological realism, but also, and principally, an ontological realism, the assertion of the immanent existence of forms. Eriugena claims that genera and species really subsist in the individuals: they are completely and simultaneously present in each of the entities which belong to them. (shrink)

In the first part of the paper we study arithmetical properties of Pascal triangles modulo a prime power; the main result is the generalization of Lucas' theorem. Then we investigate the structure N; Bpx, where p is a prime, α is an integer greater than one, and Bpx = Rem, px); it is shown that addition is first-order definable in this structure, and that its elementary theory is decidable.

This paper is an attempt to clear some philosophical questions about the nature of logic by setting up a mathematical framework. The notion of congruence in logic is defined. A logical structure in which there is no non-trivial congruence relation, like some paraconsistent logics, is called simple. The relations between simplicity, the replacement theorem and algebraization of logic are studied (including MacLane-Curry’s theorem and a discussion about Curry’s algebras). We also examine how these concepts are related to (...) such notions as semantics, truth-functionality and bivalence. We argue that a logic, which is simple, can deserve the name logic and that the opposite view is connected with a reductionist perspective (reduction of logic to algebra). (shrink)

Rationals and countable ordinals are important examples of structures with decidable monadic second-order theories. A chain is an expansion of a linear order by monadic predicates. We show that if the monadic second-order theory of a countable chain C is decidable then C has a non-trivial expansion with decidable monadic second-order theory.

This article investigates the connections between the logics of being wrong, introduced in Steinsvold (2011, Notre Dame J. Form. Log., 52, 245–253), and factive ignorance, presented in Kubyshkina and Petrolo (2021, Synthese, 198, 5917–5928). The first part of the paper provides a sound and complete axiomatization of the logic of factive ignorance that corrects errors in Kubyshkina and Petrolo (2021, Synthese, 198, 5917–5928) and resolves questions about the expressivity of the language. In the second half, it is shown (...) that the relationship between the two logics suggests an alternative axiomatization for the logic of factive ignorance, the adequacy of which is easily proved via straightforward translations. (shrink)

The central purpose of this paper is to sketch the logic of being a democrat. That is, what is involved in being a democrat will be defined and delineated. I shall proceed by first examining Richard Wollheim's alleged paradox of democratic theory. Wollheim's solution to the paradox will then be shown to be unsatisfactory. Next, the concept of being a democrat will be clarified. The stage will then be set for showing that Wollheim's alleged paradox of (...) democratic theory dissolves upon discerning what a democrat qua democrat is committed to believe. In the process of clarifying what is involved in being a democrat and dissolving the alleged paradox of democratic theory, it will become evident that one popular argument often levelled against resistance to democratic law is without foundation. This is the argument that any democrat who conscientiously disobeys valid democratic law is necessarily behaving inconsistently with his democratic principles; and, therefore, if someone does conscientiously disobey valid democratic law, it proves he is not ‘really’ a democrat after all. (shrink)

This essay aims to demonstrate a clear and significant difference, not merely expository revisions or additions, in the logical progression of Being between Hegel's two main versions of the Doctrine of Being. This controversial issue is analyzed by retracing and examining changes that international scholarship still widely neglects. Focusing on Hegel's introduction of the doubled transition of Quality and Quantity in the genesis of Measure, the essay argues that the main point of the revisions is that Hegel views (...) the whole determinateness of Being as self-­sublating its own externality, because in one determination of Being passing into another one, the first does not vanish;; instead, both remain within their relational unity. Hegel's new version of the genesis of Measure indicates an essentially qualitative appreciation of the quantitative methods of the empirical sciences. This accords with Hegel's growing acknowledgment in Berlin of the independent cognitive status of the natural sciences in regard to philosophy, and with his reassessment of the relation between intuition, representation and conceptual cognition of the objects of consciousness, to do justice to their real differences and their being for themselves within their own existence. (shrink)

In this collection of essays Béatrice Longuenesse considers the three aspects of Kant's philosophy, his epistemology and metaphysics of nature, his moral philosophy and his aesthetic theory, under one unifying standpoint: Kant's conception of our capacity to form judgements. She argues that the elements which make up our cognitive access to the world - what Kant calls the 'human point of view' - have an equally important role to play in our moral evaluations and our aesthetic judgements. Her discussion ranges (...) over Kant's account of our representations of space and time, his conception of the logical forms of judgements, sufficient reason, causality, community, God, freedom, morality, and beauty in nature and art. Her book will appeal to all who are interested in Kant and his thought. (shrink)

This chapter contains sections titled: The Problem: Perspectives on Method, Or, How to Approach Being Hegel's “Vorbegriff” of Logical Method Absolute Method and the Truth of Being The Method of the Logic of Being Conclusion.

W. V. Quine thinks logical truth can be defined in purely extensional terms, as follows: a logical truth is a true sentence that exemplifies a logical form all of whose instances are true. P. F. Strawson objects that one cannot say what it is for a particular use of a sentence to exemplify a logical form without appealing to intensional notions, and hence that Quine's efforts to define logical truth in purely extensional terms cannot succeed. Quine's reply to this criticism (...) is confused in ways that have not yet been noticed in the literature. This may seem to favour Strawson's side of the debate. In fact, however, a proper analysis of the difficulties that Quine's reply faces suggests a new way to clarify and defend the view that logical truth can be defined in purely extensional terms. (shrink)

Ontological monists hold that there is only one way of being, while ontological pluralists hold that there are many; for example, concrete objects like tables and chairs exist in a different way from abstract objects like numbers and sets. Correspondingly, the monist will want the familiar existential quantifier as a primitive logical constant, whereas the pluralist will want distinct ones, such as for abstract and concrete existence. In this paper, we consider how the debate between the monist and pluralist (...) relates to the standard test for logicality. We deploy this test and show that it favors the monist. (shrink)

Taking into account significant developments in the metaphysical thinking of E. J. Lowe over the past 20 years, _More Kinds of Being:A Further Study of Individuation, Identity, and the Logic of Sortal Terms_ presents a thorough reworking and expansion of the 1989 edition of _Kinds of Being_ Brings many of the original ideas and arguments put forth in _Kinds of Being_ thoroughly up to date in light of new developments Features a thorough reworking and expansion of the earlier (...) work, rather than just a new edition Reflects the author's conversion to what he calls 'the four-category ontology,' a metaphysical system that takes its inspiration from Aristotle Provides a unified discussion of individuation and identity that should prove to be essential reading for philosophers working in metaphysics. (shrink)

The beginning of Marx’s Capital has references to Hegel’s Logic of Being. From the individual commodity considered in isolation, Marx derives the value form as the germ cell of capitalist society. Marx’s materialist inversion of the Hegelian dialectic posits the value form as a spectral objectivity that constitutes the real abstraction specific to capitalism. As the most abstract expression of capital, it rules unconsciously the totality of social praxis as an absolute fetish. Value arises from a double mystification: (...) the reification of capitalist social relations of production in an objective abstract form, and its representation in concrete objects, as commodities and money in circulation. Value, as the real abstraction of capitalist social relations of production, is the disjunctive synthesis between the despotic command of capital in production and the reciprocity of exchange in circulation. In the final chapter on primitive accumulation, Marx identifies its historical genesis in the dispossession of the commons, which, by separating the subjective from the objective conditions of production, gives rise to the capital-wage labour relation. (shrink)

Is logic normative for reasoning? In the wake of work by Gilbert Harman and John MacFarlane, this question has been reduced to: are there any adequate bridge principles which link logical facts to normative constraints on reasoning? Hitherto, defenders of the normativity of logic have exclusively focussed on identifying adequate validity bridge principles: principles linking validity facts—facts of the form 'gamma entails phi'—to normative constraints on reasoning. This paper argues for two claims. First, for the time being (...) at least, Harman’s challenge cannot be surmounted by articulating validity bridge principles. Second, Harman’s challenge can be met by articulating invalidity bridge principles: principles linking invalidity facts of the form 'gamma does not entail phi' to normative constraints on reasoning. In doing so, I provide a novel defence of the normativity of logic. (shrink)

The paper critically examines whether the open-endedness of the set concepts mandates the use of intuitionistic logic in set theory, as some philosophers think. [The sequel to this paper is ‘The Open-Endedness of the Set Concept and the Semantics of Set Theory' published in Synthese in 2003.].

"Graeme Nicholson addresses the fundamental topic of ontology, perhaps the fundamental topic posed to philosophy and the human mind: what is being?, i.e., what is it to exist or to be? He initially shows that we humans must be understood to be "existers" and "disclosers"--terms that render Heidegger's concept Dasein. Heidegger's philosophy provides the basic viewpoint, but Professor Nicholson offers an interpretation of Heidegger that seeks to set deconstructionist and pragmatist readings to one side. Since, according to Heidegger, (...) class='Hi'>being is fundamentally a union of presence and absence, this study shows that metaphysical theories have always offered positive illustrations or interpretations of being." "Illustrations of Being then goes on to scrutinize the four most fundamental determinations of being that Western thought has adumbrated: being as substance, especially in Greek ontology; being as reality, especially in the period from Descartes to Kant, and therefore in nineteenth- and twentieth-century science; the logic of being, in which Nicholson undertakes an ontological critique of mathematical logic; and being as the transformation of form--the key idea that runs from Christian patristics, through Hegel and Marx, to modern dialectics." "Graeme Nicholson's new study is marked by its receptiveness to metaphysics in the traditional sense, and contains a critique of the deconstructionist effort to pass beyond metaphysics. It will be of interest to professional philosophers and to theologians, as well as to graduate students and to members of the general public interested in philosophical arguments about the nature of being."--BOOK JACKET.Title Summary field provided by Blackwell North America, Inc. All Rights Reserved. (shrink)

Elucidating a metaphysics of medicine is vital for framing a coherent medical ethics. In this paper, I examine the historical case of Avicenna, the eleventh century physician-philosopher. Avicenna radicalizes the dissective power of reason using a logicized Aristotelian metaphysics to clarify concepts at the metaphysical level, which I call his anatomy of being. One of the practical consequences of Avicenna’s metaphysics is a dehumanizing eschatology of death. I outline the main elements of Avicenna’s thought that constitute his anatomy of (...) being. Through an examination of his logic, metaphysics, and psychology, I show how Avicenna develops a dissective logic. I conclude that one’s epistemology, as a method of knowing, entails a metaphysics, and, in turn, results in an ethical stance to the object of knowledge. For Avicenna, mental dissective logic applied to humans results in dehumanization, thereby destroying the humanistic impulse of medicine. (shrink)

It is commonly assumed that classical logic is the embodiment of a realist ontology. In “Sets and Semantics”, however, Jonathan Lear challenged this assumption in the particular case of set theory, arguing that even if one is a set-theoretic Platonist, due attention to a special feature of set theory leads to the conclusion that the correct logic for it is intuitionistic. The feature of set theory Lear appeals to is the open-endedness of the concept of set. This article (...) advances reasons internal to Lear’s account to show that his argument for intuitionistic set theory is unsuccessful. (shrink)

This edited volume is a comprehensive presentation of views on the relations between metaphysics and logic from Aristotle through twentieth century philosophers who contributed to the return of metaphysics in the analytic tradition. The collection combines interest in logic and its history with interest in analytical metaphysics and the history of metaphysical thought. By so doing, it adds both to the historical understanding of metaphysical problems and to contemporary research in the field. Throughout the volume, essays focus on (...) metaphysica generalis, or the systematic study of the most general categories of being. Beginning with Aristotle and his Categories , the volume goes on to trace metaphyscis and logic through the late ancient and Arabic traditions, examining the views of Thomas Aquinas, Duns Scotus, and William Ockham. Moving into the early modern period, contributors engage with Leibniz's metaphysics, Kant's critique of metaphysics, the relation between logic and ontology in Hegel, and Bolzano's views. Subsequent chapters address: Charles S. Peirce's logic and metaphysics; the relevance of set-theory to metaphysics; Meinong's theory of objects; Husserl's formal ontology; early analytic philosophy; C.I. Lewis and his relation to Russell; and the relations between Frege, Carnap, and Heidegger. Surveying metaphysics through to the contemporary age, essays explore W.V. Quine's attitude towards metaphysics; Wilfrid Sellars's relation to antidescriptivism as it connects to Kripke's; the views of Putnam and Kaplan; Peter F. Strawson's and David M. Armstrong's metaphysics; Trope theory; and its relation to Popper's conception of three worlds. The volume ends with a chapter on transcendental philosophy as ontology. In each chapter, contributors approach their topics not merely in an historical and exegetical fashion, but also engage critically with the thought of the philosophers whose work they discuss, offering synthesis and original philosophical thought in the volume, in addition to very extensive and well-informed analysis and interpretation of important philosophical texts. The volume will serve as an essential reference for scholars of metaphysics and logic. (shrink)

This talk surveys a number of methods currently being developed that assist in applying logic to the evaluation of arguments used in particular cases. A case is seen as specified by a given text and context of discourse. The methods used are pragmatic, and are based on the Gricean Cooperative Principle , as implemented in several types of goal-directed conversational exchanges.

Scientists routinely solve the problem of supplementing one’s store of variables with new theoretical posits that can explain the previously inexplicable. The banality of success at this task obscures a remarkable fact. Generating hypotheses that contain novel variables and accurately project over a limited amount of additional data is so difficult—the space of possibilities so vast—that succeeding through guesswork is overwhelmingly unlikely despite a very large number of attempts. And yet scientists do generate hypotheses of this sort in very few (...) tries. I argue that this poses a dilemma: either the long history of scientific success is a miracle, or there exists at least one method or algorithm for generating novel hypotheses with at least limited projectibility on the basis of what’s available to the scientist at a time, namely a set of observations, the history of past conjectures, and some prior theoretical commitments. In other words, either ordinary scientific success is miraculous or there exists a logic of discovery at the heart of actual scientific method. (shrink)