We are pleased to present this special issue of the journal History and Philosophy of Logic dedicated to the square of opposition.The square of opposition is a diagram and a theory of opposition re...

The theory of the square of opposition has been studied for over 2,000 years and has seen a resurgence in new theories and research since the second half of the twentieth century. This volume collects papers presented at the Sixth World Congress on the Square of Opposition, held in Crete in 2018, developing an interdisciplinary exploration of the theory. Chapter authors explore subjects such as Aristotle’s ontological square, logical oppositions in Avicenna’s hypothetical logic, and the power of (...) the square of opposition to solve theological problems regarding predestination and theodicy. Other topics covered include: Hegel’s opposition to diagrams De Morgan’s unpublished octagon of opposition turnstile figures of opposition institutional model-theoretic treatment of oppositions Lacan’s four formulas of sexuation the theory of oppositional poly-simplexes The Exoteric Square of Opposition will appeal to pure logicians, historians of logic, semioticians, philosophers, theologians, mathematicians, and psychoanalysts. (shrink)

In recent decades, research in the square of opposition has increased. New interpretations, extensions, and generalizations have been suggested, both Aristotelian and non-Aristotelian ones. The paper attempts to compare different versions of the square of opposition. For this reason, we appeal to the wider categorical model-theoretic framework of the theory of institutions.

This is a collection of new investigations and discoveries on the theory of opposition (square, hexagon, octagon, polyhedra of opposition) by the best specialists from all over the world. The papers range from historical considerations to new mathematical developments of the theory of opposition including applications to theology, theory of argumentation and metalogic.

One of the manuscripts of Buridan’s Summulae contains three figures, each in the form of an octagon. At each node of each octagon there are nine propositions. Buridan uses the figures to illustrate his doctrine of the syllogism, revising Aristotle's theory of the modal syllogism and adding theories of syllogisms with propositions containing oblique terms (such as ‘man’s donkey’) and with ‘propositions of non-normal construction’ (where the predicate precedes the copula). O-propositions of non-normal construction (i.e., ‘Some S (some) P (...) is not’) allow Buridan to extend and systematize the theory of the assertoric (i.e., non-modal) syllogism. Buridan points to a revealing analogy between the three octagons. To understand their importance we need to rehearse the medieval theories of signification, supposition, truth and consequence. (shrink)

This paper presents a new, third-personal account of empathy that characterizes empathy as being sensitive to others’ concerns as opposed to remaining stuck in one’s egocentric perspective on the world. The paper also demonstrates why this account is preferable to its two main rivals, namely the simulation theory of empathy, and the direct perception theory of empathy.

In this paper, we provide an overview of some of the results obtained in the mathematical theory of intermediate quantifiers that is part of fuzzy natural logic. We briefly introduce the mathematical formal system used, the general definition of intermediate quantifiers and define three specific ones, namely, “Almost all”, “Most” and “Many”. Using tools developed in FNL, we present a list of valid intermediate syllogisms and analyze a generalized 5-square of opposition.

In 1964, a debate that attracted widespread attention occurred within Chinese philosophical circles on the question of "one divides into two" and "two combine into one." But because the scholarly questions became mixed with politics, this debate never fully developed, and the critique of "one divides into two" was hurriedly terminated. "One divides into two" was judged to be the "correct, living, and common expression of the true nature and core of the materialist dialectic — the theory of the (...) unity of opposites," and it was interpreted as representing the broad functions of the revolutionary dialectic. (shrink)

In this paper, I will show to what extent we can use our modern understanding of the Square of Opposition in order to make sense of Kant 's double standard solution to the cosmological antinomies. Notoriously, for Kant, both theses and antitheses of the mathematical antinomies are false, while both theses and antitheses of the dynamical antinomies are true. Kantian philosophers and interpreters have criticized Kant 's solution as artificial and prejudicial. In the paper, I do not dispute such claims, (...) but I show that our modern understanding of the Square of Opposition enables us to more naturally deliver the result Kant was aiming at. Accordingly, the paper does not pretend to be exegetically accurate. It is an attempt to revise the antinomies with the help of standard classical logic. And although such a revision entails some re-interpretation, in the end, it will actually help to unveil some of Kant 's thoughts. (shrink)

How do social institutions exist? How do they direct our conduct? The Opposite Mirrors defends the thesis that the existence of institutions is a conventional matter. Ultimately they exist because we believe in their existence, and because they play a role in our practical reasoning. Human action necessarily has an unpredictable aspect; human institutions perform an important task by reducing uncertainty in our interactions. The author applies this thesis to the most important institutions: the law and the monetary system. In (...) his analysis he connects many traditional topics of the philosophy of law, social philosophy and the philosophy of social sciences in a new way. He discusses the nature of rules, authority, and power and analyzes the Hobbesian presuppositions which have been dominant in legal theory and in the economic analyses of the state. The book is written for legal theorists as well as for political and social philosophers, and theoretically oriented social scientists. (shrink)

Individuation -- Will -- Continuity -- Freedom.

The theory of opposition has always been viewed as the founding principle of structuralism within contemporary linguistics and semiotics. As an analytical technique, it has remained a staple within these disciplines, where it continues to be used as a means for identifying meaningful cues in the physical form ofsigns. However, as a theory of conceptual structure it was largely abandoned under the weight of post-structuralism starting in the 1960s — the exception tothis counter trend being the work of (...) the Tartu School of semiotics. This essay revisits opposition theory not only as a viable theory for understanding conceptual structure, but also as a powerful technique for establishing the interconnectedness of language, culture, and cognition. (shrink)

For more than 50 years the Guy's Hospital physician Frederick Pavy attempted to discredit the theory of his erstwhile teacher, Claude Bernard, that liver glycogen was broken down to supply sugar to the systemic circulation. His opposition was driven by his clinical perceptions and was based on two assumptions: the first was that the kidney was a simple filter through which small molecules would diffuse, so that sugar had to be prevented from reaching the systemic circulation. For Pavy, the (...) liver was the barrier. The second was teleological: he could not believe that nature would operate in what he saw as a defective way, i.e. converting sugar into glycogen and then back again. At the beginning of his long working life Pavy regarded himself as a physiologist and was critical of the stagnancy of English physiology which was kept afloat by amateurs like himself in whatever time they could spare from busy private practice. At the end he came to see his own view of carbohydrate metabolism as symbolic of the schism between responsible clinicians and irresponsible daydreaming physiologists. (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)

A general theory of logical oppositions is proposed by abstracting these from the Aristotelian background of quantified sentences. Opposition is a relation that goes beyond incompatibility (not being true together), and a question-answer semantics is devised to investigate the features of oppositions and opposites within a functional calculus. Finally, several theoretical problems about its applicability are considered.

Various semantics for studying the square of opposition have been proposed recently. So far, only [14] studied a probabilistic version of the square where the sentences were interpreted by (negated) defaults. We extend this work by interpreting sentences by imprecise (set-valued) probability assessments on a sequence of conditional events. We introduce the acceptability of a sentence within coherence-based probability theory. We analyze the relations of the square in terms of acceptability and show how to construct probabilistic versions of the (...) square of opposition by forming suitable tripartitions. Finally, as an application, we present a new square involving generalized quantifiers. (shrink)

In this paper is constructed an analogue of the square of opposition for propositions about relations between two non-empty sets. Unlike the classical square of opposition, the proposed scheme uses all logically possible syllogistic constants, formulated in V.I. Markin’s universal language for traditional positive syllogistic theories. This scheme can be called “Logical lantern”. The basic constants of this language are representing the five basic relations between two non-empty sets: equity, strict inclusion, reversed strict inclusion, intersection and exclusion (considered are only (...) the relations between sets, but not the relations of the sets to the universe). The other relations between sets are combinations (disjunctions) of the basic ones. There are 32 constants and 32 respective propositions, and the proposed diagram expresses and/or allows to deduce the logical relations among those propositions. The constructed scheme, making it possible to visually see the logical relations among propositions about relations between two non-empty sets, allows us to suggest considering logical relations not discussed previously: many-place Aristotelian-like logical relations among propositions: exhaustive _n_-place contrariety and exhaustive _n_-place subcontrariety (_n_ is a natural number, \(n>2\) ). (shrink)

After giving a short summary of the traditional theory of the syllogism, it is shown how the square of opposition reappears in the much more powerful concept logic of Leibniz. Within Leibniz’s algebra of concepts, the categorical forms are formalized straightforwardly by means of the relation of concept-containment plus the operator of concept-negation as ‘S contains P’ and ‘S contains Not-P’, ‘S doesn’t contain P’ and ‘S doesn’t contain Not-P’, respectively. Next we consider Leibniz’s version of the so-called Quantification (...) of the Predicate which consists in the introduction of four additional forms ‘Every S is every P’, ‘Some S is every P’, ‘Every S isn’t some P’, and ‘Some S isn’t some P’. Given the logical interpretation suggested by Leibniz, these unorthodox propositions also form a Square of Opposition which, when added to the traditional Square, yields a “Cube of Opposition”. Finally it is shown that besides the categorical forms, also the non-categorical forms can be formalized within an extension of Leibniz’s logic where “indefinite concepts” X, Y, Z\ function as quantifiers and where individual concepts are introduced as maximally consistent concepts. (shrink)

Various semantics for studying the square of opposition and the hexagon of opposition have been proposed recently. We interpret sentences by imprecise (set-valued) probability assessments on a finite sequence of conditional events. We introduce the acceptability of a sentence within coherence-based probability theory. We analyze the relations of the square and of the hexagon in terms of acceptability. Then, we show how to construct probabilistic versions of the square and of the hexagon of opposition by forming suitable tripartitions of (...) the set of all coherent assessments. Finally, as an application, we present new versions of the square and of the hexagon involving generalized quantifiers. (shrink)

The theory of the square of opposition has been worked out many centuries ago as a part of Aristotelian logic of terms.In spite of its inexactness (for instance it is not possible to decide whether the termsquare of opposition is a logical or a metalogical term) this theory is included without any changes in the usual elementary course of logic.The author defines the square of opposition in the language of the logic of propositions (see Def. 1.000) and derives (...) from this definition the usual laws of the square of opposition and several new theorems. (shrink)

A version of intuitionistic type theory is extended with opposite types, allowing a different formalization of negation and obtaining a paraconsistent type theory (⁠|$\textsf{PTT} $|⁠). The rules for opposite types in |$\textsf{PTT} $| are based on the rules of the so-called constructible falsity. A propositions-as-types correspondence between the many-sorted paraconsistent logic |$\textsf{PL}_\textsf{S} $| (a many-sorted extension of López-Escobar’s refutability calculus presented in natural deduction format) and |$\textsf{PTT} $| is proven. Moreover, a translation of |$\textsf{PTT} $| into intuitionistic type (...) theory is presented and some properties of |$\textsf{PTT} $| are discussed. (shrink)

This book presents a formal and philosophical analysis of language syntax. It refers to some ideas of E.Husserl and G. Frege, to S. Leśniewski's theory of syntactic categories and K. Ajdukiewicz's conception of formal grammar, also to Ch.S. Pierces's distinction between tokens (concrete linguistic entities) and types (ideal linguistic entities) and to A.A. Markov's theory of algorithms. The central aim of the book is - in the spirit of these ideas - to provide both strict yet comprehensive lectures (...) on two axiomatic theories of languages (grammars) irrespective of specific structure of their expression and the notation used in them. The main feature of these theories are that definitions of well-formed expression allow the formulation of algorithms for the examination of syntactic correctness of expressions and that their formalizations are bi-level, in reference to opposite philosophical orientations: nominalistic and idealistic. The theoretical considerations in the book speak in favour of the former. The book contains a translation of the basic contents of the book in Polish "Teorie języków syntaktycznie kategorialnych ("Theories of syntactically categorial languages"), PWN, Warszawa-Wrocław 1985, and extensive Introduction and Final Remarks. In Introduction are discussed the main assumptions, objectives and conditionings of presented theories and intuitive foundations of these theories. Final Remarks are connected with the subject-matter of the book and the ability to build syntax theories in the opposition spirit, because of the Platonic approach to language syntax. -/- . (shrink)

A reconstruction of Johnson's main contributions to philosophy is provided. Johnson's theories are grounded on his distinction between "substantives" and "adjectives", which governs the oppositions between (1) particular and universal, (2) determinandum and determinans in thought, (3) acts of separation and discrimination, (4) subject and predicate, (5) thing and quality, (6) substance and determination, (7) proposition and fact, (8) external and internal relations, (9) extension and intension. While substantives divide between continuants and occurrents, adjectives are fundamentally distinguishable into determinables (...) and determinates. The immediate (Stout, Broad) and later (Prior, Carnap, Searle, Armstrong, Hautamäki and Johansson) reception of Johnson's distinction between determinables and determinates is also discussed. (shrink)

. Each predicate of the Aristotelian square of opposition includes the word “is”. Through a twofold interpretation of this word the square includes both classical logic and non-classical logic. All theses embodied by the square of opposition are preserved by the new interpretation, except for contradictories, which are substituted by incommensurabilities. Indeed, the new interpretation of the square of opposition concerns the relationships among entire theories, each represented by means of a characteristic predicate. A generalization of the square of opposition (...) is achieved by not adjoining, according to two Leibniz’ suggestions about human mind, one more choice about the kind of infinity; i.e., a choice which was unknown by Greek’s culture, but which played a decisive role for the birth and then the development of modern science. This essential innovation of modern scientific culture explains why in modern times the Aristotelian square of opposition was disregarded. (shrink)

The recognition and reconciliation of ‘opposites’ lies at the heart of our most personal and global problems. These problems are ‘wicked’ in the sense that they are difficult or impossible to solve and arise at the interface of interdependent polarities. By exploring the human tendency to divide the world into two parts, _Wicked Problems & the Reconciliation of Opposites_ argues that our relationship with such pairings and polarities is profoundly important to the way we recognise and resolve wicked problems. Using (...) an original theory of bi-relational development, Adam proposes that our everyday ways of knowing and being can be powerfully located and understood in terms of the creation, emergence, opposition, convergence, collapse and trans-positioning of dyadic constituents. Chapters use this concept to frame key debates in and across domains of knowledge, including education, psychology, law and theology, as well as to offer a new perspective on the most profound problems of the twenty-first century: globalisation, sustainability and secularisation. This book is a comprehensive study of dyadic structrures and relationships and provides a multidisciplinary and original approach to human development. It will be of great interest to students and academics of social psychology, psychosocial development, psychoanalysis and transpersonal psychology, but it is also relevant within the fields of education, human development and theology. (shrink)

In the system of the philosophical and sociological ideas of the Frankfurt School the "critical theory" of society occupies the central place. In the "critical theory" are interwoven all the most significant aspects of the philosophical, economic, political, sociological, psychological, aesthetic, and ethical ideas dealt with by the representatives of this school. And therefore it is not accidental that the concept of the "critical theory" of society is employed frequently as a synonym of the social philosophy of (...) the Frankfurt School. The multi-leveled problematique of the "critical theory" of society, and the contradictoriness of the theoretical positions of its adherents, complicate critical analysis. Therefore, the explanation of its methodological orientation, which can help us to understand better the existence and actual philosophical nature of this theory, has important significance for our discussion. (shrink)

In this article I develop my argument for a shallow interpretivist theory of sport by showing that whereas it applies to all oppositional sports, the standard theory of sport for the past twenty ye...

The Theory of Event Coding (TEC) is a new framework for understanding interactions between perception and action. We are concerned that the theory is underspecified, showing that it can easily be used to make exactly opposite predictions. Precise specification of the time course of activation and binding is needed to make the theory useful for understanding the perception-action interface.

During the last decades, the psychology of reasoning has identified experimentally many fallacies committed by spontaneous reasoners. Given these experimental results, some theories have been developed about this phenomenon, mainly algorithmic theories. This paper develops instead a computational modelling of these current fallacies which appear as simplifications in the treatment of information that do not respect the formal rules of classical propositional logic. These fallacies are explained as crushes in the Klein group structure and so, in squares of opposition. These (...) crushes are an effect of not to take into account the dual of the binary operator at work in the major premise of the inference. This analysis allows predictions on fallacies not identified before, which are fallacies produced when reasoning with incompatibilities. The paper concludes with consequences of the analysis on pedagogical strategies for the teaching of logic. (shrink)

This book examines the legacy of Antonio Gramsci and Leon Trotsky in the shadow of Stalinism in order to reassess the very different and distorted academic reception of the two figures, as well as to contribute to the revitalization of Marxism for our time. While Gramsci and Trotsky lived and died in a similar fashion, as revolutionary Marxist leaders and theoreticians, their reception in academia could not be more different. Gramsci has become tremendously popular, becoming a central figure in many (...) disciplines, while Trotsky remains largely ignored. Saccarelli argues that not only is Gramsci popular for the wrong reasons--being routinely distorted and depoliticized--even when rescued from his contemporary users, Gramsci remains inadequate. Conversely, the fact that Trotsky remains beyond the pale of "theory" is a terrible indictment of the current state of academic thinking. (shrink)

. In the 18th century, Gottfried Ploucquet developed a new syllogistic logic where the categorical forms are interpreted as set-theoretical identities, or diversities, between the full extension, or a non-empty part of the extension, of the subject and the predicate. With the help of two operators ‘O’ (for “Omne”) and ‘Q’ (for “Quoddam”), the UA and PA are represented as ‘O(S) – Q(P)’ and ‘Q(S) – Q(P)’, respectively, while UN and PN take the form ‘O(S) > O(P)’ and ‘Q(S) > (...) O(P)’, where ‘>’ denotes set-theoretical disjointness. The use of the symmetric operators ‘–’ and ‘>’ gave rise to a new conception of conversion which in turn lead Ploucquet to consider also the unorthodox propositions O(S) – O(P), Q(S) – O(P), O(S) > Q(P), and Q(S) > Q(P). Although Ploucquet’s critique of the traditional theory of opposition turns out to be mistaken, his theory of the “Quantification of the Predicate” is basically sound and involves an interesting “Double Square of Opposition”. (shrink)

This is a collection of new investigations and discoveries on the theory of opposition by the best specialists from all over the world. The papers range from historical considerations to new mathematical developments of the theory of opposition including applications to theology, theory of argumentation and metalogic.

In this paper I propose a set-theoretical interpretation of the logical square of opposition, in the perspective opened by generalized quantifier theory. Generalized quantifiers allow us to account for the semantics of quantificational Noun Phrases, and of other natural language expressions, in a coherent and uniform way. I suggest that in the analysis of the meaning of Noun Phrases and Determiners the square of opposition may help representing some semantic features responsible to different logical properties of these expressions. I (...) will conclude with some consideration on scope interactions between quantifiers. (shrink)

Presented as a Vorlesung in the German philosophical tradition, this book presents the most detailed account of Nelson's method of argument analysis, celebrated by many luminaries such as Karl Popper. It was written in 1921 in opposition to the relativistic, subjectivistic and nihilistic tendencies of Nelson's time. The book contains an exposition of a method that is a further development of Kant's transcendental dialectics, followed by an application to the critical analysis of arguments by many famous thinkers, including Bentham, Mill, (...) Poincaré, Leibniz, Hegel, Einstein, Bergson, Rickert, Simmel, Brentano, Stammler, Jellinek, Dingler, and Meinong. The book presents a general theory of philosophical argumentation as seen from the viewpoint of the typical fallacies committed by anybody arguing philosophically, whether professional philosophers or philosophical laypeople. Although the nature of philosophy and philosophical argumentation is one of the most recurrent objects of reflection for philosophers, this book represents the first attempt at a general theory of philosophical fallacy. According to Nelson, it is in the shape of false dilemmas that errors in reasoning always emerge, and false dilemmas are always the result of the same mechanism--the unwitting replacement of one concept for another. (shrink)

The place of the subjective -- Everything that is of a whole constitutes an obstacle to it insofar as it is included in it -- Action, manor of the subject -- The real is the impasse of formalization : formalization is the locus of the passing-into-force of the real -- Hegel : "the activity of force is essentially activity reacting against itself" -- Subjective and objective -- The subject under the signifiers of the exception -- Of force as disappearance, whose (...) effect is the whole from which it has disappeared -- Deduction of the splitting -- A la nue accablante tu? -- Any subject is a forced exception, which comes in second place -- Jewelry for the sacred of any subtraction of existence -- Lack and destruction -- The new one forbids the new one and presupposes it -- On the side of the true -- There are no class relations -- Every subject crosses a lack of being and a destruction -- The subjects antecedence to itself -- Torsion -- Theory of the subject according to Sophocles, theory of the subject according to Eeschylus -- Of the strands of the knot, knowing only the color -- A materialist reversal of materialism -- The Black sheep of materialism -- The indissoluble salt of truth -- Answering to the sphinx demands from the subject not to have to answer or the sphinx -- Algebra and topology -- Neigborhoods -- Consistency, second name of the real after the cause -- So little ontology -- Subjectivization and subjective process -- The topological opposite of the knot is not the cut-dispersion but the destruction-recomposition -- Subjectivizing anticipation, retroaction of the subjective process -- Hurry! hurry! word of the living! -- The inexistent -- Logic of the excess -- Topics of ethics -- Where? -- The subjective twist : and -- Diagonals of the imaginary -- Schema -- Ethics as the dissipation of the paradoxes of partisanship -- Classical detour -- Love what you will never believe twice. (shrink)

This book examines the legacy of Antonio Gramsci and Leon Trotsky in the shadow of Stalinism in order to reassess the very different and distorted academic reception of the two figures, as well as to contribute to the revitalization of Marxism for our time. While Gramsci and Trotsky lived and died in a similar fashion, as revolutionary Marxist leaders and theoreticians, their reception in academia could not be more different. Gramsci has become tremendously popular, becoming a central figure in many (...) disciplines, while Trotsky remains largely ignored. Saccarelli argues that not only is Gramsci popular for the wrong reasons--being routinely distorted and depoliticized--even when rescued from his contemporary users, Gramsci remains inadequate. Conversely, the fact that Trotsky remains beyond the pale of "theory" is a terrible indictment of the current state of academic thinking. (shrink)

In this paper, I propose a new way of understanding the space of possibilities in the field of mental content. The resulting map assigns separate locations to theories of content that have generally been lumped together on the more traditional map. Conversely, it clusters together some theories of content that have typically been regarded as occupying opposite poles. I make my points concrete by developing a taxonomy of theories of mental content, but the main points of the paper concern not (...) merely how to classify, but how to understand, the theories. Also, though the paper takes theories of mental content as a case study, much of the discussion is applicable to theories of other phenomena. To a first approximation, the difference between the traditional and the proposed taxonomies turns on whether we classify theories of content by, on the one hand, their implications for a non-redundant supervenience base for content facts (i.e., for facts about what contents thoughts have) or, on the other, by their constitutive accounts of content. By a "constitutive account," I mean the kind of elucidation of the nature of a phenomenon that theorists have tried to give for, for example, knowledge, justice, personal identity, consciousness, convention, heat, and limit. The tendency to taxonomize by supervenience base is encouraged, I suggest, by a failure to keep clearly in view a distinction between constitutive and modal determination. Many philosophers would accept that a constitutive account cannot be captured in purely modal terms. Giving a constitutive account is not the same as specifying modally necessary and sufficient conditions. Nevertheless, philosophers often try to cash constitutive claims in modal terms. A case in point is that theories of content tend to be conceptualized in terms of the theories' implications for a supervenience base for content facts. My thesis goes beyond the by-now somewhat familiar proposition that not all modal determinants of a phenomenon are constitutive determinants. One who has taken that point on board might nevertheless conceive of a philosophical account as an attempt to specify constitutive determinants of the target phenomenon that make up a non-redundant supervenience base for the phenomenon. Shoehorning a philosophical account into this form leaves out elements that are modally redundant, but may be explanatorily or ontologically significant. For example, when a constitutive account has multiple levels, the different levels will typically be modally redundant. Formulating the account as a specification of a supervenience base of constitutive determinants will therefore flatten the account into a single level. Many of my arguments can be illustrated by considering the place of normativity in the theory of content. The new taxonomy gives a distinct niche to normative theories of content - theories that explain a thought's having a certain content at least in part in terms of the obtaining of normative facts. By contrast, on a traditional map, normative theories are invisible as such because normative facts supervene on non-normative ones. (shrink)

The topic of truth has long been thought to be connected to scientific realism and its opposition. In this essay, I discuss the various ways that truth might be related to realism. First, I consider how truth might be of use when defining scientific realism and its opposition. Second, I consider whether various stances regarding realism require specific stances on the nature of truth. I survey "neutralist" views that argue that one's stance on realism is independent of one's view on (...) truth, and partisan positions that claim that one's attitude on realism is, in part, determined by one's theory of truth. Though partisan views have been popular, and defended by seminal figures such as Thomas Kuhn, Richard Rorty, Hilary Putnam, and Arthur Fine, I raise a number of objections for them. (shrink)

In The Structure of Biological Science I argued that the theory of natural selection is a statistical theory for reasons much like those which makes thermodynamics a statistical theory. In particular, the theory claims that fitness differences are large enough and the life span of species long enough for increases in average fitness always to appear in the long run; and this claim, I held, is of the same form as the statistical version of the second (...) law of thermodynamics.For the latter law also makes a claim about the long run, and its statistical character is due to this claim: thermodynamic systems must in the long run approach an equilibrium level of organization that maximizes entropy. Over finite times, given local boundary conditions, an isolated mechanical system, like the molecules in a container of gas, may sometimes interact so as to move the entropy of the system further from, instead of closer to the equilbrium level. But given enough interacting bodies, and enough time, the system will always eventually move in the direction prescribed by the law. Thus, we can attach much higher probabilities to the prediction that non-equilibrium systems will reflect greater entropy in future periods than we can to predictions that they will move in the opposite direction. And as we increase the amount of time and the number of bodies interacting, the strength of the probability we can attach to the prediction becomes greater and greater. (shrink)

In 1995 Slater argued both against Priest’s paraconsistent system LP (1979) and against paraconsistency in general, invoking the fundamental opposition relations ruling the classical logical square. Around 2002 Béziau constructed a double defence of paraconsistency (logical and philosophical), relying, in its philosophical part, on Sesmat’s (1951) and Blanche’s (1953) “logical hexagon”, a geometrical, conservative extension of the logical square, and proposing a new (tridimensional) “solid of opposition”, meant to shed new light on the point raised by Slater. By using n-opposition (...) theory (NOT) we analyse Beziau’s anti-Slater move and show both its right intuitions and its technical limits. Moreover, we suggest that Slater’s criticism is much akin to a well-known one by Suszko (1975) against the conceivability of many-valued logics. This last criticism has been addressed by Malinowski (1990) and Shramko and Wansing (2005), who developed a family of tenable logical counter-examples to it: trans-Suszkian systems are radically many-valued. This family of new logics has some strange logical features, essentially: each system has more than one consequence operator. We show that a new, deeper part of the aforementioned geometry of logical oppositions (NOT), the “logical poly-simplexes of dimension m”, generates new logical-geometrical structures, essentially many-valued, which could be a very natural (and intuitive) geometrical counterpart to the “strange”, new, non-Suszkian logics of Malinowski, Shramko and Wansing. By a similar move, the geometry of opposition therefore sheds light both on the foundations of paraconsistent logics and on those of many-valued logics. (shrink)