Complete deductive systems are constructed for the non-valid (refutable) formulae and sequents of some propositional modal logics. Thus, complete syntactic characterizations in the sense of Lukasiewicz are established for these logics and, in particular, purely syntactic decision procedures for them are obtained. The paper also contains some historical remarks and a general discussion on refutation systems.

In the paper rejection systems for a system of nonsense-logic are investigated. The first rejection system consists of four rejected axioms and only one rejection rule  the rule of rejection by detachment. The second one consists of one rejected axiom and two rejection rules: the rule of rejection by detachment and the rule of rejection by substitution. The aim of the paper is to present also a proof of Ł-decidability for the considered systems.

Hybrid deduction–refutation systems are deductive systems intended to derive both valid and non-valid, i.e., semantically refutable, formulae of a given logical system, by employing together separate derivability operators for each of these and combining ‘hybrid derivation rules’ that involve both deduction and refutation. The goal of this paper is to develop a basic theory and ‘meta-proof’ theory of hybrid deduction–refutation systems. I then illustrate the concept on a hybrid derivation system of natural deduction for (...) classical propositional logic, for which I show soundness and completeness for both deductions and refutations. (shrink)

The aim of this paper is to study the refutation system consisting of the refutation axiom p ∧ ¬p → q and the refutation rules: reverse substitution and reverse modus ponens (B/A, if A → B ∈ RM). It is shown that the refutation system is characteristic for the logic of the 3-element RM algebra.

Hybrid deduction-refutation systems are presented for four first degree entailment based logics. The hybrid systems are shown to deductively and refutationally sound and complete with respect to their logics. The proofs of completeness are presented in a uniform way. This paper builds on work in [6], where Goranko presented a deductively and refutationally sound and complete hybrid system for classical logic.

A sufficient condition for an extension of positive logic with strong negation to be characterized by a class of finite trees is given.

There is reason for genuine puzzlement about Hume's aim in ‘The Natural History of Religion’. Some commentators take the work to be merely a causal investigation into the psychological processes and environmental conditions that are likely to give rise to the first religions, an investigation that has no significant or straightforward implications for the rationality or justification of religious belief. Others take the work to constitute an attack on the rationality and justification of religious belief in general. In contrast to (...) these views, I argue that Hume aims to establish two important claims in ‘The Natural History of Religion’. First, almost all popular religions, including popular monotheism, are deeply superstitious. Second, superstitious monotheism is incompatible with the variety of theism supported by the argument from design. This incompatibility puts significant pressure on the rational acceptability of popular religions. (shrink)

A general theory of refutation systems is given. Some applications (concerning maximality and minimality in lattices of logics) are also discussed.

The goal of this paper is to generalize specific techniques connected with refutation rules involving certain normal forms. In particular, a method of axiomatizing both a logic L and its complement −L is introduced.

The purpose of the paper is to study syntactic refutation systems as a way of characterizing normal modal propositional logics. In particular it is shown that there is a decidable modal logic without the finite model property that has a simple finite refutation system.

Refutation systems are formal systems for inferring the falsity of formulae. These systems can, in particular, be used to syntactically characterise logics. In this paper, we explore the close connection between refutation systems and admissible rules. We develop technical machinery to construct refutation systems, employing techniques from the study of admissible rules. Concretely, we provide a refutation system for the intermediate logics of bounded branching, known as the Gabbay–de Jongh logics. We (...) show that this gives a characterisation of these logics in terms of their admissible rules. To illustrate the technique, we also provide a refutation system for Medvedev’s logic. (shrink)

In this paper we study symmetric inference systems (that is, pairs of inference systems) as refutation systems characterizing maximal logics with certain properties. In particular, the method is applied to paraconsistent logics, which are natural examples of such logics.

À la demande de Bossuet, qui voyait à travers l’idée d’ordre qui guide l’acte créateur de Dieu dans la métaphysique de Malebranche l’expression d’une forme de fatalisme, Fénelon entreprend de dénoncer à la lumière de la vérité de l’Écriture les erreurs de ce système. Théologique et apologétique dans son intention première, la critique semble toutefois recourir à des arguments esthétiques pour défendre l’idée d’une absolue liberté de Dieu. Tout en montrant que Dieu n’est pas un artisan, soumis à une nécessité (...) inflexible, ni le monde une machine imparfaite, Fénelon poursuivrait sa propre réflexion esthétique, et prolongerait, notamment à partir des notions de simplicité et de sublimité, l’argumentation des Dialogues sur l’éloquence..., tout en anticipant celle qui sera exposée dans la Lettre à l’Académie. (shrink)

An environmental ethic holds that some entities in nature or in natural states of affairs are intrinsically valuable. I argue that proposals for an environmental ethic either fail to satisfy requirements which any ethical system must satisty to be an ethic or they fail to give us reason to suppose that the values they promote are intrinsic values. If my arguments are correct, then environmental ethics is not properly ethics at all.

An environmental ethic holds that some entities in nature or in natural states of affairs are intrinsically valuable. I argue that proposals for an environmental ethic either fail to satisfy requirements which any ethical system must satisty to be an ethic or they fail to give us reason to suppose that the values they promote are intrinsic values. If my arguments are correct, then environmental ethics is not properly ethics at all.

We consider tautologies expressing equivalence‐chain properties in the spirit of Thapen and Krajíček, which are candidates for exponentially separating depth k and depth Frege proof systems. We formulate a special case where the initial member of the equivalence chain is fully specified and the equivalence‐chain implications are actually equivalences. This special case is shown to lead to polynomial size resolution refutations. Thus it cannot be used for separating depth k and depth propositional systems. We state some Håstad switching (...) lemma conditions that restrict the possible propositional proofs in more general situations. (shrink)

A refutation mechanism is introduced into logic programming, dual to the usual proof mechanism; then negation is treated via refutation. A four-valued logic is appropriate for the semantics: true, false, neither, both. Inconsistent programs are allowed, but inconsistencies remain localized. The four-valued logic is a well-known one, due to Belnap, and is the simplest example of Ginsberg’s bilattice notion. An efficient implementation based on semantic tableaux is sketched; it reduces to SLD resolution when negations are not involved. The (...) resulting system can give reasonable answers to queries that involve both negation and free variables. Also it gives the same results as Prolog when there are no negations. Finally, an implementation in Prolog is given. (shrink)

In this paper I will develop a lambda-term calculus, lambda-2Int, for a bi-intuitionistic logic and discuss its implications for the notions of sense and denotation of derivations in a bilateralist setting. Thus, I will use the Curry-Howard correspondence, which has been well-established between the simply typed lambda-calculus and natural deduction systems for intuitionistic logic, and apply it to a bilateralist proof system displaying two derivability relations, one for proving and one for refuting. The basis will be the natural deduction (...) system of Wansing's bi-intuitionistic logic 2Int, which I will turn into a term-annotated form. Therefore, we need a type theory that extends to a two-sorted typed lambda-calculus. I will present such a term-annotated proof system for 2Int and prove a Dualization Theorem relating proofs and refutations in this system. On the basis of these formal results I will argue that this gives us interesting insights into questions about sense and denotation as well as synonymy and identity of proofs from a bilateralist point of view. (shrink)

We offer a critical overview of two sorts of proof systems that may be said to characterize classical propositional logic indirectly (and non-standardly): refutation systems, which prove sound and complete with respect to classical contradictions, and rejection systems, which prove sound and complete with respect to the larger set of all classical non-tautologies. Systems of the latter sort are especially interesting, as they show that classical propositional logic can be given a paraconsistent characterization. In both (...) cases, we consider Hilbert-style systems as well as Gentzen-style sequent calculi and natural-deduction formalisms. (shrink)

Searle proposes an argument in order to prove the existence of universals and thereby solve the problem of universals: From every meaningful general term P(x) follows a tautology Vx[P(x) v -P(x)], which entails the existence of the corresponding universal P. To be convincing, this argument for existence must be valid, it must presume true premises and it must be free of any informal fallacy. First, the validity of the argument for existence in its non-modal interpretation will be proven with the (...) help of the formal deductive system F. Secondly, it will be shown that a self-contradictory tautology concept is employed, which renders the premises meaningless. Consequently, the inconsistency will be emended through redefinition and the argument's ensuing correctness will be demonstrated. Finally, it will be shown that the argument for existence presupposes the existence of universals in its premise and hence begs the question. (shrink)

The goal of this paper is to analyse Implicational Relevance Logic from the point of view of refutability. We also correct an inaccuracy in our paper “The RM paraconsistent refutation system”.

This paper considers how the terms ‘objection,’ ‘rebuttal,’ ‘attack,’ ‘refutation,’ ‘rebutting defeater’ and ‘undercutting defeater’ are used in writings on argumentation and artificial intelligence. The central focus is on the term ‘rebuttal.’ A provisional classification system is proposed that provides a normative structure within which the terms can be clarified, distinguished from each other, and more precisely defined.

It is widely, if not universally, assumed by philosophers that it is impossible to justify the reliability of memory without recourse to the use of memory. This so-called “epistemic circularity” is supposed to infect all attempts to justify memory as a source of knowledge in a noncircular way. In this paper, we argue that advances in cognitive science radically upheave the traditional, folk-psychological conception of memory which epistemologists have hitherto been subjecting to analysis. With an updated view of the nature (...) of the diverse systems typically falling under the umbrella term “memory”, it can be shown that the epistemic circularity associated with the justification of memory no longer rears its ugly head. We show that it is possible to give a noncircular justification of memory. In so doing, we believe that we have solved a perennial problem in epistemology. (shrink)

This thesis introduces a new theoretical tool to explore the notion of time and temporal order in quantum mechanics: the relativistic quantum "clock" framework. It proposes novel thought experiments showing that proper time can display quantum features, e.g. when a "clock" runs different proper times in superposition. The resulting new physical effects can be tested in near-future laboratory experiments (with atoms, molecules and photons as "clocks"). The notion of time holds the key to the regime where quantum theory and general (...) relativity overlap, which has not been directly tested yet and remains largely unexplored by the theory. The framework also applies to scenarios in which causal relations between events become non-classical and which were previously considered impossible to address without refuting quantum theory. The relativistic quantum "clock" framework offers new insights into the foundations of quantum theory and general relativity. (shrink)

SummaryThis paper attempts to develop an interpretation of Kant's transcendental idealism which is based upon his critique of transcendental realism . It is argued that given Kant's transcendental distinction, all non‐ or pre‐critical philosophies, even Berkeleian phenomenalism are transcendentally realistic. This paradoxical result is used as the basis for an analysis of Kant's resolution of the mathematical antinomies, wherein this resolution is seen both as an “indirect proof” of transcendental idealism and as a refutation of transcendental realism. Finally, it (...) is claimed that Kant's idealism, at least insofar as it is established by means of a refutation of transcendental realism, is methodological rather than metaphysical, viz. it involves a claim about how the sensible world is to be considered in transcendental reflection, not a claim about the “real nature” of this world.RésuméCet article essaye de développer une interprétation de l'idéalisme transcendental de Kant, interprétation basée sur sa critique du réalisme transcendental . L'auteur montre que, si l'on accepte la distinction transcendentale de Kant, toutes les philosophies non critiques et précritiques sont transcendentalement réalistes, y compris le phénoménalisme de Berkeley. A partir de ce résultat paradoxal, il analyse la manière dont Kant résoud les antinomies mathématiques: cette résolution apparaît à la fois comme preuve indirecte de l'idéalisme transcendental et comme une réfutation du réalisme transcendental. L'auteur est finalement d'avis que l'idéalisme de Kant, du moins lorsqu'il est justifié par une réfutation du réalisme transcendental, est plus méthodologique que métaphysique, c'est‐à‐dire qu'il déclare comment le monde sensible doit être considéré dans la réflexion transcendentale et non quelle est la véritable nature de ce monde.ZusammenfassungEs wird versucht, eine Interpretation von Kants transzendentalem Idealismus zu entwickeln, die auf seiner Kritik am transzendentalen Realismus — verstanden als derjenige Standpunkt, der systematisch Erscheinung und Ding an sich verwechselt — beruht. Es wird argumentiert, dass — einmal Kants transzendentale Unterscheidung angenommen — aile früheren, vorkritischen Systeme der Philosophie einschliesslich Berkeleys Phänomenalismus transzendental realistisch sind. Dieses paradoxale Ergebnis wird als Basis für eine Analyse von Kants Auflösung der mathematischen Antinomien verwendet, wobei dièse Auflösung sowohl als ein indirekter Beweis für den transzendentalen Idealismus als auch als eine Widerlegung des transzendentalen Realismus gedeutet wird. Es wird schliesslich nahegelegt, dass Kants Idealismus, sofern wenigstens als er sich auf Widerlegung des transzendentalen Realismus abstützt, mehr ein rnethodologischer als ein metaphysischer Idealismus ist. Er statuiert eher über die Art, wie die Sinneswelt in einer transzendentalen Reflexion betrachtet werden soll, als über die Frage, wie die Welt wirklich beschaffen sei. (shrink)

SummaryThis paper attempts to develop an interpretation of Kant's transcendental idealism which is based upon his critique of transcendental realism. It is argued that given Kant's transcendental distinction, all non‐ or pre‐critical philosophies, even Berkeleian phenomenalism are transcendentally realistic. This paradoxical result is used as the basis for an analysis of Kant's resolution of the mathematical antinomies, wherein this resolution is seen both as an “indirect proof” of transcendental idealism and as a refutation of transcendental realism. Finally, it is (...) claimed that Kant's idealism, at least insofar as it is established by means of a refutation of transcendental realism, is methodological rather than metaphysical, viz. it involves a claim about how the sensible world is to be considered in transcendental reflection, not a claim about the “real nature” of this world.RésuméCet article essaye de développer une interprétation de l'idéalisme transcendental de Kant, interprétation basée sur sa critique du réalisme transcendental. L'auteur montre que, si l'on accepte la distinction transcendentale de Kant, toutes les philosophies non critiques et précritiques sont transcendentalement réalistes, y compris le phénoménalisme de Berkeley. A partir de ce résultat paradoxal, il analyse la manière dont Kant résoud les antinomies mathématiques: cette résolution apparaît à la fois comme preuve indirecte de l'idéalisme transcendental et comme une réfutation du réalisme transcendental. L'auteur est finalement d'avis que l'idéalisme de Kant, du moins lorsqu'il est justifié par une réfutation du réalisme transcendental, est plus méthodologique que métaphysique, c'est‐à‐dire qu'il déclare comment le monde sensible doit être considéré dans la réflexion transcendentale et non quelle est la véritable nature de ce monde.ZusammenfassungEs wird versucht, eine Interpretation von Kants transzendentalem Idealismus zu entwickeln, die auf seiner Kritik am transzendentalen Realismus — verstanden als derjenige Standpunkt, der systematisch Erscheinung und Ding an sich verwechselt — beruht. Es wird argumentiert, dass — einmal Kants transzendentale Unterscheidung angenommen — aile früheren, vorkritischen Systeme der Philosophie einschliesslich Berkeleys Phänomenalismus transzendental realistisch sind. Dieses paradoxale Ergebnis wird als Basis für eine Analyse von Kants Auflösung der mathematischen Antinomien verwendet, wobei dièse Auflösung sowohl als ein indirekter Beweis für den transzendentalen Idealismus als auch als eine Widerlegung des transzendentalen Realismus gedeutet wird. Es wird schliesslich nahegelegt, dass Kants Idealismus, sofern wenigstens als er sich auf Widerlegung des transzendentalen Realismus abstützt, mehr ein rnethodologischer als ein metaphysischer Idealismus ist. Er statuiert eher über die Art, wie die Sinneswelt in einer transzendentalen Reflexion betrachtet werden soll, als über die Frage, wie die Welt wirklich beschaffen sei. (shrink)

Lewis has recently argued that Maudlin׳s contingent absorber experiment remains a significant problem for the Transactional Interpretation. He argues that the only straightforward way to resolve the challenge is by describing the absorbers as offer waves, and asserts that this is a previously unnoticed aspect of the challenge for TI. This argument is refuted in two basic ways: it is noted that the Maudlin experiment cannot be meaningfully recast with absorbers described by quantum states; instead the author replaces it with (...) an ordinary which-way experiment; and the extant rebuttals to the Maudlin challenge in its original form are not in fact subject to the alleged flaws that Lewis ascribes to them. This paper further seeks to clarify the issues raised in Lewis’ presentation concerning the distinction between quantum systems and macroscopic objects in TI. It is noted that the latest, possibilist version of TI has no ambiguity concerning macroscopic absorbers. In particular, macroscopic objects are not subject to indeterminate trajectories, since they are continually undergoing collapse. It is concluded that the Maudlin challenge poses no significant problem for the transactional interpretation. (shrink)

L'article montre que l'idée développée par Popper dans The Open Universe, et reprise par d'autres, selon laquelle la physique moderne serait foncièrement indéterminisme, repose en réalité sur une conception erronée du déterminisme. Popper n'a pas de mal à montrer que l'état initial d'un système n'étant jamais connu avec une précision absolue, il est impossible de prédire avec certitude son évolution future. Mais cela ne signifie pas pour autant que le déterminisme soit réfuté. Popper s'est attaqué à une des conséquences du (...) déterminisme, à savoir la prédictïbilité universelle, mais il laisse intact le coeur même de la doctrine du déterminisme, c'est-à-dire l'idée que chaque événement suit de manière univoque celui qui le précède. La mécanique classique est déterministe, la relativité restreinte est déterministe, et la mécanique quantique elle-même, à condition toutefois de laisser de côté l'épineux problème de l'opération de mesure, est déterministe. The article deals with an idea developed by Popper in The Open Universe, and supported afterwards by some others. Indeed, according to them, modern physics would be basically indeterministic. This idea rests in fact on a wrong conception of determinism. Popper has no difficulty in showing that, as the initial state of a system is never known with an absolute accuracy, one cannot predict with certainty what will come of it But that does not mean that determinism is refuted Popper has critized one of the consequences of determinism, that is universal predictibility, but he retains the main idea of the doctrine of determinism, which means that each event follows univocally the one which preceeds it. Classical mechanics is deterministic, special relativity is deterministic, and quantum mechanics itself is deterministic too, provided that the difficult problem of the act of measurement is put aside. (shrink)

In a recent paper, Levy, Gadd, Kerridge, and Komesaroff attempt to defend the ethicality of homeopathy by attacking the utilitarian ethical framework as a basis for medical ethics and by introducing a distinction between evidence-based medicine and modern science. This paper demonstrates that their argumentation is not only insufficient to achieve that goal but also incorrect. Utilitarianism is not required to show that homeopathic practice is unethical; indeed, any normative basis of medical ethics will make it unethical, as a defence (...) of homeopathic practice requires the rejection of modern natural sciences, which are an integral part of medical ethics systems. This paper also points out that evidence-based medicine lies at the very core of modern science. Particular arguments made by Levy et al. within the principlist medical ethics normative system are also shown to be wrong. (shrink)

In a diversity course for pre-service teachers, we explored coursework by students of color to uncover instances in which they resisted the existence systemic oppression in K12 schools. First, we examined the written responses from three students of color (Asian-Indian, Asian immigrant, and Latina) who were largely agreeable to the existence of different forms of oppression presented in the course content. Our work illuminated instances of what we have described as narrative-based resistance. Students initially referred to narratives of rugged individualism (...) or the American Dream to resist the existence of systemic barriers. As the course progressed, students shifted to deeply entrenched responses that rejected the course content to refute systemic oppression. Secondly, we developed a case study for one student, a biracial female that self-identified as White who consistently rejected systemic oppression during class interactions to the point of displaying openly defiant behaviors. The examples of resistance we encountered served as a reminder that students of color along with their White peers must be able to critically examine and understand systems of oppression that are pervasive throughout education. Furthermore, the underlying sources of the resistance were closely associated with indoctrination in Whiteness, limited understanding of systemic oppression, deeply held beliefs and understandings and the lived experiences of individuals. While we agree that teacher education must recruit and retain more teachers of color for an increasingly diverse US K12 student population, we add that preparation that meets the needs of teachers of color is essential. -/- . (shrink)

While Gödel's (first) incompleteness theorem has been used to refute the main contentions of Hilbert's program, it does not seem to have been generally used to stress that a basic ingredient of that program, the concept of formal system as a closed system - as well as the underlying view, embodied in the axiomatic method, that mathematical theories are deductions from first principles must be abandoned. Indeed the logical community has generally failed to learn Gödel's lesson that Hilbert's concept of (...) formal system as a closed system is inadequate and continues to use it as if there were no incompleteness theorem. In this paper I will stress the role of Gödel's incompleteness theorem in showing the inadequacy of such a concept of formal system and the need for a more articulated view of mathematical theories. More generally I will argue that Gödel's result entails that, as an alternative to mathematical logic, a new concept of logic is required: logic as the theory of communicating inference processes. (shrink)

This article reexamines Condillac's Traité des systêmes (1749) and the broader Enlightenment controversy over "systems." Historians have often read this work as an epistemological treatise: an expression of the empiricist rejection of seventeenth-century rationalism. Yet a different picture emerges when we consider its pedagogical aims. Condillac sought not only to refute his opponents, but also to train readers how to evaluate philosophical arguments on their own, promoting a streamlined critical technique that involved parsing texts for a reductive logical structure. (...) In the process, he helped construct an enduring stereotype of the seventeenth-century philosophers as rigidly systematic thinkers. (shrink)

In this article, I argue that Dworkin’s one-system view of law and morality is not as easy to refute or dismiss as some would suggest. In a recent article, Dindjer criticizes a new kind of opposition to legal positivism characterized by both its opposition to a two-system view of law and morality and its promotion of a one-system alternative picture. By re-examining Dworkin’s criticisms of the two-system view and by providing additional reasoning of my own, I show that Dworkin’s one-system (...) interpretative approach is not just sensible but also promising in refocusing contemporary debates in general jurisprudence on a moral and political reading of the structural features of law. (shrink)

Andrew Kliman’s Reclaiming Marx’s ‘Capital’ sets out to refute the ‘myth’ that Marx’s original presentation of the theory of the value is internally inconsistent. A century ago, Bortkiewicz purported to demonstrate that Marx’s mistake was his failure to adopt simultaneous valuation. Thereafter, twentieth-century Marxian economics worked out a ‘corrected’ version of Marx’s original theory, culminating in Steedman’s 1977 Marx after Sraffa. Conclusions Marx himself deemed central were dropped, prominently including the law of the tendential fall in the rate of profit. (...) But simultaneous valuation is absolutely incompatible with Marx’s first and fundamental premise, the determination of value by labour-time. On the other hand, if Marx’s major theoretical conclusions do consistently follow from his premises, including the transformation of values into prices of production, then the quantitative dimension of his value-theory is internally consistent after all and stands in no need of correction on this score. Advocating a temporal, single-system interpretation, Kliman shows how ‘two simple modifications’ eliminate ‘all of the alleged inconsistencies in the quantitative dimension of Marx’s value theory’: valuation is temporal, and values and prices are determined interdependently. Kliman’s refutation is sound, but his claim to know Marx’s intentions, in E.D. Hirsch’s sense, is questionable. (shrink)

An error that medicine has long shared is to attribute to a desire or an effect of the mother’s imagination during gestation, the deformities, growths or spots that a child bears at birth. The imagination would be capable of imprinting external modifications on a matter and would have an impact on the perceptions and sensory development of the fetus. Returning briefly to the genealogy and posterity of the topos, this article focuses on the successes and refutations of the Malebranchist paradigm (...) in the 18th century, through a corpus of medical popularization texts where the debates oppose the supporters of the imagination for whom emotion alters the organs of the fetus and the detractors of this thesis who only see it as prejudice. Mechanistic systems had in common that they avoided the soul to explain life. Although each era has its hermeneutic system of representations, and that medicine—closely dependent on the philosophical and moral conceptions of its time—is also a cultural production, it is nevertheless not uninteresting to question on the fortune of a motive and the scientific topicality of the question. What does the baby perceive in utero? Does he feel his mother’s pain? If so, what is the biological impact? To what extent can the maternal imagination and experience mark the child’s body? Informed by functional imaging technologies, recent research returns to the symbiotic link of mother-fetus interactions. Convergences appear between this 18th century and our 21st century. In no case did we want to contrast today’s scientists who are firmly in touch with reality and their predecessors who are prey to imagination. Science, whatever the era, always feeds on imagination. (shrink)

Postmodernism, globalism & the New Age -- Who are the traditionalists? -- What is the New Age? -- New Age authorities : a divided house -- The shadows of God -- The war against love -- Ufos & traditional metaphysics : a postmodern demonology -- Vigilance at the eleventh hour : a refutation of The only tradition -- Comparative eschatology -- Facing apocalypse.

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Aristotle on False Reasoning: Language and the World in the Sophistical RefutationsMarina Berzins McCoyAristotle on False Reasoning: Language and the World in the Sophistical Refutations. Scott Schreiber. Albany: SUNY Press, 2003. pp. 240. $68.50, hardcover; $22.95, paperback.Scott Schreiber's Aristotle on False Reasoning is the first full-length English commentary on Aristotle's Sophistical Refutations in the last century. Aristotle's Sophistical Refutations is a text that has received relatively little attention (...) in the last century of scholarship, despite a revival of interest in other aspects of Aristotle's work concerned with the nature of good argument and rhetoric. (The 1995 French translation and commentary by Loius-Andre Dorion is a notable exception.) Schreiber finds the primary reason [End Page 92] for inattention to this text to lie in the tendency of contemporary Anglo-American philosophy to resolve problems in reasoning through linguistic clarification (xiv). Aristotle's claim that some errors are due to language while others lie outside the realm of linguistic error is not one to which contemporary analytic philosophy has been particularly sympathetic. The Sophistical Refutations has been neglected in light of contemporary logic. Schreiber's book attempts to return to Aristotle's project on his own philosophical terms, in order to better understand why Aristotle classified errors in reasoning as he did. Schreiber's approach is to examine each of the twelve types of false reasoning that Aristotle lays out in the Sophistical Refutations, with particular attention to Aristotle's examples, in order to understand the principles behind the overall system.Schreiber argues that Aristotle had good reason for separating errors due to language from those outside of language: Aristotle's classification of error is tied to his notion of the resolution of false arguments. To understand how to resolve a sophistical argument, we must first understand how it could have been believed to be true. Since Aristotle's aim in the Sophistical Refutations is to show why certain sorts of arguments are deceptive to some who hear them, his method of explaining errors is less a pure examination of their logical errors than of how such erroneous arguments can deceive. Aristotle is concerned with two types of problems with sophistical argument: first, why such an argument is false; and second, why it might appear to be true. Schreiber shows that most commentators have not given sufficient attention to the second of these concerns in their attempts to understand Aristotle's taxonomy. As Schreiber puts it, "Examples of false reasoning are unified into groups and differentiated into subgroups not by the nature of the confusions that they engender but by the different ways that confusion is cleared up" (54). False reasoning is due not only to mistakes in logic, but also to mistaken beliefs about language and reality. Careful examination of Aristotle's thinking allows us to see the importance of beliefs about the world in good and bad argument.For the most part, Schreiber's examinations of Aristotle's examples are lucid and helpful in understanding both the particular example at hand as well as the general picture of Aristotle's classifications. Schreiber continually returns to the importance of Aristotle's own view of language and argument in contrast to the approaches of contemporary linguistics and logic. For example, while some twentieth-century scholars have attempted to explain Aristotle's distinction between homonymy and amphiboly in terms of the contemporary distinction between semantics and syntax, [End Page 93] Aristotle seems to distinguish the two according to whether a general predicate signifies many particulars regardless of context, or in a propositional context (31). In the end, Schreiber does not think that the categories of homonymy and amphiboly can be completely distinct, even on Aristotle's own grounds, but still finds the categories useful. Schreiber is also careful to provide criticism of Aristotle's categories when warranted, both defending Aristotle against his contemporary critics when he thinks they have misunderstood him, and pointing out genuine weaknesses in Aristotle's arguments.Schreiber's book is clearly intended as a response to the contemporary Anglo-American reading of Aristotle. Much of the book assumes at least some familiarity with the ways in... (shrink)

ArgumentThis article documents the reasoning in a mathematical work by Mei Wending, one of the most prolific mathematicians in seventeenth-century China. Based on an analysis of the mathematical content, we present Mei’s systematic treatment of this particular genre of problems,fangcheng, and his efforts to refute the traditional practices in works that appeared earlier. His arguments were supported by the epistemological values he utilized to establish his system and refute the flaws in the traditional approaches. Moreover, in the context of the (...) competition between the Chinese and Western approaches to mathematics, Mei was motivated to demonstrate that the genre offangchengproblems was purely a “Chinese” achievement, not discussed by the Jesuits. Mei’s motivations were mostly expressed primarily in the prefaces to his works, in his correspondence with other scholars, in synopses of his poems, and in biographical records of some of his contemporaries. (shrink)

This article argues against the non-cognitivist theory of vision that has been formulated in the work of Nico Orlandi. It shows that, if we understand ‘representation’ in the way Orlandi recommends, then the visual system’s response to abstract regularities must involve the formation of representations. Recent experiments show that those representations must be used by the visual system in the production of visual experiences. Their effects cannot be explained by taking them to be non-visual effects involving attention or memory. This (...) contradicts Orlandi’s version of the non-cognitivist hypothesis, but does so while vindicating her methodological position. (shrink)

We investigate the semantics of the logical systems obtained by introducing the modalities and into the family of substructural implication logics (including relevant, linear and intuitionistic implication). Then, in the spirit of the LDS (Labelled Deductive Systems) methodology, we "import" this semantics into the classical proof system KE. This leads to the formulation of a uniform labelled refutation system for the new logics which is a natural extension of a system for substructural implication developed by the first (...) two authors in a previous paper. (shrink)

Hume’s famous and influential contributions to the philosophy of religion pursue two broad themes that have deep links with his general sceptical and naturalistic commitments throughout his philosophy as a whole.1 The first is his sceptical critique of the philosophical arguments and doctrines of various (Christian) theological systems. The second is his naturalistic account of the origins and roots of religion in human nature. Taken together, these two themes serve to advance Hume’s “Lucretian mission”, which was to discredit and (...) dislodge the role of religion in human life. In this paper I consider the criticism that Hume’s entire Lucretian mission is fundamentally misguided and misconceived as judged in terms of his own claims and hypotheses concerning religion. More specifically, it may be argued that if Hume is right about the foundations of religion in human nature and the human predicament, then his Lucretian mission is neither wise nor achievable. His project is, in other words, both theoretically self-refuting and practically self-defeating. Drawing from Hume’s writings on this subject, I will suggest a set of replies and responses to these criticisms. (shrink)

This book seeks to defend Marx’s theory in Capital against the long-standing criticism of logical inconsistency, which has provided the main justification for the rejection of Marx’s theory over the last century. This book presents a new interpretation of Marx’s theory that has emerged over the last several decades called the ‘temporal single-system’ interpretation. Kliman argues that the TSSI eliminates all of the alleged logical inconsistencies in Marx’s theory, and therefore logical inconsistency is not a valid reason to reject Marx’s (...) theory. I agree in general with much of this book, but I disagree on some points, especially the use of one-commodity models and its interpretation of the transformation-problem. (shrink)

Abstract This paper addresses the role that argumentation schemes and argument visualization software tools can play in helping to find and counter objections to a given argument one is confronted with. Based on extensive analysis of features of the argumentation in these two examples, a practical four-step method of finding objections to an argument is set out. The study also applies the Carneades Argumentation System to the task of finding objections to an argument, and shows how this system has some (...) capabilities that are especially useful. Content Type Journal Article Pages 1-23 DOI 10.1007/s10503-012-9261-z Authors Douglas Walton, Centre for Research in Reasoning, Argumentation and Rhetoric (CRRAR), University of Windsor, 2500 University Ave. W., Windsor, ON N9B 3Y1, Canada Journal Argumentation Online ISSN 1572-8374 Print ISSN 0920-427X. (shrink)