In his (1994) "Feminism, Argumentation, and Coalescence", Michael Gilbert argues that the "Critical Thinking Industry" is antagonistic to women. Because the critical-logical skills in which the industry deals tend to be gender-specific. its adoption as the dominant mode of discourse disenfranchises women, making its overhaul a moral imperative. Following a variety offeminist epistemologists. this conclusion is reached by confiating "critical reasoning" with "communicating about ideas," as though the two were inseparable. In this paper it is argued (...) that the inclusion of feminist modes of communication and evaluating ideas are not at odds with the Critical-Logical model of reasoning. Rather, the very critical features embedded in the feminist approach would seem to represent the best means of arriving at the truth. (shrink)

This paper discusses critically what simulation models of the evolution ofcooperation can possibly prove by examining Axelrod’s “Evolution of Cooperation” and the modeling tradition it has inspired. Hardly any of the many simulation models of the evolution of cooperation in this tradition have been applicable empirically. Axelrod’s role model suggested a research design that seemingly allowed to draw general conclusions from simulation models even if the mechanisms that drive the simulation could not be identified empirically. But this research design (...) was fundamentally flawed, because it is not possible to draw general empirical conclusions from theoretical simulations. At best such simulations can claim to prove logical possibilities, i.e. they prove that certain phenomena are possible as the consequence of the modeling assumptions built into the simulation, but not that they are possible or can be expected to occur in reality I suggest several requirements under which proofs of logical possibilities can nevertheless be considered useful. Sadly, most Axelrod-style simulations do not meet these requirements. I contrast this with Schelling’s neighborhood segregation model, thecore mechanism of which can be retraced empirically. (shrink)

This paper discusses critically what simulation models of the evolution of cooperation can possibly prove by examining Axelrod’s “Evolution of Cooperation” (1984) and the modeling tradition it has inspired. Hardly any of the many simulation models in this tradition have been applicable empirically. Axelrod’s role model suggested a research design that seemingly allowed to draw general conclusions from simulation models even if the mechanisms that drive the simulation could not be identified empirically. But this research design was fundamentally flawed. (...) At best such simulations can claim to prove logical possibilities, i.e. they prove that certain phenomena are possible as the consequence of the modeling assumptions built into the simulation, but not that they are possible or can be expected to occur in reality. I suggest several requirements under which proofs of logical possibilities can nevertheless be considered useful. Sadly, most Axelrod-style simulations do not meet these requirements. It would be better not to use this kind of simulations at all. (shrink)

This article takes off from Johan van Benthem’s ruminations on the interface between logic and cognitive science in his position paper “Logic and reasoning: Do the facts matter?”. When trying to answer Van Benthem’s question whether logic can be fruitfully combined with psychological experiments, this article focuses on a specific domain of reasoning, namely higher-order social cognition, including attributions such as “Bob knows that Alice knows that he wrote a novel under pseudonym”. For intelligent interaction, it is important that the (...) participants recursively model the mental states of other agents. Otherwise, an international negotiation may fail, even when it has potential for a win-win solution, and in a time-critical rescue mission, a software agent may depend on a teammate’s action that never materializes. First a survey is presented of past and current research on higher-order social cognition, from the various viewpoints of logic, artificial intelligence, and psychology. Do people actually reason about each other’s knowledge in the way proscribed by epistemic logic? And if not, how can logic and cognitive science productively work together to construct more realistic models of human reasoning about other minds? The paper ends with a delineation of possible avenues for future research, aiming to provide a better understanding of higher-order social reasoning. The methodology is based on a combination of experimental research, logic, computational cognitive models, and agent-based evolutionary models. (shrink)

This article takes off from Johan van Benthem’s ruminations on the interface between logic and cognitive science in his position paper “Logic and reasoning: Do the facts matter?”. When trying to answer Van Benthem’s question whether logic can be fruitfully combined with psychological experiments, this article focuses on a specific domain of reasoning, namely higher-order social cognition, including attributions such as “Bob knows that Alice knows that he wrote a novel under pseudonym”. For intelligent interaction, it is important that the (...) participants recursively model the mental states of other agents. Otherwise, an international negotiation may fail, even when it has potential for a win-win solution, and in a time-critical rescue mission, a software agent may depend on a teammate’s action that never materializes. First a survey is presented of past and current research on higher-order social cognition, from the various viewpoints of logic, artificial intelligence, and psychology. Do people actually reason about each other’s knowledge in the way proscribed by epistemic logic? And if not, how can logic and cognitive science productively work together to construct more realistic models of human reasoning about other minds? The paper ends with a delineation of possible avenues for future research, aiming to provide a better understanding of higher-order social reasoning. The methodology is based on a combination of experimental research, logic, computational cognitive models, and agent-based evolutionary models. Keywords Epistemic logic - Cognitive science - Intelligent interaction - Cognitive modeling. (shrink)

In this paper I develop a cross-cultural critique of contemporary critical thinking education in the United States, the United Kingdom, and those educational systems that adopt critical thinking education from the standard model used in the US and UK. The cross-cultural critique rests on the idea that contemporary critical thinking textbooks completely ignore contributions from non-western sources, such as those found in the African, Arabic, Buddhist, Jain, Mohist and Nyāya philosophical traditions. The exclusion of these traditions (...) leads to the conclusion that critical thinking educators, by using standard textbooks are implicitly sending the message to their students that there are no important contributions to the study of logic and argumentation that derive from non-western sources. As a case study I offer a sustained analysis of the so-called Hindu Syllogism that derives from the Nyāya School of classical Indian philosophy. I close with a discussion of why contributions from non-western sources, such as the Hindu Syllogism, belong in a Critical Thinking course as opposed to an area studies course, such as Asian Philosophy. (shrink)

A common reaction to Hegel’s suggestion that we collapse Kant’s distinction between form and content is that, since such a move would also deprive us of any way of distinguishing the merely logical from the real possibility of our concepts, it is incoherent and ought to be rejected. It is true that these two distinctions are intimately related in Kant, such that if one goes, the other does as well. But it is less obvious that giving them up as (...) Kant conceives them is as incoherent a proposal as many of Hegel’s critics think. It has been the point of a recent account of Hegel’s idealism to demonstrate that his critique of Kant’s dichotomy between form and content or concept and intuition does not commit him to the view that human cognition is materially creative of its content in the manner of a God-like or intuitive intellect—does not, in other words, signify a return to a pre-Critical metaphysics. This is the interpretative stance I adopt here as well, in hope of giving defenders of Kant reasons for taking Hegel more seriously. (shrink)

Bohr’s atomic model is one of the better known examples of empirically successful, albeit inconsistent, theoretical schemes in the history of physics. For this reason, many philosophers use this model to illustrate their position for the occurrence and the function of inconsistency in science. In this paper, I proceed to a critical comparison of the structure and the aims of Bohr’s research program – the starting point of which was the formulation of his model – with (...) some of its contemporary philosophical readings. My study comes to conclude that the attempt of certain philosophers to accommodate Bohr’s model to a form of paraconsistent logic obliterates essential aspects of scientists' actual practice and reasoning. (shrink)

Individuating the logic of scientific discovery appears a hopeless enterprise. Less hopeless is trying to figure out a logical way to model the epistemic attitude distinguishing the practice of scientists. In this paper, we claim that classical logic cannot play such a descriptive role. We propose, instead, one of the three-valued logics in the Kleene family that is often classified as the less attractive one, namely Hallden’s logic. By providing it with an appropriate epistemic interpretation, we can informally (...) model the scientific attitude. (shrink)

We aim to show that Kant’s theory of time is consistent by providing axioms whose models validate all synthetic a priori principles for time proposed in the Critique of Pure Reason. In this paper we focus on the distinction between time as form of intuition and time as formal intuition, for which Kant’s own explanations are all too brief. We provide axioms that allow us to construct ‘time as formal intuition’ as a pair of continua, corresponding to time as ‘inner (...) sense’ and the external representation of time as a line Both continua are replete with infinitesimals, which we use to elucidate an enigmatic discussion of ‘rest’ in the Metaphysical foundations of natural science. Our main formal tools are Alexandroff topologies, inverse systems and the ring of dual numbers. (shrink)

Aristotle is oftentimes viewed through a strictly philosophical lens as heir to Plato and has having introduced logical rigor where an emphasis on the theory of Forms formerly prevailed. It must be appreciated that Aristotle was the son of a physician, and that his inculcation of the thought of other Greek philosophers addressing health and the natural elements led to an extremely broad set of biologically- and medically-related writings. As this article proposes, Aristotle deepened the fourfold theory of the (...) elements with anatomic and physiologic observations. In books like History of Animals, Parts of Animals, and the lost Anatomai, he actively dissected organisms and recorded his findings. The corpus of medically-related literature Aristotle developed had a direct influence on subsequent Greek thinkers, including Galen, and on Medieval Islamic and modern Western practitioners such as William Harvey. Aristotle's ideas continue to influence modern medical thinkers in Europe and America through both his interpretation by European philosophers gaining the attention of medical humanists, and his writings' enduring impact on medical researchers balancing scientific with more personalistic approaches to medicine. (shrink)

In this paper I develop a cross-cultural critique of contemporary critical thinking education in the United States, the United Kingdom, and those educational systems that adopt critical thinking education from the standard model used in the US and UK. The cross-cultural critique rests on the idea that contemporary critical thinking textbooks completely ignore contributions from non-western sources, such as those found in the African, Arabic, Buddhist, Jain, Mohist and Nyāya philosophical traditions. The exclusion of these traditions (...) leads to the conclusion that critical thinking educators, by using standard textbooks are implicitly sending the message to their students that there are no important contributions to the study of logic and argumentation that derive from non-western sources. As a case study I offer a sustained analysis of the so-called Hindu Syllogism that derives from the Nyāya School of classical Indian philosophy. I close with a discussion of why contributions from non-western sources, such as the Hindu Syllogism, belong in a Critical Thinking course as opposed to an area studies course, such as Asian Philosophy. (shrink)

This thesis consists in six articles and a comprehensive summary. • The pourpose of the summary is to introduce the AGM theory of belief change and to exemplify the diversity and significance of the research that has been inspired by the AGM article in the last 25 years. The research areas associated with AGM was divided in three parts: criticisms, where we discussed some of the more common criticisms of AGM. Extensions where the most common extensions and variations of AGM (...) are presented and applications where we provided an overview of applications and connections with other areas of research. • Article I elaborates on the connection between partial meet contractions [AGM85] and kernel contractions [Han94a] in belief change theory. Also both functions are equivalent in belief sets, there are notequivalent in belief bases. A way to define incision functions from selection functions and vice versa is presented. It is explained under which conditions there are exact correspondences between selection and incision functions so that the same contraction operations can be obtained by using either of them. • Article II proposes an axiomatic characterization for ensconcement-based contraction functions, belief base functions proposed byWilliams and relates this function with other kinds of base contraction functions. • Article III adapts the Fermé and Hansson model of Shielded Contraction [FH01] as well as Hansson et all Credibility-Limited Revision [HFCF01] for belief bases, to join two of the many variations of the AGM model [AGM85], i.e. those in which knowledge is represented through belief bases instead of logic theories, and those in which the object of the epistemic change does not get the priority over the existing information as it is the case in the AGM model. • Article IV introduces revision by comparison a refined method for changing beliefs by specifying constraints on the relative plausibility of propositions. Like the earlier belief revision models, the method proposed is a qualitative one, in the sense that no numbers are needed in order to specify the posterior plausibility of the new information. The method uses reference beliefs in order to determine the degree of entrenchment of the newly accepted piece of information. Two kinds of semantics for this idea are proposed and a logical characterization of the new model is given. • Article V focuses on the extension of AGM that allows change for a belief base by a set of sentences instead of a single sentence. In [FH94], Fuhrmann and Hansson presented an axiomatic for Multiple Contraction and a construction based on the AGM Partial Meet Contraction. This essay proposes for their model another way to construct functions: Multiple Kernel Contraction, that is a modification of Kernel Contraction,proposed by Hansson [Han94a] to construct classical AGM contractions and belief base contractions. • Article VI relates AGM model with the DFT model proposed by Carlos Alchourrón [Alc93]. Alchourrón devoted his last years to the analysis of the notion of defeasible conditionalization. His definition of the defeasible conditional is given in terms of strict implication operator and a modal operator f which is interpreted as a revision function at the language level. This essay points out that this underlying revision function is more general than AGM revision. In addition, a complete characterization of that more general kind of revision that permits to unify models of revision given by other authors is given. (shrink)

Logical reconstruction is a fundamental philosophical method for achieving clarity concerning the prerequisites, presuppositions and the logical structure of natural language arguments. The scope and limits of this method have become visible not least through its intense application to Anselm of Canterbury’s notorious proofs for the existence of God. This volume collects, on the one hand, reconstructions of Anselmian arguments that take account of the problems of reconstruction and, on the other hand, theoretical reflections on reconstruction with a (...) view to Anselm. We hope that this will allow the reader to critically assess the merits of the theoretical accounts in the light of the reconstructions and the merits of the reconstructions in the light of the theoretical accounts. In general, by considering the example of an outstanding thinker in one or the other way, this volume aims at advancing the methodology and the practice of logical reconstruction. The following remarks explain and motivate this undertaking: What purposes does logical reconstruction serve? What purposes does the reflection on logical reconstruction serve? In which ways can the practice and theory of reconstruction profit particularly from studying Anselm’s reasoning? How can the resulting problems be addressed? – Finally, a short overview over the contributions to this volume is offered. (shrink)

A system of logic usually comprises a language for which a model-theory and a proof-theory are defined. The model-theory defines the semantic notion of model-theoretic logical consequence (⊨), while the proof-theory defines the proof- theoretic notion of logical consequence (or logical derivability, ⊢). If the system in question is sound and complete, then the two notions of logical consequence are extensionally equivalent. The concept of full formalization is a more restrictive one and requires (...) in addition the preservation of the standard meanings of the logical terms in all the admissible interpretations of the logical calculus, as it is proof-theoretically defined. Although classical first-order logic is sound and complete, its standard formalizations fall short to be full formalizations since they allow non-intended interpretations. This fact poses a challenge for the logical inferentialism program, whose main tenet is that the meanings of the logical terms are uniquely determined by the formal axioms or rules of inference that govern their use in a logical calculus, i.e., logical inferentialism requires a categorical calculus. This paper is the first part of a more elaborated study which will analyze the categoricity problem from its beginning until the most recent approaches. I will first start by describing the problem of a full formalization in the general framework in which Carnap (1934/1937, 1943) formulated it for classical logic. Then, in sections IV and V, I shall discuss the way in which the mathematicians B.A. Bernstein (1932) and E.V. Huntington (1933) have previously formulated and analyzed it in algebraic terms for propositional logic and, finally, I shall discuss some critical reactions Nagel (1943), Hempel (1943), Fitch (1944), and Church (1944) formulated to these approaches. (shrink)

ABSTRACT This paper aims to show that intuitionistic Kripke models are a powerful tool for interpreting Kant’s ‘Critical Philosophy’. Part I reviews some old work of mine that applies these models to provide a reading of Kant’s second antinomy about the divisibility of matter and to answer several attacks on Kant’s antinomies. But it also points out three shortcomings of that original application. First, the reading fails to account for Kant’s second antinomy claim that matter is divisible ‘ad infinitum’ (...) and his first antinomy claim that empirical space extends only ‘ad indefinitum’. Secondly, in conformity with the ‘assertability’ heuristics for Kripke models, it attributes an assertability semantics to Kant. In fact, it attributes a pair of assertability semantics to Kant, but neither of these accords with modern assertabilism. And finally, one must wonder the propriety of using contemporary assertability and contemporary formal logic to save an eighteenth-century text. Part II goes historical to solve the problems about assertability. It outlines the Descartes–Leibniz dialectic about the infinite/indefinite distinction and demonstrates how each position reflects larger philosophical positions. It then demonstrates that Kant’s two versions of assertability and his version of the infinite/indefinite dichotomy emerge naturally from his attempts to resolve a tension in Leibniz’s philosophy. In light of this demonstration, Part III adapts the Kripke model interpretation so that it does reflect that dichotomy. It then refines the Kripke semantics in order to model some of Kant’s signature critical doctrines, and it shows how Kant’s critical version of the infinite/indefinite distinction differs from all those of his predecessors and from his own pre-critical version. It also addresses the question of using contemporary logical machinery to interpret Kant. Part IV turns the tables and uses what we have learned about Kant and modern semantics in order to address a pair of issues in the contemporary critical foundations of logic. (shrink)

The paper begins with a more carefully stated version of ontologically neutral (ON) logic, originally introduced in (Hailperin, 1997). A non-infinitistic semantics which includes a definition of potential infinite validity follows. It is shown, without appeal to the actual infinite, that this notion provides a necessary and sufficient condition for provability in ON logic.

I thank the editors for inviting me to contribute to this issue on critical views of logic. Kant invented the critical philosophy. He fashioned its doctrines (Understanding versus Reason, synthetic...

The First International Workshop brings together researchers from the theoretical ends of the logic programming and artificial intelligence communities to discuss their mutual interests. Logic programming deals with the use of models of mathematical logic as a way of programming computers, where theoretical AI deals with abstract issues in modeling and representing human knowledge and beliefs. One common ground is nonmonotonic reasoning, a family of logics that includes room for the kinds of variations that can be found in human reasoning. (...) Topics covered: Stable Semantics. Default Logic. AutoEpistemic Logic. Truth Maintenance Systems. Implementation Issues. Diagnosis. Applications. Inheritance Reasoning. Logics of Belief. Inconsistency and Non-Monotonicity. (shrink)

The current state of the world suggests we have some difficulty in developing effective policy. This paper demonstrates two methods for the objective analysis of logic models within policy documents. By comparing policy models, we will be better able to compare policies and so determine which policy is best. Our ability to develop effective policy is reflected across the social sciences where our ability to create effective theoretical models is being called into question. The broad scope of this issue suggests (...) a source as deep as our unconscious ways of thinking. Specifically, our reliance on modern and postmodern thinking has limited our ability to develop more effective policy, and more particularly, logic models. The move in some quarters toward “integral” thinking may provide insights that support the creation of more useful policy models. However, some versions of that thinking seem to be unwittingly mired in modern and postmodern thinking. This paper identifies how integral thought may be clarified, allowing us to advance beyond postmodern thinking. Usefully, this “neo-integral” form of thinking supports the creation of more mature policy models by encompassing greater complexity and a careful understanding of interrelationships that may be identified within the logic models that are commonly found in policy analyses. Neo-integral thinking is related to more complex forms of systems thinking and both are found in recent conversations within the nascent field of metatheory. And, to some extent, a logic model within a policy operates as a kind of theoretical model because both may be used to inform understanding and decision-making. Therefore, it seems reasonable to apply neo-integral thinking and metatheoretical methodologies to conduct critical comparisons of logic models. In the present paper, these methodologies are applied to critically compare two logic models. The structure of each model is analyzed to objectively determine its complexity and formal robustness. The complexity is determined by quantifying the concepts and connections within each model. The robustness of a model is a measure of its internal integrity, based on the ratio between the total number of aspects and the number of concatenated aspects. In this analysis, one policy model is found to have a robustness of 0.08, while another is found to have a robustness of 0.67. The more robust policy is expected to be much more effective in application. Implications for policy development and policy application are discussed. (shrink)

Critical Thinking: An Introduction to Analytical Reading and Reasoning, Second Edition, provides a nontechnical vocabulary and analytic apparatus that guide students in identifying and articulating the central patterns found in reasoning and in expository writing more generally. Understanding these patterns of reasoning helps students to better analyze, evaluate, and construct arguments and to more easily comprehend the full range of everyday arguments found in ordinary journalism. Critical Thinking, Second Edition, distinguishes itself from other texts in the field by (...) emphasizing analytical reading as an essential skill. It also provides detailed coverage of argument analysis, diagnostic arguments, diagnostic patterns, and fallacies. Opening with two chapters on analytical reading that help students recognize what makes reasoning explicitly different from other expository activities, the text then presents an interrogative model of argument to guide them in the analysis and evaluation of reasoning. This model allows a detailed articulation of "inference to the best explanation" and gives students a view of the pervasiveness of this form of reasoning. The author demonstrates how many common argument types--from correlations to sampling--can be analyzed using this articulated form. He then extends the model to deal with several predictive and normative arguments and to display the value of the fallacy vocabulary. Ideal for introductory courses in critical thinking, critical reasoning, informal logic, and inductive reasoning, Critical Thinking, Second Edition, features hundreds of exercises throughout and includes worked-out solutions and additional exercises at the end of each chapter. An Instructor's Manual--offering solutions to the text's unanswered exercises and featuring other pedagogical aids--is available on the book's Companion Website at www.oup.com/us/wright. (shrink)

University Abstract Philosophers have sought to improve upon the logical empiricists’ model of scientific reduction. While opportunities for integration between the cognitive and the neural sciences have increased, most philosophers, appealing to the multiple realizability of mental states and the irreducibility of consciousness, object to psychoneural reduction. New Wave reductionists offer a continuum of comparative goodness of intertheoretic mapping for assessing reductions. Their insistence on a unified view of intertheoretic relations obscures epistemically significant crossscientific relations and engenders dismissive (...) conclusions about psychology. Richer, more sensitive accounts of explanatory pluralism and mechanistic explanation in science advocate multi-level approaches in cross-scientific settings and criticize the distance of the standard philosophical objections from working scientists’ practices and discoveries. The Heuristic Identity Theory, a new, scientifically informed version of the psycho-physical identity theory, incorporates these insights, showing how multiple realizability is an argument for (not against) identities in science and why, therefore, consciousness is not irreducible. (shrink)

Philosophical Logic is a clear and concise critical survey of nonclassical logics of philosophical interest written by one of the world's leading authorities on the subject. After giving an overview of classical logic, John Burgess introduces five central branches of nonclassical logic, focusing on the sometimes problematic relationship between formal apparatus and intuitive motivation. Requiring minimal background and arranged to make the more technical material optional, the book offers a choice between an overview and in-depth study, and it balances (...) the philosophical and technical aspects of the subject.The book emphasizes the relationship between models and the traditional goal of logic, the evaluation of arguments, and critically examines apparatus and assumptions that often are taken for granted. Philosophical Logic provides an unusually thorough treatment of conditional logic, unifying probabilistic and model-theoretic approaches. It underscores the variety of approaches that have been taken to relevantistic and related logics, and it stresses the problem of connecting formal systems to the motivating ideas behind intuitionistic mathematics. Each chapter ends with a brief guide to further reading.Philosophical Logic addresses students new to logic, philosophers working in other areas, and specialists in logic, providing both a sophisticated introduction and a new synthesis. (shrink)

Featuring an exceptionally clear writing style and a wealth of real-world examples and exercises, Logic, Second Edition, shows how logic relates to everyday life, demonstrating its applications in such areas as the workplace, media and entertainment, politics, science and technology, student life, and elsewhere.Thoroughly revised and expanded in this second edition, the text now features 2600 exercises, more than 1000 of them new; three new chapters on legal arguments, moral arguments, and analyzing a long essay; enhanced pedagogy; and much more.FEATURES* (...) 2600 exercises--more than 1000 of them new--breathe new life into logic* Real-world examples help bring logic down to earth for students* A unique, extended explanation or model of the answer to the first question of each "Check Your Understanding" section shows students what is expected of their answers* An additional 25% of the exercises are answered at the back of the book* "Profiles in Logic" provide short sketches of logicians, philosophers, mathematicians, and others associated with logic* "Logic Challenge" problems present puzzles and paradoxes that end each chapter on a fun note* Additional pedagogical elements--marginal definitions, key terms, a glossary, reference boxes, and bulleted chapter summaries--make the material even more accessible* Detailed guides help students learn to create "truth tables" and Venn diagramsSUPPORT PACKAGEAn Instructor's Manual with Computerized Test Bank on CD includes: Solutions to all exercises in the book, enhanced by explanations and answers that elucidate the details of the correct answersKey Terms and a summary for each chapterA customizable Computerized Test Bank--with multiple-choice, true/false, and fill-in-the-blank questions--that allows instructors to give exams or homework problems that can be auto-gradedA traditional "pencil-and-paper" Test Bank and answer key containing the same questions as the Computerized Test BankPowerPoint-based lecture outlinesThe Instructor's Manual with Computerized Test Bank and the traditional Test Bank are also available in printed format.A Companion Website offers:Instructor Resources :A downloadable version of the Instructor's Manual PowerPoint-based lecture outlinesStudent Resources:Brief chapter summariesInteractive Flash Cards with key terms and definitionsWeb links and other media resourcesPractice quizzes with answers and explanations The Learning Management System Cartridges include, in a fully downloadable format:Instructor's Manual and Computerized Test Bank Student material from the companion websiteThe Perfect Text for Your Course... No Matter How You Teach ItYour course is unique; you have your own teaching philosophy and style. Whether you teach traditional Introduction to Logic, Critical Thinking/Informal Logic, or Formal Logic, Baronett: Logic, Second Edition, can be tailored to fulfill your course needs.We'll make it easy for you; choose one of our Alternate Editions or build the book you want, chapter by chapter.Option 1. Author Stan Baronett has suggested four Alternate Editions that may work for you. Each Alternate Edition comes in full color, with answers to problems, a full glossary, and an index. The books are in stock and available for ordering. Please see the ISBN information below.Logic: Concise EditionChapters 1, 3, 4, 5, 6, 7, 8Order using ISBN: 978-0-19-994129-2Logic: An Emphasis on Critical Thinking and Informal LogicChapters 1, 2, 3, 4, 10, 11, 12, 13 A-E, 14, 15Order using ISBN: 978-0-19-994128-5Logic: An Emphasis on Formal LogicChapters 1, 5, 6, 7, 8, 9Order using ISBN: 978-0-19-994126-1Logic: With Diagramming used in Chapter 4. Informal FallaciesFull textOrder using ISBN: 978-0-19-997081-0Option 2. Create your own customized textbook by choosing the specific chapters that you need for your course. Please contact your Oxford University Press Sales Representative or call 800.280.0280 for details. (shrink)

In this paper, a criticism of the traditional theories of approximation and idealization is given as a summary of previous works. After identifying the real purpose and measure of idealization in the practice of science, it is argued that the best way to characterize idealization is not to formulate a logical model – something analogous to Hempel's D-N model for explanation – but to study its different guises in the praxis of science. A case study of it (...) is then made in thermostatistical physics. After a brief sketch of the theories for phase transitions and critical phenomena, I examine the various idealizations that go into the making of models at three difference levels. The intended result is to induce a deeper appreciation of the complexity and fruitfulness of idealization in the praxis of model-building, not to give an abstract theory of it. (shrink)

To understand logic is, first and foremost, to understand logical consequence. This Element provides an in-depth, accessible, up-to-date account of and philosophical insight into the semantic, model-theoretic conception of logical consequence, its Tarskian roots, and its ideas, grounding, and challenges. The topics discussed include: the passage from Tarski's definition of truth to his definition of logical consequence, the need for a non-proof-theoretic definition, the idea of a semantic definition, the adequacy conditions of preservation of truth, formality, (...) and necessity, the nature, structure, and totality of models, the logicality problem that threatens the definition of logical consequence, a general solution to the logicality, formality, and necessity problems/challenges, based on the isomorphism-invariance criterion of logicality, philosophical background and justification of the isomorphism-invariance criterion, and major criticisms of the semantic definition and the isomorphism-invariance criterion. (shrink)

The goal of this paper is to review and critically discuss the philosophical aspects of probabilistic seismic hazard analysis (PSHA). Given that estimates of seismic hazard are typically riddled with uncertainty, diferent epistemic values (related to the pursuit of scientifc knowledge) compete in the selection of seismic hazard models, in a context infuenced by non-epistemic values (related to practical goals and aims) as well. We frst distinguish between the diferent types of uncertainty in PSHA. We claim that epistemic and nonepistemic (...) considerations are closely related in the selection of the appropriate estimate of seismic hazard by the experts. Finally, we argue that the division of scientifc responsibility among the experts can lead to responsibility gaps. This raises a problem for the ownership of the results (“no one’s model” problem) similar to the “problem of many hands” in the ethics of technology. We conclude with a plea for a close collaboration between philosophy and engineering. (shrink)

The basic idea of logical expressivism in the Brandomian tradition is that logic makes inferential relations explicit and thereby accessible to critical discussion. But expressivists have not given a convincing explanation of what the point of logical theories is. Peregrin provides a starting point by observing a distinction between making explicit and explication in Carnap’s sense of replacing something unclear and vague by something clear and exact. Whereas logical locutions make inferential relations explicit within a language, (...) logical theories use formal languages to explicate inferential roles and meanings of ordinary-language expressions. But Peregrin also holds that the whole point of logical theories is to provide perspicuous models of inferential structures in ordinary language practice. This turns explication into a mere continuation of making explicit by other means, and it leads to a one-sided conception of logic which has no room for evaluating inferential practice in light of logical theories. As a more convincing alternative, I suggest that expressivists rely on the method of reflective equilibrium. This approach is closely related to Carnapian explication, but it has the potential of correcting informal inferential practice without dubious ambitions to replace ordinary languages by logical formalisms. (shrink)

This paper discusses abductive reasoning---that is, reasoning in which explanatory hypotheses are formed and evaluated. First, it criticizes two recent formal logical models of abduction. An adequate formalization would have to take into account the following aspects of abduction: explanation is not deduction; hypotheses are layered; abduction is sometimes creative; hypotheses may be revolutionary; completeness is elusive; simplicity is complex; and abductive reasoning may be visual and non-sentential. Second, in order to illustrate visual aspects of hypothesis formation, the paper (...) describes recent work on visual inference in archaeology. Third, in connection with the evaluation of explanatory hypotheses, the paper describes recent results on the computation of coherence. (shrink)

Free Energy Principle underlies a unifying framework that integrates theories of origins of life, cognition, and action. Recently, FEP has been developed into a Markovian monist perspective. The paper expresses scepticism about the validity of arguments for Markovian monism. The critique is based on the assumption that Markovian models are scientific models, and while we may defend ontological theories about the nature of scientific models, we could not read off metaphysical theses about the nature of target systems from our theories (...) of nature of scientific models. The paper draws attention to different ways of understanding Markovian models, as material entities, fictional entities, and mathematical structures. I argue that none of these interpretations contributes to the defence of a metaphysical stance. This is because scientific representation is a sophisticated process, and properties of Markovian models—such as the property of being neither physical nor mental—could not be projected onto their targets to determine the ontological properties of targets easily. (shrink)

This volume presents the proceedings from the Eleventh Brazilian Logic Conference on Mathematical Logic held by the Brazilian Logic Society in Salvador, Bahia, Brazil. The conference and the volume are dedicated to the memory of professor Mario Tourasse Teixeira, an educator and researcher who contributed to the formation of several generations of Brazilian logicians. Contributions were made from leading Brazilian logicians and their Latin-American and European colleagues. All papers were selected by a careful refereeing processs and were revised and updated (...) by their authors for publication in this volume. There are three sections: Advances in Logic, Advances in Theoretical Computer Science, and Advances in Philosophical Logic. Well-known specialists present original research on several aspects of model theory, proof theory, algebraic logic, category theory, connections between logic and computer science, and topics of philosophical logic of current interest. Topics interweave proof-theoretical, semantical, foundational, and philosophical aspects with algorithmic and algebraic views, offering lively high-level research results. (shrink)

Engineering is often said to be ‘scientific’, but the nature of knowledge in engineering is different to science. Engineering has a different ontological basis—its theories address different entities and are judged by different criteria. In this paper I use Popper’s three worlds ontological framework to propose a model of engineering theories, and provide an abstract logical view of engineering theories analogous to the deductive-nomological view of scientific theories. These models frame three key elements from definitions of engineering: requirements, (...) designs of artefacts, and theories for reasoning about how artefacts will meet requirements. In a subsequent paper I use this ontological basis to explore methodological issues in the growth of engineering knowledge from the perspective of critical rationalism. (shrink)

Many criticisms of epistemic logic have centered around its use of devices such as idealized knowers with logical omniscience and perfect self-knowledge. One possible response to such criticisms is to say that these idealizations are normative devices, and that epistemic logic tells us how agents ought to behave. This paper will take a different approach, treating epistemic logic as descriptive, and drawing the analogy between its formal models and idealized scientific models on that basis. Treating it as descriptive matches (...) the way in which some philosophers, including one of its founders, Jaako Hintikka, have thought about epistemic logic early in its history. Further, the analogy between the two fields will give us a way to defuse criticisms that see epistemic logic as unrealistic. For example, criticizing models of epistemic logic in which agents know all propositional tautologies as being unrealistic would be like criticizing frictionless planes in physics for being unrealistic. Each one would certainly be an unsuitable model for studying some kinds of phenomena, but is entirely appropriate for others. After outlining the analogy between epistemic and scientific models, we will discuss some ways in which idealizations are used by different research programs in epistemic logic. (shrink)

In his classic 1936 essay "On the Concept of Logical Consequence", Alfred Tarski used the notion of satisfaction to give a semantic characterization of the logical properties. Tarski is generally credited with introducing the model-theoretic characterization of the logical properties familiar to us today. However, in his book, The Concept of Logical Consequence, Etchemendy argues that Tarski's account is inadequate for quite a number of reasons, and is actually incompatible with the standard model-theoretic account. (...) Many of his criticisms are meant to apply to the model-theoretic account as well. In this paper, I discuss the following four critical charges that Etchemendy makes against Tarski and his account of the logical properties: (1) (a) Tarski's account of logical consequence diverges from the standard model-theoretic account at points where the latter account gets it right. (b) Tarski's account cannot be brought into line with the model-theoretic account, because the two are fundamentally incompatible. (2) There are simple counterexamples (enumerated by Etchemendy) which show that Tarski's account is wrong. (3) Tarski committed a modal fallacy when arguing that his account captures our pre-theoretical concept of logical consequence, and so obscured an essential weakness of the account. (4) Tarski's account depends on there being a distinction between the "logical terms" and the "non-logical terms" of a language, but (according to Etchemendy) there are very simple (even first-order) languages for which no such distinction can be made. Etchemendy's critique raises historical and philosophical questions about important foundational work. However, Etchemendy is mistaken about each of these central criticisms. In the course of justifying that claim, I give a sustained explication and defense of Tarski's account. Moreover, since I will argue that Tarski's account and the model theoretic account really do come to the same thing, my subsequent defense of Tarski's account against Etchemendy's other attacks doubles as a defense against criticisms that would apply equally to the familiar model-theoretic account of the logical properties. (shrink)

John Burgess is the author of a rich and creative body of work which seeks to defend classical logic and mathematics through counter-criticism of their nominalist, intuitionist, relevantist, and other critics. This selection of his essays, which spans twenty-five years, addresses key topics including nominalism, neo-logicism, intuitionism, modal logic, analyticity, and translation. An introduction sets the essays in context and offers a retrospective appraisal of their aims. The volume will be of interest to a wide range of readers across philosophy (...) of mathematics, logic, and philosophy of language. (shrink)

Experimental engineering models have been used both to model general phenomena, such as the onset of turbulence in fluid flow, and to predict the performance of machines of particular size and configuration in particular contexts. Various sorts of knowledge are involved in the method - logical consistency, general scientific principles, laws of specific sciences, and experience. I critically examine three different accounts of the foundations of the method of experimental engineering models (scale models), and examine how theory, practice, (...) and experience are involved in employing the method to obtain practical results. Models of machines and mechanisms can be (and generally are) involved in establishing criteria for similar phenomena, which provide guidance in using events to model other events. Conversely, models of phenomena such as events that model other events can be (and generally are) involved in experimentation on models of machines. I conclude that often it is not more detailed models or the more precise equations they engender that leads to better understanding, but rather an insightful use of knowledge at hand to determine which similarity principles are appropriate in allowing us to infer what we do not know from what we are able to observe. (shrink)

My purpose in this paper is to shed some light on two questions: In what sense is logic philosophical? And what is philosophical logic? I take these two questions as co-extensive: an answer to one of them is also (or can easily be converted into) an answer to the other. I approach the problem from three perspectives: a conceptual, a descriptive and a prescriptive perspective. In other words, I try to answer the following questions: (i) In what sense can logic (...) be taken as philosophical? (ii) In what sense has logic been taken as philosophical? (iii) In what sense should logic be taken as philosophical? To this end, I analyze excerpts from five works in which meanings are attributed to the expression “philosophical logic”. The meanings are then object of critical analysis: I try to assess which of these semantical alternatives do not hold up as satisfactory answers to (iii). The result of this analysis is then used as a starting point for my own answer to question (iii). (shrink)

This essay consists of two parts. In the first part, I focus my attention on the remarks that Frege makes on consistency when he sets about criticizing the method of creating new numbers through definition or abstraction. This gives me the opportunity to comment also a little on H. Hankel, J. Thomae—Frege’s main targets when he comes to criticize “formal theories of arithmetic” in Die Grundlagen der Arithmetik (1884) and the second volume of Grundgesetze der Arithmetik (1903)—G. Cantor, L. E. (...) J. Brouwer and D. Hilbert (1899). Part 2 is mainly devoted to Hilbert’s proof theory of the 1920s (1922–1931). I begin with an account of his early attempt to prove directly, and thus not by reduction or by constructing a model, the consistency of (a fragment of) arithmetic. In subsequent sections, I give a kind of overview of Hilbert’s metamathematics of the 1920s and try to shed light on a number of difficulties to which it gives rise. One serious difficulty that I discuss is the fact, widely ignored in the pertinent literature on Hilbert’s programme, that his language of finitist metamathematics fails to supply the conceptual resources for formulating a consistency statement qua unbounded quantification. Along the way, I shall comment on W. W. Tait’s objection to an interpretation of Hilbert’s finitism by Niebergall and Schirn, on G. Gentzen’s allegedly finitist consistency proof for Peano Arithmetic as well as his ideas on the provability and unprovability of initial cases of transfinite induction in pure number theory. Another topic I deal with is what has come to be known as partial realizations of Hilbert’s programme, chiefly advocated by S. G. Simpson. Towards the end of this essay, I take a critical look at Wittgenstein’s views about (in)consistency and consistency proofs in the period 1929–1933. I argue that both his insouciant attitude towards the emergence of a contradiction in a calculus and his outright repudiation of metamathematical consistency proofs are unwarranted. In particular, I argue that Wittgenstein falls short of making a convincing case against Hilbert’s programme. I conclude with some philosophical remarks on consistency proofs and soundness and raise a question concerning the consistency of analysis. (shrink)

The first chapter explores the theory developed in Kripke's "Outline of a Theory of Truth." A tension in Kripke's account of the concept of truth is revealed--a conflict between two intuitions. The first intuition, called the "fixed point conception of truth," is that the whole meaning of the truth predicate is given by the formula "we may assert of a sentence that it is true iff we may assert that sentence." The second intuition, called the "thesis of the supervenience of (...) semantics," is that the interpretation of the truth predicate is determined by the interpretations of all the other non-logical constants of the language. I show that these two intuitions cannot be reconciled within the context of Kripke's theory, and I argue for the choice of the fixed point conception of truth over the principle of the supervenience of semantics. Chief among the considerations that I advance is the fact that the fixed point conception of truth yields a natural logic of truth. In the second chapter I present that logic of truth in the form of a cut-free sequent calculus. I then turn, in chapter three, to a discussion of the significance of such cut-free sequent calculi. I argue that we may view the sequent calculus introduction rules for a logical constant as giving the meaning of that constant, under certain conditions. In particular, we can see our logic of truth as providing an explication of our intuitive concept of truth which complements Kripke's original model-theoretic explication. The fourth chapter takes up some criticisms of Kripke's theory which center on the logic of truth. In addition, the general ideas developed in the first three chapters are applied in a discussion of the various schemes of three-valued logic which can be used in the development of Kripke's approach. Finally, in the last chapter, it is shown that Kripke's technical concepts, and the logical ideas developed in the second and third chapters, can be used to provide a unified account of many contexts in which paradox arises. (shrink)

Consider the proposition, "Informal logic is a subdiscipline of philosophy". The best chance of showing this to be true is showing that informal logic is part of logic, which in turn is a part of philosophy. Part 1 is given over to the task of sorting out these connections. If successful, informal logic can indeed be seen as part of philosophy; but there is no question of an exclusive relationship. Part 2 is a critical appraisal of the suggestion that (...) informal logic is applied epistemology. Part 3 examines the claim that informal logic has failed to penetrate into mainstream philosophy, and suggestions for amelioration are considered. (shrink)