This paper examines the role of a proper opponent (phyi rgol yang dag) in debate from the standpoint of the Tibetan Buddhist theory of argumentation. A proper opponent is a person who is engaged in the process of truth-seeking. He is not a debater who undertakes to refute the tenets of a proponent. But rather, he is the model debater to whom a proponent can teach truth by using a probative argument in the most effective way. A proper opponent is (...) thus the model thinker conceived by Tibetan Buddhist scholars, especially by the dGe lugs pa exegetes, to explain the idea of “inference for others.” The term phyi rgol yang dag figures in many text books of the dGe lugs pa school. And the germ of the dGe lugs pa's idea of ``proper opponent'' is found in early Tibetan tshad ma literature, too. The present paper shows that the dGe lugs pa scholars are largely concerned with the process by which one obtains an inferential knowledge about the unknown object, and also that they, when talking about a proper opponent, emphasize the pedagogical role of dialectic conversation rather than the competitive feature of debates. (shrink)
Erratum to: Stanley Peters and Dag Westerståhl: Quantifiers in language and logic Content Type Journal Article Category Erratum Pages 1-1 DOI 10.1007/s10988-011-9094-5 Authors Edward L. Keenan, Department of Linguistics, University of California at Los Angeles, 3125 Campbell Hall, Los Angeles, CA 90095-1543, USA Denis Paperno, Department of Linguistics, University of California at Los Angeles, 3125 Campbell Hall, Los Angeles, CA 90095-1543, USA Journal Linguistics and Philosophy Online ISSN 1573-0549 Print ISSN 0165-0157.
if and only if for every W in V, W is independent of the set of all its non-descendants conditional on the set of its parents. One natural question that arises with respect to DAGs is when two DAGs are “statistically equivalent”. One interesting sense of “statistical equivalence” is “d-separation equivalence” (explained in more detail below.) In the case of DAGs, d-separation equivalence is also corresponds to a variety of other natural senses of statistical equivalence (such as representing the same (...) set of distributions). Theorems characterizing d-separation equivalence for directed acyclic graphs and that can be used as the basis for polynomial time algorithms for checking d-separation equivalence were provided by Verma and Pearl (1990), and Frydenberg (1990). The question we will examine is how to extend these results to cases where a DAG may have latent (unmeasured) variables or selection bias (i.e. some of the variables in the DAG have been conditioned on.) D-separation equivalence is of interest in part because there are algorithms for constructing DAGs with latent variables and selection bias that are based on observed conditional independence relations. For this class of algorithms, it is impossible to determine which of two d-separation equivalent causal structures generated a given probability distribution, given only the set of conditional independence and dependence relations true of the observed distribution. We will describe a polynomial (in the number of vertices) time algorithm for determining when two DAGs which may have latent variables or selection bias are d-separation equivalent. (shrink)
Quantifiers in Language and Logic (QLL) is a major contribution to natural language semantics, specifically to quantification. It integrates the extensive recent work on quantifiers in logic and linguistics. It also presents new observations and results. QLL should help linguists understand the mathematical generalizations we can make about natural language quantification, and it should interest logicians by presenting an extensive array of quantifiers that lie beyond the pale of classical logic. Here we focus on those aspects of QLL we judge (...) to be of specific interest to linguists, and we contribute a few musings of our own, as one mark of a worthy publication is whether it stimulates the reader to seek out new observations, and QLL does. QLL is long and fairly dense, so we make no attempt to cover all the points it makes. But QLL has a topic index, a special symbols index and two tables of contents, a detailed one and an overview one, all of which help make it user friendly. QLL is presented in four parts: I, The Logical Conception of Quantifiers and Quantification with an introductory section Quantification . II, Quantifiers of Natural Language , the most extensive section in the book and of the most direct interest to linguists. III, Beginnings of a Theory of Expressiveness, Translation, and Formalization introduces notions of expressive power and definability, and IV, presents recent work and techniques concerning quantifier definability over finite domains, making accessible to linguists recent work in finite model theory. (shrink)
By means of ‘means that’ and propositional quantification, we can define a truth predicate. This also allows the construction of liar sentences, either by self-reference or by means of quantification. In order to avoid inconsistency, restrictions on expressive power must be imposed, and the question is how far such restrictions will limit our ability to say of what is intuitively described as ‘‘meaningful’’ that it is precisely meaningful.
In a recent paper Asher and Pustejovsky propose a type theoretical approach to account for cases of copredication which had motivated Pustejovsky to introduce dot types in the Generative Lexicon. In this paper I will propose an alternative treatment to that given by Asher and Pustejovsky using type theory with records. I will suggest that using record types not only gives us a simple and intuitive account of dot types but also makes an important connection between copredication and (...) the use of hypothetical contexts in dynamic generalized quantifiers I have proposed in earlier work. More generally it allows us to preserve the intuitive feature structure based accounts of lexical analysis proposed in Pustejovsky’s original work on the Generative Lexicon while at the same time introducing functions and binding in the way that is necessary for giving formal accounts of compositional semantics. (shrink)
The focus of this paper are the meaning-theoretical arguments against classical logic that Dummett bases on consideration about the meanings of negation. Using Dummettian principles, I shall outline three such arguments, of increasing strength, and show that they are unsuccessful by giving responses to each argument on behalf of the classical logician. What is crucial is that in responding to these arguments a classicist need not challenge any of the basic assumptions of Dummett's outlook on the theory of meaning. In (...) particular, I shall grant Dummett his general bias towards verificationism or justificationism, encapsulated in the slogan `meaning is use'. The second general assumption I see no need to question is Dummett's particular breed of molecularism. Some of Dummett's assumptions will have to be given up, if classical logic is to be vindicated in his meaning-theoretical framework. A major result of this paper will be that the meaning of negation cannot be defined by rules of inference in the Dummettian framework. (shrink)
The fundamental assumption of Dummett’s and Prawitz’ proof-theoretic justification of deduction is that ‘if we have a valid argument for a complex statement, we can construct a valid argument for it which finishes with an application of one of the introduction rules governing its principal operator’. I argue that the assumption is flawed in this general version, but should be restricted, not to apply to arguments in general, but only to proofs. I also argue that Dummett’s and Prawitz’ project of (...) providing a logical basis for metaphysics only relies on the restricted assumption. (shrink)
I argue for a kind of logical pluralism on the basis of a difficulty with defining the meaning of negation in the framework of Dummett's and Prawitz' proof-theoretic semantics.
I present an argument that negation is a problem for proof-theoretic semantics: it's meaning cannot be defined by rules of inference, and that's particularly problematic for Dummett's and Prawitz' Justification of Deduction. I won the Jacobsen Essay Price of the University of London for this essay a few years ago.
In this paper, I'll present a general way of "reading off" introduction/elimination rules from elimination/introduction rules, and define notions of harmony and stability on the basis of it.
Ethics in business and economics is often attacked for being too superficial. By elaborating the conclusions of two such critics of business ethics and welfare economics respectively, this article will draw the attention to the ethics behind these apparently well-intended, but not always convincing constructions, by help of the fundamental ethics of Emmanuel Levinas. To Levinas, responsibility is more basic than language, and thus also more basic than all social constructions. Co-operation relations in organizations, markets and value networks are generated (...) from personal relations and personal responsibilities. It is not sufficient to integrate ethics in an impersonal, rational system, neither in business organizations nor in the world economy. Ethics has its source not in rationality, but in the personal. (shrink)
According to a main idea of Gentzen the meanings of the logical constants are reflected by the introduction rules in his system of natural deduction. This idea is here understood as saying roughly that a closed argument ending with an introduction is valid provided that its immediate subarguments are valid and that other closed arguments are justified to the extent that they can be brought to introduction form. One main part of the paper is devoted to the exact development of (...) this notion. Another main part of the paper is concerned with a modification of this notion as it occurs in Michael Dummett’s book The Logical Basis of Metaphysics. The two notions are compared and there is a discussion of how they fare as a foundation for a theory of meaning. It is noted that Dummett’s notion has a simpler structure, but it is argued that it is less appropriate for the foundation of a theory of meaning, because the possession of a valid argument for a sentence in Dummett’s sense is not enough to be warranted to assert the sentence. (shrink)
What is the appropriate notion of truth for sentences whose meanings are understood in epistemic terms such as proof or ground for an assertion? It seems that the truth of such sentences has to be identified with the existence of proofs or grounds, and the main issue is whether this existence is to be understood in a temporal sense as meaning that we have actually found a proof or a ground, or if it could be taken in an abstract, tenseless (...) sense. Would the latter alternative amount to realism with respect to proofs or grounds in a way that would be contrary to the supposedly anti-realistic standpoint underlying the epistemic understanding of linguistic expressions? Before discussing this question, I shall consider reasons for construing linguistic meaning epistemically and relations between such reasons and reasons for taking an anti-realist point of view towards the discourse in question. (shrink)
We give a condensed survey of recent research on generalized quantifiers in logic, linguistics and computer science, under the following headings: Logical definability and expressive power, Polyadic quantifiers and linguistic definability, Weak semantics and axiomatizability, Computational semantics, Quantifiers in dynamic settings, Quantifiers and modal logic, Proof theory of generalized quantifiers.
Truth’s universal knowability entails its discovery. This threatens antirealism, which is thought to require it. Fortunately, antirealism is not committed to it. Avoiding it requires adoption (and extension) of Dag Prawitz’s position in his long-term disagreement with Michael Dummett on the notion of provability involved in intuitionism’s identification of it with truth. Antirealism (intuitionism generalized) must accommodate a notion of lost-opportunity truth (a kind of recognition-transcendent truth), and even truth consisting in the presence of unperformable verifications. Dummett’s position cannot abide (...) this, while Prawitz’s can. Antirealism’s epistemic notion of truth derives from general features of its meaning theory, not from a universal knowability principle. (shrink)
Michael Dummett and Dag Prawitz have argued that a constructivist theory of meaning depends on explicating the meaning of logical constants in terms of the theory of valid inference, imposing a constraint of harmony on acceptable connectives. They argue further that classical logic, in particular, classical negation, breaks these constraints, so that classical negation, if a cogent notion at all, has a meaning going beyond what can be exhibited in its inferential use.I argue that Dummett gives a mistaken elaboration of (...) the notion of harmony, an idea stemming from a remark of Gerhard Gentzen"s. The introduction-rules are autonomous if they are taken fully to specify the meaning of the logical constants, and the rules are harmonious if the elimination-rule draws its conclusion from just the grounds stated in the introduction-rule. The key to harmony in classical logic then lies in strengthening the theory of the conditional so that the positive logic contains the full classical theory of the conditional. This is achieved by allowing parametric formulae in the natural deduction proofs, a form of multiple-conclusion logic. (shrink)
Starting from the familiar observation that no straightforward treatment of pure quotation can be compositional in the standard (homomorphism) sense, we introduce general compositionality, which can be described as compositionality that takes linguistic context into account. A formal notion of linguistic context type is developed, allowing the context type of a complex expression to be distinct from those of its constituents. We formulate natural conditions under which an ordinary meaning assignment can be non-trivially extended to one that is sensitive to (...) context types and satisfies general compositionality. As our main example we work out a Fregean treatment of pure quotation, but we also indicate that the method applies to other kinds of context, e.g. intensional contexts. (shrink)
Bolzano’s definition of consequence in effect associates with each set X of symbols (in a given interpreted language) a consequence relation X . We present this in a precise and abstract form, in particular studying minimal sets of symbols generating X . Then we present a method for going in the other direction: extracting from an arbitrary consequence relation its associated set C of constants. We show that this returns the expected logical constants from familiar consequence relations, and that, restricting (...) attention to sets of symbols satisfying a strong minimality condition, there is an isomorphism between the set of strongly minimal sets of symbols and the set of corresponding consequence relations (both ordered under inclusion). (shrink)
The idea of an ?inversion principle?, and the name itself, originated in the work of Paul Lorenzen in the 1950s, as a method to generate new admissible rules within a certain syntactic context. Some fifteen years later, the idea was taken up by Dag Prawitz to devise a strategy of normalization for natural deduction calculi (this being an analogue of Gentzen's cut-elimination theorem for sequent calculi). Later, Prawitz used the inversion principle again, attributing it with a semantic role. Still working (...) in natural deduction calculi, he formulated a general type of schematic introduction rules to be matched ? thanks to the idea supporting the inversion principle ? by a corresponding general schematic Elimination rule. This was an attempt to provide a solution to the problem suggested by the often quoted note of Gentzen. According to Gentzen ?it should be possible to display the elimination rules as unique functions of the corresponding introduction rules on the basis of certain requirements?. Many people have since worked on this topic, which can be appropriately seen as the birthplace of what are now referred to as ?general elimination rules?, recently studied thoroughly by Sara Negri and Jan von Plato. In this study, we retrace the main threads of this chapter of proof-theoretical investigation, using Lorenzen's original framework as a general guide. (shrink)
The paper elaborates two points: i) There is no principal opposition between predicate logic and adherence to subject-predicate form, ii) Aristotle's treatment of quantifiers fits well into a modern study of generalized quantifiers.
In the analysis of the ethicalproblems of online research, there is much tobe learned from the work that has already beendone on research ethics in the socialsciences and the humanities. I discuss thestructure of norms in the Norwegian ethicalguidelines for research in the social scienceswith respect to their relevance for the ethicalissues of Internet research. A four-stepprocedure for the ethical evaluation ofresearch is suggested. I argue that eventhough, at one level, the problems of onlineresearch are very similar to those (...) we find intraditional areas of social scientificresearch, there still are some issues that areunique to research online. A general model forthe analysis of privacy and data protection issuggested. This model is then used tocharacterize the special problems pertaining tothe protection of privacy in online contexts,and to argue that one cannot assume a simpledistinction between the private and the publicwhen researching in such contexts. (shrink)
Logic and Knowledge -/- Editor: Carlo Cellucci, Emily Grosholz and Emiliano Ippoliti Date Of Publication: Aug 2011 Isbn13: 978-1-4438-3008-9 Isbn: 1-4438-3008-9 -/- The problematic relation between logic and knowledge has given rise to some of the most important works in the history of philosophy, from Books VI–VII of Plato’s Republic and Aristotle’s Prior and Posterior Analytics, to Kant’s Critique of Pure Reason and Mill’s A System of Logic, Ratiocinative and Inductive. It provides the title of an important collection of papers (...) by Bertrand Russell (Logic and Knowledge. Essays, 1901–1950). However, it has remained an underdeveloped theme in the last century, because logic has been treated as separate from knowledge. -/- This book does not hope to make up for a century-long absence of discussion. Rather, its ambition is to call attention to the theme and stimulating renewed reflection upon it. The book collects essays of leading figures in the field and it addresses the theme as a topic of current debate, or as a historical case study, or when appropriate as both. Each essay is followed by the comments of a younger discussant, in an attempt to transform what might otherwise appear as a monologue into an ongoing dialogue; each section begins with an historical essay and ends with an essay by one of the editors. -/- Carlo Cellucci is Emeritus Professor of Philosophy at the University of Rome ‘La Sapienza,’ Italy. He is currently completing a book entitled, Remaking Logic: What is Logic Really? -/- Emily Grosholz is Professor of Philosophy at the Pennsylvania State University, USA. She is the author of Representation and Productive Ambiguity in Mathematics and the Sciences (Oxford University Press, 2007). -/- Emiliano Ippoliti is a Research Fellow at the University of Rome ‘La Sapienza,’ Italy. His main interests are heuristics, the logic of discovery, and problem-solving. He is currently working on a book, Ampliating Knowledge: Data, Hypotheses and Novelty. -/- TABLE OF CONTENTS -/- Foreword .................................................................................................... ix Acknowledgements ................................................................................. xxv -/- Section I: Logic and Knowledge -/- Chapter One................................................................................................. 3 The Cognitive Importance of Sight and Hearing in Seventeenthand Eighteenth-Century Logic (Mirella Capozzi) Discussion .............................................................................................. 26 (Chiara Fabbrizi) Chapter Two .............................................................................................. 33 Nominalistic Content (Jody Azzouni) Discussion ............................................................................................... 52 (Silvia De Bianchi) Chapter Three ............................................................................................ 57 A Garden of Grounding Trees (Göran Sundholm) Discussion.......................................................................................... .. 75 (Luca Incurvati) Chapter Four .............................................................................................. 81 Logics and Metalogics (Timothy Williamson) Discussion.......................................................................................... 101 (Cesare Cozzo) Chapter Five ............................................................................................ 109 Is Knowledge the Most General Factive Stative Attitude? (Cesare Cozzo) Discussion.......................................................................................... 117 (Timothy Williamson) Chapter Six .............................................................................................. 123 Classifying and Justifying Inference Rules (Carlo Cellucci) Discussion.......................................................................................... 143 (Norma B. Goethe) -/- Section II: Logic and Science -/- Chapter Seven.......................................................................................... 151 The Universal Generalization Problem and the Epistemic Status of Ancient Medicine: Aristotle and Galen (Riccardo Chiaradonna) Discussion.......................................................................................... 168 (Diana Quarantotto) Chapter Eight........................................................................................... 175 The Empiricist View of Logic (Donald Gillies) Discussion.......................................................................................... 191 (Paolo Pecere) Chapter Nine............................................................................................ 197 Artificial Intelligence and Evolutionary Theory: Herbert Simon’s Unifying Framework (Roberto Cordeschi) Discussion.......................................................................................... 216 (Francesca Ervas) Chapter Ten ............................................................................................. 221 Evolutionary Psychology and Morality: The Renaissance of Emotivism? (Mario De Caro) Discussion.......................................................................................... 232 (Annalisa Paese) Chapter Eleven ........................................................................................ 237 Between Data and Hypotheses (Emiliano Ippoliti) Discussion.......................................................................................... 262 (Fabio Sterpetti) -/- Section III: Logic and Mathematics -/- Chapter Twelve ....................................................................................... 273 Dedekind Against Intuition: Rigor, Scope and the Motives of his Logicism (Michael Detlefsen) Discussion.......................................................................................... 290 (Marianna Antonutti) Chapter Thirteen...................................................................................... 297 Mathematical Intuition: Poincaré, Polya, Dewey (Reuben Hersh) Discussion.......................................................................................... 324 (Claudio Bernardi) Chapter Fourteen ..................................................................................... 329 On the Finite: Kant and the Paradoxes of Knowledge (Carl Posy) Discussion.......................................................................................... 358 (Silvia Di Paolo) Chapter Fifteen ........................................................................................ 363 Assimilation: Not Only Indiscernibles are Identified (Robert Thomas) Discussion.......................................................................................... 380 (Diego De Simone) Chapter Sixteen ....................................................................................... 385 Proofs and Perfect Syllogisms (Dag Prawitz) Discussion.......................................................................................... 403 (Julien Murzi) Chapter Seventeen ................................................................................... 411 Logic, Mathematics, Heterogeneity (Emily Grosholz) Discussion.......................................................................................... 427 (Valeria Giardino) -/- Contributors........................................................................................ ..... 433 Index............................................................................................... ......... 437 -/- Price Uk Gbp: 49.99 Price Us Usd: 74.99 -/- Website: http://www.c-s-p.org/Flyers/Logic-and-Knowledge1-4438-3008-9.htm. 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The theme of these notes is the relation between verificationism and Quine's approach to philosophy of language. The main thesis is that a tenable theory of meaning along verificationist lines must distinguish between canonical and indirect verification and that this distinction is related to observable features of language use. It is argued that a theory of meaning along such lines is not vulnerable to Quine's arguments against verificationism, and suggested that, on the whole, a verificationism of this kind is compatible (...) with Quine's basic approach to philosophy of language. (shrink)
Albertus Magnus favours the Aristotelian definition of the soul as the first actuality or perfection of a natural body having life potentially. But he interprets Aristotle's vocabulary in a way that it becomes compatible with the separability of the soul from the body. The term “perfectio” is understood as referring to the soul's activity only, not to its essence. The term “forma” is avoided as inadequate for defining the soul's essence. The soul is understood as a substance which exists independently (...) of its actions and its body. The article shows that Albertus' terminological decisions continue a tradition reaching from the Greek commentators, and John Philoponos in particular, to Avicenna. Albertus' position on another important issue is also influenced by Arabic sources. His defense of the unity of the soul's vegetative, animal and rational parts rests on arguments from Avicenna and Averroes. It is shown that Averroes' position on the problem is not clearcut: he advocates the unity thesis, but also teaches the plurality of the generic and individual forms in man. This double stance is visible in the Latin reception of Averroes' works, and also in Albertus, who presents Averroes both as supporter and opponent of the plurality thesis. (shrink)
Ordinary semantic compositionality (meaning of whole determined from meanings of parts plus composition) can serve to explain how a hearer manages to assign an appropriate meaning to a new sentence. But it does not serve to explain how the speaker manages to find an appropriate sentence for expressing a new thought. For this we would need a principle of inverse compositionality, by which the expression of a complex content is determined by the expressions of it parts and the mode of (...) composition. But this presupposes that contents have constituent structure, and this cannot be taken for granted. However, it can be proved that if a certain principle of substitutivity is valid for a particular language, then the meanings expressed by its sentences can justifiably be treated as structured. In its simplest form, this principle says that if in a complex expression a constituent is replaced by another constituent with a different meaning, the new complexhas a meaning different from the original. This principle is again inversely related to the normal compositional principle of substitutivity. The combination of ordinary and inverse compositionality is here called strong compositionality. The proof is carried out in the algebraic framework developed by Wilfrid Hodges and Dag Westerståhl. (shrink)
How should the policies of search engines and other information intermediaries be ethically evaluated? It is argued that Kant’s principles for the public use of reason are useful starting points for the formulation of criteria for such an evaluation. The suggestion is, furthermore, that a search engine can be seen to provide a testimony to the user concerning what information that is most relevant to her query. This suggestion is used as the basis for the development of a broadly Kantian (...) account of a rational searcher. It is argued that the search engine companies are morally required to publish their information policies and act in accordance with them but given the threat of search engine spam they can have no obligation to publish the details of their algorithms. (shrink)
At IAPS Ljubljana conference (September 2007) Dag Vidar Hanstad and Sigmund Loland presented a paper on elite-level athletes' duty to provide information on their whereabouts, to decide between two opposing positions: is this WADA demand justifiable anti-doping work or an indefensible surveillance regime? They concluded that on moral grounds this regime is conditionally acceptable, the condition being the acceptability of a general framework and objectives embodied in anti-doping global legislative foundations (the World Anti-Doping Code). But, as they said, principled objections (...) against the system have more universal relevance, which has to be taken seriously . To take this ambiguous and intriguing conclusion a step further, I propose a legal rather than ethical approach, from the aspect of constitutional and international human rights law, and the possible clash of two legally acknowledged values - the concept of elite sport without doping, and the concept of individual human rights. This conflict between ideological or moral values and the legality of individual rights is not a novelty. This paper presents three instances of this conflict: Bernard de Mandeville's differentiation between public and private values; Eug ne Sue's parallel legal and civil morals; and the contemporary moralisation of law which conflates legality into morality. The subordination of legality to morality has potentially dangerous consequences: here, Agamben's 'state of exception' comes to mind, with his analysis of potestas and auctoritas. However, in the case of sport and the war against doping, the origin of power is not in the nation state; it originates in civil society's non-governmental national and international bodies recognised as autonomous sources of legal order. (shrink)
The problem, or cluster of problems, of the unity of the proposition, along with the cluster of problems that tend to go under the name of Bradley’s regress, has recently again become a going concern for philosophers, after having for some time been regarded as primarily of historical interest. However, while I find the problems of sufficient interest that this tendency is in some ways laudable, my view, roughly put, is that when confusions and conflations are set aside, relatively easy (...) solutions – perhaps one might say dissolutions – can be given of these problems. In this paper, I distinguish between the different problems that tend to be brought up under the heading of the unity of the proposition, and the different regress arguments brought up in connection with these problems, arguing that the problems, once clearly distinguished, can be dealt with rather straightforwardly. Along the way, I discuss solutions to these problems due, or purported to be due, to Russell, Frege and Wittgenstein, as well as more recent ideas defended by Jeffrey King, D.M. Armstrong and Chris Swoyer. (shrink)
The aim of this paper is to make a critical assessment of Krister Segerberg''s theory of action. The first part gives a critical presentation of the key concepts in Segerberg''s informal theory of action. These are the ideas that motivate the formal models he develops. In the second part it is argued that if one takes all of Segerberg''s motivating ideas seriously, problems are forthcoming. The main problem is that on this theory the agents seem to be bound to realize (...) all of their intentions, a problem that stems from Segerberg''s attempt to individuate actions in terms of the agent''s intentions. On the ground that this unfortunate result is forthcoming in both of Segerberg''s approaches to the logic of action it is concluded that the conceptual basis of the theory is problematic. (shrink)
A semantics may be compositional and yet partial, in the sense that not all well-formed expressions are assigned meanings by it. Examples come from both natural and formal languages. When can such a semantics be extended to a total one, preserving compositionality? This sort of extension problem was formulated by Hodges, and solved there in a particular case, in which the total extension respects a precise version of the fregean dictum that the meaning of an expression is the contribution it (...) makes to the meanings of complex phrases of which it is a part. Hodges' result presupposes the so-called Husserl property, which says roughly that synonymous expressions must have the same category. Here I solve a different version of the compositional extension problem, corresponding to another type of linguistic situation in which we only have a partial semantics, and without assuming the Husserl property. I also briefly compare Hodges' framework for grammars in terms of partial algebras with more familiar ones, going back to Montague, which use many-sorted algebras instead. (shrink)
Quantification is a topic which brings together linguistics, logic, and philosophy. Quantifiers are the essential tools with which, in language or logic, we refer to quantity of things or amount of stuff. In English they include such expressions as no, some, all, both, and many. Peters and Westerstahl present the definitive interdisciplinary exploration of how they work - their syntax, semantics, and inferential role. Quantifiers in Language and Logic is intended for everyone with a scholarly interest in the exact treatment (...) of meaning. It presents a broad view of the semantics and logic of quantifier expressions in natural languages and, to a slightly lesser extent, in logical languages. The authors progress carefully from a fairly elementary level to considerable depth over the course of sixteen chapters; their book will be invaluable to a broad spectrum of readers, from those with a basic knowledge of linguistic semantics and of first-order logic to those with advanced knowledge of semantics, logic, philosophy of language, and knowledge representation in artificial intelligence. (shrink)
We study generalized quantifiers on finite structures.With every function : we associate a quantifier Q by letting Q x say there are at least (n) elementsx satisfying , where n is the sizeof the universe. This is the general form ofwhat is known as a monotone quantifier of type .We study so called polyadic liftsof such quantifiers. The particular lifts we considerare Ramseyfication, branching and resumption.In each case we get exact criteria fordefinability of the lift in terms of simpler quantifiers.
The rich and interconnected universe of Śākya Mchog Ldan’s views, including those on the buddha-essence, cannot be limited to or summarized in a few neat categories. Nevertheless, the following two interrelated ideas are crucial for understanding Śākya Mchog Ldan’s interpretation of the buddha-essence: 1) only Mahāyāna āryas (’phags pa) have the buddha-essence characterized by the purity from adventitious stains (glo bur rnam dag).
A new formalism for predicate logic is introduced, with a non-standard method of binding variables, which allows a compositional formalization of certain anaphoric constructions, including donkey sentences and cross-sentential anaphora. A proof system in natural deduction format is provided, and the formalism is compared with other accounts of this type of anaphora, in particular Dynamic Predicate Logic.
This volume is the product of the Proceedings of the 9th International Congress of Logic, Methodology and Philosophy of Science and contains the text of most of ...
We describe anytime search procedures that (1) find disjoint subsets of recorded variables for which the members of each subset are d-separated by a single common unrecorded cause, if such exists; (2) return information about the causal relations among the latent factors so identified. We prove the procedure is point-wise consistent assuming (a) the causal relations can be represented by a directed acyclic graph (DAG) satisfying the Markov Assumption and the Faithfulness Assumption; (b) unrecorded variables are not caused by recorded (...) variables; and (c) dependencies are linear. We compare the procedure with standard approaches over a variety of simulated structures and sample sizes, and illustrate its practical value with brief studies of social science data sets. Finally, we consider generalizations for non-linear systems. Keywords: latent variable models, causality, graphical models.. (shrink)
I present three reasons why philosophers of science should be more concerned about violations of causal faithfulness (CF). In complex evolved systems, mechanisms for maintaining various equilibrium states are highly likely to violate CF. Even when such systems do not precisely violate CF, they may nevertheless generate precisely the same problems for inferring causal structure from probabilistic relationships in data as do genuine CF-violations. Thus, potential CF-violations are particularly germane to experimental science when we rely on probabilistic information to uncover (...) the DAG, rather than already knowing the DAG from which we could predict the right experiments to ‘catch out’ the hidden causal relationships. (shrink)
We study definability in terms of monotone generalized quantifiers satisfying Isomorphism Closure, Conservativity and Extension. Among the quantifiers with the latter three properties – here called CE quantifiers – one finds the interpretations of determiner phrases in natural languages. The property of monotonicity is also linguistically ubiquitous, though some determiners like an even number of are highly non-monotone. They are nevertheless definable in terms of monotone CE quantifiers: we give a necessary and sufficient condition for such definability. We further identify (...) a stronger form of monotonicity, called smoothness, which also has linguistic relevance, and we extend our considerations to smooth quantifiers. The results lead us to propose two tentative universals concerning monotonicity and natural language quantification. The notions involved as well as our proofs are presented using a graphical representation of quantifiers in the so-called number triangle. (shrink)
Levinas did not present any new ethical theories; he did not even give any normative recommendations. But his phenomenological investigations help us to understand how the idea of ethics emerges and how we try to cope with it. The purpose of this paper is to suggest some implications from a reading of Levinas on how ethical challenges are handled within a management perspective. The paper claims that management, both in theory and in practice, is necessarily egocentric and thus ethically biased. (...) Therefore, ethics, defined as the idea that it is possible to do otherwise than pursue one's own interest, must have its source outside the scope of management. Levinas identifies this source as the call for responsibility from the Other, beyond the reach of managerial control. He also suggests how this idea of ethics is put into practice, especially in economic life: the existence of money makes it both possible and necessary to compare unique and incomparable others. Management tools may be used in the service of always more justice, as it also may be used for the opposite purpose. Instead of trying to draw a normative conclusion from Levinas, we may distinguish between two ways of experiencing reality: one through language and knowledge, covering both descriptive and normative knowledge, including business ethics, and the other through the particular events of encounters, from where this knowledge is continuously questioned through the call for responsibility, and thereby may provide possibilities for continuous improvements towards always more justice. (shrink)
The paper has three parts. First, a survey and analysis is given ofthe structure of individual rights in the recent EU Directive ondata protection. It is argued that at the core of this structure isan unexplicated notion of what the data subject can `reasonablyexpect' concerning the further processing of information about himor herself. In the second part of the paper it is argued thattheories of privacy popular among philosophers are not able to shed much light on the issues treated in (...) the Directive, whichare, arguably, among the central problems pertaining to theprotection of individual rights in the information society. Inthe third part of the paper, some suggestions are made for a richerphilosophical theory of data protection and privacy. It is arguedthat this account is better suited to the task of characterizingthe central issues raised by the Directive. (shrink)
A Bayesian network consists of two distinct parts: a directed acyclic graph (DAG or belief-network structure) and a set of parameters for the DAG. The DAG in a Bayesian network can be used to represent both causal hypotheses and sets of probability distributions. Under the causal interpretation, a DAG represents the causal relations in a given population with a set of vertices V when there is an edge from A to B if and only if A is a direct cause (...) of B relative to V. (We adopt the convention that sets of variables are capitalized and boldfaced, and individual variables are capitalized and italicized.) Under the statistical interpretation a DAG G can be taken to represent a set of all distributions all of which share a set of conditional independence relations that are entailed by satisfying a local directed Markov property (defined below). (shrink)
In this paper, we compare several cut-free sequent systems for propositional intuitionistic logic Intwith respect to polynomial simulations. Such calculi can be divided into two classes, namely single-succedent calculi (like Gentzen's LJ) and multi-succedent calculi. We show that the latter allow for more compact proofs than the former. Moreover, for some classes of formulae, the same is true if proofs in single-succedent calculi are directed acyclic graphs (dags) instead of trees. Additionally, we investigate the effect of weakening rules on the (...) structure and length of dag proofs.The second topic of this paper is the effect of different embeddings from Int to S4. We select two different embeddings from the literature and show that translated (propositional) intuitionistic formulae have sometimes exponentially shorter minimal proofs in a cut-free Gentzen system for S4than the original formula in a cut-free single-succedent Gentzen system for Int. Moreover, the length and the structure of proofs of translated formulae crucially depend on the chosen embedding. (shrink)
This paper introduces a class of graphical independence models that is closed under marginalization and conditioning but that contains all DAG independence models. This class of graphs, called maximal ancestral graphs, has two attractive features: there is at most one edge between each pair of vertices; every missing edge corresponds to an independence relation. These features lead to a simple parameterization of the corresponding set of distributions in the Gaussian case.
This is a reply to H. Ben-Yami, 'Generalized quantifiers, and beyond' (this journal, 2009), where he argues that standard GQ theory does not explain why natural language quantifiers have a restricted domain of quantification. I argue, on the other hand, that although GQ theory gives no deep explanation of this fact, it does give a sort of explanation, whereas Ben-Yami's suggested alternative is no improvement.
We characterize the generalized quantifiers Q which satisfy the scheme $QxQy\phi \leftrightarrow QyQx\phi$ , the so-called self-commuting quantifiers, or quantifiers with the Fubini property.
with the meaning function [[·]] appearing on both sides. (1) is commonly construed as a prescription for computing the meaning of a based on the parts of a and their mode of combination. As equality is symmetric, however, we can also read (1) from right to left, as a constraint on the meaning [[b]] of a term b that brings in the wider context where b may occur, in accordance with what Dag Westerst˚ahl has recently described as “one version of (...) Frege’s famous Context Principle”. (shrink)
This paper is an argument to the effect that a certain view about mental representing, together with some very liberal constraints on the brain as a dynamic system, entails that the organism will tend to form adaptive mental representations of its environment. To show this, it will first be argued that although mental representing is a common thing indeed, representationalism, in the most important sense of that term (indirect representationalism), is false. Three different views about pictorial thinking (mental imagery, intuitive (...) representing) are then contrasted, two of which are tied to this brand of representationalism and one of which is not. The latter view, versions of which have sometimes been presented as ”simulation” theories of imagery, is here generalised to cover all kinds of mental representation. Two models of the brain are then presented in which learning of adaptive representations follows from this theory together with certain biologically plausible constraints. (shrink)
The category of heroic action is important in both everyday life and the wider social context. This article argues that interest in the notion of heroic actions and heroic defeats also brings out an important set of sociological problems, such as disagreements on identity, norms, and rational choice explanations. Illustrations are provided from recent analyses of union militancy in Britain and Italy, and of the student movement in Beijing. Different versions of the critique of rational choice theory often take norm-guided (...) action as a point of departure. Another version of this critique is represented by theories of new social movements and identity maintenance. The article suggests that rational choice theory is more useful than some of its opponents would have it; yet the general argument favors a mixed motivation approach. The discussion points out some of the strengths and limitations of different explanatory perspectives, and some of the links between them. (shrink)
This paper presents an argument to the effect that the relation of exact similarity with respect to properties that are supervenient cannot be transitive. The point of departure is that, while a difference in respect of supervenient properties entails a difference in respect of subvenient properties, exact similiarity in respect of supervenient properties is compatible with differences in respect of subvenient properties. It is logically possible that two such sets of differences that each individually is insufficient for a difference as (...) regards the supervenient property together are sufficient for such a supervenient difference. This possibility claim is incompatible with the necessity claim entailed by the transitivity of exact similarity. Several objections to this argument are then considered. (shrink)
