This is a short introduction to a book symposium on Paul Gowder's recent book, _The Rule of Law in thee Real World_ (Cambridge University Press, 2016). The book symposium will appear in the St. Luis University Law Journal, 62 St. Louis U. L.J., -- (2018), with commentaries on Gowder's book by colleen Murphy, Robin West, Chad Flanders, and Matthew Lister, along with replies by Paul Gowder.

: This introduction highlights two of Mondzain's contributions in the chapter reproduced here, "Iconic Space and the Rule of Lands." The first is her discussion of a link between images and power, which stresses the formal characteristics of paintings rather than their narratives. The second is her examination of the specific task which representation is called on to perform in religious as opposed to secular contexts, where spiritual, otherworldly figures are given physical shape and form.

This introduction highlights two of Mondzain's contributions in the chapter reproduced here, "Iconic Space and the Rule of Lands." The first is her discussion of a link between images and power, which stresses the formal characteristics of paintings rather than their narratives. The second is her examination of the specific task which representation is called on to perform in religious as opposed to secular contexts, where spiritual, otherworldly figures are given physical shape and form.

This introduction highlights two of Mondzain's contributions in the chapter reproduced here, “Iconic Space and the Rule of Lands.” The first is her discussion of a link between images and power, which stresses the formal characteristics of paintings rather than their narratives. The second is her examination of the specific task which representation is called on to perform in religious as opposed to secular contexts, where spiritual, otherworldly figures are given physical shape and form.

This paper argues that Lemmon-style proof systems (those that consist of only introduction and elimination inference rules) have several pedagogical benefits over Copi-style systems (those that make use of inference rules and equivalence rules). It is argued that Lemmon-style systems are easier to learn as they do not require memorizing as many rules, they do not require learning the subtle distinction between a rule of inference and a rule of replacement, and deriving material conditionals is (...) more straightforward. Finally, it is argued that the need for learning provisional assumptions in Lemmon-style rules is not a significant enough reason for choosing the Copi-style system. (shrink)

This paper argues that Lemmon-style proof systems (those that consist of only introduction and elimination inference rules) have several pedagogical benefits over Copi-style systems (those that make use of inference rules and equivalence rules). It is argued that Lemmon-style systems are easier to learn as they do not require memorizing as many rules, they do not require learning the subtle distinction between a rule of inference and a rule of replacement, and deriving material conditionals is (...) more straightforward. Finally, it is argued that the need for learning provisional assumptions in Lemmon-style rules is not a significant enough reason for choosing the Copi-style system. (shrink)

This paper studies a formalisation of intuitionistic logic by Negri and von Plato which has general introduction and elimination rules. The philosophical importance of the system is expounded. Definitions of ‘maximal formula’, ‘segment’ and ‘maximal segment’ suitable to the system are formulated and corresponding reduction procedures for maximal formulas and permutative reduction procedures for maximal segments given. Alternatives to the main method used are also considered. It is shown that deductions in the system convert into normal form and (...) that deductions in normal form have the subformula property. (shrink)

Introducing this issue’s triptych on algorithms and culture, this article argues that prevailing modes of analysis that focus on the prospects for algorithms “taking over” are no longer useful. It advocates the need for a new conceptual vocabulary, which recognizes that algorithmic and cultural reasoning processes are already enmeshed with each other. The introduction suggests a need for an enterprise of algorithmic epistemology attuned to the fine structure of the ways in which culture and code have interacted in the (...) past and continue to interact today. (shrink)

In An Introduction to Non-Classical Logic: From If to Is Graham Priest presents branching rules in Free Logic, Variable Domain Modal Logic, and Intuitionist Logic. I propose a simpler, non-branching rule to replace Priest's rule for universal instantiation in Free Logic, a second, slightly modified version of this rule to replace Priest's rule for universal instantiation in Variable Domain Modal Logic, and third and fourth rules, further modifying the second rule, to replace Priest's branching universal and particular (...) instantiation rules in Intuitionist Logic. In each of these logics the proposed rule leads to tableaux with fewer branches. In Intuitionist logic, the proposed rules allow for the resolution of a particular problem Priest is grappling with throughout the chapter. In this paper, I demonstrate that the proposed rules can greatly simplify tableaux and argue that they should be used in place of the rules given by Priest. (shrink)

A natural extension of Natural Deduction was defined by Schroder-Heister where not only formulas but also rules could be used as hypotheses and hence discharged. It was shown that this extension allows the definition of higher-level introduction and elimination schemes and that the set $\{ \vee, \wedge, \rightarrow, \bot \}$ of intuitionist sentential operators forms a {\it complete} set of operators modulo the higher level introduction and elimination schemes, i.e., that any operator whose introduction and elimination (...) rules are instances of the higher-level schemes can be defined in terms of $\{ \vee, \wedge, \rightarrow, \bot \}$.The aim of the present work is to extend the well-known connections between Proof Theory and Category Theory to higher-level Natural Deduction. To be precise, we will show how an adjointness between cartesian closed categories with finite coproducts can be associated, in a systematic way, with any operator $\phi$ defined by the higher-level schemes. The objects in the categories will be rules instead of formulas. (shrink)

"Descartes is rightly considered the father of modern philosophy" - Schopenhauer "The effect of this man on his age and the new age cannot be imagined broadly enough... René Descartes is indeed the true beginner of modern philosophy, insofar as it makes thinking the principle. "- Hegel "Descartes was the first to bring to light the idea of a transcendental science, which is to contain a system of knowledge of the conditions of possibility of all knowledge." - Kant A new (...) 2023 translation directly from the original manuscripts into English of Descartes' famous work "Rules for the Direction of the Mind" (Règles pour la direction de l'esprit). This edition contains a new introduction and afterword from the translator, as well as a timeline of Descartes' life and summaries of each of his works. Here, Descartes lays out a method for approaching problems and seeking knowledge. The importance of this work lies in the fact that it established the scientific method as a way of investigating the world, and had a significant influence on the development of modern science. This work is one of the foundational texts of Western Philosophy. (shrink)

Analytical commentary -- Fruits upon one tree -- The continuation of the early draft into philosophy of mathematics -- Hidden isomorphism -- A common methodology -- The flatness of philosophical grammar -- Following a rule 185-242 -- Introduction to the exegesis -- Rules and grammar -- The tractatus and rules of logical syntax -- From logical syntax to philosophical grammar -- Rules and rule-formulations -- Philosophy and grammar -- The scope of grammar -- Some morals -- (...) Exegesis 185-8 -- Accord with a rule -- Initial compass bearings -- Accord and the harmony between language and reality -- Rules of inference and logical machinery -- Formulations and explanations of rules by examples -- Interpretations, fitting and grammar -- Further misunderstandings -- Exegesis 189-202 -- Following rules, mastery of techniques and practices -- Following a rule -- Practices and techniques -- Doing the right thing and doing the same thing -- Privacy and the community view -- On not digging below bedrock -- Private linguists and private linguists : Robinson Crusoe sails again -- Is a language necessarily shared with a community of speakers? -- Innate knowledge of a language -- Robinson Crusoe sails again -- Solitary cavemen and monolinguists -- Private languages and private languages -- Exegesis 203-37 -- Agreement in definitions, judgements, and form of life -- The scaffolding of facts -- The role of our nature -- Forms of life -- Agreement : consensus of human beings and their actions -- Exegesis 238-42 -- Grammar and necessity -- Setting the stage -- Leitmotifs -- External guidelines -- Necessary propositions and norms of representation -- Concerning the truth and falsehood of necessary propositions -- What necessary truths are about illusions of correspondence : ideal objects, kinds of reality, and ultra-physics -- The psychology of the A priori -- Knowledge -- Belief -- Certainty -- Surprise -- Discoveries and conjectures -- Compulsion -- Propositions of logic and laws of thought -- Alternative forms of representation -- The arbitrariness of grammar -- A kinship to the non-arbitrary -- Proof in mathematics -- Conventionalism. (shrink)

Natural deduction with alternatives extends Gentzen–Prawitz-style natural deduction with a single structural addition: negatively signed assumptions, called alternatives. It is a mildly bilateralist, single-conclusion natural deduction proof system in which the connective rules are unmodi_ed from the usual Prawitz introduction and elimination rules — the extension is purely structural. This framework is general: it can be used for (1) classical logic, (2) relevant logic without distribution, (3) affine logic, and (4) linear logic, keeping the connective rules (...) fixed, and varying purely structural rules. The key result of this paper is that the two principles that introduce kinds of irrelevance to natural deduction proofs: (a) the rule of explosion (from a contradiction, anything follows); and (b) the structural rule of vacuous discharge; are shown to be two sides of a single coin, in the same way that they correspond to the structural rule of weakening in the sequent calculus. The paper also includes a discussion of assumption classes, and how they can play a role in treating additive connectives in substructural natural deduction. (shrink)

The interplay of introduction and elimination rules for propositional connectives is often seen as suggesting a distinguished role for intuitionistic logic. We prove three formal results about intuitionistic propositional logic that bear on that perspective, and discuss their significance.

Philosophy of logic is a fundamental part of philosophical study, and one which is increasingly recognized as being immensely important in relation to many issues in metaphysics, metametaphysics, epistemology, philosophy of mathematics, and philosophy of language. This textbook provides a comprehensive and accessible introduction to topics including the objectivity of logical inference rules and its relevance in discussions of epistemological relativism, the revived interest in logical pluralism, the question of logic's metaphysical neutrality, and the demarcation between logic and (...) mathematics. Chapters in the book cover the state of the art in contemporary philosophy of logic, and allow students to understand the philosophical relevance of these debates without having to contend with complex technical arguments. This will be a major new resource for students working on logic, as well as for readers seeking a better understanding of philosophy of logic in its wider context. (shrink)

Effective altruism is the project of using resources like time and money to help others as much as possible. Those who engage in this project—effective altruists—tend to focus on three ways of helping.First, effective altruists focus on helping people living in extreme poverty and typically support interventions that prevent diseases such as malaria, trachoma, and schistosomiasis. These interventions have been shown to be highly cost-effective. For example, it costs on average about $4,500 to prevent someone from dying of malaria.Second, effective (...) altruists focus on reducing animal suffering. For example, tens of billions of animals are raised each year on factory farms. The conditions on these farms are so poor that the animals’ lives are probably not worth living. A host of charities aim to improve conditions on these farms or reduce the number of animals raised on them.Finally, effective altruists focus on improving the long-term future. This often takes the form of safeguarding the very existence of humanity's future by reducing risks of existential catastrophe posed by threats like nuclear weapons, pandemics, and artificial intelligence. It is frequently argued that, since there is vast value in avoiding such catastrophes, reducing the risk of any of them even fractionally has relatively high expected value.Each of these three ways of helping has been argued to be the most cost-effective way to help, that is, what makes the biggest positive difference, per dollar donated (or hour of time volunteered). There is disagreement among effective altruists over which of these areas, if any, should be the top priority.The effective altruism social movement has been around since about 2011 and now has thousands of supporters and is backed by billions of dollars in donations. At the same time, the project, underlying philosophy, and social movement of effective altruism have attracted substantial criticism, voiced in very visible venues. The present special issue of PAQ deals with a range of philosophical issues at the heart of this ongoing public debate. Below is a very brief overview of the articles in this issue.In “Why Not Effective Altruism?” Richard Yetter Chappell takes a careful look at criticisms that have been offered against effective altruism. He focuses on four ideas associated with effective altruism that have received particular attention, including moral prioritization, earning to give, billionaire philanthropy, and longtermism. Chappell argues that, in each case, the core moral claims of effective altruism cannot reasonably be rejected.In “Effective Altruists Need Not Be Pronatalist Longtermists,” Tina Rulli offers a sustained rebuttal to the argument for longtermism presented by William MacAskill in his recent book What We Owe the Future. In particular, she objects to pronatalist longtermism, which favors extensively populating the future, provided the future will be on balance good. Rulli argues that taking account of moral considerations most would recognize shows this position to be implausible. Her view is nonetheless compatible with versions of longtermism that focus on preventing harms to future people.In “How (Not) to Fear Death,” Susanne Burri provides a fresh perspective on the ancient question of whether we should fear death. She argues that, on a wide range of theories of well-being, it can be fitting to fear death. Burri argues that having a proper philosophical understanding of our reasons to fear death is in fact essential to reducing our death-related fears. This, she argues, provides an example of philosophical therapy, a neglected type of intervention effective altruists should consider. Given that the dissemination of valuable philosophical insight is so cheap, and could significantly benefit so many, it can and should be pursued alongside more resource-intensive interventions such as distributing malaria nets or reducing existential risks.In “Effective Altruism and Requiring Reasons to Help Others,” Thomas Sinclair provides a response to one of the main claims of my recent (2023) book The Rules of Rescue. I claim that each of us has a requiring reason (or pro tanto duty) to prevent harm to others, whenever we have the opportunity to do so. I argue that since these opportunities are ubiquitous, so, too, are requiring reasons. In response, Sinclair argues that we have requiring reasons to help others only when we engage with the plights of these others in a certain way. That engagement is not ubiquitous; it is present in cases of nearby emergency rescues, but it is not present simply whenever we can donate to effective charities.Philosophical debates surrounding effective altruism have developed rapidly over the past decade or so. As the articles in this special issue suggest, there is still much to be explored. (shrink)

The introduction of connectionist or parallel distributed processing (PDP) systems to model cognitive functions has raised the question of the possible relations between these models and traditional information processing models which employ rules to manipulate representations. After presenting a brief account of PDP models and two ways in which they are commonly interpreted by those seeking to use them to explain cognitive functions, I present two ways one might relate these models to traditional information processing models and so (...) not totally repudiate the tradition of modelling cognition through systems of rules and representations. The proposal that seems most promising is that PDP-type structures might provide the underlying framework in which a rule and representation model might be implemented. To show how one might pursue such a strategy, I discuss recent research by Barsalou on the instability of concepts and show how that might be accounted for in a system whose microstructure had a PDP architecture. I also outline how adopting a multi-leveled view of the mind, where on one level the mind employed a PDP-type system and at another level constituted a rule processing system, would allow researchers to relocate some problems which seemed difficult to explain at one level, such as the capacity for concept learning, to another level where it could be handled in a straightforward manner. (shrink)

An extension L + of the non-associative Lambek calculus Lis defined. In L + the restriction to formula-conclusion sequents is given up, and additional left introduction rules for the directional implications are introduced. The system L + is sound and complete with respect to a modification of the ternary frame semantics for L.

In proof-theoretic semantics the meaning of an atomic sentence is usually determined by a set of derivations in an atomic system which contain that sentence as a conclusion (see, in particular, Prawitz, 1971, 1973). The paper critically discusses this standard approach and suggests an alternative account which proceeds in terms of subatomic introduction and elimination rules for atomic sentences. A simple subatomic normal form theorem by which this account of the semantics of atomic sentences and the terms from (...) which they are composed is underpinned, shows moreover that the proof-theoretic analysis of first-order logic can be pursued also beneath the atomic level. (shrink)

Many results of modern physics—those of quantum mechanics, for instance—come in a probabilistic guise. But what do probabilistic statements in physics mean? Are probabilities matters of objective fact and part of the furniture of the world, as objectivists think? Or do they only express ignorance or belief, as Bayesians suggest? And how are probabilistic hypotheses justified and supported by empirical evidence? Finally, what does the probabilistic nature of physics imply for our understanding of the world? This volume is the first (...) to provide a philosophical appraisal of probabilities in all of physics. Its main aim is to make sense of probabilistic statements as they occur in the various physical theories and models and to provide a plausible epistemology and metaphysics of probabilities. The essays collected here consider statistical physics, probabilistic modelling, and quantum mechanics, and critically assess the merits and disadvantages of objectivist and subjectivist views of probabilities in these fields. In particular, the Bayesian and Humean views of probabilities and the varieties of Boltzmann's typicality approach are examined. The contributions on quantum mechanics discuss the special character of quantum correlations, the justification of the famous Born Rule, and the role of probabilities in a quantum field theoretic framework. Finally, the connections between probabilities and foundational issues in physics are explored. The Reversibility Paradox, the notion of entropy, and the ontology of quantum mechanics are discussed. Other essays consider Humean supervenience and the question whether the physical world is deterministic. (shrink)

This chapter contains sections titled: Textual Problems The Trinitarian Structure within the Introduction to the Philosophy of History The Trinitarian Structure in History The Role of Race in History List of Abbreviations of Works by Hegel References.

The intention here is that of giving a formal underpinning to the idea of ‘meaning-is-use’ which, even if based on proofs, it is rather different from proof-theoretic semantics as in the Dummett–Prawitz tradition. Instead, it is based on the idea that the meaning of logical constants are given by the explanation of immediate consequences, which in formalistic terms means the effect of elimination rules on the result of introduction rules, i.e. the so-called reduction rules. For that (...) we suggest an extension to the Curry– Howard interpretation which draws on the idea of labelled deduction, and brings back Frege’s device of variable-abstraction to operate on the labels (i.e., proof-terms) alongside formulas of predicate logic. (shrink)

We investigate introduction and elimination rules for truth-functional connectives, focusing on the general questions of the existence, for a given connective, of at least one such rule that it satisfies, and the uniqueness of a connective with respect to the set of all of them. The answers are straightforward in the context of rules using general set/set sequents of formulae, but rather complex and asymmetric in the restricted (but more often used) context of set/formula sequents, as also (...) in the intermediate set/formula-or-empty context. (shrink)

In several applications of sequent calculi going beyond pure logic, an introduction of suitably defined rules seems to be more profitable than addition of extra axiomatic sequents. A program of formalization of mathematical theories via rules of special sort was developed successfully by Negri and von Plato. In this paper a general theorem on possible ways of transforming axiomatic sequents into rules in sequent calculi is proved. We discuss its possible applications and provide some case studies (...) for illustration. (shrink)

Introduction -- Instrumental rationality -- Social order -- Deontic constraint -- Intentional states -- Preference noncognitivism -- A naturalistic perspective -- Transcendental necessity -- Weakness of will -- Normative ethics.

Providing a comprehensive introduction to political philosophy, this 2006 book combines discussion of historical and contemporary figures, together with numerous real-life examples. It ranges over an unusually broad range of topics in the field, including the just distribution of wealth, both within countries and globally; the nature and justification of political authority; the meaning and significance of freedom; arguments for and against democratic rule; the problem of war; and the grounds for toleration in public life. It also offers an (...) accessible, non-technical discussion of perfectionism, utilitarianism, theories of the social contract, and of recently popular forms of critical theory. Throughout, the book challenges readers to think critically about political arguments and institutions that they might otherwise take for granted. It will be a provocative text for any student of philosophy or political science. (shrink)

This book provides a rich, systematic, and accessible introduction to moral psychology, aimed at undergraduate philosophy and psychology majors. There are eight chapters, in addition to a short introduction, prospective conclusion, and extensive bibliography. The recipe for each chapter will be: a) to introduce a philosophical topic (e.g., altruism, virtue, preferences, rules) and some prominent positions on it, without assuming prior acquaintance on the part of the reader b) to canvass and explain the relevance of a particular (...) domain of empirical inquiry (e.g., evolutionary psychology, behavioral economics, neuroscience) to the topic c) to argue for some tentative conclusions about the topic d) to suggest further avenues for conceptual and empirical research The guiding theme of the book is that moral philosophy without psychological content is empty, whereas psychological investigation without philosophical insight is blind. Thus, I advocate a holistic approach that pictures moral psychology as a project of collaborative inquiry into the descriptive and normative aspects of the human condition. Ideally, students will come away from (a course built around) the book with the sense that, though philosophy may not be the queen of the sciences, its role is not merely to interpret scientific results. (shrink)

The intention here is that of giving a formal underpinning to the idea of 'meaning-is-use' which, even if based on proofs, it is rather different from proof-theoretic semantics as in the Dummett-Prawitz tradition. Instead, it is based on the idea that the meaning of logical constants are given by the explanation of immediate consequences, which in formalistic terms means the effect of elimination rules on the result of introduction rules, i. e. the so-called reduction rules. For (...) that we suggest an extension to the Curry-Howard interpretation which draws on the idea of labelled deduction, and brings back Frege's device of variable-abstraction to operate on the labels (i. e., proof-terms) alongside formulas of predicate logic. (shrink)

I examine Paul Boghossian's recent attempt to argue for scepticism about logical rules. I argue that certain rule- and proof-theoretic considerations can avert such scepticism. Boghossian's 'Tonk Argument' seeks to justify the rule of tonk-introduction by using the rule itself. The argument is subjected here to more detailed proof-theoretic scrutiny than Boghossian undertook. Its sole axiom, the so-called Meaning Postulate for tonk, is shown to be false or devoid of content. It is also shown that the rules (...) of Disquotation and of Semantic Ascent cannot be derived for sentences with tonk dominant. These considerations deprive Boghossian's scepticism of its support. (shrink)

This paper is an introduction to a virtual special issue of AI and Law exploring the legacy of the influential HYPO system of Rissland and Ashley. The papers included are: Arguments and cases: An inevitable intertwining, BankXX: Supporting legal arguments through heuristic retrieval, Modelling reasoning with precedents in a formal dialogue Game, A note on dimensions and factors, An empirical investigation of reasoning with legal cases through theory construction and application, Automatically classifying case texts and predicting outcomes, A factor-based (...) definition of precedential constraint and An improved factor based approach to precedential constraint. After describing HYPO, in this introduction to the special issue I look at various aspects of its influence on AI and Law: the developments led by Rissland at Amherst; the developments led by Ashley in Pittsburgh; the expression of these ideas in terms of rule based systems, and their subsequent formalisation; value based theories, which were inspired by a critique of HYPO; and contemporary approaches which revive the idea of dimensions. (shrink)

The concept of _substructural logic_ was originally introduced in relation to limitations of Gentzen’s structural rules of Contraction, Weakening and Exchange. Recent years have witnessed the development of substructural logics also challenging the Tarskian properties of Reflexivity and Transitivity of logical consequence. In this introduction we explain this recent development and two aspects in which it leads to a reassessment of the bounds of classical logic. On the one hand, standard ways of defining the notion of logical consequence (...) in classical logic naturally induce substructural logics when admitting more than two truth values; on the other hand, these substructural logics give rise to hierarchies of _metainferences_ that can be used to approximate classical logic at different levels. (shrink)

“Imagination may be thought of as a ‘work-around.’ It is a resourceful tactic to ‘undo’ a rule by creating a path around it without necessarily defying it.... Transgression, on the other hand, is rule breaking. There is no pretense of reinterpretation; it is defiance pure and simple. Whether imagination or disobedience is the source, constraints need not constrain, ties need not bind.” So writes Kenneth A. Shepsle in his introduction to Rule Breaking and Political Imagination. Institutions are thought to (...) channel the choices of individual actors. But what about when they do not? Throughout history, leaders and politicians have used imagination and transgression to break with constraints upon their agency. Shepsle ranges from ancient Rome to the United States Senate, and from Lyndon B. Johnson to the British House of Commons. He also explores rule breaking in less formal contexts, such as vigilantism in the Old West and the CIA’s actions in the wake of 9/11. Entertaining and thought-provoking, Rule Breaking and Political Imagination will prompt a reassessment of the nature of institutions and remind us of the critical role of political mavericks. (shrink)

Logic was revered in the thirteenth century, perhaps more highly than it has been revered before or since. In the Muslim East, logic was an integral part of the syllabus of schools and found to be especially helpful for legal studies. It was at this time that The Canons of Logic was composed by Najm al-Din al-Katibi, a scholar of the Shafi'i school of law. The Rules of Logic is the most widely read introduction to logic in the (...) Arabic-speaking world. It has probably enjoyed a longer shelf-life than any other logic textbook ever written, having been in use by madrasa students from the early fourteenth century up until the present day. Building on the theories of Avicenna, al-Razi, and other pioneers of logic, al-Katibi discusses the many pitfalls of building arguments and setting out unambiguous claims in natural language. The enduring nature of the text is a testament to al-Katibi and his impact on concepts of formal discourse and argument. This new translation of The Canons of Logic provides new life to an influential text that has shaped the work of scholars of logic for centuries. (shrink)

This book is exceptional in the sense that it provides an introduction to law in general rather than the law of one specific jurisdiction, and it presents a unique way of looking at legal education. It is crucial for lawyers to be aware of the different ways in which societal problems can be solved and to be able to discuss the advantages and disadvantages of different legal solutions. In this respect, being a lawyer involves being able to reason like (...) a lawyer, even more than having detailed knowledge of particular sets of rules. Introduction to Law reflects this view by focusing on the functions of rules and on ways of arguing the relative qualities of alternative legal solutions. Where 'positive' law is discussed, the emphasis is on the legal questions that must be addressed by a field of law, and on the different solutions which have been adopted by, for instance, the common law and civil law tradition. The law of specific jurisdictions is discussed to illustrate possible answers to questions such as when the existence of a valid contract is assumed. (shrink)

§1 According to the paradigmatic formula offered by Kant, the philosopher’s task consists of demonstrating “how we ought to think” as opposed to “how we do think” – that is, logical rules or norms must be separated from the functioning principles of the human mind or from psychological laws. As it is well-known, in the “Preface” to the second edition of the Critique of Pure Reason, the German philosopher stands against “some moderns” who “have thought to enlarge” logic “interpolating (...) psycholo... (shrink)

The question whether corporations should be used as a means for administering distributive justice is crucial. There are two fundamental issues associated with this. Firstly, would the introduction of rules have any distributional effect? Secondly, what would be the efficiency cost? In this paper, we explore both questions with reference to a job-security corporate rule. We show that the job-security rule will always produce distributional consequences which are consistent with its objectives. However, whether or not it is a (...) socially desirable policy depends on whether the economy is at an efficient allocation and what motivated the policy. It can be shown that under some conditions, even if the initial allocation is efficient, yet not the socially desirable one, a corporate rule—like the job security one—may produce socially desirable gains. The same can be said in the case where the initial allocation is inefficient even in the presence of competitive markets (dueto incompleteness problems). However, these social gains would come at the expense of competitiveness. In an internationally open environment this may offset the initial social gains from this policy. Whether or not this happens would then depend on whether agents have a social dimension to their preferences or not. If they do, their response to the initiative may offset the initial loss of competitiveness. Alternatively, society may face the dilemma whether to remain open to uphold local conceptions of distributive justice. (shrink)

The intention here is that of giving a formal underpinning to the idea of ‘meaning-is-use’ which, even if based on proofs, it is rather different from proof-theoretic semantics as in the Dummett–Prawitz tradition. Instead, it is based on the idea that the meaning of logical constants are given by the explanation of immediate consequences, which in formalistic terms means the effect of elimination rules on the result of introduction rules, i.e. the so-called reduction rules. For that (...) we suggest an extension to the Curry– Howard interpretation which draws on the idea of labelled deduction, and brings back Frege’s device of variable-abstraction to operate on the labels (i.e., proof-terms) alongside formulas of predicate logic. (shrink)

We investigate introduction and elimination rules for truth-functional connectives, focusing on the general questions of the existence, for a given connective, of at least one such rule that it satisfies, and the uniqueness of a connective with respect to the set of all of them. The answers are straightforward in the context of rules using general set/set sequents of formulae, but rather complex and asymmetric in the restricted (but more often used) context of set/formula sequents, as also (...) in the intermediate set/formula-or-empty context. (shrink)

The topic of this special issue of Synthese is hyperintensionality. This introduction offers a brief survey of the very notion of hyperintensionality followed by a summary of each of the papers in this collection. The papers are foundational studies of hyperintensionality accompanied by ample philosophical applications.Hyperintensionality concerns the individuation of non-extensional entities such as propositions and properties, relations-in-intension and individual roles, as well as, for instance, proofs and judgments and computational procedures, in case these do not reduce to any (...) of the former. Hyperintensional individuation is frequently also referred to as ‘fine-grained’ or sometimes simply ‘intensional’ individuation, when ‘intensional’ is not understood in the specific sense of possible-world semantics or in the pejorative sense of flouting various logical rules of extensional logic. A principle of individuation qualifies as hyperintensional as soon as it is finer than necessary .. (shrink)

First published in 1949. This title provides an introduction into the subject of aesthetics, and the problems associated with it. Aesthetics is not strictly a criterion or rule for production or appreciation, and cannot directly alter our aesthetic experiences, but only helps us to understand them. _An Introduction to Aesthetics _explores this theory, and will be of interest to students of both art and philosophy.

I examine Paul Boghossian's recent attempt to argue for scepticism about logical rules. I argue that certain rule- and proof-theoretic considerations can avert such scepticism. Boghossian's 'Tonk Argument' seeks to justify the rule of tonk-introduction by using the rule itself. The argument is subjected here to more detailed proof-theoretic scrutiny than Boghossian undertook. Its sole axiom, the so-called Meaning Postulate for tonk, is shown to be false or devoid of content. It is also shown that the rules (...) of Disquotation and of Semantic Ascent cannot be derived for sentences with tonk dominant. These considerations deprive Boghossian's scepticism of its support. (shrink)

In an old paper of our group in Milano a formalism was introduced for the continuous monitoring of a system during a certain interval of time in the framework of a somewhat generalized approach to quantum mechanics. The outcome was a distribution of probability on the space of all the possible continuous histories of a set of quantities to be considered as a kind of coarse grained approximation to some ordinary quantum observables commuting or not. In fact the main aim (...) was the introduction of a classical level in the context of QM, treating formally a set of basic quantities, to be considered as beables in the sense of Bell, as continuously taken under observation. However the effect of such assumption was a permanent modification of the Liouville-von Neumann equation for the statistical operator by the introduction of a dissipative term which is in conflict with basic conservation rules in all reasonable models we had considered. Difficulties were even encountered for a relativistic extension of the formalism. In this paper I propose a modified version of the original formalism which seems to overcome both difficulties. First I study the simple models of an harmonic oscillator and a free scalar field in which a coarse grain position and a coarse grained field respectively are treated as beables. Then I consider the more realistic case of spinor electrodynamics in which only certain coarse grained electric and magnetic fields are introduced as classical variables and no matter related quantities. (shrink)