This collection of new essays offers a 'state-of-the-art' conspectus of major trends in the philosophy of logic and philosophy of mathematics. A distinguished group of philosophers addresses issues at the centre of contemporary debate: semantic and set-theoretic paradoxes, the set/class distinction, foundations of set theory, mathematical intuition and many others. The volume includes Hilary Putnam's 1995 Alfred Tarski lectures, published here for the first time.

Originally published in 1961. Michael Polanyi was a polymath who influenced economics and the sciences as well as philosophy. His wide-ranging research in physical science is as well-known as his work on freedom and knowledge and his arguments against positivism and reductionism. This collection of essays written for him touches on all aspects of his influence but rotates around his published lectures Personal Knowledge: Towards a Post-Critical Philosophy. The contributors address four areas – The Scientist as Knower, Historical Perspectives, (...) The Knowledge of Society and the Knowledge of Living Things. (shrink)

Originally published in 1961. Michael Polanyi was a polymath who influenced economics and the sciences as well as philosophy. His wide-ranging research in physical science is as well-known as his work on freedom and knowledge and his arguments against positivism and reductionism. This collection of essays written for him touches on all aspects of his influence but rotates around his published lectures _Personal Knowledge: Towards a Post-Critical Philosophy._ The contributors address four areas – The Scientist as Knower, Historical Perspectives, (...) The Knowledge of Society and the Knowledge of Living Things. (shrink)

TWENTIETH-CENTURY ETHICS. AFTER NIETZSCHE -/- Preface This book tells the story of twentieth-century ethics or, in more detail, it reconstructs the history of a discussion on the foundations of ethics which had a start with Nietzsche and Sidgwick, the leading proponents of late-nineteenth-century moral scepticism. During the first half of the century, the prevailing trends tended to exclude the possibility of normative ethics. On the Continent, the trend was to transform ethics into a philosophy of existence whose self-appointed task was (...) that of describing the human condition as consisting of choices, as unavoidable as arbitrary, without any attempt at providing criteria for making such choices. In the Anglo-Saxon countries, the heir of ethics was a philosophy of morality, that is, an analysis of the language of morality that intended to clarify valuations without trying to justify them. 1958 was the year of the normative turn that led to the Rehabilitation of practical philosophy, a turn followed by decades of controversies between distinct kinds of normative ethics: utilitarian, Kantian, virtue ethics. While the controversy was raging, a quiet revolution took place, that of applied ethics which surprisingly dissolved the controversy's very subject matter by providing methods for making convergence possible on intermediate principles even when no agreement was available about first principles. The normative turn and the revolution of applied ethics have led us, at the turn of the century, to a goal that was quite far from the starting point. Instead of scepticism and relativism that was the fashion at the beginning of the century, at the beginning of the third millennium impartial and universal moral arguments seem to hold the spot being supported, if not by a final rational foundation, at least by reasonableness, the most precious legacy of the Enlightenment. -/- ● TABLE OF CONTENTS -/- ● I Anglo-Saxon philosophy: naturalism 1. Dewey beyond evolutionism and utilitarianism 2. Dewey and anti-essentialist moral epistemology 3. Dewey and naturalist moral ontology 4. Dewey and normative ethics of conduct and function 5. Perry and semantic naturalism -/- ● II Anglo-Saxon philosophy: ideal utilitarianism and neo-intuitionism 1. Moore's critique of utilitarian empiricism 2. Moore on the naturalistic fallacy 3. Moore on the nature of intrinsic value 4. Moore on ideal utilitarianism 5. Prichard on the priority of the right over the good 6. Ross's coherentist moral epistemology 7. Ross's moral ontology: realism, pluralism, and non-naturalism 8. Ross's normative ethics of prima facie duties -/- The chapter reconstructs the background of ideas, concerns and intentions out of which Moore's early essays, the preliminary version, and then the final version of Principia Ethica originated. It stresses the role of religious concerns, as well as that of the Idealist legacy. It argues that PE is more a patchwork of somewhat diverging contributions than a unitary work, not to say the paradigm of a new school in Ethics. -/- ●III Anglo-Saxon philosophy: non-cognitivism 1. The Scandinavian School, the Vienna circle and proto-emotivism 2. Wittgenstein and the ineffability of ethics 3. Russell's and Ayer's radical emotivism 4. Stevenson and moderate emotivism 5. Stevenson and the pragmatics of moral language 6. Stevenson and the methods for solving ethical disagreement 7. Hare and prescriptivism The chapter reconstructs first the discussion after Moore. The naturalistic-fallacy argument was widely accepted but twisted to prove instead that the intuitive character of the definition of 'good', its non-cognitive meaning, in a first phase identified with 'emotive' meaning. Alfred Julius Ayer is indicated as a typical proponent of such non-cognitivist meta-ethics. More detailed discussion is dedicated to Bertrand Russell's ethics, a more nuanced and sophisticated doctrine, arguing that non-cognitivism does not condemn morality to arbitrariness and that the project of rational normative ethics is still possible, heading finally to the justification of a kind of non-hedonist utilitarianism. Stevenson's theory, another moderate version of emotivism is discussed at some length, showing how the author comes close to the discovery of the role of a pragmatic dimension of language as a basis for ethical argument. A section reconstructs the discussion from the Forties about Hume's law, mentioning Karl Popper's argument and Richard Hare's early non-cognitivist but non-emotivist doctrine named prescriptivism. -/- ●IV Anglo-Saxon philosophy: critics of non-cognitivism 1. Neo-naturalism and its objections to the naturalistic fallacy argument 2. Objections to Hume's law 3. Clarence Lewis and the pragmatic contradiction 4. Toulmin and the good reasons approach 5. Baier and moral reasons 5. Baier, social moralities and the absolute morality 6. Baier and the moral point of view 7. Baier and the contents of absolute ethics -/- ● V Continental philosophy: the philosophy of values 1. Max Weber and the polytheism of values 2. Phenomenology against psychologism and rationalism 3. Reinach and the theory of social acts 4. Scheler and the material ethics of values 5. Hartmann and the ontology of values 6. Plessner, Gehlen and the Philosophische Anthropologie -/- The chapter illustrates first the idea of phenomenology and the Husserl's project of a phenomenological ethic as illustrated in his 1908-1914 lectures. The key idea is dismissing psychology and trying to ground a new science of the apriori of action, within which a more restricted field of inquiry will be the science of right actions. Then the chapter illustrates the criticism of modern moral philosophy conducted in the 1920 lectures, where the main target is naturalism, understood in the Kantian meaning of primacy of common sense. The third point illustrate is Adolph Reinach's theory of social acts as a key the grounding of norms, a view that sketches the ideas 'discovered' later by Clarence I. Lewis, John Searle, Karl-Otto Apel and Jürgen Habermas. A final section discusses Nicolai Hartman, who always refused to define himself a phenomenologist and yet developed a more articulated and detailed theory of 'values' – with surprising affinities with George E. Moore - than philosophers such as Max Scheler, who claimed to be Husserl's legitimate heirs. -/- ● VI Continental philosophy: the critics of the philosophy of values 1. Freud, the Superego and Civilization 2. Heidegger on original ethos against ethics 3. Sartre and de Beauvoir on authenticity and ambiguity 4. Adorno and Horkheimer on emancipation and immoralism -/- ●VII Post-liberal theologians and religious thinkers 1. Barth on the autonomy of faith from ethics 2. Developments of Reformed moral theology after Barth 3. Bonhoeffer on the concrete divine command and ethics of penultimate realities 4. Developments of Reformed and Catholic moral theology after world war II 5. Baeck and the transformation of liberal Judaism 6. Rosenzweig against liberal Judaism 7. Buber and religion as the vital lymph of morality 8. Heschel and Judaism as a science of actions -/- The chapter examines the main protagonists of Christian theology and Jewish religious thinking in the twentieth century. It stresses how the main dilemmas of contemporary philosophical ethics lie at the root of the various path of inquiry taken by these thinkers. -/- ● VIII Normative ethics: neo-Utilitarianism 1. The discussion on act and rule utilitarianism 2. Hare on two-tiered preference utilitarianism 3. Harsanyi, Gauthier and rational choice ethics 4. Parfit, utilitarianism and the idea of a person 5. Brandt and indirect conscience utilitarianism -/- The chapter addresses the issue of the complex process of self-transformation Utilitarianism underwent after Sidgwick's and Moore's fatal criticism and the unexpected Phoenix-like process of rebirth of a doctrine refuted. Two examples give the reader a glimpse at this uproarious process. The first is Roy Harrod Wittgensteinian transformation of utilitarianism in pure normative ethics depurated from hedonism as well as from whatsoever theory of the good. This transformation results in preference utilitarianism combined with a 'Kantian' version of rule utilitarianism. The second is Richard Hare's two-level preference utilitarianism, where act utilitarianism plays the function of the eventual rational justification of moral judgments and rule-utilitarianism that of an action-guiding practical device. -/- ● IX Normative ethics: neo-Aristotelianism and virtue ethics 1. Hannah Arendt, action and judgement 2. Hans-Georg Gadamer and phronesis 3. Alasdair MacIntyre on practices, virtues, and traditions 5. Stuart Hampshire on deliberation 6. Bernard Williams and moral complexity 7. Feminist ethics -/- Sect 1 reconstructs the post-war rediscovery of ethics by many German thinkers and its culmination in the Sixties in the movement named 'Rehabilitation of practical philosophy' is described. Heidegger's most brilliant disciples were the promoters of this Rehabilitation. Hans-Georg Gadamer is a paradigmatic example. His reading of Aristotle's lesson I reconstructed, starting with Heidegger's lesson but then subtly subverting its outcome thanks to the recovery of the significant role of the notion of phronesis. Sect 3 discusses the three theses defended by Anscombe in 'Modern Moral Philosophy'. It argues that: a) her answer to the question "why should I be moral?" requires a solution of the problem of theodicy, and ignores any attempts to save the moral point of view without recourse to divine retribution; b) her notion of divine law is an odd one more neo-Augustinian than Biblical or Scholastic; c) her image of Kantian ethics and intuitionism is the impoverished image manufactured by consequentialist opponents for polemical purposes and that she seems strangely accept it; d) the difficulty of identifying the "relevant descriptions" of acts is not an argument in favour of an ethics of virtue and against consequentialism or Kantian ethics, and indeed the role of judgment in the latter is a response to the difficulties raised by the case of judgment concerning future action. The chapter gives a short look at further developments in the neo-naturalist current trough a reconstruction of Philippa Foot's and Peter Geach's critiques to the naturalist-fallacy argument and Alasdair MacIntyre's grand reconstruction of the origins and allegedly inevitable failure of the Enlightenment project of an autonomous ethic. -/- ● X Normative ethics: Kantian and rights-based ethics 1. Dialogical constructivism 2. Apel, Habermas and discourse ethics 3. Gewirth and rights-based ethics 4. Nagel on agent-relative reasons 5. Donagan and persons as ends in themselves Parallel to the neo-Aristotelian trend, there was in the Rehabilitation of practical philosophy a Kantian current. This current started with the discovery of the pragmatic dimension of language carried out by Charles Peirce and the Oxford linguistic philosophy. On this basis, Karl-Otto Apel singled out as the decisive proponent of the linguistic and Kantian turn in German-speaking ethics, worked out the performative-contradiction argument while claiming that this was able to provide a new rational and universal basis for normative ethics. The chapter offers an examination of his argument in some detail, followed by a more cursory reconstruction of Jürgen Habermas's elaboration on Apel's theory. -/- ● XI The applied ethics renaissance 1. Elisabeth Anscombe on the atom bomb 2. From medical ethics to bioethics 3. Rawls and public ethics 3. Nozick, Dworkin and further developments of public ethics 5. Sen and the revival of economic ethics -/- The chapter presents the revolution of applied ethics while stressing its methodological novelty, exemplified primarily by Beauchamp and Childress principles approach and then by Jonsen and Toulmin's new casuistry. The chapter argues that Rawls's distinction between a "political" and a "metaphysical" approach to the theory of justice, one central part of ethical theory, is a formulation of the same basic idea at the root of both the principles approach and the new casuistry, both discussed in the following chapter. The idea is that it is possible to reach an agreement concerning positive moral judgments even though the discussion is still open – and in Rawls' view never will be close – on the essential criteria for judgment. -/- ● XII Fin-de-siècle metaethics 1. Deontic logics 2. Anti-realism 3. External realism 4. Internal realism 5. Kantian constructivism -/- The chapter illustrates the fresh start of meta-ethical discussion in the Eighties and Nineties and the resulting new alignments: metaphysical naturalism, internal realism, anti-realism, and constructivism. (shrink)

This paper introduces two new paradoxes for standard deontic logic (SDL). They are importantly related to, but distinct from Ross' paradox. These two new paradoxes for SDL are the simple weakening paradox and the complex weakening paradox. Both of these paradoxes arise in virtue of the underlaying logic of SDL and are consequences of the fact that SDL incorporates the principle known as weakening. These two paradoxes then show that SDL has counter-intuitive implications related to disjunctive obligations (...) that arise in virtue of deontic weakening and in virtue of decisions concerning how to discharge such disjunctive obligations. The main result here is then that theorem T1 is a problematic component of SDL that needs to be addressed. (shrink)

A considerable number of books and papers have analyzed normative concepts using new techniques developed by logicians; however, few have bridged the gap between the English legal culture and the Continental tradition in legal philosophy. This book addresses this issue by offering an introductory study on the many possibilities that logical analysis offers the study of legal systems. The volume is divided into two sections: the first covers the basic aspects of classical and deontic logic and its connections, (...) advancing an explanation of the most important topics of the discipline by comparing different systems of deontic logic and exploring some of the most important paradoxes in its domain. The second section deals with the role of logic in the analysis of legal systems by discussing in what sense deontic logic and the logic of norm-propositions are useful tools for a proper understanding of the systematic structure of law. (shrink)

Several years ago I came across a marvelous little paper in which Hector-Neri Castaneda shows that standard versions of act utilitarian l ism are formally incoherent. I was intrigued by his argument. It had long seemed to me that I had a firm grasp on act utilitarianism. Indeed, it had often seemed to me that it was the clearest and most attractive of normative theories. Yet here was a simple and relatively uncontrover sial argument that showed, with only some trivial (...) assumptions, that the doctrine is virtually unintelligible. The gist of Castaneda's argument is this: suppose we understand act utilitarianism to be the view that an act is obligatory if and only if its utility exceeds that of each alternative. Suppose it is obligatory for a certain person to perform an act with two parts - we can call it 'A & B'. Then, obviously enough, it is also obligatory for this person to perform the parts, A and B. If act utilitarianism were true, we appar ently could infer that the utility of A & B is higher than that of A, and higher than that of B (because A & B is obligatory, and the other acts are alternatives to A & B). (shrink)

There seems to be no clear consensus in the existing literature about the role of deontic logic in legal knowledge representation — in large part, we argue, because of an apparent misunderstanding of what deontic logic is, and a misplaced preoccupation with the surface formulation of legislative texts. Our aim in this paper is to indicate, first, which aspects of legal reasoning are addressed by deontic logic, and then to sketch out the beginnings of (...) a methodology for its use in the analysis and representation of law.The essential point for which we argue is that deontic logic — in some form or other —needs to be taken seriously whenever it is necessary to make explicit, and then reason about, the distinction between what ought to be the case and what is the case, or as we also say, between the ideal and the actual. We take the library regulations at Imperial College as the main illustration, and small examples from genuinely legal domains to introduce specific points. In conclusion, we touch on the role of deontic logic in the development of the theory of normative positions. (shrink)

I am idebted to members of the Wellington Logic Seminar for useful discussions of work of which this essay forms part, in particular to M. J. Cresswell for comments in the earlier stages of the investigation and to R. I. Goldblatt who suggested the definition ofB infD supu and made numerous other suggestions.

If deontic logic is to cast light on any of the normative sciences, such as legal reasoning, then certain problems regarding its logical constants must be faced. Recent studies in the area of deontic logic have tended to assume that it is our responses to the “paradoxes” of deontic implication which are fundamental to resolving problems with the use of deontic logic to investigate various branches of normative reasoning. In this paper I wish (...) to show that the paradoxes are of secondary importance; that they are merely by‐products of the central issue, namely the ability of certain syntactic forms to embody natural language structures used in reasoning about norms. An investigation of modal syntax is proffered as the best starting‐point from which to tackle the questions that still dog the legitimacy of deontic logic. Part I provides some philosophical background to the discussion of deontic logical constants. Part II addresses in greater detail issues concerning the representation of normative concepts; and Part III offers a few remarks on the general issue of deontic logic's fruitfulness as an analytical tool. (shrink)

In this collection of essays, which were first delivered as lectures at the International Academy of Philosophy in the Principality of Liechtenstein in 1998, distinguished philosopher Peter Geach confronts some of the most difficult issues in philosophy with the precision of a logician and the grace and wit of an accomplished stylist. These essays constitute a significant addition to Professor Geach's esteemed body of work in philosophy, as he addresses not only problems of logic and analytic philosophy, but (...) also of epistemology and ethics. Geach's engaging discussions of human nature, truth, goodness, and love provide probing insight into perennial themes in an appealing, highly readable style which is nevertheless forceful and exacting. Geach knows the subjectivity of his own experience and belief and is able to illuminate that experience and belief by submitting it to a rational and philosophical inquiry. His avowed Catholic perspective is neither a weapon nor a shield. It is an integral part of the sustained, systematic, and constructive approach to philosophy demonstrated in these essays. They will certainly provoke serious reflection even in those inclined to disagree with Geach's conclusions. (shrink)

The book is a collection of papers addressing the role of logic in forming and developing philosophy. In particular, on the ground of modern development of logic, it is shown that philosophy can be established (and, in fact, to a large extent is established) as a modern science. The following problems are addressed: general relationship between philosophy and science (especially from a logical viewpoint); the use of logic in ordinary language; names and descriptions; Quine's pragmatic extensional Platonism (...) and predicate-functor logic; philosophical and logical aspects of Gödel's onto-theological system. In the last two chapters, an early critique and emendement of algebraic logic by Croatian philosophers Franjo Marković and Mate Meršić, respectively, is examined. (shrink)

Noted logician and philosopher addresses various forms of mathematical logic, discussing both theoretical underpinnings and practical applications. After historical survey, lucid treatment of set theory, model theory, recursion theory and constructivism and proof theory. Place of problems in development of theories of logic, logic’s relationship to computer science, more. Suitable for readers at many levels of mathematical sophistication. 3 appendixes. Bibliography. 1981 edition.

Kant's views on logic and logical theory play an important role in his critical writings, especially the Critique of Pure Reason. However, since he published only one short essay on the subject, we must turn to the texts derived from his logic lectures to understand his views. The present volume includes three previously untranslated transcripts of Kant's logic lectures: the Blumberg Logic from the 1770s; the Vienna Logic (supplemented by the recently discovered Hechsel (...) Logic) from the early 1780s; and the Dohna-Wundlacken Logic from the early 1790s. Also included is a new translation of the Jasche Logic, compiled at Kant's request and published in 1800 but which also appears to stem in part from a transcript of his lectures. Together these texts provide a rich source of evidence for Kant's evolving views on logic, on the relations between logic and other disciplines, and on a variety of topics (e.g. analysis and synthesis) central to Kant's mature philosophy. They also provide a portrait of Kant as lecturer, a role in which he was both popular and influential. This volume contains substantial editorial apparatus: a general introduction, linguistic and factual notes, glossaries of key terms (both German/English and English/German) and concordances relating Kant's lectures to Georg Frederich Meier's Excerpts from the Doctrine of Reason, the book on which Kant lectured throughout his life and in which he left extensive notes. (shrink)

This volume comprises systematic as well as historical essays, including contributions intended to give comprehensive overviews of such areas as genetic phenomenology, transcendental phenomenology, philosophy and history of logic and mathematics, Kant, hermeneutics, Hegel, and philosophy of language. The book is addressed to phenomenologists, particularly those who are interested in some or all of the areas mentioned. In his introduction Joseph J. Kockelmans indicates that these diverse areas enter into dialogue in the work of Thomas M. Seebohm, whom the (...) editors and authors wish to honor, and the systematic papers mirror the state of the art of research in the above-mentioned disciplines. (shrink)

Kant's views on logic and logical theory play an important part in his critical writings, especially the Critique of Pure Reason. However, since he published only one short essay on the subject, we must turn to texts derived from his logic lectures to understand his views. This volume includes three previously untranslated transcripts of Kant's logic lectures: the Blomberg Logic, the Vienna Logic supplemented by the recently discovered Hechsel Logic, and the Dohna-Wundlacken (...) Logic. Also included is a new translation of the Jäsche Logic, compiled at Kant's request from his lectures and published in 1800, and concordances relating Kant's lectures to Georg Friedrich Meier's Excerpts from the Doctrine of Reason, the book on which Kant lectured throughout his life and in which he left extensive notes. (shrink)

I am honoured with and touched by the invitation of delivering the opening address of this Congress. Firstly, to see paraconsistent logic flourishing and growing, as we can readily see by simply glacing over the programme of this conference, is among one of my greatest joys. Secondly, and equally important, because this congress takes place in the University of Toruń.I am honoured for having lectured here, a most congenial and stimulating place, and could not think of a better place (...) for a conference dedicated to the memory of Stanisław Jaśkowski. In particular, I am delighted for having had a correspondence with him, and although I was deprived of the pleasure of meeting him personally, I was fortunate enough for having collaborated with some of his disciples, such as L. Dubikajtis and T. Kotas. All and all, Toruń in particular and Poland in general are for me a second home, for all the kindness and care everyone has shown to me over several years, since my very first visit to this country. (shrink)

This book includes Emerson's re-written version of his early book, Nature, along with various essays, including: The American Scholar (1836), The Divinity School Address (1838), Literary Ethics (1838), The Method of Nature (1841), Man the Reformer (1841), Lecture on the Times (1841), The Conservative (1841), The Transcendentalist (1842), The Young American (1844).

The book is a collection of the author’s selected works in the philosophy and history of logic and mathematics. Papers in Part I include both general surveys of contemporary philosophy of mathematics as well as studies devoted to specialized topics, like Cantor's philosophy of set theory, the Church thesis and its epistemological status, the history of the philosophical background of the concept of number, the structuralist epistemology of mathematics and the phenomenological philosophy of mathematics. Part II contains essays in (...) the history of logic and mathematics. They address such issues as the philosophical background of the development of symbolism in mathematical logic, Giuseppe Peano and his role in the creation of contemporary logical symbolism, Emil L. Post's works in mathematical logic and recursion theory, the formalist school in the foundations of mathematics and the algebra of logic in England in the 19th century. The history of mathematics and logic in Poland is also considered.This volume is of interest to historians and philosophers of science and mathematics as well as to logicians and mathematicians interested in the philosophy and history of their fields. (shrink)

Lewis, D. Semantic analyses for dyadic deontic logic.--Salomaa, A. Some remarks concerning many-valued propositional logics.--Chellas, B. F. Conditional obligation.--Jeffrey, R.C. Remarks on interpersonal utility theory.--Hintikka, J. On the proper treatment of quantifiers in Montague semantics.--Mayoh, B.H. Extracting information from logical proofs.--Åqvist, L. A new approach to the logical theory of actions and causality.--Pörn, I. Some basic concepts of action.--Bouvère, K. de. Some remarks concerning logical and ontological theories.--Hacking, I. Combined evidence.--Äberg, C. Solution to a problem raised by Stig (...) Kanger and a set theoretical statement equivalent to the axiom of choice.--Lindström, P. On characterizing elementary logic.-- Scott, D. Rules and derived rules.--Hansson, B. A program for pragmatics.--Hermerén, G. Models.--Fenstad, J.E. Remarks on logic and probability.--Stenlund, S. Analytic and synthetic arithmetical statements. (shrink)

The third part, Cognition, concerns abstract questions about knowledge and truth as well as more concrete questions about the usefulness and tractability of various graphic representations of information. The book would be of special interest to Research Institutes in Computer Science, Researchers in Philosophical Logic, Deontic Logic, Applied Logic, Artificial Intelligence, and Cognitive Science.

In a career that spans 60 years so far, W.W. Tait has made many highly influential contributions to logic, the philosophy of mathematics, and their history. The present collection of new essays - contributed by former students, colleagues, and friends - is a Festschrift, i.e., a celebration of his life and work. The essays address a variety of themes prominent in his work or related to it. The collection starts with an introduction in which Tait's contributions are sketched and (...) put into context. The eleven essays that follow are arranged in three parts: Part I. Proof Theory and its History; Part II. Logic and Philosophy of Mathematics; and Part III. History of Logic and Philosophy of Mathematics. Each of the essays contributes substantially to one or several of these areas. The authors included are: Steve Awodey, Solomon Feferman, Michael Friedman, Warren Goldfarb, Geoffrey Hellman, William Howard, Stephen Menn, Rebecca Morris, Charles Parsons, Erich Reck, Thomas Ricketts, and Wilfried Sieg. The editor, Erich H. Reck is Professor of Philosophy at the University of California at Riverside. (shrink)

The book is a collection of the author¿s selected works in the philosophy and history of logic and mathematics. Papers in Part I include both general surveys of contemporary philosophy of mathematics as well as studies devoted to specialized topics, like Cantor's philosophy of set theory, the Church thesis and its epistemological status, the history of the philosophical background of the concept of number, the structuralist epistemology of mathematics and the phenomenological philosophy of mathematics. Part II contains essays in (...) the history of logic and mathematics. They address such issues as the philosophical background of the development of symbolism in mathematical logic, Giuseppe Peano and his role in the creation of contemporary logical symbolism, Emil L. Post's works in mathematical logic and recursion theory, the formalist school in the foundations of mathematics and the algebra of logic in England in the 19th century. The history of mathematics and logic in Poland is also considered. This volume is of interest to historians and philosophers of science and mathematics as well as to logicians and mathematicians interested in the philosophy and history of their fields. (shrink)

Robert E. Butts (1928-1997) was a philosopher and historian of science whose central concerns were the distinction between the rational and the irrational. He viewed scientific rationality as our major defence against the various conditions that encourage witch hunts and similar outbursts of irrationality, with all their attendant pain and terror. Butts saw himself as a pragmatic realist, combining what he took to be the best aspects of logical empiricism with a historically informed pragmatism, deeply appreciative of the methods of (...) science, trying to describe a kind of rationality essential in the struggle to preserve human values. This volume gathers previously unpublished essays and lectures with some previously published, thematically related essays. It includes essays and lectures on philosophical aspects of the European witch hunt, on scientific rationality and methodology, and on the relationships between science and philosophy exhibited in the writings of such historically significant figures as Leibniz, D'Alembert, Hume, Kant, Carnap and Kuhn. (shrink)

This volume also contains a long introductory essay by Hilary Putnam on the mathematics of continuity.

In recent years, mathematical logic has developed in many directions, the initial unity of its subject matter giving way to a myriad of seemingly unrelated areas. The articles collected here, which range from historical scholarship to recent research in geometric model theory, squarely address this development. These articles also connect to the diverse work of Väänänen, whose ecumenical approach to logic reflects the unity of the discipline.

The deontic status of tautologies and contradictions is one of the major puzzles for authors of early works on deontic logic. It is well-known that von Wright addresses this problem by adopting a Principle of Deontic Contingency, which says that tautologies are not necessarily obligatory and contradictions are not necessarily forbidden. A more radical solution is proposed by Anderson within a reductionist approach to deontic logic and consists in restricting the range of application of (...) deontic modalities to contingent propositions. Anderson’s solution has not received much attention in the literature, despite reflecting a typical feature of ordinary deontic reasoning, where non-contingent propositions are rarely, if ever, taken into account. In the present article we explore some of its formal consequences, providing a taxonomy of the properties of the Andersonian operators of obligation and permission for contingent propositions, O′ and P′, in the class of normal alethic systems. (shrink)

When one side is illuminated, the other side remains in darkness.My reason for addressing the topic for this article is to attempt a philosophical reconstruction of the "logic of not" in such a way as to guide us into entertaining a holistic mode of thinking. In preparation for this investigation, for comparative purposes I will engage a conceptual paradigm that is dominant in the Western philosophical tradition, namely the paradigm that is framed in terms of an either-or, ego-logical dualistic (...) stance and that undergirds our daily life in knowing and understanding thing-events. I will use the phrase "thing-event" throughout this article as a way of attempting to capture a sense of the whole rather than thematizing... (shrink)

Arthur Prior was a truly philosophical logician. Though he believed formal logic to be worthy of study in its own right, of course, the source of Prior’s great passion for logic was his faith in its capacity for clarifying philosophical issues, untangling philosophical puzzles, and solving philosophical problems. Despite the fact that he has received far less attention than he deserves, Prior has had a profound influence on the development of philosophical and formal logic over the past (...) forty years, a fact to which the present volume bears eloquent witness. The genesis of the volume was the 1989 Arthur Prior Memorial Conference, held appropriately enough at the University of Canterbury in Christchurch, New Zealand, where Prior had his first appointment in philosophy. However, this is not a volume of proceedings. Only eight of the twenty-two essays were actually presented at the conference. The rest were solicited by the editor specially for the volume. The subtitle—Essays on the Legacy of Arthur Prior—is an appropriate one. Few of the essays devote much space to Prior’s work per se. Rather, most address issues that, if not first raised by Prior, were revisited by him and subjected to his typically keen and distinctively original analysis. The papers themselves divide pretty evenly into the technical and the less technical. In this short review I will focus on the latter. (shrink)

This collection of papers is written in the spirit of what is nowadays called 'Logical Philosophy.' The topics addressed include: skepticism and the criterion of truth, situational semantics, computational aspects of possible worlds semantics and question-answer systems, occurrent beliefs, the logical omniscience paradox, paraconsistency, and models of explanatory procedures. (Series: Development in Humanities - Vol. 12).

In this exciting new collection, a distinguished international group of philosophers contribute new essays on central issues in philosophy of language and logic, in honor of Michael Dummett, one of the most influential philosophers of the late twentieth century. The essays are focused on areas particularly associated with Professor Dummett. Five are contributions to the philosophy of language, addressing in particular the nature of truth and meaning and the relation between language and thought. Two contributors discuss time, in particular (...) the reality of the past. The last four essays focus on Frege and the philosophy of mathematics. The volume represents some of the best work in contemporary analytical philosophy. (shrink)

In this paper, the set-theoretic approach in the logical theory of normative systems is extended using Broome’s definition of the normative code function. The syntax and semantics for first order metanormative language is defined, and metanormative language is applied in the formalization of the basic principles in Broome’s approach and in the construction of a logical typology of normative systems. Special attention is given to the types of normative systems which are not definable in terms of the properties of singular (...) sets of requirements (e.g. the realization equivalence of codes, the social compatibility of codes, and the compatibility of codes issued by different normative sources). Examples are given of the application of the typology in the interpretation of philosophical texts. Von Wright’s hypothesis on the connection of logical properties of normative systems, conceived set-theoretically, with standard deontic logic is proved by introducing the translation function between the metanormative language and the restricted language of standard deontic logic. The translation reveals that von Wright’s hypothesis must be appended. The problems of narrow and wide scope readings of the deontic conditionals and of the meaning of iterated deontic operators are addressed using the distinction between relative and absolute normative codes. The theorem on the existence of a realization equivalent absolute code for any relative code is proved. (shrink)

I read Stefan Collini’s What are Universities For? last week with very mixed feelings. In the past, I’ve much admired his polemical essays on the REF, “impact”, the Browne Report, etc. in the London Review of Books and elsewhere: they speak to my heart. If you don’t know those essays, you can get some of their flavour from his latest article in the Guardian yesterday. But I found the book a disappointment. Perhaps the trouble is that Collini is too decent, (...) too high-minded, has too unrealistically exalted a view about what actually happens in universities which is too coloured by attitudes appropriate to the traditional humanities. And he is optimistic to the point of fantasy if he thinks that people are so susceptible to “the romance of ideas and the power of beauty” that they will want, or can be brought to want, lots and lots of universities in order to promote the ideas (as if they would suppose that the task of “conserving, understanding, extending and handing on to subsequent generations the intellectual, scientific, and artistic heritage of mankind” was clearly ill-served when there were only forty universities in England, as opposed to a hundred and whatever). (shrink)