We distinguish three different readings of the intuitionistic notions of validity, soundness, and completeness with respect to the quantification occurring in the notion of validity, and we establish certain relations between the different readings. For each of the meta-logical notions considered we suggest that the “most natural” reading (which is not the same for all cases) is precisely the one which is required by the recent intuitionistic completeness theorems for IPC.

We distinguish three different readings of the intuitionistic notions of validity, soundness, and completeness with respect to the quantification occurring in the notion of validity, and we establish certain relations between the different readings. For each of the meta-logicalnotions considered we suggest that the "most natural" reading (which is not the same for all cases) is precisely the one which is required by the recent intuitionistic completeness theorems for IPC.

IPC, the intuitionistic predicate calculus, has the property(i) Vc(A c /x) xA.Furthermore, for certain important , IPC has the converse property (ii) xA Vc(A c /x). (i) may be given up in various ways, corresponding to different philosophic intuitions and yielding different systems of intuitionistic free logic. The present paper proves the strong completeness of several of these with respect to Kripke style semantics. It also shows that giving up (i) need not force us to abandon the analogue of (ii).

It is argued that the tensed theory of the creative subject provides a natural formulation of the logic underlying Brouwer's notion of unextendable order and explains the link between that notion and virtual order. The tensed theory of the creative subject is also shown to be a useful tool for interpreting recent evidence about the stages of Brouwer's thinking concerning these two notions of order.

Robert C. Scharff has written what we might call, after Nietzsche, a timely meditation. It is timely in that it is aimed at our particular time , and it is a meditation on timeliness, on what it means to do philosophy within time and history . These two topics meet in his depiction of our time as one that is either not fully aware of or that actively suppresses its own timeliness, its own determination by its time and historical context, (...) due largely to analytic philosophy’s remaining caught in the vestigial grips of positivism and the dominance of science. We may be “After Positivism,” but we are not wholly past positivism. Scharff considers this ahistorical approach untenable because, as he informs us in the book’s second sentence, all meditations are timely: time and historical context inescapably determine how and what we meditate on, especially the attempts to escape them.Scharff identifies our place in history as “after posi .. (shrink)

This book develops an Aristotelian account of the virtue of practical intelligence or "phronesis"--an excellence of deliberating and making choices--which ...

MICHAEL DUMMETT, Elements of intuitionism. With the assistance of Robert Minio. Oxford: Oxford University Press, 1977. xii + 466 pp. No price stated.

The Statesman is Plato's neglected political work, but it is crucial for an understanding of the development of his political thinking. In some respects it continues themes from the Republic, particularly the importance of knowledge as entitlement to rule. But there are also changes: Plato has dropped the ambitious metaphysical synthesis of the Republic, changed his view of the moral psychology of the citizen, and revised his position on the role of law and institutions. In its presentation of the statesman's (...) expertise, the Statesman modifies, as well as defending in original ways, this central theme of the Republic. (shrink)

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

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

Though my title speaks of Kant’s mathematical realism, I want in this essay to explore Kant’s relation to a famous mathematical anti-realist. Specifically, I want to discuss Kant’s influence on L. E. J. Brouwer, the 20th-century Dutch mathematician who built a contemporary philosophy of mathematics on constructivist themes which were quite explicitly Kantian. Brouwer’s theory is perhaps most notable for its belief that constructivism requires us to abandon the traditional logic of mathematical reasoning in favor of different canon of reasoning, (...) called intuitionistic logic. Brouwer thought that classical logic is intrinsically bound up with a nonconstructive view of mathematics. This means that, according to Brouwer, when we do mathematics we must give up bivalence, we must no longer use such familiar logical laws as excluded middle, and we must sometimes forebear from the classic method of reductio ad absurdum. All of these are intuitionistically invalid classical principles. (shrink)

After sketching the essentials of L. E. J. Brouwer’s intuitionistic mathematics—separable mathematics, choice sequences, the uniform continuity theorem, and the intuitionistic continuum—this chapter outlines the main philosophical tenets that go hand in hand with Brouwer’s technical achievements. It presents his views about general and mathematical phenomenology and shows how these views ground his positive epistemological and ontological positions and his stinging criticisms of classical mathematics and logic. The chapter then turns to intuitionistic logic and its philosophical side. It first sets (...) out the basic meta-logical technical results, then discusses the relevant philosophical views—those of Arend Heyting and Michael Dummett. It concludes by tracing intuitionism’s philosophical and technical roots in Aristotle and Kant. (shrink)

The current debate over aesthetic testimony typically focuses on cases of doxastic repetition — where, when an agent, on receiving aesthetic testimony that p, acquires the belief that p without qualification. I suggest that we broaden the set of cases under consideration. I consider a number of cases of action from testimony, including reconsidering a disliked album based on testimony, and choosing an artistic educational institution from testimony. But this cannot simply be explained by supposing that testimony is usable for (...) action, but unusable for doxastic repetition. I consider a new asymmetry in the usability aesthetic testimony. Consider the following cases: we seem unwilling to accept somebody hanging a painting in their bedroom based merely on testimony, but entirely willing to accept hanging a painting in a museum based merely on testimony. The switch in intuitive acceptability seems to track, in some complicated way, the line between public life and private life. These new cases weigh against a number of standing theories of aesthetic testimony. I suggest that we look further afield, and that something like a sensibility theory, in the style of John McDowell and David Wiggins, will prove to be the best fit for our intuitions for the usability of aesthetic testimony. I propose the following explanation for the new asymmetry: we are willing to accept testimony about whether a work merits being found beautiful; but we are unwilling to accept testimony about whether something actually is beautiful. (shrink)

Metaphysicians speak of laws of nature in terms of necessity and universality; scientists, in terms of symmetry and invariance. In this book van Fraassen argues that no metaphysical account of laws can succeed. He analyzes and rejects the arguments that there are laws of nature, or that we must believe there are, and argues that we should disregard the idea of law as an adequate clue to science. After exploring what this means for general epistemology, the author develops the empiricist (...) view of science as a construction of models to represent the phenomena. (shrink)

Philosophy has as much to do with feelings as it does with thoughts and thinking. Philosophy, accordingly, requires not only emotional sensitivity but an understanding of the emotions, not as curious but marginal psychological phenomena but as the very substance of life. In this, the second book in a series devoted to his work on the emotions, Robert Solomon presents a defense of the emotions and of sentimentality against the background of what he perceives as a long history of abuse (...) in philosophy and social thought and art and literary criticism. The title piece reopens a classic debate about the role of sentimentality in art and literature. In subsequent chapters, Solomon discusses not only such "moral sentiments" as sympathy and compassion but also grief, gratitude, love, horror, and even vengeance. He also defends, with appropriate caution, the "seven deadly sins." The emotions, at least some emotions--are essential to a well-lived life. They are or can be virtues, features of the human condition without which civilized life would be unimaginable. (shrink)

Kant's views about mathematics were controversial in his own time, and they have inspired or infuriated thinkers ever since. Though specific Kantian doctrines fell into disrepute earlier in this century, the past twenty-five years have seen a surge of interest in and respect for Kant's philosophy of mathematics among both Kant scholars and philosophers of mathematics. The present volume includes the classic papers from the 1960s and 1970s which spared this renaissance of interest, together with updated postscripts by their authors. (...) It also includes the most important recent work on Kant's philosophy of mathematics. The essays bring to bear a wealth of detailed Kantian scholarship, together with powerful new interpretative tools drawn from modern mathematics, logic and philosophy. The cumulative effect of this collection upon the reader will be a deeper understanding of the centrality of mathematics in all aspects of Kant's thought and a renewed respect for the power of Kant's thinking about mathematics. The essays contained in this volume will set the agenda for further work on Kant's philosophy of mathematics for some time to come. (shrink)

Mark Jay Steiner, a brilliant and influential philosopher of mathematics, whose interests and accomplishments extended beyond that field as well, passed away on.

The Cambridge History of Renaissance Philosophy, published in 1988, offers a balanced and comprehensive account of philosophical thought from the middle of the fourteenth century to the emergence of modern philosophy. This was the first volume in English to synthesise for a wider audience the substantial and sophisticated research now available. The volume is organised by branch of philosophy rather than by individual philosopher or school, and the intention has been to present the internal development of different aspects of the (...) subject in their own historical context. The structure also naturally emphasises the international nature of philosophy in the Renaissance. (shrink)

L. E. J. Brouwer, the founder of mathematical intuitionism, believed that mathematics and its objects must be humanly graspable. He initiated a program rebuilding modern mathematics according to that principle. This book introduces the reader to the mathematical core of intuitionism – from elementary number theory through to Brouwer's uniform continuity theorem – and to the two central topics of 'formalized intuitionism': formal intuitionistic logic, and formal systems for intuitionistic analysis. Building on that, the book proposes a systematic, philosophical foundation (...) for intuitionism that weaves together doctrines about human grasp, mathematical objects and mathematical truth. (shrink)

The authors present a case study involving truth telling responsibilities in the setting of nonepileptic seizures. Specifically, over the course of several suspected nonepileptic seizures, a patient’s seizures stopped after he received a saline flush meant to precede the administration of anti-seizure medication. The patient and his surrogate believed he had received the medication each time, and the team wondered whether they should disclose the truth. Some worried that disclosure would reinforce the suspected psychogenic behavior, exacerbating the patient’s condition. In (...) this way, the case study presents a twist on the traditional truth telling archetype. While most truth telling cases center on navigating cultural differences or worries about emotional harm, this case presented concerns about medical harm in the form of exacerbating the patient’s condition. The authors describe the complex patient-family-team dynamic that preceded this ethical dilemma, describe the case, analyze the ethical issue, and describe the outcome. (shrink)

The late 1960s saw the emergence of new philosophical interest in Kant's philosophy of mathematics, and since then this interest has developed into a major and dynamic field of study. In this state-of-the-art survey of contemporary scholarship on Kant's mathematical thinking, Carl Posy and Ofra Rechter gather leading authors who approach it from multiple perspectives, engaging with topics including geometry, arithmetic, logic, and metaphysics. Their essays offer fine-grained analysis of Kant's philosophy of mathematics in the context of his Critical (...) philosophy, and also show sensitivity to its historical background. The volume will be important for readers seeking a comprehensive picture of the current scholarship about the development of Kant's philosophy of mathematics, its place in his overall philosophy, and the Kantian themes that influenced mathematics and its philosophy after Kant. (shrink)

Artikelen en lezingen uit de periode 1970-1982.

Kant says patently conflicting things about infinity and our grasp of it. Infinite space is a good case in point. In his solution to the First Antinomy, he denies that we can grasp the spatial universe as infinite, and therefore that this universe can be infinite; while in the Aesthetic he says just the opposite: ‘Space is represented as a given infinite magnitude’. And he rests these upon consistently opposite grounds. In the Antinomy we are told that we can have (...) no intuitive grasp of an infinite space, and in the Aesthetic he says that our grasp of infinite space is precisely intuitive. (shrink)

Three standard psychometric tests were administered to parents who volunteered their children for a randomised, double-blind placebo-controlled trial of a new asthma drug and to a control group of parents whose children were eligible for the trial but had declined the invitation. The trial took place at a children's hospital in Australia. The subjects comprised 68 parents who had volunteered their children and 42 who had not, a participation rate of 94 per cent and 70 per cent, respectively. The responses (...) of these parents to the Gordon Survey of Interpersonal Values Questionnaire, the Coopersmith Self-Esteem Inventory and the Cattell Sixteen Personality Factor Questionnaire were analysed by computer. There was a marked difference between the psychological profiles of the two groups of parents. Volunteering parents put more value on benevolence while non-volunteering parents were more concerned with power and prestige. The self-esteem of volunteering parents was much lower than that of non-volunteering parents. Finally, volunteering parents were more introverted, exhibited greater anxiety and low supergo, while non-volunteering parents appeared to have greater social confidence and emotional stability. Since an individual's values, self-esteem and personality may be important antecedents of behaviour, these findings suggest that parents who volunteer their children for clinical research are not only socially disadvantaged and emotionally vulnerable, but may also be psychologically predisposed to volunteering. Furthermore, these findings provide evidence for the existence of a psychosocial 'filter' effect of the informed consent procedure, which may be discouraging the better educated, more privileged and psychologically resilient members of society from participation as research subjects. (shrink)

In this dialogue Plato shows the pretensions of the leading sophist, Protagoras, challenged by the critical arguments of Socrates. The dialogue broadens out to consider the nature of the good life and the role of intellect and pleasure.

Kant says patently conflicting things about infinity and our grasp of it. Infinite space is a good case in point. In his solution to the First Antinomy, he denies that we can grasp the spatial universe as infinite, and therefore that this universe can be infinite; while in the Aesthetic he says just the opposite: ‘Space is represented as a given infinite magnitude’ (A25/B39). And he rests these upon consistently opposite grounds. In the Antinomy we are told that we can (...) have no intuitive grasp of an infinite space, and in the Aesthetic he says that our grasp of infinite space is precisely intuitive. (shrink)