A Brief History of Time: From the Big Bang to Black Holes is a popular-science book on cosmology (the study of the origin and evolution of the universe) by British physicist Stephen Hawking. It was first published in 1988. Hawking wrote the book for readers who have no prior knowledge of the universe and people who are interested in learning.

Einstein said that the most incomprehensible thing about the universe is that it is comprehensible. But was he right? Can the quantum theory of fields and Einstein's general theory of relativity, the two most accurate and successful theories in all of physics, be united in a single quantum theory of gravity? Two of the world's most famous physicists - Stephen Hawking and Roger Penrose - disagree. Here they explain their positions in a work based on six lectures with a (...) final debate, all originally presented at the Isaac Newton Institute for Mathematical Sciences at the University of Cambridge. (shrink)

From Descartes to Popper, philosophers have criticized and tried to improve the strategies of reasoning invoked in science and in everyday life. In recent years leading cognitive psychologists have painted a detailed, controversial, and highly critical portrait of common sense reasoning. Stephen Stich begins with a spirited defense of this work and a critique of those writers who argue that widespread irrationality is a biological or conceptual impossibility.Stich then explores the nature of rationality and irrationality: What is it that (...) distinguishes good reasoning from bad? He rejects the most widely accepted approaches to this question approaches which unpack rationality by appeal to truth, to reflective equilibrium or conceptual analysis. The alternative he defends grows out of the pragmatic tradition in which reasoning is viewed as a cognitive tool. Stich's version of pragmatism leads to a radical epistemic relativism and he argues that the widespread abhorrence of relativism is ill founded. (shrink)

In this book, Stephen Read sets out to rescue logic from its undeserved reputation as an inflexible, dogmatic discipline by demonstrating that its technicalities and processes are founded on assumptions which are themselves amenable to philosophical investigation. He examines the fundamental principles of consequence, logical truth and correct inference within the context of logic, and shows that the principles by which we delineate consequences are themselves not guaranteed free from error. Central to the notion of truth is the beguiling (...) issue of paradox. Its philosophical value, Read shows, lies in exposing the invalid assumption on which the paradox is built. Thinking About Logic also discusses logical puzzles which introduce questions relating to language, the world, and their relationship. (shrink)

Connectionist models provide a promising alternative to the traditional computational approach that has for several decades dominated cognitive science and artificial intelligence, although the nature of connectionist models and their relation to symbol processing remains controversial. Connectionist models can be characterized by three general computational features: distinct layers of interconnected units, recursive rules for updating the strengths of the connections during learning, and “simple” homogeneous computing elements. Using just these three features one can construct surprisingly elegant and powerful models of (...) memory, perception, motor control, categorization, and reasoning. What makes the connectionist approach unique is not its variety of representational possibilities or its departure from explicit rule-based models, or even its preoccupation with the brain metaphor. Rather, it is that connectionist models can be used to explore systematically the complex interaction between learning and representation, as we try to demonstrate through the analysis of several large networks. (shrink)

Anti-exceptionalism about logic is the doctrine that logic does not require its own epistemology, for its methods are continuous with those of science. Although most recently urged by Williamson, the idea goes back at least to Lakatos, who wanted to adapt Popper's falsicationism and extend it not only to mathematics but to logic as well. But one needs to be careful here to distinguish the empirical from the a posteriori. Lakatos coined the term 'quasi-empirical' `for the counterinstances to putative mathematical (...) and logical theses. Mathematics and logic may both be a posteriori, but it does not follow that they are empirical. Indeed, as Williamson has demonstrated, what counts as empirical knowledge, and the role of experience in acquiring knowledge, are both unclear. Moreover, knowledge, even of necessary truths, is fallible. Nonetheless, logical consequence holds in virtue of the meaning of the logical terms, just as consequence in general holds in virtue of the meanings of the concepts involved; and so logic is both analytic and necessary. In this respect, it is exceptional. But its methodologyand its epistemology are the same as those of mathematics and science in being fallibilist, and counterexamples to seemingly analytic truths are as likely as those in any scientic endeavour. What is needed is a new account of the evidential basis of knowledge, one which is, perhaps surprisingly, found in Aristotle. (shrink)

A comprehensive reassessment of the concept of mimesis in the history of ancient Greek aesthetics and philosophy of art, with particular attention to Plato, Aristotle, Hellenistic philosophy, and neoplatonism. There is also a wide-ranging review of arguments pro and contra the idea of artistic mimesis from the Renaissance to modern literar theory. The book challenges standard accounts in numerous respects and builds a new dialectical model with which to make sense of the entire history of mimeticist thinking in aesthetics.

The field of neuroimaging has reached a watershed. Brain imaging research has been the source of many advances in cognitive neuroscience and cognitive science over the last decade, but recent critiques and emerging trends are raising foundational issues of methodology, measurement, and theory. Indeed, concerns over interpretation of brain maps have created serious controversies in social neuroscience, and, more important, point to a larger set of issues that lie at the heart of the entire brain mapping enterprise. In this volume, (...) leading scholars -- neuroimagers and philosophers of mind -- reexamine these central issues and explore current controversies that have arisen in cognitive science, cognitive neuroscience, computer science, and signal processing. The contributors address both statistical and dynamical analysis and modeling of neuroimaging data and interpretation, discussing localization, modularity, and neuroimagers' tacit assumptions about how these two phenomena are related; controversies over correlation of fMRI data and social attributions ; and the standard inferential design approach in neuroimaging. Finally, the contributors take a more philosophical perspective, considering the nature of measurement in brain imaging, and offer a framework for novel neuroimaging data structures. Contributors: William Bechtel, Bharat Biswal, Matthew Brett, Martin Bunzl, Max Coltheart, Karl J. Friston, Joy J. Geng, Clark Glymour, Kalanit Grill-Spector, Stephen José Hanson, Trevor Harley, Gilbert Harman, James V. Haxby, Rik N. Henson, Nancy Kanwisher, Colin Klein, Richard Loosemore, Sébastien Meriaux, Chris Mole, Jeanette A. Mumford, Russell A. Poldrack, Jean-Baptiste Poline, Richard C. Richardson, Alexis Roche, Adina L. Roskies, Pia Rotshtein, Rebecca Saxe, Philipp Sterzer, Bertrand Thirion, Edward Vul The hardcover edition does not include a dust jacket. (shrink)

Inferentialism claims that expressions are meaningful by virtue of rules governing their use. In particular, logical expressions are autonomous if given meaning by their introduction-rules, rules specifying the grounds for assertion of propositions containing them. If the elimination-rules do no more, and no less, than is justified by the introduction-rules, the rules satisfy what Prawitz, following Lorenzen, called an inversion principle. This connection between rules leads to a general form of elimination-rule, and when the rules have this form, they may (...) be said to exhibit “general-elimination” harmony. Ge-harmony ensures that the meaning of a logical expression is clearly visible in its I-rule, and that the I- and E-rules are coherent, in encapsulating the same meaning. However, it does not ensure that the resulting logical system is normalizable, nor that it satisfies the conservative extension property, nor that it is consistent. Thus harmony should not be identified with any of these notions. (shrink)

"There is no scientist today whose books I look forward to reading with greater anticipation of enjoyment and enlightenment than Stephen Jay Gould."—Martin Gardner Among scientists who write, no one illuminates as well as Stephen Jay Gould doesthe wonderful workings of the natural world. Now in a new volume of collected essays—his sixth since Ever Since Darwin—Gould speaks of the importance of unbroken connections within our own lives and to our ancestralgenerations. Along with way, he opens to us (...) the mysteries of fish tails, frog calls, and other matters, and shows once and for all why we must take notice when a seemingly insignificant creature is threatened, like the land snail Partula from Moorea, whose extinction he movingly relates. (shrink)

Leibniz often refers to the Principle of Sufficient Reason (PSR) as something like a first principle. In some texts, however, he attempts to give positive arguments in its favor. I examine two such arguments, and find them wanting. The first argument has two defects. First, it is question-begging; and second, when the question-begging step is excised, the principle one can in fact derive is highly counter-intuitive. The second argument is valid, but has the defect of only reaching a nearly trivial (...) conclusion. (shrink)

In the eighth chapter of the Bodhicaryāvatāra, the Buddhist philosopher Śāntideva has often been interpreted as offering an argument that accepting the ultimate nonexistence of the self (anātman) rationally entails a commitment to altruism, the view that one should care equally for self and others. In this essay, I consider reconstructions of Śāntideva’s argument by contemporary scholars Paul Williams, Mark Siderits and John Pettit. I argue that all of these various reconfigurations of the argument fail to be convincing. This suggests (...) that, for Madhyamaka Buddhists, an understanding of anātman does not entail acceptance of the Bodhisattva path, but rather is instrumental to achieving it. Second, it suggests the possibility that in these verses, Śāntideva was offering meditational techniques, rather than making an argument for altruism from the premise of anātman. (shrink)

Jan Lukasiewicz's treatise on Aristotle's Syllogistic, published in the 1950s, has been very influential in framing contemporary understanding of Aristotle's logical systems. However, Lukasiewicz's interpretation is based on a number of tendentious claims, not least, the claim that the syllogistic was intended to apply only to non-empty terms. I show that this interpretation is not true to Aristotle's text and that a more coherent and faithful interpretation admits empty terms while maintaining all the relations of the traditional square of opposition.

This article explores the defense Indian Buddhist texts make in support of their conceptions of lives that are good for an individual. This defense occurs, largely, through their analysis of ordinary experience as being saturated by subtle forms of suffering . I begin by explicating the most influential of the Buddhist taxonomies of suffering: the threefold division into explicit suffering , the suffering of change , and conditioned suffering . Next, I sketch the three theories of welfare that have been (...) most influential in contemporary ethical theory. I then argue that Buddhist texts underdetermine which of these theories would have been accepted by ancient Indian Buddhists. Nevertheless, Buddhist ideas about suffering narrow the shape any acceptable theory of welfare may take. In my conclusion, I argue that this narrowing process itself is enough to reconstruct a philosophical defense of the forms of life endorsed in Buddhist texts. (shrink)

I examine the (mediated) correspondence between Spinoza and Robert Boyle concerning the latter’s account of fluidity and his experiments on reconstitution of niter in the light of the epistemology and doctrine of method contained in the Treatise on the Emendation of the Intellect. I argue that both the Treatise and the correspondence reveal that for Spinoza, the proper method of science is not experimental, and that he accepted a powerful under-determination thesis. I argue that, in contrast to modern versions, Spinoza’s (...) form of naturalism was a highly rationalist and anti-empirical one. I conclude with a brief account of the value of experience and experimentation for Spinoza’s scientific method. (shrink)

Roger Swyneshed, in his treatise on insolubles, dating from the early 1330s, drew three notorious corollaries from his solution. The third states that there is a contradictory pair of propositions both of which are false. This appears to contradict what Whitaker, in his iconoclastic reading of Aristotle’s De Interpretatione, dubbed “The Rule of Contradictory Pairs”, which requires that in every such pair, one must be true and the other false. Whitaker argued that, immediately after defining the notion of a contradictory (...) pair, in which one statement affirms what the other denies of the same thing, Aristotle himself gave counterexamples to the rule. This gives some credence to Swyneshed’s claim that his solution to the logical paradoxes is not contrary to Aristotle’s teaching, as many of Swyneshed’s contemporaries claimed. Insolubles are false, he said, because they falsify themselves; and their contradictories are false because they falsely deny that the insoluble itself is false. Swyneshed’s solution depends crucially on the revision he makes to the acount of truth and falsehood, brought out in his first thesis: that a false proposition can signify as it is, or as Paul of Venice, who took up and developed Swyneshed’s solution some sixty years later, puts it, a false proposition can have a true significate. Swyneshed gave a further counterexample to when he claimed that some insolubles, like future contingents, are neither true nor false. Dialetheism, the contemporary claim that some propositions are both true and false, is wedded to the Rule, and in consequence divorces denial from the assertion of the contradictory negation. Consequently, Swyneshed’s logical heresy is very different from that found in dialetheism. (shrink)

The traditional view according to which we adults tacitly consent to a state’s lawful actions just by living within its borders—the residence theory—is now widely rejected by political philosophers. According to the critics, this theory fails because consent must be (i) intentional, (ii) informed, and (iii) voluntary, whereas one’s continued residence within a state is typically none of these things. Few people intend to remain within the state in which they find themselves, and few realize that by remaining they are (...) consenting to the state’s lawful actions. In addition, the various obstacles standing in the way of us leaving the state render our remaining involuntary. Thus, the critics conclude, few if any people can be considered to have consented through their residence. I argue that these objections fail and that the residence theory remains a viable option, at least for those who are not committed incompatibilists. (shrink)

Leslie Stephen (1832–1904) was a writer, philosopher and literary critic whose work was published widely in the nineteenth century. As a young man Stephen was ordained deacon, but he later became agnostic and much of his work reflects his interest in challenging popular religion. This two-volume work, first published in 1876, is no exception: it focuses on the eighteenth-century deist controversy and its effects, as well as the reactions to what Stephen saw as a revolution in thought. (...) Comprehensive and full of detailed analysis, this is an important work in the history of ideas. Volume 2 focuses on eighteenth-century moral philosophy, political philosophy and literature, and on the literary and religious reactions to the revolution in thought. Utilitarianism is discussed at length, as well as the work of thinkers such as Shaftesbury, Mandeville, Burke and Adam Smith. (shrink)

For serious yoga practitioners curious to know the ancient origins of the art, Stephen Phillips, a professional philosopher and sanskritist with a long-standing personal practice, lays out the philosophies of action, knowledge, and devotion as well as the processes of meditation, reasoning, and self-analysis that formed the basis of yoga in ancient and classical India and continue to shape it today. In discussing yoga's fundamental commitments, Phillips explores traditional teachings of hatha yoga, karma yoga, _bhakti_ yoga, and tantra, and (...) shows how such core concepts as self-monitoring consciousness, karma, nonharmfulness, reincarnation, and the powers of consciousness relate to modern practice. He outlines values implicit in _bhakti_ yoga and the tantric yoga of beauty and art and explains the occult psychologies of _koshas_, _skandhas_, and _chakras_. His book incorporates original translations from the early Upanishads, the _Bhagavad Gita_, the _Yoga Sutra_, the _Hatha Yoga Pradipika_, and seminal tantric writings of the tenth-century Kashmiri Shaivite, Abhinava Gupta. A glossary defining more than three hundred technical terms and an extensive bibliography offer further help to nonscholars. A remarkable exploration of yoga's conceptual legacy, _Yoga, Karma, and Rebirth_ crystallizes ideas about self and reality that unite the many incarnations of yoga. (shrink)

As Nair-Collins and Joffe note, the concern that our tests for brain death do not successfully show that all brain functions have stopped is not new (Nair-Collins and Joffe 2023). As our abilities...

Some philosophers contend that the past must be finite in duration, because otherwise reaching the present would have involved the sequential occurrence of an actual infinity of events, which they regard as impossible. I recently developed a new objection to this finitist argument, to which Andrew Ter Ern Loke and Travis Dumsday have replied. Here I respond to the three main points raised in their replies.

Logical inferentialism claims that the meaning of the logical constants should be given, not model-theoretically, but by the rules of inference of a suitable calculus. It has been claimed that certain proof-theoretical systems, most particularly, labelled deductive systems for modal logic, are unsuitable, on the grounds that they are semantically polluted and suffer from an untoward intrusion of semantics into syntax. The charge is shown to be mistaken. It is argued on inferentialist grounds that labelled deductive systems are as syntactically (...) pure as any formal system in which the rules define the meanings of the logical constants. (shrink)

Leibniz argues that there must be a fundamental level of simple substances because composites borrow their reality from their constituents and not all reality can be borrowed. I contend that the underlying logic of this ‘borrowed reality argument’ has been misunderstood, particularly the rationale for the key premise that not all reality can be borrowed. Contrary to what has been suggested, the rationale turns neither on the alleged viciousness of an unending regress of reality borrowers nor on the Principle of (...) Sufficient Reason, but on the idea that composites are phenomena and thus can be real only insofar as they have a foundation in substances, from which they directly ‘borrow’ their reality. The claim that composites are phenomena rests in turn on Leibniz's conceptualism about relations. So understood, what initially looked like a disappointingly simple argument for simples turns out to be a rather rich and sophisticated one. (shrink)

Some twenty-five centuries after the Buddha started teaching, his message continues to inspire people across the globe, including those living in predominantly secular societies. But what does it mean to adapt religious practices to secular contexts? Stephen Batchelor, an internationally known author and teacher, is committed to a secularized version of the Buddha's teachings. The time has come, he feels, to articulate a coherent ethical, contemplative, and philosophical vision of Buddhism for our age. _After Buddhism, _the culmination of four (...) decades of study and practice in the Tibetan, Zen, and Theravada traditions, is his attempt to set the record straight about who the Buddha was and what he was trying to teach. Combining critical readings of the earliest canonical texts with narrative accounts of five of the Buddha’s inner circle, Batchelor depicts the Buddha as a pragmatic ethicist rather than a dogmatic metaphysician. He envisions Buddhism as a constantly evolving culture of awakening, its long survival due to its capacity to reinvent itself and interact creatively with each society it encounters. This original and provocative book presents a new framework for understanding the remarkable spread of Buddhism in today’s globalized world. It also reminds us of what was so startling about the Buddha’s vision of human flourishing. (shrink)

In Watching Sport, Stephen Mumford distinguishes two ways in which sport can be seen. A purist sees it aesthetically while a partisan sees it competitively. But this overlooks the obvious point that most sports fans are neither entirely purist nor entirely partisan. The norm will be some moderate position in between with the purist and partisan as ideal limits. What is then the point of considering these pure aesthetic and pure competitive ways of seeing? In this discussion note, I (...) consider possible accounts of the way in which the moderate spectator watches. After rejecting what I call a pure perception theory and a mixed view, I defend an oscillation theory. This means that the moderate sports fan is one who switches, sometimes rapidly, between the aesthetic and competitive perceptions of sport. A pay-off of this account is that we do not need a further, third way of perceiving sport in order to account for the moderate. It has been explained in terms of our original two forms of perception. This fills a lacuna in Mumford's account. (shrink)

The proposition that man is the only animal capable of laughter is at least as old as Aristotle . In a strictly physical sense, this is probably false; but it is undoubtedly true that as a psychologically expressive and socially potent means of communication, laughter is a distinctively human phenomenon. Any attempt to study sets of cultural attitudes towards laughter, or the particular types of personal conduct which these attitudes shape and influence, must certainly adopt a wider perspective than a (...) narrowly physical definition of laughter will allow. Throughout this paper, which will attempt to establish part of the framework of such a cultural analysis for the Greek world of, broadly speaking, the archaic and classical periods, ‘laughter’ must be taken, by a convenient synecdoche, to encompass the many behavioural and affective patterns which are associated with, or which characteristically give scope for, uses of laughter in the literal sense of the word. My concern, then, is with a whole network of feelings, concepts and actions; and my argument will try to elucidate the practices within which laughter fulfils a recognizable function in Greek societies, as well as the dominant ideas and values which Greek thought brings to bear upon these practices. The results of the enquiry will, I believe, give us some reason to accept a rapprochement between the universalist assumption for which my epigraph from Johnson speaks and the recognition of cultural specificity in laughter's uses for which many anthropologists would argue, as emphatically asserted, from a Marxizing point of view, in the quotation from Vladimir Propp. (shrink)

This paper reconstructs an Indian Buddhist response to the overdemandingness objection, the claim that a moral theory asks too much of its adherents. In the first section, I explain the objection and argue that some Mahāyāna Buddhists, including Śāntideva, face it. In the second section, I survey some possible ways of responding to the objection as a way of situating the Buddhist response alongside contemporary work. In the final section, I draw upon writing by Vasubandhu and Śāntideva in reconstructing a (...) Mahāyāna response to the objection. An essential component of this response is the psychological transformation that the bodhisattva achieves as a result of realizing the nonexistence of the self. This allows him to radically identify his well-being with the well-being of others, thereby lessening the tension between self and others upon which the overdemandingness objection usually depends. Emphasizing the attention Mahāyāna authors pay to lessening moral demandingness in this way increases our appreciation of the philosophical sophistication of their moral thought and highlights an important strategy for responding to the overdemandingness objection that has been underdeveloped in contemporary work. (shrink)

Kearns (2021) argues that there is a parody version of Anselm's ontological argument (a "gontological argument") which shows that God does not exist. I show that Anselm considers one of the key premises in Kearns' gontological argument, and explicitly gives an argument which entails its falsity, and hence the unsoundness of the supposed parody argument. -/- .

A compelling investigation into one of the most coveted and cherished ideals, "Wisdom" also chronicles the efforts of modern science to penetrate the mysterious nature of this timeless virtue.

In recent years, speech-act theory has mooted the possibility that one utterance can signify a number of different things. This pluralist conception of signification lies at the heart of Thomas Bradwardine’s solution to the insolubles, logical puzzles such as the semantic paradoxes, presented in Oxford in the early 1320s. His leading assumption was that signification is closed under consequence, that is, that a proposition signifies everything which follows from what it signifies. Then any proposition signifying its own falsity, he showed, (...) also signifies its own truth and so, since it signifies things which cannot both obtain, it is simply false. Bradwardine himself, and his contemporaries, did not elaborate this pluralist theory, or say much in its defence. It can be shown to accord closely, however, with the prevailing conception of logical consequence in England in the fourteenth century. Recent pluralist theories of signification, such as Grice’s, also endorse Bradwardine’s closure postulate as a plausible constraint on signification, and so his analysis of the semantic paradoxes is seen to be both well-grounded and plausible. (shrink)

I agree fully that a “clearer picture of how vulnerability might manifest and how it can be accommodated, ideally without resorting to mere exclusion from research, is needed” (Friesen et al. 2023,...

:Neuroprosthetic speech devices are an emerging technology that can offer the possibility of communication to those who are unable to speak. Patients with ‘locked in syndrome,’ aphasia, or other such pathologies can use covert speech—vividly imagining saying something without actual vocalization—to trigger neural controlled systems capable of synthesizing the speech they would have spoken, but for their impairment.We provide an analysis of the mechanisms and outputs involved in speech mediated by neuroprosthetic devices. This analysis provides a framework for accounting for (...) the ethical significance of accuracy, control, and pragmatic dimensions of prosthesis-mediated speech. We first examine what it means for the output of the device to be accurate, drawing a distinction between technical accuracy on the one hand and semantic accuracy on the other. These are conceptual notions of accuracy.Both technical and semantic accuracy of the device will be necessary for the user to have sufficient control over the device. Sufficient control is an ethical consideration: we place high value on being able to express ourselves when we want and how we want. Sufficient control of a neural speech prosthesis requires that a speaker can reliably use their speech apparatus as they want to, and can expect their speech to authentically represent them. We draw a distinction between two relevant features which bear on the question of whether the user has sufficient control: voluntariness of the speech and the authenticity of the speech. These can come apart: the user might involuntarily produce an authentic output or might voluntarily produce an inauthentic output. Finally, we consider the role of the interlocutor in interpreting the content and purpose of the communication.These three ethical dimensions raise philosophical questions about the nature of speech, the level of control required for communicative accuracy, and the nature of ‘accuracy’ with respect to both natural and prosthesis-mediated speech. (shrink)

In this essay several challenges are raised to the project of classifying Śāntideva’s ethical reasoning given in his Bodhicaryāvatāra, or Guide to the Way of the Bodhisattva, as a species of ethical theory such as consequentialism or virtue ethics. One set of difficulties highlighted here arises because Śāntideva wrote this text to act as a manual of psychological transformation, and it is therefore often difficult to determine when his statements indicate his own ethical views. Further, even assuming we can identify (...) a set of statements that accurately portray the moral position of Śāntideva, it is argued that these statements underdetermine which foundational normative theory should be ascribed to him. (shrink)

Some brain injured patients are left in a permanent vegetative state, i.e., they have irreversibly lost their capacity for consciousness but retained some autonomic physiological functions, such as breathing unaided. Having discussed the controversial nature of the permanent vegetative state as a diagnostic category, we turn to the question of the patients’ ontological status. Are the permanently vegetative alive, dead, or in some other state? We present empirical data from interviews with relatives of patients, and with experts, to support the (...) view that the ontological state of permanently vegetative patients is unclear: such patients are neither straightforwardly alive nor simply dead. Having defended this view from counter-arguments we turn to the practical question as to how these patients ought to be treated. Some relatives and experts believe it is right for patients to be shifted from their currently unclear ontological state to that of being straightforwardly dead, but many are concerned or even horrified by the only legally sanctioned method guaranteed to achieve this, namely withdrawal of clinically assisted nutrition and hydration. A way of addressing this distress would be to allow active euthanasia for these patients. This is highly controversial; but we argue that standard objections to allowing active euthanasia for this particular class of permanently vegetative patients are weakened by these patients’ distinctive ontological status. (shrink)

" In 'Vagueness and Alternative Logic' (Realism and Reason, Cambridge 1983, pp. 271-86, especially 285-6), Hilary Putnam puts forward a suggestion for a formal treatment of the logic of vagueness. … Putnam admits that, at the time of writing, he had not thought this idea through. What will already be apparent to the alert reader is that, in order to disclose serious difficulties for the proposal, Putnam would not have had to think far.".

Although the theory of the assertoric syllogism was Aristotle's great invention, one which dominated logical theory for the succeeding two millenia, accounts of the syllogism evolved and changed over that time. Indeed, in the twentieth century, doctrines were attributed to Aristotle which lost sight of what Aristotle intended. One of these mistaken doctrines was the very form of the syllogism: that a syllogism consists of three propositions containing three terms arranged in four figures. Yet another was that a syllogism is (...) a conditional proposition deduced from a set of axioms. There is even unclarity about what the basis of syllogistic validity consists in. Returning to Aristotle's text, and reading it in the light of commentary from late antiquity and the middle ages, we find a coherent and precise theory which shows all these claims to be based on a misunderstanding and misreading. (shrink)