A common reaction to Hegel’s suggestion that we collapse Kant’s distinction between form and content is that, since such a move would also deprive us of any way of distinguishing the merely logical from the real possibility of our concepts, it is incoherent and ought to be rejected. It is true that these two distinctions are intimately related in Kant, such that if one goes, the other does as well. But it is less obvious that giving them up as Kant (...) conceives them is as incoherent a proposal as many of Hegel’s critics think. It has been the point of a recent account of Hegel’s idealism to demonstrate that his critique of Kant’s dichotomy between form and content or concept and intuition does not commit him to the view that human cognition is materially creative of its content in the manner of a God-like or intuitive intellect—does not, in other words, signify a return to a pre-Critical metaphysics. This is the interpretative stance I adopt here as well, in hope of giving defenders of Kant reasons for taking Hegel more seriously. (shrink)

Hegels Denken ist keineswegs von bloß historischem Interesse, sondern erweist sich stets von neuem als gegenwartsrelativ systematisch faszinierend. Dies gilt in besonderem Maße für jenes Werk, das für gründlichstes und systematisch anspruchsvollstes Denken unserer Tradition steht: die "Wissenschaft der Logik". Diese Logik ist keine weltlose, sondern schlechthin überall, wo wir auch leben und hinblicken, ist sie ausgebreitet wirklich und gegenständlich - in organischen Bildungen, Gefühlen, Meinungen, Institutionen, Kunstwerken, religiösen Formen, bis hin zu Konstrukten und Zahlen. Alles Natürliche und Geistige ist (...) eine realphilosophisch zu fassende Wirklichkeitsweise von Logischem. Dieser nachzuspüren wird in den Beiträgen dieses Bandes unternommen. Beiträge von Johannes Berchtold, Leo Dorner, Max Gottschlich, Friedrich Grimmlinger, Leo Hemetsberger, Thomas Sören Hoffmann, Heimo Hofmeister, Michael Höfler, Hans-Dieter Klein, Wilhelm Lütterfelds, Wolfgang Pesendorfer, Urs Richli, Josef Simon, Michael Wladika, Kurt Walter Zeidler. (shrink)

The history of contemporary modal logic dates back to the writings of C. S. Lewis in the early part of this century. Since then, a growing body of literature has attested to professional interest in the area, and in a number of related issues in philosophical logic which have received wide attention. The recent development of powerful formal techniques for modal system building, together with an increasing interest in modal logic as a tool for philosophical analysis, have (...) created a need for an up-to-date text to introduce students to this material. Snyder's book attempts to answer this need. Assuming an understanding of elementary propositional logic, Snyder introduces a reductive technique called cancellation for detecting the theorems of a system of logic. This technique, analogous to the construction of Smullyan trees but more compact, is extended to modal and quantified contexts. Cancellation versions of the systems M and Mn of G. H. von Wright, and S4 and S5 of Lewis are developed. Snyder uses a Hintikka type of semantics, showing how the various formal systems are differentiated at the semantic level by differing conditions which must be imposed on the model systems used as interpretations for them. These model systems, and the conditions imposed upon them, are in turn described by means of a metalanguage which is essentially first-order quantificational logic. The power of this technique stems from the fact that for every object language formula of a system, there is a corresponding formula in the metalanguage which describes the conditions an interpretation must meet in order to satisfy the original formula. The conditions that the interpretations of a given system of logic must meet are reflected in this metalanguage as "antecedent assumptions," and these in turn correspond to cancellation rules for the object language. This correspondence is constructed in such a way that the metalinguistic counterpart of each theorem of the system will be a theorem of first-order logic. Snyder's primary interest is in showing how modal logic can be used, with the help of these techniques, to build a large variety of formal systems and to "tailor" such systems to meet a variety of analytical tasks. Simple modal systems are developed for the articulation of a number of modal concepts, in addition to the classic alethic ones. Examples are taken from temporal, deontic, and epistemic logic to show how specific interpretations of the meanings of the relevant operators lead to the incorporation of appropriate conditions in the formal systems used to articulate them. An entire chapter is devoted to a discussion of the paradoxes of material and strict implication, and to an attempt to articulate the notion of entailment through the development of formal systems which include a dyadic modal operator that is free of these paradoxes. The final chapter discusses such classical issues as proper names, reference, fictional entities, definite descriptions, and existence presuppositions. Appendices deal with such matters as the equivalence of the cancellation systems to more classical axiomatic-deduction systems, and the sketch of a proof of soundness and completeness for all the modal systems presented. While designed as a text, this volume should be of interest to both logicians and those working in metaphysics and language analysis, since the primary concern of the author is to develop techniques that will facilitate the usefulness of modal logic as a tool for philosophical analysis. The instructor's manual contains many suggestions derived from the author's experience in teaching this non-standard treatment of the subject.--K. T. (shrink)

We reconstruct as much as we can the part of al-Fārābī's treatment of modal logic that is missing from the surviving pages of his Long Commentary on the Prior Analytics. We use as a basis the quotations from this work in Ibn Sīnā, Ibn Rushd and Maimonides, together with relevant material from al-Fārābī's other writings. We present a case that al-Fārābī's treatment of the dictum de omni had a decisive effect on the development and presentation of Ibn Sīnā's (...) modal logic. We give further evidence that the Harmonisation of the Opinions of Plato and Aristotle was not written by al-Fārābī. (shrink)

From the reviews: "A good textbook can improve a lecture course enormously, especially when the material of the lecture includes many technical details. Van Dalen's book, the success and popularity of which may be suspected from this steady interest in it, contains a thorough introduction to elementary classical logic in a relaxed way, suitable for mathematics students who just want to get to know logic. The presentation always points out the connections of logic to other parts (...) of mathematics. The reader immediately see the logic is "just another branch of mathematics" and not something more sacred." Acta Scientiarum Mathematicarum, Hungary. (shrink)

This article takes off from Johan van Benthem’s ruminations on the interface between logic and cognitive science in his position paper “Logic and reasoning: Do the facts matter?”. When trying to answer Van Benthem’s question whether logic can be fruitfully combined with psychological experiments, this article focuses on a specific domain of reasoning, namely higher-order social cognition, including attributions such as “Bob knows that Alice knows that he wrote a novel under pseudonym”. For intelligent interaction, it is (...) important that the participants recursively model the mental states of other agents. Otherwise, an international negotiation may fail, even when it has potential for a win-win solution, and in a time-critical rescue mission, a software agent may depend on a teammate’s action that never materializes. First a survey is presented of past and current research on higher-order social cognition, from the various viewpoints of logic, artificial intelligence, and psychology. Do people actually reason about each other’s knowledge in the way proscribed by epistemic logic? And if not, how can logic and cognitive science productively work together to construct more realistic models of human reasoning about other minds? The paper ends with a delineation of possible avenues for future research, aiming to provide a better understanding of higher-order social reasoning. The methodology is based on a combination of experimental research, logic, computational cognitive models, and agent-based evolutionary models. (shrink)

A comprehensive introduction to formal logic, Logic and Philosophy: A Modern Introduction is a rigorous yet accessible text, appropriate for students encountering the subject for the first time. Abundant, carefully crafted exercise sets accompanied by a clear, engaging exposition build to an exploration of sentential logic, first-order predicate logic, the theory of descriptions, identity, relations, set theory, modal logic, and Aristotelian logic. And as its title suggests, Logic and Philosophy is devoted not only (...) to logic but also to the philosophical debates that led to the development of the field. Much new material has been added for the 13th edition. An introduction to set theory and its relationship to logic and mathematics, including philosophical issues, is now part of Chapter 13. Chapter 15 is an introduction to modal logic and Kripke semantics, concluding with a discussion of philosophical problems with any logical accommodation of modalities. Instructors who do not wish to present proof methods will find chapters on truth trees for both sentential and first-order logic, and a presentation of trees for modal logic. Special features of this text include presentations of the history of logic, alternatives to traditional methods of conditional and indirect proof, and a discussion of semantic problems with universal and existential instantiations. Throughout, the authors are sensitive to philosophical issues that arise from the relationship between ordinary language, symbolic logic, and justifications for the syntax and semantics of the various symbolic languages. Discussions range from the justification of the truth table for the sentential rendering of if... then statements to semantic and syntactic paradoxes, including some troubling paradoxes that arise in ordinary language (e.g., the so-called hangman or surprise quiz paradox). Logic and Philosophy includes ample material for a one-semester or two-semester course and provides a thorough preparation for more advanced logic courses. (shrink)

Modal logic is one of philosophy’s many children. As a mature adult it has moved out of the parental home and is nowadays straying far from its parent. But the ties are still there: philosophy is important to modal logic, modal logic is important for philosophy. Or, at least, this is a thesis we try to defend in this chapter. Limitations of space have ruled out any attempt at writing a survey of all the work going on (...) in our field—a book would be needed for that. Instead, we have tried to select material that is of interest in its own right or exemplifies noteworthy features in interesting ways. Here are some themes that have guided us throughout the writing: • The back-and-forth between philosophy and modal logic. There has been a good deal of give-and-take in the past. Carnap tried to use his modal logic to throw light on old philosophical questions, thereby inspiring others to continue his work and still others to criticise it. He certainly provoked Quine, who in his turn provided—and continues to provide—a healthy challenge to modal logicians. And Kripke’s and David Lewis’s philosophies are connected, in interesting ways, with their modal logic. Analytic philosophy would have been a lot different without modal logic! • The interpretation problem. The problem of providing a certain modal logic with an intuitive interpretation should not be conflated with the problem of providing a formal system with a model-theoretic semantics. An intuitively appealing model-theoretic semantics may be an important step towards solving the interpretation problem, but only a step. One may compare this situation with that in probability theory, where definitions of concepts like ‘outcome space’ and ‘random variable’ are orthogonal to questions about “interpretations” of the concept of probability. • The value of formalisation. Modal logic sets standards of precision, which are a challenge to—and sometimes a model for—philosophy. Classical philosophical questions can be sharpened and seen from a new perspective when formulated in a framework of modal logic. On the other hand, representing old questions in a formal garb has its dangers, such as simplification and distortion. • Why modal logic rather than classical (first or higher order) logic? The idioms of modal logic—today there are many!—seem better to correspond to human ways of thinking than ordinary extensional logic. (Cf. Chomsky’s conjecture that the NP + VP pattern is wired into the human brain.) In his An Essay in Modal Logic (1951) von Wright distinguished between four kinds of modalities: alethic (modes of truth: necessity, possibility and impossibility), epistemic (modes of being known: known to be true, known to be false, undecided), deontic (modes of obligation: obligatory, permitted, forbidden) and existential (modes of existence: universality, existence, emptiness). The existential modalities are not usually counted as modalities, but the other three categories are exemplified in three sections into which this chapter is divided. Section 1 is devoted to alethic modal logic and reviews some main themes at the heart of philosophical modal logic. Sections 2 and 3 deal with topics in epistemic logic and deontic logic, respectively, and are meant to illustrate two different uses that modal logic or indeed any logic can have: it may be applied to already existing (non-logical) theory, or it can be used to develop new theory. (shrink)

Being a supporter of the “Logic of Smysl” approach (LS), the author is highlighting four its main aspects in assurance that they can increase the number of such supporters. First, it responds to the searches being carried out in European culture and to serious and multi­faceted criticism of academic philosophy. So, it has the potential to overcome this crisis on the path to discovering Smysl as a real “thing” (res), as well as to overcome the notori­ous and bored dichotomy (...) of analytical and hermeneutic approaches. Secondly, the philos­ophy proceeding from the LS starts from the very beginnings of thinking, from the meta­physical idea of ​​Wholeness-Smysl, comes to socio-political implications, thus following the Russian traditions of integral, whole knowledge. Thirdly, LS, preserving the problem of consciousness as a problem, fundamental and peculiar to modernity, can become a complex of new researches, leading cognitive science to the study of other ways of thinking of the world. Fourthly, the author sees in LS an ethical project: as a goal it is reviving and re-interpreting the well-known Russian philosophy ideal of all-humanity, taking into account the real otherness of the Other and using the material of philosophical Oriental studies – it is the ideal of friendship and brotherhood. (shrink)

This paper is concerned with counterfactual logic and its implications for the modal status of mathematical claims. It is most directly a response to an ambitious program by Yli-Vakkuri and Hawthorne, who seek to establish that mathematics is committed to its own necessity. I demonstrate that their assumptions collapse the counterfactual conditional into the material conditional. This collapse entails the success of counterfactual strengthening, which is controversial within counterfactual logic, and which has counterexamples within pure and applied (...) mathematics. I close by discussing the dispensability of counterfactual conditionals within the language of mathematics. (shrink)

This article takes off from Johan van Benthem’s ruminations on the interface between logic and cognitive science in his position paper “Logic and reasoning: Do the facts matter?”. When trying to answer Van Benthem’s question whether logic can be fruitfully combined with psychological experiments, this article focuses on a specific domain of reasoning, namely higher-order social cognition, including attributions such as “Bob knows that Alice knows that he wrote a novel under pseudonym”. For intelligent interaction, it is (...) important that the participants recursively model the mental states of other agents. Otherwise, an international negotiation may fail, even when it has potential for a win-win solution, and in a time-critical rescue mission, a software agent may depend on a teammate’s action that never materializes. First a survey is presented of past and current research on higher-order social cognition, from the various viewpoints of logic, artificial intelligence, and psychology. Do people actually reason about each other’s knowledge in the way proscribed by epistemic logic? And if not, how can logic and cognitive science productively work together to construct more realistic models of human reasoning about other minds? The paper ends with a delineation of possible avenues for future research, aiming to provide a better understanding of higher-order social reasoning. The methodology is based on a combination of experimental research, logic, computational cognitive models, and agent-based evolutionary models. Keywords Epistemic logic - Cognitive science - Intelligent interaction - Cognitive modeling. (shrink)

This unique compendium presents a comprehensive and self-contained theory of material development under imperfect information and its applications. The book describes new approaches to synthesis and selection of materials with desirable characteristics. Such approaches provide the ability of systematic and computationally effective analysis in order to predict composition, structure and related properties of new materials. The volume will be a useful advanced textbook for graduate students. It is also suitable for academicians and practitioners who wish to have fundamental models (...) in new material synthesis and selection. (shrink)

"Usually, we read news to form opinions and expand our knowledge. However, especially in the past years, more and more publications are moving apart from being objective. Therefore, we get biased knowledge. In this article, we aim to observe the way information is passed from a logical and rhetorical point of view in different publications. By this, we do not aim to evaluate the morality of the publications or journalists in questions, our aim is purely theoretical (i.e. logical and rhetorical). (...) In order to be able to provide such an analysis, we picked different pieces of news with the same topic from various publications. The chosen topic is irrelevant to the theoretical content, therefore we do not aim to focus on its political or social implications. The decision was made in order to have sufficient material to provide a proper theoretical analysis. It should also be added that any evaluative terms that are going to be used in this article (e.g. ‘biased’, ‘subjective’, ‘not objective’, ‘one-sided’, etc.) are strictly directed to a theoretical perspective, not a moral, social or political one. As already mentioned, our aim is as theoretical as possible: we are interested in the logical and rhetorical structure of a piece of information. Keywords: logical fallacies, manipulation, rhetoric, arguments. ". (shrink)

The main purpose of the paper is to outline the formal-logical, general theory of language treated as a particular ontological being. The theory itself is called the ontology of language, because it is motivated by the fact that the language plays a special role: it reflects ontology and ontology reflects the world. Language expressions are considered to have a dual ontological status. They are understood as either concretes, that is tokens – material, physical objects, or types – classes of (...) tokens, which are abstract objects. Such a duality is taken into account in the presented logical theory of syntax, semantics and pragmatics. We point to the possibility of building it on two different levels; one which stems from concretes, language tokens of expressions, whereas the other one – from their classes, types conceived as abstract, ideal beings. The aim of this work is not only to outline this theory as taking into account the functional approach to language, with respect to the dual ontological nature of its expressions, but also to show that the logic based on it is ontologically neutral in the sense that it abstracts from accepting some existential assumptions, related with the ontological nature of these linguistic expressions and their extra-linguistic ontological counterparts (objects). (shrink)

This revision of an important and lucid account of the various systems of axiomatic set theory preserves the basic format and essential ingredients of its highly regarded original. Quine's innovative exploitation of the virtual theory of classes in order to develop a considerable portion of set theory without ontological commitment to the existence of classes remains unchanged. So, too, does the list of topics treated--the theory of sets up to transfinite ordinal and cardinal numbers, the axiom of choice and its (...) equivalents, and a beautiful comparison of the various major formulations of set theory. There have, however, been a number of important changes, generally in the interest of greater elegance and clarity. One of the most notable of these is in the treatment of ordinal numbers. In the fourth section of that chapter an axiom schema is added to the effect that if α is a function and x an ordinal number, then there exists a class identical with the image of x under α. Although Quine, in general prefers to limit his existence assumptions as severely as possible, this added item possesses two attractive and closely related advantages: it yields the existence of all classes up to the size of any ordinal, and it greatly simplifies the subsequent treatment of ordinals and of transfinite recursion. The treatment of this latter subject, incidentally, has also been extensively modified to square with some difficulties first pointed out by Charles Parsons in The Journal of Symbolic Logic in 1964. Another important change consists in a considerable reworking of the section on infinite cardinals. The result is a more simplified and natural treatment. Finally, some new material on the theory of types and consequences of the axiom schema of comprehension has been added. Particularly with regard to the theory of types, this new material--due largely to the work of David Kaplan--has enabled Quine to drop, at one point, the assumption that there exists an object of lowest type. Altogether, this is a generally improved version of an originally masterful and brilliant work.--H. P. K. (shrink)

The main goal of this paper is to outline a general formal-logical theory of language construed as a particular ontological being. The theory itself will be referred to as an ontology of language, because it is motivated by the fact that language plays a special role: it reflects ontology, and ontology reflects the world. Linguistic expressions will be regarded as having a dual ontological status: they are to be understood as either concreta – i.e. tokens, in the sense of (...) class='Hi'>material, physical objects – or types, in the sense of classes of tokens – i.e. abstract objects. Such a duality will then be taken into account in the logical theory of syntax, semantics and pragmatics presented here. We point to the possibility of constructing the latter on two different levels, one stemming from concreta, construed as linguistic tokens of expressions, the other from their classes – namely types, conceived as abstract, ideal beings. The aim of this work is not only to outline such a theory with respect to the dual ontological nature of the expressions of language in terms that take into account a functional approach to language itself, but also to show that the logic based on it is ontologically neutral in the sense that it is abstracted from the level at which certain existential assumptions relating to the ontological nature of these linguistic expressions and their extra-linguistic ontological counterparts (objects) would have to be embraced. (shrink)

Two connectives are of special interest in metalogical investigations — the connective of implication which is important due to its connections to the notion of inference, and the connective of equivalence. The latter connective expresses, in the material sense, the fact that two sentences have the same logical value while in the strict sense it expresses the fact that two sentences are interderivable on the basis of a given logic. The process of identification of equivalent sentences relative to (...) theories of a logic C defines a class of abstract algebras. The members of the class are called Lindenbaum-Tarski algebras of the logic C. One may abstract from the origin of these algebras and examine them by means of purely algebraic methods. (shrink)

In recent years, I have published a number of papers addressing various aspect of inferentialism. These papers, I believe, do provide for a relatively multifaceted picture of (my version of) this enterprise; though still a picture that is in some respects patchy. This has made me start working on this book – it should bring my ideas of various aspects and dimensions of inferentialism to a desirable synthesis. Building the individual chapters, I usually start from taking parts of my published (...) papers as basic building blocks, putting them togethether and then trying to make them fit together with each other, and with the rest of the book, seamlessly. As a result, material from the older papers gets upgraded so that the chapters no longer contain many pieces of the papers in their original form. As inferentialism is a new and unsettled matter, I am not only putting forward some new ideas, but in some cases I also have to put together new frameworks to enable me to articulate these ideas intelligibly in the first place. I think that doing this with a reasonable outcome is not possible without some feadback. I do get some from my colleagues, but I will be grateful to anybody who would like to comment on anything presented here. (shrink)

The anti-metaphysical attitude of the neo-positivist movement is notorious. It is an essential mark of what its members regarded as the scientific world view. The paper focuses on a metaphysical variation of the scientific world view as proposed by Heinrich Scholz and his Münster group, who can be regarded as a peripheral part of the movement. They used formal ontology for legitimizing the use of logical calculi. Scholz's relation to the neo-positivist movement and his contributions to logic and foundations (...) are discussed. His heuristic background can be drawn from a set of six methodological ‘articles of faith’, formulated in 1942 and published here for the first time. I would like to thank Gudrun Mikus (Paderborn) for her assistance in collecting the material, Neil Tennant (Ohio State University, Columbus) for his efforts to improve the paper not only in lingual aspects, and Christian Thiel (Erlangen) and two anonymous referees for their helpful comments. CiteULike Connotea Del.icio.us What's this? (shrink)

In this paper, we explore the architecture of downward causation on the basis of three central cases. We set out by answering the question of how top-down causation is possible in the universe. The universe is not causally closed, because of irreducible randomness at the quantum level. What is more, contextual effects can already be observed at the level of quantum physics, where higher levels can modify the nature of lower-level elements by changing their context, or even creating them. As (...) one moves up through higher levels, contextual effects on lower levels occur on various scales within nature, which is crucial in biology in general and the brain in particular. We then argue that there are important logical downward causes.objects have causal effects on material-energetic systems. It can be shown that abstract objects have measurable effects on lower levels, which needs to be accounted for by successful explanations of real phenomena such as intentional action. Intentional action has the form of deductive causation from logical structures to human agency. Without this assumption, we would not be warranted in believing that our physical theories latch onto a universe that is essentially the way we discover it to be. Denying top-down causation on account of the idea that the universe permits only bottom-up constitution of wholes from lower-level elements leads to undermining the very possibility of knowledge and science. Thus, it can be rejected as a global form of explanation. We sketch a model for mind-body interaction according to which the various levels of a human organism together enable the emergence of mental top-down effects. They are necessary conditions for the emergence of human mindedness. Once it is clear that downward causation is a widespread natural phenomenon, the apparent mystery of mental causation is, in principle, solved. (shrink)

This paper puts Jane Bennett’s vital materialism into dialogue with Luce Irigaray’s ontology of sexuate difference. Together these thinkers challenge the image of dead or intrinsically inanimate matter that is bound up with both the instrumentalization of the earth and the disavowal of sexual difference and the maternal. In its place they seek to affirm a vital, generative materiality: an ‘active matter’ whose differential becomings no longer oppose activity to passivity, subject to object, or one body, self or entity to (...) its ‘other’. For both thinkers, displacing the hylomorphic conceptual structures that have tended to dominate western metaphysical thought is inseparable from critiquing the model of the individual subject as bounded, autonomous and self-identical. Such individualism is countered by the relational ontologies figured in Bennett’s ‘distributed agencies’ and Irigaray’s ‘placental economy’, and by a shared attentiveness to the capacities of the human body to bear others within. Nonetheless, this paper argues that each thinker renders this ‘other within’ in very different ways. On the one hand, Bennett’s approach complements and expands Irigaray’s notion of the elemental by affording a greater attentiveness to inorganic and non-sexuate matters. On the other, Irigaray’s conception of generative relationality and the ontological priority of the in-between allows us to think such material entanglements in ways that more fully displace the twinned logics of individualism and instrumentalization. Her project thereby affirms the relational and irreducible differences on which the ‘vitality’ of a vital materiality depends. If there is no more “earth” to press down/repress, to work, to represent, but also and always to desire, no opaque matter which in theory does not know herself, then what pedestal remains for the ex-sistence of the “subject”? If the earth turned and more especially turned upon herself, the erection of the subject might thereby be disconcerted and risk losing its elevation and penetration. For what would there be to rise up from and exercise his power over? And in? Irigaray, Speculum of the Other Woman Jane Bennett has recently argued that “the image of dead or thoroughly instrumentalized matter feeds human hubris and our earth-destroying fantasies of conquest and consumption”, continuing that: “The figure of an intrinsically inanimate matter may be one of the impediments to the emergence of more ecological and more materially sustainable modes of production and consumption”.11J. Bennett, Vibrant Matter: A Political Ecology of Things, Durham and London: Duke University Press, 2010, ix. Henceforth VM. View all notes This insight is prefigured and re-affirmed by the work of Irigaray. Her sustained analysis of western thought and culture shows how its constitutive disavowal of sexual difference and the maternal is inextricably bound up with an equally deep-rooted disavowal of matter and corporeality. As the above passage from Speculum suggests,22L. Irigaray, Speculum of the Other Woman, trans. G. Gill, Ithaca: Cornell University Press, 1985, 133. Henceforth S. View all notes Irigaray seeks to expose woman's reduction to an object for a subject and a maternal-material resource for man's speculations; but in disentangling woman from her symbolic identification with the earth, she also seeks to release the earth from its identification with a passive and manipulable matter. Her work thus bears directly on the revaluation required to transform human beings' relations to materiality: both their own, and that of the earth they inhabit. At the centre of this revaluation is Irigaray's work to displace the image of dead or intrinsically inanimate matter that Bennett also critiques, and to affirm instead a sexuate materiality that is both living and generative. Her consistent troubling of hylomorphism is as unsettling for the subject as her question: “But what if the ‘object’ started to speak?” This question is echoed in Bennett's concern with “the moment when the object becomes the Other, when the sardine can looks back, when the mute idol speaks”.33 VM, 2, citing W.J.T. Mitchell, What Do Pictures Want?, Chicago, Chicago University Press, 2005, 157. View all notes As this passage indicates, Bennett's own project is more concerned with the agency of non-human materialities – including their role in the constitution of the human – than with specifically sexed bodies or a materiality inflected by sexual difference. It is these crucial differences in emphasis, I will suggest, that allow the work of these two thinkers to be brought together in productive dialogue. On the one hand, Bennett's approach affords a greater attentiveness to inorganic and non-sexuate matter; on the other, Irigaray's twinned ontology of sexual difference and maternal relation is better able to affirm the relational differences on which the “vitality” of a vital materiality depends. The paper begins by outlining several key elements of Irigaray's philosophy of sexual difference to show how it leads necessarily to a rethinking of matter. This rethinking is especially helpful for shifting away from the hylomorphism that has been a dominant strand in western thought, informing an understanding of the earth as a fundamentally inert and ever-ready resource. As I will show, the figures through which Irigaray re-articulates female specificity also allow her to refigure the earth as active matter that “turns upon herself ” in generative flux. In the second section, I will situate Irigaray's re-thinking of matter in relation to Bennett's “vital materiality”.44Bennett can be aligned with a number of thinkers who have come to be grouped under the heading “new materialisms”. See S. Alaimo and S. Hekman, eds., Material Feminisms, Bloomington & Indianapolis: Indiana University Press, 2008; D. Coole and S. Frost, eds., New Materialisms: Ontology, Agency, and Politics, Durham and London: Duke University Press, 2010. View all notes An advantage of this concept is that it refuses the separation between humans and matter still implicit in concepts such as “the environment”. By attending to “our own constitution as vital materiality”, as well as the ways our “own” bodies are never “fully or exclusively human”, Bennett adjusts the status of human actants while re-evaluating non-human bodies “as actants rather than as objects”. As I will show, her approach provides a constructive critical perspective on Irigaray's work by drawing attention to the specifically non-sexuate nature of the elemental. Equally, however, Irigaray's insistence on sexuate difference problematises any appeal to a generic notion of “the human”. This is especially helpful, I will suggest, in relation to contemporary descriptions of climate change as “anthropogenic”. By homogenising human beings, such descriptions make it more difficult to address the ways in which current ecological problems are inseparable from global patterns of social, political and economic inequity. For both thinkers, challenging hylomorphism needs to be matched with a critique of the dominant modern model of the subject as bounded, autonomous and self-identical. And for both, this model is displaced and undone by the capacity of the human body to bear others within, in ways that engender and sustain human life. Yet as I will discuss in the final two sections, each thinker renders this “other within” in very different ways, with significant implications for the ethics and politics of a “vital materiality”. In the end it is Irigaray's rendering of a distinctively female capacity to bear an other within, explored via the generative relationality of a placental economy, that more fully escapes the individualism of the One and the Same. Together, Irigaray and Bennett show that to take seriously the ecological crises that currently confront us means overcoming the disavowal of both human beings' own fundamental materiality and our dependency on the sustaining materialities of the earth. In contrast, a dominant strand in contemporary responses to these crises is an environmental politics of “enlightened self-interest”55I borrow this phrase from H. Kopnina's critical discussion in “Forsaking Nature? Contesting ‘Biodiversity’ Through Competing Discourses of Sustainability”, Journal of Education for Sustainable Development 7, no. 1 : 51–63. that precludes any serious re-evaluation of human beings' relations to matter and the earth. If human beings can be persuaded that current levels of environmental degradation are damaging to them, threatening perhaps their very survival, they are more likely to take decisive steps to alter their behaviour. Insofar as such approaches demand action only for the sake of human interests and ends, they are both anthropocentric and spring from the same instrumentalising rationality that has engendered the ecological crises we currently face. They may well be successful in prompting action. But by foregrounding the survival of “the human species” per se, such approaches foreclose discussion of whose interests are served if survival is all that is allowed to be at stake, and whose lives are thereby consigned to ongoing exploitation. Moreover, as I will argue below, the instrumental rationality that serves survival is at odds with an affirmation of life, as a becoming that depends on difference. With this in mind, I will problematise Bennett's proposed politics of “expanded self-interest”, while seeking to retain many of the insights her approach brings. To more fully displace the “rational” self-interest that has encouraged human exploitation of the earth, we might take up Bennett's “vital materiality” in ways informed by Irigaray's conception of generative difference and the relational space-time of the in-between. (shrink)

While there are numerous differences between the approaches taken by Maurice Merleau-Ponty and James J. Gibson, the basic motivation of the two thinkers, as well as the internal logic of their respective views, is extraordinarily close. Both were guided throughout their lives by an attempt to overcome the dualism of subject and object, and both devoted considerable attention to their "Gestaltist" predecessors. There can be no doubt but that it is largely because of this common cause that the subsequent (...) development of their ideas is so similar. It is not my objective in what follows merely to demonstrate a similarity between two lines of thought. Instead, I will try to show that each approach gains considerably from attention to the other. There are numerous ways to begin such a project, each about as arbitrary as the next. For present purposes, I shall take as of central importance the question of the character of the perceived world, both in relation to the traditionally opposed mental and material "substances", and in relation to its identification and individuation of things vis a vis one another and vis a vis ourselves. This will implicate especially Gibson's "affordances" and Merleau-Ponty's thesis concerning the "materiality of meaning.". (shrink)

This volume began as a remembrance of Alonzo Church while he was still with us and is now finally complete. It contains papers by many well-known scholars, most of whom have been directly influenced by Church's own work. Often the emphasis is on foundational issues in logic, mathematics, computation, and philosophy - as was the case with Church's contributions, now universally recognized as having been of profound fundamental significance in those areas. The volume will be of interest to logicians, (...) computer scientists, philosophers, and linguists. The contributions concern classical first-order logic, higher-order logic, non-classical theories of implication, set theories with universal sets, the logical and semantical paradoxes, the lambda-calculus, especially as it is used in computation, philosophical issues about meaning and ontology in the abstract sciences and in natural language, and much else. The material will be accessible to specialists in these areas and to advanced graduate students in the respective fields. (shrink)

We are used to the idea that computers operate on numbers, yet another kind of data is equally important: the syntax of formal languages, with variables, binding, and alpha-equivalence. The original application of nominal techniques, and the one with greatest prominence in this paper, is to reasoning on formal syntax with variables and binding. Variables can be modelled in many ways: for instance as numbers (since we usually take countably many of them); as links (since they may `point' to a (...) binding site in the term, where they are bound); or as functions (since they often, though not always, represent `an unknown'). None of these models is perfect. In every case for the models above, problems arise when trying to use them as a basis for a fully formal mechanical treatment of formal language. The problems are practical—but their underlying cause may be mathematical. The issue is not whether formal syntax exists, since clearly it does, so much as what kind of mathematical structure it is. To illustrate this point by a parody, logical derivations can be modelled using a Gödel encoding (i.e., injected into the natural numbers). It would be false to conclude from this that proof-theory is a branch of number theory and can be understood in terms of, say, Peano's axioms. Similarly, as it turns out, it is false to conclude from the fact that variables can be encoded e.g., as numbers, that the theory of syntax-with-binding can be understood in terms of the theory of syntax-without-binding, plus the theory of numbers (or, taking this to a logical extreme, purely in terms of the theory of numbers). It cannot; something else is going on. What that something else is, has not yet been fully understood. In nominal techniques, variables are an instance of names, and names are data. We model names using urelemente with properties that, pleasingly enough, turn out to have been investigated by Fraenkel and Mostowski in the first half of the 20th century for a completely different purpose than modelling formal language. What makes this model really interesting is that it gives names distinctive properties which can be related to useful logic and programming principles for formal syntax. Since the initial publications, advances in the mathematics and presentation have been introduced piecemeal in the literature. This paper provides in a single accessible document an updated development of the foundations of nominal techniques. This gives the reader easy access to updated results and new proofs which they would otherwise have to search across two or more papers to find, and full proofs that in other publications may have been elided. We also include some new material not appearing elsewhere. (shrink)

The article covers such issues as the relevance of the theory of perception as a multi-level information processing, the methodological role of the concept of representation and the relation of neurodynamic structures to subjective experience. The author critically reviews the philosophical presumptions underlying the various concepts of “local rationality,” the core of which is constituted by the belief that large ethnic cultures generate or are based on their own rationality and their own logic. Three statements are successively considered: thinking (...) is based on the inherent rules of rationality, logic is an extract of rationality, and types of rationality are geographically consistent with large ethnocultural communities. Empirical arguments are presented that demonstrate equivocality of the first two theses. In particular, firstly, it is shown that the genuine rationality of thinking lies not in following the rules that are immanent to it, but in the development of thinking and, more broadly, cognitive operations towards optimization of certain indicators of the cognitive or motor system that are important for survival and adaptation. In addition, this rationality is multivariate, and the choice between variants is often weakly determined or even random. Thus, the first statement turns out to be refuted. Secondly, by reference to the well-known experiments, it is shown that most people do not explicitly follow some declared logical rules in solving even logical or mathematical problems, and yet there is reason to consider their behavior rational. The third thesis, as shown with some limited empirical material, appears to be partially confirmed. Nevertheless, the demonstration of the doubtfulness of the first two theses makes the conclusion that different nations have different logics insufficiently substantiated. (shrink)

In this paper we provide a mathematical model of Kant’s temporal continuum that yields formal correlates for Kant’s informal treatment of this concept in theCritique of Pure Reasonand in other works of his critical period. We show that the formal model satisfies Kant’s synthetic a priori principles for time and that it even illuminates what “faculties and functions” must be in place, as “conditions for the possibility of experience”, for time to satisfy such principles. We then present a mathematically precise (...) account of Kant’s transcendental theory of time—the most precise account to date.Moreover, we show that the Kantian continuum which we obtain has some affinities with the Brouwerian continuum but that it also has “infinitesimal intervals” consisting of nilpotent infinitesimals; these allow us to capture Kant’s theory of rest and motion in theMetaphysical Foundations of Natural Science.While our focus is on Kant’s theory of time the material in this paper is more generally relevant for the problem of developing a rigorous theory of the phenomenological continuum, in the tradition of Whitehead, Russell, and Weyl among others. (shrink)

The first beginning logic text to employ the tree method--a complete formal system of first-order logic that is remarkably easy to understand and use--this text allows students to take control of the nuts and bolts of formal logic quickly, and to move on to more complex and abstract problems. The tree method is elaborated in manageable steps over five chapters, in each of which its adequacy is reviewed; soundness and completeness proofs are extended at each step, and (...) the decidability proof is extended at the step from truth functions to the logic of nonoverlapping quantifiers with a single variable, after which undecidability is demonstrated by example. The first three chapters are bilingual, with arguments presented twice, in logical notation and in English. The last three chapters consider the discoveries defining the scope and limits of formal methods that marked logic’s coming of age in the 20th century: Godel’s completeness and incompleteness theorems for first and second-order logic, and the Church-Turing theorem on the undecidability of first-order logic. This new edition provides additional problems, solutions to selected problems, and two new Supplements: Truth-Functional Equivalence reinstates material on that topic from the second edition that was omitted in the third, and Variant Methods, in which John Burgess provides a proof regarding the possibility of modifying the tree method so that it will always find a finite model when there is one, and another, which shows that a different modification—once contemplated by Jeffrey--can result in a dramatic speed--up of certain proofs. (shrink)

This work is an introduction to logic, covering what is most commonly taught in the first term of a two-term sequence in logic at four-year colleges and universities. It is designed for use by community college students who plan to transfer credits to four-year institutions. The material covered seeks to maintain logic's place in philosophical thought systems, and avoids political examples in order to appeal to reason and study rather than ill-conceived jokes that often offend students' (...) varying policitcal beliefs. This work concludes with studies in proof constructions and rules and provides explanations of various grading decisions commonly made in logic courses, a unique feature helpful to students and teachers alike. (shrink)

Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set (...) theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science. (shrink)

This inquiry is addressed to two questions: (1) what if any logical relations might exist between the concepts of desire and action (as they and the distinctions to which they commit us are ensconced in ordinary parlance), and (2) what if any causal or significant non-causal (i.e., material) relations might ever exist between instances of desire and action? -/- It is held that any credible move to deal with such questions must initially, and at some length, specify the employment (...) conditions for the terms 'want' and 'desire'. This is accomplished in the first two chapters wherein a set of premises is generated for the argument of the inquiry which is presented in full and concluded in the third and final chapter. Premises generated devolve from treatment of the following major topics: (a) the grammar of 'want' and 'desire', (b) the ontological status of wants, (c) first-person and third-person want ascriptions, (d) the sorts of things which may be desired (desiderabilia), (e) wants and lacks, (f) wants and wishes, (g) the 'conflicts' of desires and reason and desire, (h) four major candidates for logical relations between wants and acts, (i) the issue of causation, and (j) the placement of Desire in an adequate ontology of persons. -/- It is argued that every major candidate for a logical relation between wants and acts (or our warrant for believing that such a connection exists) breaks down upon analysis; that little warrant exists for construing wants as causes of acts; that wants and acts are related in significant non-logical and non-causal (i.e., material) respects; and that any fully adequate theory of human action must undertake ontology, placing the category of Desire squarely in the foreground. This project represents neither a general theory of desire nor a general theory of human action. It is rather conceived as a propaedeutic to any such inquiry. It is essentially revisionist in intent, setting out on the one hand to challenge existing claims about wants and acts and, on the other hand, proposing a more satisfactory approach to the issue. In no sense is it suggested that recent Anglo-American contributions are without merit. It is rather argued that they are often inadequate contributions vis-a-vis the larger requirements for an adequate theory of human action. (shrink)

A collection of material on Husserl's Logical Investigations, and specifically on Husserl's formal theory of parts, wholes and dependence and its influence in ontology, logic and psychology. Includes translations of classic works by Adolf Reinach and Eugenie Ginsberg, as well as original contributions by Wolfgang Künne, Kevin Mulligan, Gilbert Null, Barry Smith, Peter M. Simons, Roger A. Simons and Dallas Willard. Documents work on Husserl's ontology arising out of early meetings of the Seminar for Austro-German Philosophy.

This book treats ancient logic: the logic that originated in Greece by Aristotle and the Stoics, mainly in the hundred year period beginning about 350 BCE. Ancient logic was never completely ignored by modern logic from its Boolean origin in the middle 1800s: it was prominent in Boole’s writings and it was mentioned by Frege and by Hilbert. Nevertheless, the first century of mathematical logic did not take it seriously enough to study the ancient (...) class='Hi'>logic texts. A renaissance in ancient logic studies occurred in the early 1950s with the publication of the landmark Aristotle’s Syllogistic by Jan Łukasiewicz, Oxford UP 1951, 2nd ed. 1957. Despite its title, it treats the logic of the Stoics as well as that of Aristotle. Łukasiewicz was a distinguished mathematical logician. He had created many-valued logic and the parenthesis-free prefix notation known as Polish notation. He co-authored with Alfred Tarski’s an important paper on metatheory of propositional logic and he was one of Tarski’s the three main teachers at the University of Warsaw. Łukasiewicz’s stature was just short of that of the giants: Aristotle, Boole, Frege, Tarski and Gödel. No mathematical logician of his caliber had ever before quoted the actual teachings of ancient logicians. -/- Not only did Łukasiewicz inject fresh hypotheses, new concepts, and imaginative modern perspectives into the field, his enormous prestige and that of the Warsaw School of Logic reflected on the whole field of ancient logic studies. Suddenly, this previously somewhat dormant and obscure field became active and gained in respectability and importance in the eyes of logicians, mathematicians, linguists, analytic philosophers, and historians. Next to Aristotle himself and perhaps the Stoic logician Chrysippus, Łukasiewicz is the most prominent figure in ancient logic studies. A huge literature traces its origins to Łukasiewicz. -/- This Ancient Logic and Its Modern Interpretations, is based on the 1973 Buffalo Symposium on Modernist Interpretations of Ancient Logic, the first conference devoted entirely to critical assessment of the state of ancient logic studies. (shrink)

The aim of this paper is to clarify the truth-functional interpretation of the logical connective of the material implication. The importance of such clarification lies in the fact that it allows avoiding the supposed paradoxes introduced by C. I. Lewis (1918). I argue that an adequate understanding of the history and purposes of logic is enough to dissolve them away. The defense is based on an exposition of propositional compositionalism. To compare, I also present Stalnaker’s (1968) alternative that (...) seeks to explain the implicit concept of conditionality of conditionals assertions. In order to reinforce my aim I expound the twelve different meanings of ‘implication’ stated by Corcoran (1993) in order to hold that a proper understanding of these meanings allows us to avoid ambiguities and confusions. Finally, I expect to show that despite the possible alternatives, compositionalism is still the best explanation for the truth-functionality account of logical connectives. (shrink)

The Joint International Conference on Logic Programming, sponsored by the Association for Logic Programming, is a major forum for presentations of research, applications, and implementations in this important area of computer science. Logic programming is one of the most promising steps toward declarative programming and forms the theoretical basis of the programming language Prolog and its various extensions. Logic programming is also fundamental to work in artificial intelligence, where it has been used for nonmonotonic and commonsense (...) reasoning, expert systems implementation, deductive databases, and applications such as computer-aided manufacturing. Krzysztof R. Apt is project leader at the Centre for Mathematics and Computer Science in Amsterdam and part-time Professor in Computer Science at the University of Amsterdam. Topics covered: Theory Foundations. Programming Languages. Implementation. Programming Methodologies and Tools. Applications. Deductive Databases. Artificial Intelligence. Parallelism. (shrink)

Samson Abramsky’s wide-ranging contributions to logical and structural aspects of Computer Science have had a major influence on the field. This book is a rich collection of papers, inspired by and extending Abramsky’s work. It contains both survey material and new results, organised around six major themes: domains and duality, game semantics, contextuality and quantum computation, comonads and descriptive complexity, categorical and logical semantics, and probabilistic computation. These relate to different stages and aspects of Abramsky’s work, reflecting its exceptionally (...) broad scope and his ability to illuminate and unify diverse topics. Chapters in the volume include a review of his entire body of work, spanning from philosophical aspects to logic, programming language theory, quantum theory, economics and psychology, and relating it to a theory of unification of sciences using dual adjunctions. The section on game semantics shows how Abramsky’s work has led to a powerful new paradigm for the semantics of computation. The work on contextuality and categorical quantum mechanics has been highly influential, and provides the foundation for increasingly widely used methods in quantum computing. The work on comonads and descriptive complexity is building bridges between currently disjoint research areas in computer science, relating Structure to Power. The volume also includes a scientific autobiography, and an overview of the contributions. The outstanding set of contributors to this volume, including both senior and early career academics, serve as testament to Samson Abramsky’s enduring influence. It will provide an invaluable and unique resource for both students and established researchers. (shrink)

Although logic’s thinking of thinking overcomes the difference between subject and object of knowing, subjectivity and objectivity have distinct logical determinations presupposed by objectivity in nature and subjectivity in rational agency. An analysis of Hegel’s account of subjectivity and objectivity in his Logic of the Concept shows how both can be differentiated without relying upon any contents of nature and spirit. This logical distinction of subjectivity and objectivity is then employed to clarify how objectivity in nature can be (...) irreducible to objectivity in logic, independently of any empirical material, an insight bearing upon the whole relation between logic and reality and its formulation by Burbidge, Maker, and Halper. (shrink)

This is the first book-length treatment of hybrid logic and its proof-theory. Hybrid logic is an extension of ordinary modal logic which allows explicit reference to individual points in a model. This is useful for many applications, for example when reasoning about time one often wants to formulate a series of statements about what happens at specific times. There is little consensus about proof-theory for ordinary modal logic. Many modal-logical proof systems lack important properties and the (...) relationships between proof systems for different modal logics are often unclear. In the present book we demonstrate that hybrid-logical proof-theory remedies these deficiencies by giving a spectrum of well-behaved proof systems for a spectrum of different hybrid logics. (shrink)

This article presents a detailed, novel account of the emergence of (the meaning of) empirical concepts. Acquiring experience and empirical concepts is shown to be the result of multifaceted, cognitive processes, which require both material realization and conceptual interpretation. Generally speaking, the meaning of empirical concepts consists of several distinct components, but it includes at least a structuring and an abstracting component. These two meaning components are abstract entities, which can be justifiably interpreted as real objects. On this basis, (...) I address the subject of emergence. The primary claim is that the abstracting meaning component (but not the structuring one) emerges from its underlying empirical processes: it both depends on and transcends these processes. This claim is expounded by discussing relevant similarities and dissimilarities between the emergence of abstract meanings and a range of central features of emergence prominent in recent debates on this topic. The conception of empirical concepts with emergent abstracting meaning components involves an interpretation that avoids the problematic extremes of both empiricism and Platonism. (shrink)

Dynamic Epistemic Logic This article tells the story of the rise of dynamic epistemic logic, which began with epistemic logic, the logic of knowledge, in the 1960s. Then, in the late 1980s, came dynamic epistemic logic, the logic of change of knowledge. Much of it was motivated by puzzles and paradoxes. The number … Continue reading Dynamic Epistemic Logic →.

This paperback is a programed text designed for teaching introductory logic, either in conjunction with a standard text based upon traditional logic or as a do-it-yourself supplement for students taking courses stressing symbolic logic. The student learns logical theory by answering a variety of short answer, objective type exercises. The correct answer is given directly below each question or exercise, and the student is required to cover the answer while working the exercise; the purpose of this immediate (...) access to the answer is to enable the student to determine quickly whether or not he comprehends the material. The content of the book concentrates primarily upon categorical statements, presenting both the existential and hypothetical interpretations of the square of opposition, but unfortunately continues to promulgate the historically inaccurate terminology of "Aristotelian" and "Boolean." [Categorical statements were first expressed as existential statements by Franz Brentano in 1874.] Categorical statements not in standard form are standardized, e.g., "No roaches feel despair" is standardized by being rewritten as "No roaches are entities who feel despair." In addition to considering the logical relations of opposition with respect to A, E, I, O statements, these same relations are extended to non-categorical statements, e.g., "George Washington did not die in Europe" and "George Washington did not die in Asia" are subcontraries, while "There is philosophical activity on Venus" and "There is philosophical activity in the universe" are alterns. Determining validity of syllogisms is based upon the distribution of terms, and also by the use of Venn diagrams. The traditional figures and moods of the syllogism are ignored, as is the distinction between major and minor terms, with these latter two being lumped together as end terms. Immediate inferences and non-syllogistic arguments are treated by Venn diagrams. One-, two-, three- and four-term Venn diagrams are utilized throughout a substantial part of the book.--T. G. N. (shrink)

An Essay on Metaphysics is one of the finest works of the great Oxford philosopher R. G. Collingwood : in it he considers the nature of philosophy, especially of metaphysics, and puts forward his original and influential theories of absolute presuppositions, causation, and the logic of question and answer. Three fascinating unpublished pieces by Collingwood have been added for this revised edition: they illuminate and amplify the ideas of the Essay, to which they are closely related. The editor Rex (...) Martin contributes a substantial introduction telling the story of the composition of all these works, discussing their major themes, and setting them in the context of Collingwood's philosophy as a whole. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Deleuze, Bergson, Merleau-Ponty: The Logics and Pragmatics of Creation, Affective Life, and Perception by Dorothea E. OlkowskiElodie BoublilOLKOWSKI, Dorothea E. Deleuze, Bergson, Merleau-Ponty: The Logics and Pragmatics of Creation, Affective Life, and Perception. Bloomington: Indiana University Press, 2021. 180 pp. Cloth, $63.00; paper, $28.00[End Page 152]Dorothea E. Olkowski's latest book carefully examines "the relationship between the creation of ideas and their actualization in relation to semiology, logic (...) and the cosmos in the philosophies of Deleuze, Bergson, and Merleau-Ponty." However, this work is neither an extensive or historical account of Deleuze's, Bergson's, and Merleau-Ponty's philosophies, nor an attempt to homogenize their views on space, time, or perception. Instead, it subtly compares their differences and similarities to move beyond metaphysical dualism, and fruitfully rethinks the relations between formal logic and ontology. Indeed, the author aims to draw a "theory of form," based on the logic of sensation, ultimately designed "to take the place of a theory of the real, of material physical forces."Chapter 1 retraces the history of postmodernist claims and their philosophical legacy. Olkowski explains that postmodernism is not first and foremost a political worldview or a debunking of objectivity in natural sciences. Instead, "it begins as a formal system or series of formal systems." Olkowski explores how Deleuze draws on the knowledge of modern science and logic (Bolzano, Cavaillès) and on Bergson's critical analysis of it to elaborate his logic of sensation. Bergson's conception of affectivity impacted Deleuze's and Merleau-Ponty's theories of corporeality and sensation, and their understanding of perception. Bergson's concept of "body image" specifically influenced Deleuze's elaboration of the concept of "movement-image," through which he tried to overcome the dichotomy set up by mind–body dualism.Chapter 2 focuses on Deleuze and Guattari's critique of logic as an attempt to find a third way between idealism and materialism and to overcome the disconnection between formal logic and lived experience. It reviews their critique of Euclidean geometry, their objections to formal logic as set out by Frege and Russell, and their assessment of phenomenology in order to eventually show Deleuze's affinity with Peirce's pragmatist approach. Then, the author aims to determine if Deleuze's attempt could be compatible with the phenomenology of Merleau-Ponty and Bergson's understanding of quality and multiplicity.Chapter 3 focuses on Bergson. Recalling the controversy with Russell, Einstein, and Langevin, Olkowski refers to Merleau-Ponty's defense of Bergson's concept of intuition to prove the accuracy of his reflection on creative forces and pure duration. As she explains, "[T]he intent here is to clarify the relations between these different aspects of Bergson's thought and draw out how Deleuze makes use of these structures derived from Bergson's philosophy." This leads her to explore, more specifically, how Deleuze reworks the concept of "multiplicity" along the lines of Bergson's analysis of the élan vital.In chapter 4 the author focuses on Deleuze's work on cinema to deepen the philosophical correlation between Bergson's concepts, Deleuze's analysis, and the influences of Merleau-Ponty and Pierce. It aims to rethink the relation between movement and time, notably through the notions of time-image and movement-image. Olkowski notably showcases Deleuze's concept of destiny, "which is the pure power of time that [End Page 153] overflows all possible reaction. It defeats, immobilizes, and petrifies figures in their own affectivity; it sends them to their fate, destroying conventions along the way. For Merleau-Ponty, as for Bergson, acts are still possible in a network of temporal relations so that motion and time are destiny but differently than for Deleuze."Chapter 5 addresses the Phenomenology of Perception and how Merleau-Ponty provides an opportunity to rethink perception. In this book and his Courses on Nature, Merleau-Ponty "does not dismiss either position—that of objective science or that of the natural attitude—but argues that although each contains an element of truth, it is perception and only perception that allows us to bridge the gap between physical reality and behavior/comportment." Deleuze will depart from... (shrink)

This is a collection of essays about logic and its applications to various philosophical problems. In general, it is argued that logic constitutes an important device of philosophical analysis. Concerning the nature of logic the author defends the thesis that first-order logic is the logic. Among the philosophical problems to which logic is applied in the essays are: truth, consistency, realism, foundations of semantics, psychologism, undetermination of theories by empirical data, modalities, value concepts, identity, (...) vagueness, God's existence, transcendentals, legal reasoning, category mistakes, bivalence, the cognitive relation, and meaningfulness. (shrink)

The paper begins with a more carefully stated version of ontologically neutral (ON) logic, originally introduced in (Hailperin, 1997). A non-infinitistic semantics which includes a definition of potential infinite validity follows. It is shown, without appeal to the actual infinite, that this notion provides a necessary and sufficient condition for provability in ON logic.

The beginning of the 20th century coincides with the establishment of the modern disciplines of the social sciences, chiefly in the United States but on a smaller scale in Western Europe as well. These disciplinary structures, which varied from country to country, provide the organizing principle of this handbook.The immediate context of the disciplinarization of sociology was the transformation of two fields, statistics and history, which shed large chunks of content as they took their current shape. The principal body of (...) thought that is excluded from the discipline of history, for example, was philosophy of history. Émile Durkheim provided the earliest and most coherent reconciliation of this fundamental tension, and it is striking how similar the lists of intellectual sources and problems actually were between these principal solutions to the common problem of constructing a “science” out of the materials and topics in question. Durkheim's analytic strategy in this chapter relies on the preexisting methodological tradition about cause and statistics that was established in Mill's System of Logic, but rejected Mill's own understanding of the role of probability in favor of the method of concomitant variation, which Mill had thought was inapplicable in social science. (shrink)

`This book grew out of the conviction, not in itself strange or startling, that the ordinary person can and should think straight rather than crooked.' Patrick Shaw has written a commonsense introduction to the use of logic in everyday thought and argument. It explains some of the rules of good argument and some of the ways in which arguments can fail, drawing illustrations from a variety of contemporary and international sources, such as the press, radio, and television. Symbols and (...) technicalities are kept to a minimum in this thorough and provocative investigation of the rational approach to thought - and its limitations. Logic and Its Limits emphasizes the use of logic in helping to settle and clarify disputes. It will help the reader to avoid bad arguments, to detect them in others, and so to think and argue more effectively. A wide range of thought-provoking examples and exercises concerned with contemporary social and political issues make this a readable and stimulating guide for the student and general reader alike. (shrink)