This paper examines the historical rise of both cardiopulmonary resuscitation and the do-not-resuscitate order and the wisdom of their continuing status in U.S. hospital practice and policy. The practice of universal presumed consent to CPR and the resulting DNR policy are the products of a particular time and were responses to particular problems. In order to keep the excesses of technology in check, the DNR policies emerged as a response to the in-hospital universal presumed consent to CPR. We live with (...) this historical concretion, which seems to perpetuate a false culture that the patient's wishes must be followed. The authors are critical of the current U.S. climate, where CPR and DNR are viewed as two among a panoply of patient choices, and point to UK practice as an alternative. They conclude that physicians in the United States should radically rethink approaches to CPR and DNR. (shrink)

Hegel's Science of Logic makes the just not low claim to be an absolute, ultimate-grounded knowledge. This project, which could not be more ambitious, has no good press in our post-metaphysical age. However: That absolute knowledge absolutely cannot exist, cannot be claimed without self-contradiction. On the other hand, there can be no doubt about the fundamental finiteness of knowledge. But can absolute knowledge be finite knowledge? This leads to the problem of a self-explication of (...) logic (in the sense of Hegel) and further, as will be shown, to a new definition of the dialectical procedure. The stringency of which results from the fact that always exactly that implicit content is explicated that was generated by the preceding explication step itself and is thus concretely comprehensible. At the same time, a new implicit content is generated by this act of explication, which requires a new explication step, and so forth. In the dialectical procedure reinterpreted in this way, dialectical arguments are not beheld, guessed at or even surreptitiously obtained, but are methodically accountable. Thereby dialectics is understood as a self-explication of logic by logical means and thus as a proof of the possibility of ultimate-grounding in the form of absolute and nevertheless finite – and thus also fallible – knowledge. (shrink)

In this paper we apply social epistemology to mathematical proofs and their role in mathematical knowledge. The most famous modern collaborative mathematical proof effort is the Classification of Finite Simple Groups. The history and sociology of this proof have been well-documented by Alma Steingart (2012), who highlights a number of surprising and unusual features of this collaborative endeavour that set it apart from smaller-scale pieces of mathematics. These features raise a number of interesting philosophical issues, but have received (...) very little attention. In this paper, we will consider the philosophical tensions that Steingart uncovers, and use them to argue that the best account of the epistemic status of the Classification Theorem will be essentially and ineliminably social. This forms part of the broader argument that in order to understand mathematical proofs, we must appreciate their social aspects. (shrink)

The key question I pursue in this book can be captured as follows: How can reference to the world be justified in a non-relational conception of intentionality? The overarching context of this proj...

In this paper we present a finitary sequent calculus for the S5 multi-modal system with common knowledge. The sequent calculus is based on indexed hypersequents which are standard hypersequents refined with indices that serve to show the multi-agent feature of the system S5. The calculus has a non-analytic right introduction rule. We prove that the calculus is contraction- and weakening-free, that (almost all) its logical rules are invertible, and finally that it enjoys a syntactic cut-elimination procedure. Moreover, the use (...) of the non-analytic rule can be restricted so that the calculus can be considered as suitable for proof search. (shrink)

This chapter suggests a new interpretation of Spinoza’s concept of mind claiming that the goal of the equation of the human mind with the idea of the body is not to solve the mind-body problem, but rather to show how we can, within the framework of Spinoza’s rationalism, conceive of finite minds as irreducibly distinguishable individuals. To support this view, the chapter discusses the passage from E2p11 to E2p13 against the background of three preliminaries, i.e. the notion of a (...) union between mind and body as it appears in Thomas Aquinas’ refutation of Averroism, Spinoza’s views on knowledge of actually existing things in E2p8c, and the phenomenological character of E2a2-4. It argues that while this view on the human mind does not undermine radical rationalism, it does require its amendment by some irreducibly empirical concessions. (shrink)

Nonmonotonic reasoning is a discipline of computer science, epistemology, and cognition: It models inferences where classical logic is inadequate in symbolic AI, defines normative models for reasoning with defeasible information in epistemology, and models human reasoning under information change in cognition. Its building blocks are defeasible rules formalised as DeFinetti conditionals. In this thesis, Christian Eichhorn examines qualitative and semi-quantitative inference relations on top said conditionals, using the conditional structure of the knowledge base and Spohn’s Ordinal Conditional Functions, using (...) established properties. Converting network approaches from probabilistics, he shows how to approach the relations with regard to implementation. (shrink)

Neo-Fregeanism contends that knowledge of arithmetic may be acquired by second-order logical reflection upon Hume's principle. Heck argues that Hume's principle doesn't inform ordinary arithmetical reasoning and so knowledge derived from it cannot be genuinely arithmetical. To suppose otherwise, Heck claims, is to fail to comprehend the magnitude of Cantor's conceptual contribution to mathematics. Heck recommends that finite Hume's principle be employed instead to generate arithmetical knowledge. But a better understanding of Cantor's contribution is achieved if (...) it is supposed that Hume's principle really does inform arithmetical practice. More generally, Heck's arguments misconceive the epistemological character of neo-Fregeanism. (shrink)

A system of finite mathematics is proposed that has all of the power of classical mathematics. I believe that finite mathematics is not committed to any form of infinity, actual or potential, either within its theories or in the metalanguage employed to specify them. I show in detail that its commitments to the infinite are no stronger than those of primitive recursive arithmetic. The finite mathematics of sets is comprehensible and usable on its own terms, without appeal (...) to any form of the infinite. That makes it possible to, without circularity, obtain the axioms of full Zermelo-Fraenkel Set Theory with the Axiom of Choice (ZFC) by extrapolating (in a precisely defined technical sense) from natural principles concerning finite sets, including indefinitely large ones. The existence of such a method of extrapolation makes it possible to give a comparatively direct account of how we obtain knowledge of the mathematical infinite. The starting point for finite mathematics is Mycielski's work on locally finite theories. (shrink)

The view that chances are relative frequencies of occurrence within actual, finite reference classes has long been written off. I argue that it ought to be reconsidered. Focusing on non-deterministic chance, I defend a version of finite frequentism in which reference classmates are required to have qualitatively identical pasts. While my analysis can evade or resist several standard objections, it has a counterintuitive consequence: non-trivial chances entail the existence of past light cones that are perfect intrinsic duplicates. In (...) mitigation, I argue that our scientific knowledge is consistent with the hypothesis that there are many such duplicates in the actual world. Moreover, my analysis has some striking advantages: it is simple, it is metaphysically undemanding, and it makes possible a satisfying explanation of the chance–credence connection. 1 Introduction2 Target3 Sketch and Skirmish4 Articulation5 Standard Worries5.1 Frequency tolerance5.2 Leibniz’s dictum5.3 Single case chance5.4 Missing values5.5 Explanation5.6 Counterfactual chances6 Chance and Credence6.1 An indefeasible indifference intuition6.2 Articulating the credence principle6.3 Appraising the credence principle7 Confirmation8 Laws9 Summing Up. (shrink)

In the current paper we consider theories with vocabulary containing a number of binary and unary relation symbols. Binary relation symbols represent labeled edges of a graph and unary relations represent unique annotations of the graph's nodes. Such theories, which we call annotation theories^ can be used in many applications, including the formalization of argumentation, approximate reasoning, semantics of logic programs, graph coloring, etc. We address a number of problems related to annotation theories over finite models, including satisfiability, querying (...) problem, specification of preferred models and model checking problem. We show that most of considered problems are NPTime- or co-NPTime-complete. In order to reduce the complexity for particular theories, we use second-order quantifier elimination. To our best knowledge none of existing methods works in the case of annotation theories. We then provide a new second-order quantifier elimination method for stratified theories, which is successful in the considered cases. The new result subsumes many other results, including those of [2, 28, 21]. (shrink)

In his paper ‘Scmantic Theory and Tacit Knowlcdgc’, Gareth Evans uscs a familiar kind of cxamplc in ordcr to render vivid his account of tacit knowledge. We arc to consider a finite language, with just one hundrcd scntcnccs. Each scntcncc is made up of a subjcct (a name) and a prcdicatc. The names are ‘a’, ‘b’, . . ., T. The prcdicatcs arc ‘F’, ‘G’, . . ., ‘O’. Thc scntcnccs have meanings which dcpcnd in a systematic way (...) upon their construction. Thus, all scntcnccs containing ‘a’ mean something about john; all scntcnccs containing ‘b’ mean something about Harry; all scntcnccs containing ‘F’ mean something about being bald; all scntcnccs containing ‘G’ mean something about being happy; and so 011. For this vcry simple language L, wc arc to consider various semantic theories. We could consider thcorics whosc dclivcranccs about wholc scntcnccs are of.. (shrink)

When physicist Alan Sokal recently submitted an article to the postmodernist journal Social Text, the periodical's editors were happy to publish it--for here was a respected scientist offering support for the journal's view that science is a subjective, socially constructed discipline. But as Sokal himself soon revealed in Lingua Franca magazine, the essay was a spectacular hoax--filled with scientific gibberish anyone with a basic knowledge of physics should have caught--and the academic world suddenly awoke to the vast gap that (...) has opened between the scientific community and their mould-be critics. But the truth is that not only postmodern critics but Americans in general have a weak grasp on scientific principles and facts. In Connected Knowledge, physicist Alan Cromer offers a way to bridge the chasm, with a lively, lucid account of scientific thinking and a provocative new agenda for American education. Science, Cromer argues, is anything but common sense: It requires a particular habit of mind that does not come naturally. For example, something as simple as buoyancy can only be explained through Archimedes' principle--that a body in a fluid is subject to an upward force equal to the weight of fluid it displaces--yet few scientists could arrive at this ancient concept by trial and error. School children, however, are often given a ball and a tank of water, and asked to explain buoyancy any way they can. Today's de emphasis on teaching pupils necessary facts and principles, he argues, "far from empowering them, makes them slaves of their own subjective opinions." This movement in education, known as Constructivism, has close ties to postmodern critics (such as the editors of Social Text) who question the objectivity of science, and with it the existence of an objective reality. Cromer offers a ringing defense of the knowability of the world, both as an objective reality and as a finite landscape of discovery. The advance of scientific knowledge, he argues, is not unlike the mapping of the continents; at this point, we have found them all. He shows how the advent of quantum mechanics, rather than making knowledge less certain, actually offers a more precise understanding of the behavior of atoms and electrons. Turning from philosophy to education, he argues that instead of allowing students to flounder, however creatively, schools should follow a progressive curriculum that returns theoretical knowledge to the classroom. Connected Knowledge, however, goes much farther. As a discipline that insists upon connecting theory with measurable reality, physical science offers a new direction for reforming the social sciences. Cromer also shows how some of the hottest issues in public policy--including the debates over special education and group variations in I.Q., can be resolved through clear, hard headed thinking. For example, he argues for use of the G.E.D. as a national educational standard, with a new "politics of intelligence" to guide the distribution of school resources. Always forthright and articulate, Alan Cromer offers a startling new vision for integrating science, philosophy, and education. (shrink)

Genevieve Lloyd’s Spinoza is quite a different thinker from the arch rationalist caricature of some undergraduate philosophy courses devoted to “The Continental Rationalists”. Lloyd’s Spinoza does not see reason as a complete source of knowledge, nor is deductive rational thought productive of the highest grade of knowledge. Instead, that honour goes to a third kind of knowledge—intuitive knowledge (scientia intuitiva), which provides an immediate, non-discursive knowledge of its singular object. To the embarrassment of some hard-nosed (...) philosophers, intellectual intuition has an affective component; it is a form of love, and ultimately given that human beings are finite modes of God/Nature (Deus sive Natura), it is a form of the intellectual love of God (amor Dei intellectualis). Some philosophers do not know what to make of this mysterious aspect of Spinoza’s philosophy, which is nonetheless firmly anchored in a reading of Part V of the Ethics. Nonetheless, this note will insist with Lloyd’s “Reconsidering Spinoza’s Rationalism” that such doctrine is an integral part of Spinoza’s philosophy. Moreover, it will be shown that Spinoza is well aware of the limitations of reason (ratio) in gaining scientific knowledge of the world and requires intuition precisely because of the inability of reason to represent individuals in their full particularity. Imagination too has a role to play in shaping scientific knowledge, although reason performs a vital critical role in disciplining and liberating the human mind from inadequate imaginary ideas. The result is an interpretation of Spinoza’s epistemology as both rationalist and intuitionist. DOI: 10.1080/24740500.2021.1962652. (shrink)

The concept of practical knowledge is central to G.E.M. Anscombe's argument in Intention, yet its meaning is little understood. There are several reasons for this, including a lack of attention to Anscombe's ancient and medieval sources for the concept, and an emphasis on the more straightforward concept of knowledge "without observation" in the interpretation of Anscombe's position. This paper remedies the situation, first by appealing to the writings of Thomas Aquinas to develop an account of practical knowledge (...) as a distinctive form of thought that "aims at production" of things that lie within an agent's power; and then by showing how this Thomistic understanding of practical cognition seems to have been Anscombe's, too. Having done this, I question whether the thesis that agential knowledge is practical knowledge entails that an agent always has non-observational knowledge of what she is intentionally doing. I answer "Not": Anscombe's claims to the contrary rest on a misleading assimilation of human beings' finite agency to that of an infinite agent like God. (shrink)

We study the topological models of a logic of knowledge for topological reasoning, introduced by Larry Moss and Rohit Parikh (1992). Among our results is the confirmation of a conjecture by Moss and Parikh, as well as the finite satisfiability property and decidability for the theory of topological models.

There are many aspects of the Ethics that seem to suggest, or perhaps even require the possibility of deducing finite modes from the infinite substance. Nonetheless, as many have noted even during Spinoza’s own time, it is far from clear that such a deduction can be successfully performed. In this chapter I argue that the expectation of a top-down deduction is unwarranted, and that interestingly enough, it is not only unwarranted with regard to Spinoza but with regard to Descartes (...) as well. I show this by pointing to the crucial role confusion plays for both, noting that our epistemic journey to clear and distinct or adequate knowledge begins with confusion, and that this trajectory is one of emending initially confused ideas. This shows that epistemically a bottom-up trajectory necessarily precedes a top-down one. My claim, however, goes beyond this point regarding the order of discovery. I argue that the state of confusion presupposes a plurality of finite modes, in Spinoza’s case, and substances and modes in Descartes’s. Confusion, I claim, amounts to an inadequate perception of an amalgam of ideas of a real plurality of things. Recognizing the metaphysical ground of confusion along with its central epistemic role brings to light the artificiality, and indeed ultimately the impossibility of a top-down deduction which is divorced from a preceding bottom-up analysis. (shrink)

Written by a highly respected scholar of Thomas Aquinas's writings, this volume offers a comprehensive presentation of Aquinas's metaphysical thought. It is based on a thorough examination of his texts organized according to the philosophical order as he himself describes it rather than according to the theological order. -/- In the introduction and opening chapter, John F. Wippel examines Aquinas's view on the nature of metaphysics as a philosophical science and the relationship of its subject to divine being. Part One (...) is devoted to his metaphysical analysis of finite being. It considers his views on the problem of the One and the Many in the order of being, and includes his debt to Parmenides in formulating this problem and his application of analogy to finite being. Subsequent chapters are devoted to participation in being, the composition of essence and esse in finite beings, and his appeal to a kind of relative nonbeing in resolving the problem of the One and the Many. Part Two concentrates on Aquinas's views on the essential structure of finite being, and treats substance-accident composition and related issues, including, among others, the relationship between the soul and its powers and unicity of substantial form. It then considers his understanding of matter-form composition of corporeal beings and their individuation. Part Three explores Aquinas's philosophical discussion of divine being, his denial that God's existence is self-evident, and his presentation of arguments for the existence of God, first in earlier writings and then in the "Five Ways" of his Summa theologiae. A separate chapter is devoted to his views on quidditative and analogical knowledge of God. The concluding chapter revisits certain issues concerning finite being under the assumption that God's existence has now been established. -/- John F. Wippel, professor of philosophy at The Catholic University of America, was recently awarded the prestigious Aquinas Medal by the American Catholic Philosophical Association. In addition to numerous articles and papers, Wippel has coauthored or edited several other works, including Metaphysical Themes in Thomas Aquinas and The Metaphysical Thought of Godfrey of Fontaines, both published by CUA Press. (shrink)

From the author: This dissertation undertakes a critical examination of one central problem in Hegelian philosophy: viz., whether the final realization of “absolute knowledge” is logically consistent with significant epistemic progress in the system’s continuing development. Serious consideration of the concept of systematic completeness, as interpreted on Hegel’s terms, uncovers the existence of a profound paradox. On the one hand, if the Truth is the Whole, then the truth of any finite part or aspect of that Whole depends (...) upon its place within the system as a totality. In order to grasp the part and comprehend it correctly, one must already have a systematically ordered knowledge of the universe in its entirety. Yet the methodological open-endedness of dialectical thinking precludes the acceptance of any particular theoretical formulation as final or complete in itself. Hegel interprets the history of philosophy as a progression of successive formulations of the Truth, each of which improves on its predecessors by reconciling their internal contradictions, but no one of which is adequate in itself. Hence, no theoretical world view, including Hegel’s own, can rest content within its limits, for the inevitable advance of thought must in the end throw it down. (shrink)

A uniform construction for sequent calculi for finite-valued first-order logics with distribution quantifiers is exhibited. Completeness, cut-elimination and midsequent theorems are established. As an application, an analog of Herbrand’s theorem for the four-valued knowledge-representation logic of Belnap and Ginsberg is presented. It is indicated how this theorem can be used for reasoning about knowledge bases with incomplete and inconsistent information.

Contents: Foreword. Wolfgang BALZER and C. ULISES MOULINES: Introduction. José A. DÍEZ CALZADA: Structuralist Analysis of Theories of Fundamental Measurement. Adolfo GARCÍA DE LA SIENRA and Pedro REYES: The Theory of Finite Games in Extensive Form. Hans Joachim BURSCHEID und Horst STRUVE: The Theory of Stochastic Fairness - its Historical Development, Formulation and Justification. Wolfgang BALZER and Richard MATTESSICH: Formalizing the Basis of Accounting. Werner DIEDERICH: A Reconstruction of Marxian Economics. Bert HAMMINGA and Wolfgang BALZER: The Basic Structure of (...) Neoclassical General Equilibrium Theory. Klaus MANHART: Balance Theories: Two Reconstructions and the Problem of Intended Applications. Rainer WESTERMANN: Festinger's Theory of Cognitive Dissonance: A Structuralist Theory-Net. Rainer REISENZEIN: Wundt's Three-Dimensional Theory of Emotion. Pablo LORENZANO: Classical Genetics and the Theory-Net of Genetics. Hinne HETTEMA and Theo A.F. KUIPERS: The Formalisation of the Periodic Table. C. ULISES MOULINES: The Basic Core of Simple Equilibrium Thermodynamics. Thomas BARTELBORTH: An Axiomatization of Classical Electrodynamics. Author's Index. Subject Index. (shrink)

The single greatest challenge facing managers in the developed countries of the world is to raise the productivity of knowledge and service workers. This challenge, which will dominate the management agenda for the next several decades, will ultimately determine the competitive performance of companies. Even more important, it will determine the very fabric of society and the quality of life of every industrialized nation. … Unless this challenge is met, the developed world will face increasing social tensions, increasing polarization, (...) increasing radicalization, possibly even class war. (shrink)

A primary problem in the area of natural language processing has been semantic analysis. This book looks at the semantics of natural languages in context. It presents an approach to the computational processing of English text that combines current theories of knowledge representation and reasoning in Artificial Intelligence with the latest linguistic views of lexical semantics. The book will interest postgraduates and researchers in computational linguistics as well as industrial research groups specializing in natural language processing.

Husserl and Aquinas -- Knowledge, truth, being -- Actual and ideal being, species, type, and likeness (fragment) -- Sketch of a foreword to Finite and eternal being (fragment) -- Ways to know God.

The spectacular development of medical knowledge over the last two centuries has brought intrusive advances in the capabilities of medical technology. These advances have been remarkable over the last century, but especially over the last few decades, culminating in such high technology interventions as heart transplants and renal dialysis. These increases in medical powers have attracted societal interest in acquiring more such knowledge. They have also spawned concerns regarding the use of human subjects in research and regarding the (...) byproducts of basic research as in the recent recombinant DNA debate. As a consequence of the development of new biomedical knowledge, physicians and biomedical scientists have been placed in positions of new power and responsibility. The emergence of this group of powerful and knowledgeable experts has occasioned debates regarding the accountability of physicians and biomedical scientists. But beyond that, the very investment of resources in the acquisition of new knowledge has been questioned. Societies must decide whether finite resources would not be better invested at this juncture, or in general, in the alleviation of the problems of hunger or in raising general health standards through interventions which are less dependent on the intensive use of high technology. To put issues in this fashion touches on philosophical notions concerning the claims of distributive justice and the ownership of biomedical knowledge. (shrink)

: This paper reconstructs the evolution of Novalis’ thought concerning being, nature, and knowledge. In his earlier writings (above all the Fichte-Studies) he argues that unitary being underlies finite phenomena and that we can never know, but only strive towards knowledge of, being. In contrast, his later writings, principally the Allgemeine Brouillon, maintain that the unitary reality underlying finite things can be known, because it is an organic whole which develops and organises itself according to an (...) intelligible pattern. Novalis equates this whole with nature. However, because this organic whole exercises spontaneity in assuming particular forms of organisation, we can never know why it assumes just these particular forms; nature therefore remains partly unintelligible to us. I argue that Novalis’ intellectual shift towards the idea that the whole can be known is motivated by his concern to explain how the modern, “disenchanted,” view of nature could be overcome. I also argue that by recognising this shift, we can resolve the dispute between Frank and Beiser as to whether Novalis thinks that the absolute can be known. (shrink)

One of the many problems that would have t o be solved by a satisfactory theory of empirical knowledge, perhaps the most central is a general structural problem which I shall call the epistemic regress problem: the problem of how to avoid an in- finite and presumably vicious regress of justification in ones account of the justifica- tion of empirical beliefs. Foundationalist theories of empirical knowledge, as we shall see further below, attempt t o avoid the regress (...) by locating a class of empirical beliefs whose justification does not depend on that of other empirical beliefs. Extemalist theories, the topic of the present paper, represent one species of foundationalism. (shrink)

The article explores the idea that according to Spinoza finite thought and substantial thought represent reality in different ways. It challenges “acosmic” readings of Spinoza's metaphysics, put forth by readers like Hegel, according to which only an infinite, undifferentiated substance genuinely exists, and all representations of finite things are illusory. Such representations essentially involve negation with respect to a more general kind. The article shows that several common responses to the charge of acosmism fail. It then argues that (...) we must distinguish the well-founded ideality of representations of finite things from mere illusoriness, insofar as for Spinoza we can have true knowledge of what is known only abstractly. Finite things can be seen as well-founded beings of reason. The article also proposes that within Spinoza's framework it is possible to represent a finite thing without drawing on representations of mind-dependent entities. (shrink)

Mutual perceptual knowledge is a prevalent feature of our everyday lives, yet appears to be exceptionally difficult to characterise in an acceptable way. This paper argues for a renewed understanding of Stephen Schiffer’s iterative approach to mutual knowledge, according to which mutual knowledge requires an infinite number of overlapping, embedded mental states. It is argued that the charge of ‘psychological implausibility’ that normally accompanies discussion of this approach can be offset by identifying mutual knowledge, not with (...) the infinite iterations themselves, but with the finite base which Schiffer proves is capable of generating those iterations. An understanding of this finite base as a primitive, relational property holding between two or more people, allows us to understand the iterations as an implicit and ‘harmless’ intrapersonal feature of what is an interpersonal phenomenon. The paper concludes by relating the account to joint attention in infant interaction. (shrink)

Spinoza unequivocally states in the Ethics that intuitive knowledge is more powerful than reason. Nonetheless, it is not clear what exactly this greater power promises in the face of the passions. Does this mean that intuitive knowledge is not liable to akrasia? Ronald Sandler offers what, to my knowledge, is the only explicit answer to this question in recent Spinoza scholarship. According to Sandler, intuitive knowledge, unlike reason, is not susceptible to akrasia. This is because, intuitive (...) knowledge enables the knower to greater power over the passions due to its immediacy, its foundation and because it engenders the boundlessly powerful intellectual love of God. In this paper, I consider to what extent intuitive knowledge is liable to akrasia by exploring whether Sandler's claim can justifiably be attributed to Spinoza. I argue that, given our modal status, it is not plausible to claim that akrasia would never apply to intuitive knowledge. Since intuitive ideas are the ideas of a finite .. (shrink)

Introduction: contemporary conditions and diagrammatic trajectory -- From joy to the gap: the accessing of the infinite by the finite (Spinoza, Nietzsche, Bergson) -- The care of the self versus the ethics of desire: two diagrams of the production of subjectivity (and of the subject's relation to truth) (Foucault versus Lacan) -- The aesthetic paradigm: from the folding of the finite-infinite relation to schizoanalytic metamodelisation (to biopolitics) (Guattari) -- The strange temporality of the subject: life in-between the infinite (...) and the finite (Deleuze contra Badiou) -- Desiring-machines, chaoids, probeheads: towards a speculative production of subjectivity (Deleuze and Guattari) -- Conclusion: composite diagram and relations of adjacency. (shrink)

reprinted as 'Can We Know the Nature of Reality As It Is In Itself' in Galen Strawson, Real Materialism, 2008: Many hold that it is impossible in principle for finite creatures like ourselves to know anything of the nature of non-mental concrete reality as it is in itself, even if we can be said to know the nature of the qualitative character of our own experiences (as it is in itself) just in having them. I argue that there is (...) no insuperable obstacle to knowledge of the nature of non-mental concrete reality as it is in itself, even if we have very little as a matter of fact. (shrink)

Renaissance philosopher, mathematician, and theologian Nicholas of Cusa (1401-1464) said that there is no proportion between the finite mind and the infinite. He is fond of saying reason cannot fully comprehend the infinite. That our best hope for attaining a vision and understanding of infinite things is by mathematics and by the use of contemplating symbols, which help us grasp "the absolute infinite". By the late 19th century, there is a decisive intervention in mathematics and its philosophy: the philosophical (...) mathematician Georg Cantor (1845-1918) says that between the realm of the finite and the absolute infinite, there is an intermediate realm partaking in properties in a certain sense of both the finite and the infinite: the transfinite realm. Like the finite, the transfinite realm is a realm of mathematical objects, numbers, and knowledge. Like the absolute infinite, the transfinite is a form of infinity insofar as transfinite sets and numbers transcend any finite number. Echoing Cusanus and neo-Platonism, Cantor says that the transfinite sequence of all ordinals is a symbol of the absolutely infinite, that is, God. Moreover, Cantor envisioned his transfinite set theory (Mengenlehre) as providing the analytical methods and techniques necessary for a comprehensive, organic, non-reductive description of nature, a Naturphilosophie. Thus Cantor’s novel mathematics is presented as part of a long tradition, to which Cusanus, Bruno, Spinoza, Leibniz and others belong, in which the infinity and infinite character of organic life forms is appreciated, and is in some sense a mirror or symbol of the divine. The doctrine of symbolism and their different approach to the laws of logic present in both the work of Cusanus and Cantor enables these thinkers to articulate a transcendental apophatic approach to divinity. (shrink)

This paper presents a bimodal logic for reasoning about knowledge during knowledge acquisitions. One of the modalities represents (effort during) non-deterministic time and the other represents knowledge. The semantics of this logic are tree-like spaces which are a generalization of semantics used for modeling branching time and historical necessity. A finite system of axiom schemes is shown to be canonically complete for the formentioned spaces. A characterization of the satisfaction relation implies the small model property and (...) decidability for this system. (shrink)

Default logic is computationally expensive. One of the most promising ways of easing this problem and developing powerful implementations is to split a default theory into smaller parts and compute extensions in a modular, local way. This paper compares two recent approaches, Turner's splitting and Cholewinski's stratification. It shows that the approaches are closely related – in fact the former can be viewed as a special case of the latter.

This paper deals with two different problems in which infinity plays a central role. I first respond to a claim that infinity renders counting knowledge-level beliefs an infeasible approach to measuring and comparing how much we know. There are two methods of comparing sizes of infinite sets, using the one-to-one correspondence principle or the subset principle, and I argue that we should use the subset principle for measuring knowledge. I then turn to the normalizability and coarse tuning objections (...) to fine-tuning arguments for the existence of God or a multiverse. These objections center on the difficulty of talking about the epistemic probability of a physical constant falling within a finite life-permitting range when the possible range of that constant is infinite. Applying the lessons learned regarding infinity and the measurement of knowledge, I hope to blunt much of the force of these objections to fine-tuning arguments. (shrink)

Contents: Foreword. Wolfgang BALZER and C. ULISES MOULINES: Introduction. José A. DÍEZ CALZADA: Structuralist Analysis of Theories of Fundamental Measurement. Adolfo GARCÍA DE LA SIENRA and Pedro REYES: The Theory of Finite Games in Extensive Form. Hans Joachim BURSCHEID und Horst STRUVE: The Theory of Stochastic Fairness - its Historical Development, Formulation and Justification. Wolfgang BALZER and Richard MATTESSICH: Formalizing the Basis of Accounting. Werner DIEDERICH: A Reconstruction of Marxian Economics. Bert HAMMINGA and Wolfgang BALZER: The Basic Structure of (...) Neoclassical General Equilibrium Theory. Klaus MANHART: Balance Theories: Two Reconstructions and the Problem of Intended Applications. Rainer WESTERMANN: Festinger's Theory of Cognitive Dissonance: A Structuralist Theory-Net. Rainer REISENZEIN: Wundt's Three-Dimensional Theory of Emotion. Pablo LORENZANO: Classical Genetics and the Theory-Net of Genetics. Hinne HETTEMA and Theo A.F. KUIPERS: The Formalisation of the Periodic Table. C. ULISES MOULINES: The Basic Core of Simple Equilibrium Thermodynamics. Thomas BARTELBORTH: An Axiomatization of Classical Electrodynamics. Author's Index. Subject Index. (shrink)

Les "Seconds analytiques" contiennent les concepts et méthodes de la science aristotélicienne qui se retrouvent en acte dans les écrits biologistes. Cette étude s'intéresse aux passages sur la définition de l'âme, où Aristote use de deux procédés, la division et la démonstration. Elle met en évidence le caractère méthodique de l'argumentation et propose des solutions aux difficultés du texte.

As an important corollary of this interpretation of absolute knowledge, the dissertation concludes with the suggestion that Hegelian philosophy need not be regarded merely as an interesting curiosity in the history of ideas, but rather that it can serve as a vital and potentially rewarding source of fresh theoretical insights. ;Instead, the concrete completeness of speculative philosophy can only consist in the activity of a dynamical, ceaselessly self-examining and self-regulating intellectual community. In one sense, of course, no finite (...) system can ever be complete, insofar as it will inevitably be guilty of errors and misconceptions. Yet at the same time, the infinite System is perfect and complete, insofar as it contains within itself the means whereby its own unavoidable flaws will be discovered, corrected, and "forgiven"--i.e. aufgehoben into vanishing moments of a universal totality. ;In opposition to most traditional interpretations of Hegel, the position is maintained that Hegel himself deliberately faced this problem, and that a true understanding of his proposed solution requires a radical Aufhebung of the concept of cognition as such. Relying primarily on the penultimate chapters of the Phenomenology of Spirit, the dissertation argues that absolute knowledge can neither be a finalized system of fully explicit content, nor an endless movement toward such an ideal state. ;This dissertation undertakes a critical examination of one central problem in Hegelian philosophy: viz., whether the final realization of "absolute knowledge" is logically consistent with significant epistemic progress in the system's continuing development. Serious consideration of the concept of systematic completeness, as interpreted on Hegel's terms, uncovers the existence of a profound paradox. On the one hand, if the Truth is the Whole, then the truth of any finite part or aspect of that Whole depends upon its place within the system as a totality. In order to grasp the part and comprehend it correctly, one must already have a systematically ordered knowledge of the universe in its entirety. Yet the methodological open-endedness of dialectical thinking precludes the acceptance of any particular theoretical formulation as final or complete in itself. Hegel interprets the history of philosophy as a progression of successive formulations of the Truth, each of which improves on its predecessors by reconciling their internal contradictions, but no one of which is adequate in itself. Hence, no theoretical world view, including Hegel's own, can rest content within its limits, for the inevitable advance of thought must in the end throw it down. (shrink)

Robert Aumann argues that common knowledge of rationality implies backward induction in finite games of perfect information. I have argued that it does not. A literature now exists in which various formal arguments are offered in support of both positions. This paper argues that Aumann's claim can be justified if knowledge is suitably reinterpreted.

Logic and Knowledge -/- Editor: Carlo Cellucci, Emily Grosholz and Emiliano Ippoliti Date Of Publication: Aug 2011 Isbn13: 978-1-4438-3008-9 Isbn: 1-4438-3008-9 -/- The problematic relation between logic and knowledge has given rise to some of the most important works in the history of philosophy, from Books VI–VII of Plato’s Republic and Aristotle’s Prior and Posterior Analytics, to Kant’s Critique of Pure Reason and Mill’s A System of Logic, Ratiocinative and Inductive. It provides the title of an important collection (...) of papers by Bertrand Russell (Logic and Knowledge. Essays, 1901–1950). However, it has remained an underdeveloped theme in the last century, because logic has been treated as separate from knowledge. -/- This book does not hope to make up for a century-long absence of discussion. Rather, its ambition is to call attention to the theme and stimulating renewed reflection upon it. The book collects essays of leading figures in the field and it addresses the theme as a topic of current debate, or as a historical case study, or when appropriate as both. Each essay is followed by the comments of a younger discussant, in an attempt to transform what might otherwise appear as a monologue into an ongoing dialogue; each section begins with an historical essay and ends with an essay by one of the editors. -/- Carlo Cellucci is Emeritus Professor of Philosophy at the University of Rome ‘La Sapienza,’ Italy. He is currently completing a book entitled, Remaking Logic: What is Logic Really? -/- Emily Grosholz is Professor of Philosophy at the Pennsylvania State University, USA. She is the author of Representation and Productive Ambiguity in Mathematics and the Sciences (Oxford University Press, 2007). -/- Emiliano Ippoliti is a Research Fellow at the University of Rome ‘La Sapienza,’ Italy. His main interests are heuristics, the logic of discovery, and problem-solving. He is currently working on a book, Ampliating Knowledge: Data, Hypotheses and Novelty. -/- TABLE OF CONTENTS -/- Foreword .................................................................................................... ix Acknowledgements ................................................................................. xxv -/- Section I: Logic and Knowledge -/- Chapter One................................................................................................. 3 The Cognitive Importance of Sight and Hearing in Seventeenthand Eighteenth-Century Logic (Mirella Capozzi) Discussion .............................................................................................. 26 (Chiara Fabbrizi) Chapter Two .............................................................................................. 33 Nominalistic Content (Jody Azzouni) Discussion ............................................................................................... 52 (Silvia De Bianchi) Chapter Three ............................................................................................ 57 A Garden of Grounding Trees (Göran Sundholm) Discussion.......................................................................................... .. 75 (Luca Incurvati) Chapter Four .............................................................................................. 81 Logics and Metalogics (Timothy Williamson) Discussion.......................................................................................... 101 (Cesare Cozzo) Chapter Five ............................................................................................ 109 Is Knowledge the Most General Factive Stative Attitude? (Cesare Cozzo) Discussion.......................................................................................... 117 (Timothy Williamson) Chapter Six .............................................................................................. 123 Classifying and Justifying Inference Rules (Carlo Cellucci) Discussion.......................................................................................... 143 (Norma B. Goethe) -/- Section II: Logic and Science -/- Chapter Seven.......................................................................................... 151 The Universal Generalization Problem and the Epistemic Status of Ancient Medicine: Aristotle and Galen (Riccardo Chiaradonna) Discussion.......................................................................................... 168 (Diana Quarantotto) Chapter Eight........................................................................................... 175 The Empiricist View of Logic (Donald Gillies) Discussion.......................................................................................... 191 (Paolo Pecere) Chapter Nine............................................................................................ 197 Artificial Intelligence and Evolutionary Theory: Herbert Simon’s Unifying Framework (Roberto Cordeschi) Discussion.......................................................................................... 216 (Francesca Ervas) Chapter Ten ............................................................................................. 221 Evolutionary Psychology and Morality: The Renaissance of Emotivism? (Mario De Caro) Discussion.......................................................................................... 232 (Annalisa Paese) Chapter Eleven ........................................................................................ 237 Between Data and Hypotheses (Emiliano Ippoliti) Discussion.......................................................................................... 262 (Fabio Sterpetti) -/- Section III: Logic and Mathematics -/- Chapter Twelve ....................................................................................... 273 Dedekind Against Intuition: Rigor, Scope and the Motives of his Logicism (Michael Detlefsen) Discussion.......................................................................................... 290 (Marianna Antonutti) Chapter Thirteen...................................................................................... 297 Mathematical Intuition: Poincaré, Polya, Dewey (Reuben Hersh) Discussion.......................................................................................... 324 (Claudio Bernardi) Chapter Fourteen ..................................................................................... 329 On the Finite: Kant and the Paradoxes of Knowledge (Carl Posy) Discussion.......................................................................................... 358 (Silvia Di Paolo) Chapter Fifteen ........................................................................................ 363 Assimilation: Not Only Indiscernibles are Identified (Robert Thomas) Discussion.......................................................................................... 380 (Diego De Simone) Chapter Sixteen ....................................................................................... 385 Proofs and Perfect Syllogisms (Dag Prawitz) Discussion.......................................................................................... 403 (Julien Murzi) Chapter Seventeen ................................................................................... 411 Logic, Mathematics, Heterogeneity (Emily Grosholz) Discussion.......................................................................................... 427 (Valeria Giardino) -/- Contributors........................................................................................ ..... 433 Index............................................................................................... ......... 437 -/- Price Uk Gbp: 49.99 Price Us Usd: 74.99. 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A large class of games is that of non-cooperative, extensive form games of perfect information. When the length of these games is finite, the method used to reach a solution is that of a backward induction. Working from the terminal nodes, dominated strategies are successively deleted and what remains is a unique equilibrium. Game theorists have generally assumed that the informational requirement needed to solve these games is that the players have common knowledge of rationality. This assumption, however, (...) has given rise to several problems and paradoxes. Most notably, it has been shown that the common knowledge assumption makes the theory of the game inconsistent at some information set. The present paper shows that a) no common knowledge of rationality need be assumed for the backward induction solution to hold. Rather, it is sufficient that the players have a number of levels of knowledge proportional to the length of the game, and b) it is also necessary that the number of levels of knowledge is finite and proportional to the length of the game. For a higher number of levels of knowledge, inconsistencies arise. (shrink)

In this paper we investigate first order common knowledge logics; i.e., modal epistemic logics based on first order logic with common knowledge operators. It is shown that even rather weak fragments of first order common knowledge logics are not recursively axiomatizable. This applies, for example, to fragments which allow to reason about names only; that is to say, fragments the first order part of which is based on constant symbols and the equality symbol only. Then formal properties (...) of "quantifying into" epistemic contexts are investigated. The results are illustrated by means of epistemic representations of Nash Equilibria for finite games with mixed strategies. (shrink)