Hermann Cohen, as it is well known, criticised the Kantian notion of the thing-in-itself. And before him the Kantian thing-in-itself was criticised by Fichte and other German idealists. Probably for this reason, Hermann Cohen is sometimes regarded as a person who said things similar to Fichte. This gives a completely wrong perspective, making it impossible to understand the philosopher's ideas. The basis for his critique of the Kantian thing-in-itself is quite different from the motives, determining the criticism of Kant in (...) the classical German Idealism. Such interpretation does not allow to see close connection of Cohen's theoretical philosophy with revolution in physics which took place at the turn of the nineteenth and twentieth centuries. The article explains how Cohen's demand that pure thinking must form its own content is connected with transformations taking place in physics and mathematics, and the peculiarity of Cohen's understanding of idealism is demonstrated: for him, correct idealism must realize that autonomous, free thinking should work seriously with sense data. The closeness of Cohen's ideas to the postpositivist thesis of the theory-ladenness of observation is explained. For Cohen, serious work with sense data is opposite to uncritical acceptance of them as given. The origin of scientific thinking is thinking itself. It responds to the challenge of sensory material by creating its own constructs. Mathematized natural science becomes for Cohen both an example and a confirmation of this thesis. For him, what is real is what is described in the language of mathematical analysis, i.e. continuous processes, in spite of the fact that any data are discrete. It is shown that the source of Cohen's assertions on this issue is in Kant's Critique of Pure Reason, namely in the doctrine of the Principles of pure natural science and, more specifically, in the Anticipations of Perception. Cohen's conviction of the constructive character of the theories of mathematized natural science is confirmed in the article by references to the authority of A. Einstein. (shrink)

The connection of Hermann Сohen’s “The Logic of Pure Knowledge” with the revolutionary transformations in physics and mathematics at the end of the 19th century is shown. Сohen criticised Kant’s answer to the question “How is mathematics possible”? If Kant refers to a priori forms of pure intuition, Сohen sees in it a restriction of freedom of mathematical thinking by limits of intuition. It has been shown that Cohen's position is in accordance with the main development (...) of mathematics in the last decades of the 19th century, in particular, with K. Weierstrass’ striving to get rid of geometrical or mechanical images and intuitions in the mathematical analysis. Cohen was also well informed about the latest ideas in physics of his time. They are also discussed in “The Logic of Pure Knowledge.” The revolutionary spirit of physics and mathematics was appealing to Cohen, and he felt a corresponding enthusiasm for it. The ongoing scientific revolution is consonant with Cohen’s assertion that the foundations of science are hypotheses. The purity of pure thinking does not guarantee the correctness of any of its constructions. Each step in the development of science requires a critique of existing notions. The development of knowledge from the naive to the critical one shows a movement from a picture of the world as a set of stable things to a picture of continuous movement and change, where change is more important than what changes. Cohen sees such a development in an evolution of the concept of substance in modern physics and he welcomes the replacement of material substance by energy, seeing this movement as a confirmation of critical idealism. Finally, it is discussed whether we can speak of the actuality of Cohen’s logic of pure knowledge. (shrink)

The notions of common knowledge or common belief play an important role in several areas of computer science , in philosophy, game theory, artificial intelligence, psychology and many other fields which deal with the interaction within a group of “agents”, agreement or coordinated actions. In the following we will present several deductive systems for common knowledge above epistemic logics –such as K, T, S4 and S5 –with a fixed number of agents. We focus on structural and proof-theoretic properties (...) of these calculi. (shrink)

We present a complete, decidable logic for reasoning about a notion of completely trustworthy evidence and its relations to justifiable belief and knowledge, as well as to their explicit justifications. This logic makes use of a number of evidence-related notions such as availability, admissibility, and “goodness” of a piece of evidence, and is based on an innovative modification of the Fitting semantics for Artemovʼs Justification Logic designed to preempt Gettier-type counterexamples. We combine this with ideas from (...) belief revision and awareness logics to provide an account for explicitly justified knowledge based on conclusive evidence that addresses the problem of omniscience. (shrink)

Baltag, Moss, and Solecki proposed an expansion of classical modal logic, called logic of epistemic actions and knowledge (EAK), in which one can reason about knowledge and change of knowledge. Kurz and Palmigiano showed how duality theory provides a flexible framework for modeling such epistemic changes, allowing one to develop dynamic epistemic logics on a weaker propositional basis than classical logic (for example an intuitionistic basis). In this paper we show how the techniques of (...) Kurz and Palmigiano can be further extended to define and axiomatize a bilattice logic of epistemic actions and knowledge (BEAK). Our propositional basis is a modal expansion of the well-known four-valued logic of Belnap and Dunn, which is a system designed for handling inconsistent as well as potentially conflicting information. These features, we believe, make our framework particularly promising from a computer science perspective. (shrink)

One of the cornerstone books of Western philosophy, Critique of Pure Reason is Kant's seminal treatise, where he seeks to define the nature of reason itself and builds his own unique system of philosophical thought with an approach known as transcendental idealism. He argues that human knowledge is limited by the capacity for perception and attempts a logical designation of two varieties of knowledge: a posteriori, the knowledge acquired through experience; and a priori, knowledge not (...) derived through experience. This accurate translation by J. M. D. Meiklejohn offers a simple and direct rendering of Kant's work that is suitable for readers at all levels. (shrink)

We present a bimodal logic suitable for formalizing reasoning about points and sets, and also states of the world and views about them. The most natural interpretation of the logic is in subset spaces , and we obtain complete axiomatizations for the sentences which hold in these interpretations. In addition, we axiomatize the validities of the smaller class of topological spaces in a system we call topologic . We also prove decidability for these two systems. Our results on (...) topologic relate early work of McKinsey on topological interpretations of S4 with recent work of Georgatos on topologic. Some of the results of this paper were presented at the 1992 conference on Theoretical Aspects of Reasoning about Knowledge. (shrink)

The logic of ‘being informed’ gives a formal analysis of a cognitive state that does not coincide with either belief, or knowledge. To Floridi, who first proposed the formal analysis, the latter is supported by the fact that unlike knowledge or belief, being informed is a factive, but not a reflective state. This paper takes a closer look at the formal analysis itself, provides a pure and an applied semantics for the logic of being informed, (...) and tries to find out to what extent the formal analysis can contribute to an information-based epistemology. (shrink)

Although the concept of “pure knowledge” is one of the most interesting and singular concepts in the philosophical work of Vasily Seseman, it can only be presented after a comprehensive analysis of the philosopher’s numerous works devoted to ontological, epistemological and logical problems. Seseman believes that the main philosophical trends at the beginning of the twentieth century, namely neo-Kantianism, intuitionism and phenomenology, could not present this concept, although they did try. According to the philosopher, the main reason for (...) the inability of neo-Kantianism, intuitionism and phenomenology to start talking about pure knowledge is their inability to assert the essential difference between objective and non-objective knowledge. Sesemann pays special attention when substantiating his concept of “pure knowledge” to the difference between his approach and that of the founder of modern phenomenology. The philosopher points out that even Husserl, who concentrated attention on the specifics of inner experience, puts this specific, in the end, in dependence on the process of cognition and reflection, completely ignoring its ontological foundations. While pure knowledge, according to Seseman, is neither non-objective, nor objective knowledge, nor non-objective, nor objective being, it, in fact, is non-knowledge and non-being. It is precisely this understanding by the philosopher of this phenomenon that allows him to characterize pure knowledge as premiseless and limitless and, in general, as free from any ontological or epistemological determinations. However, on the other hand, Sesemann insists that the phenomenon of pure knowledge has the meaning of not just a regulatory idea, an infinitely distant ideal, but also a real constitutive meaning, as a principle that reveals and determines the human striving for knowledge as an interconnected and necessary process that ascends from the onto-gnoseological stage of non-objective knowledge to the epistemological, and then the logical stage of objective knowledge. (shrink)

The difference between Hermann Cohen’s systematic philosophy and his philosophy of religion can be determined via the logical “Judgment of Contradiction,” viewed as an “Authority of Annihilation.” In Cohen’s Logic of Pure Knowledge the “Judgment of Contradiction” acts as a “means of protection” against “falsifications” that may have arisen on the pathway through the previous judgments of “origin” and “identity.” Cohen thematizes these operations in his Religion of Reason Out of the Sources of Judaism, too. However, there (...) they do not form the grounding for natural science but rather for the knowledge of nature as creation in a strict correlation to God’s uniqueness. Any admixture between God and nature is the falseness that must be excluded via the “Authority of Annihilation.” The Being of God places the world over against the possibility of its own radical Non-Being. Yet at the same time, a second mode of Negation, a relative Nothing providing continuity for the world’s being-there, grounded in the “Logic of Origin,” retains its validity. In Cohen’s view a Creation “in the beginning” stands side by side with a continuous “renewal of the world”. (shrink)

A new semantics is presented for the logic of proofs (LP), [1, 2], based on the intuition that it is a logic of explicit knowledge. This semantics is used to give new proofs of several basic results concerning LP. In particular, the realization of S4 into LP is established in a way that carefully examines and explicates the role of the + operator. Finally connections are made with the conventional approach, via soundness and completeness results.

As a multi-layered theory of the foundations of “‘mathematicizing’ logic”, Husserlian pure logic is stratified on three levels (sub-theoretical, theoretical, meta-theoretical), which are then themselves transversally split in two sides (apophantic and ontological). This paper investigates how symbolic knowledge works in this framework—viz. in terms of ‘How can the subjective operating with symbols be justified in the process of obtaining objective contents of knowledge?’ To do so, it innovates in showing how Husserl’s theory of semiotic (...) intentionality provides the epistemological-transcendental foundation for the syntactic-semantic correspondence of the meaning relationship that is operative at the kernel of pure logic—i.e. on the theoretical level, between systems of axioms and formal manifolds. And thereby, it bridges the gap between the two volumes of the first edition of the Logical Investigations (namely, the Prolegomena and the six Investigations). (shrink)

The Nyãya philosophy is primarily concerned with the conditions of valid thought and the means of acquiring true knowledge of objects. Its ultimate end, like that of the other systems of Indian philosophy, is liberation-a state of pure existence- which is free from both pleasure and pain. For the attainment of this liberation, a true knowledge of objects is the surest means. Hence the theory of knowledge is the very foundation of the Nyãya system. The Nyãya (...) Theory of Knowledge is the first systematic, critical and comparative treatment of the Nyãya epistemology. It reveals how, as a thorough-going realistic view of the universe, the Nyãya philosophy supplies an important Eastern parallel to the triumphant modern Realism of the West, and contains anticipations of as well as possible alternatives to many contemporary realistic theories. This book is important as much for the correct understanding of ancient Indian philosophy, as for the evaluation of modern Western philosophy. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Michael Wreen THE LOGIC OF IONESCO'S THE LESSON As men abound in copiousness of language, so they become more wise, or more mad than ordinary. Hobbes, Leviathan, chap. 4 (L a RiTHMETic leads to philology, and philology leads to crime."1 This is both XXthe plot and die pessimism of Ionesco's The Lesson. As the drama unfolds, the spectator watches the world of progress-through-education crumble and a world oflust (...) and murder rise in its ruins. What has gone wrong? In a word, the life oflogic has become the logic oflife. To understand Ionesco's lesson, we must examine the (largely implicit) logic and philosophy of language of his Lesson. Logic, whether die classical syllogistic logic of Aristode, the modern symbolic logic of Russell and Whitehead, or die dialectical logic of Hegel, has two essentia ] components: a syntax, which distinguishes permissible from impermissible combinations and inferences, and a semantics, which allows interpretation and thus fills out the purely formal shell provided by the former. Ionesco's strategy is to show how each of these components as diey have come to be developed philosophically is inadequate to its real content — life, and how, together, they lead, at least metaphorically, to life's devastation. These diree conceptual moments correspond to the three dramatic divisions of the play, marked out by the interruptions of die maid. Ionesco begins with the methodology of logic, syntax, and focuses on arithmetic, which, we are told, "is more a method than a science" (p. 50). Since the time of Descartes, arithmetic, or more generally mathematics, has been the academic discipline par excellence, the study diat all of the empirical sciences have aspired to. So completely has the idea of the mathematical nature of reality impressed itself upon us diat for many people it has acquired the status of an 229 230Philosophy and Literature unquestioned, and even unquestionable, assumption. And for many in this group, including the Professor, it is more dianjust an assumption; it is a way of life. "Let us arithmetize a little," he says to his pupil (p. 51), and his neologism refers not just to a subject matter, arithmetic, but to a way of dealing with subject matters and, ultimately, to a way of dealing with the whole of reality. The noun "arithmetic" has become a verb, and the ascendancy of abstract method has begun. Formal logic, in adi diree of its classic Western forms, is now subjected to sustained and specific criticism. Generally speaking, the Pupil represents Aristotelian and Russellian humanism, a view based on an optimistic belief in man's capacity for direct knowledge, in understanding through analysis by fine distinctions between terms, and in the elimination of paradoxes, both in logic and life. The Professor, again roughly speadcing, represents Hegeliainism, a view based on an optimistic belief in die capacity of reason to unify all oppositions and to overcome, through a higher syndiesis, the fundamentally paradoxical nature of all phenomena, including life itself. Thus, at die level of formal logic and ontology, the Professor amd the Pupil aire diametrically opposed, united only in their uncritical reliatnce upon a method of reason. This philosophical opposition is in turn correlated with a psycho-physical opposition: the Professor is male, old, retiring, and initially lifeless; the Pupil is female, young, forwaurd, amd initiadly vivacious. The confrontation of the two embodied philosophical/ psychological principles over die matter of arithmetic makes dieir opposition manifest and demonstrates, for the first time in the play, die utter inability of bodi philosophical traditions to maintain a grip on reality. This confrontation is also a struggle, one which the fresh, straightforward, vital Pupil begins with great success. She is "magnificent" in addition, and claims she can "count to infinity" — an ability which would vindicate her confident, optimistic belief in man's mental capacities, but an ability, nevertheless, which is logically impossible to possess, since "infinity" is not the name of a particulatrly large number, ais she seems to think. Her claim to understand reveals her as limited and ignorant of the deeper and paradoxical nature of her subject, and thus as in need of further, more abstract lessons. "One must also be able to subtract," die Professor... (shrink)

The paper introduces a semantics for the language of classical first order logic supplemented with the additional operators and . This semantics understands formulas as tasks. An agent , working as a slave for its master , can carry out the task αβ if it can carry out any one of the two tasks α, β, depending on which of them was requested by the master; similarly, it can carry out xα if it can carry out α for any (...) particular value for x selected by the master; an agent can carry out α→β if it can carry out β as long as it has, as a slave , an agent who carries out α; finally, carrying out P, where P is an atomic formula, simply means making P true; in particular, is a task that no agent can carry out. When restricted to the language of classical logic, the meaning of formulas is isomorphic to their classical meaning, which makes our semantics a conservative extension of classical semantics.This semantics can claim to be a formalization of the resource philosophy associated with linear logic, if resources are understood as agents carrying out tasks. The classical operators of our language correspond to the multiplicative operators of linear logic, while and correspond to the additive conjunction and universal quantifier, respectively.Our formalism may also have a potential to be used in AI as an alternative logic of planning and action. Its main appeal is that it is immune to the frame problem and the knowledge preconditions problem.The paper axiomatically defines a logic L in the above language and proves its soundness and completeness with respect to the task semantics in the following intuitive sense: L α iff α can be carried out by an agent who has nothing but its intelligence for carrying out tasks. This logic is shown to be semidecidable in the full language and decidable when the classical quantifier is forbidden in it. (shrink)

First Professor of Logic and Metaphysics at Main Pedagogical Institute and then also St. Petersburg University, Carpatho-Rusyn P. D. Lodij spent a quarter of a century teaching philosophy and law in the Russian Empire in the first third of the 19th century. His knowledge of Kant’s philosophy and his attitude to Kant’s criticism are estimated diametrically opposed in the research literature. An analysis of his main philosophical work, “Logical Precepts which Lead to Cognition and the Distinction of the (...) True from the False” (1815), convincingly proves that Lodij was an excellent scholar of Kant’s philosophy. In Russia, he was the first thinker who spoke about the differences between the first and second editions of the “Critique of Pure Reason”. Lodij also was the first who noted both the revolutionary role of Kant’s Copernican turn, and the importance of Humeʼs causality problem for the formation of critical philosophy. In Russia, Lodij was the first who proposed a detailed description of Kant’s transcendental idealism. At the same time, Lodij’s general attitude to Kant was rather skeptical. In his own logic, he does not follow Kant’s division of logic into pure and applied, but he returns to pre-Kant’s split into theoretical and practical logics. Lodij disputes with the basic conclusions about the space derived from the transcendental aesthetic, denies synthetic judgments a priori and the rooting of the cognizing reason in illusions. Despite his unequivocal claims regarding Kant’s philosophy, “Logical Precepts” and its author were persecuted during the so-called “professorsʼ affair” of the 1820s. As a result, Lodij was suspended from teaching philosophy, and his logic textbook was withdrawn from teaching for both “disgrace” and imaginary Kantianism. (shrink)

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to (...) be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

The publication of the Critique of Pure Reason by Immanuel Kant marked the beginning of an intellectual revolution not only in Philosophy, but also in other spheres of intellectual activity. Every year interest to this work is only growing up, especially in the context of the development of cognitive sciences and technologies related to the development and implementation of artificial intelligence systems. However, both Kant’s contemporaries and subsequent generations of researchers had questions about the basic concepts, outlined in the (...) first Critique. Nikolay Lossky became one of such outstanding experts in Kant’s philosophy, who carried out a metacritique of transcendental idealism. His analysis is interesting because it is characterized by consistency, depth and inclusiveness, despite the fact that he was not a supporter of Kant’s philosophy. The proposed article explicates the main points of the metacritique of pure reason carried out by Lossky. The aim is to systematize the advantages and disadvantages of transcendental idealism highlighted by him in order to assess the validity of objections and identify points that paradoxically escaped Lossky’s attention. In particular, it is shown that the highest evaluation of Lossky is awarded to Kant’s efforts to create an epistemology that does not rely as presuppositions on any other branches of human knowledge; the resolution of contradictions between Empiricism and Rationalism; the creation of the doctrine of synthetic rationality and transcendental logic; the idea of the need for the immanence of knowledge to consciousness. Lossky identified as the key shortcomings of transcendental idealism a range of contradictions grouped around such concepts as the things in themselves, affection, experience, inner sense, transcendental schema, and unity of apperception. At the same time, it is shown that such a key concept for Kant’s theoretical philosophy as transcendental reflection has disappeared from the Lossky’s field of consideration. The study is preceded by a brief description of Lossky’s characteristics, including personal ones, as a meta-critic of pure reason. (shrink)

This research article revisits Hempel’s logic of confirmation in light of recent developments in categorical proof theory. While Hempel advocated several logical conditions in favor of a purely syntactical definition of a general non-quantitative concept of confirmation, we show how these criteria can be associated to specific logical properties of monoidal modal deductive systems. In addition, we show that many problems in confirmation logic, such as the tacked disjunction, the problem of weakening with background knowledge and the (...) problem of irrelevant conjunction, are also associated with specific logical properties and, incidentally, with some of Hempel’s logical conditions of adequacy. We discuss the raven paradox together with further objections against Hempel’s approach, showing how our analysis enables a clear understanding of the relationships between Hempel’s conditions, the problems in confirmation logic, and the properties of deductive systems. (shrink)

We begin with a theory of thought as a biocognition not precisely situated in the individual, and still less in the brain alone, but deriving from a shared field of bioinformation. The structure of associations among elements of speech may reflect the structure of this field. Then we demonstrate that the analysis of the structure of the scientific discourse applied within this logic shows the fractal structure of the field of bioinformation. We also show that scientific culture can be (...) interpreted as a cultural model. So, scientific culture would be the elaboration of a cultural scenario in which each human being is another "myself" according to circumstances, an identification making a relationship of aid possible. This aid relationship is governed by an energy equilibrium defined by the cultural scenario, and may be calculated according to fractal theory. The result is a fractal model of consciousness and of the energies at work, whose equilibrium is necessary for the correct functioning of the human being. The consequences are determined concerning the reinsertion of the logic of the culture within the purely objective logic of medicine, in particular that of "giving-receiving" inherent in all cultures, even at the levels of giving birth in the context of modern medicine. We thank R. Ruiz-Banos for a long-time fruitful collaboration in the field of scientometrics. (shrink)

This paper deals with two opposite metaphilosophical doctrines concerning the nature of philosophy. More specifically, it is a study of the naturalistic view that philosophical, hence also epistemological, knowledge cannot be distinguished from empirical knowledge, and of the antinaturalistic view that philosophical, hence also epistemological, knowledge, is pure, that is, independent of empirical knowledge and particularly of the special sciences. The conditions of the possibility of naturalistic and of pure epistemology are studied in terms (...) of phenomenological philosophy. It is concluded that pure epistemology is possible under relatively strong conditions but that the version of naturalistic epistemology which denies the pure basis leads to contradiction. That, however, does not shake the possibility of cognitive science. Following Husserl, we may argue that studies of human cognition are possible on the condition that a first basis is assumed which is not naturalized. (shrink)

Kant is the last classical practitioner of foundationalist epistemology in the Cartesian tradition, a tradition which saw the major problem of the theory of knowledge as one of providing a metaphysical account of the way in which the subjective contents of the individual mind come to have indubitable objective reference. But he is also the inaugurator of a very different approach to epistemology, one that sees methodology or rules of cognitive procedure as fundamental in determining the objectivity of (...) class='Hi'>knowledge. An examination of Kant's reconstruction of the traditional form-matter distinction and his application of it to the manifold of intuition in the Critique of Pure Reason brings out the transitional character of his philosophy with particular force, and shows the immense impact of his work on the central epistemological issues of representation, explanation, and justification. While Kant continues to employ the traditional term Vorstellung , he extends its signification beyond that of a subjective mental content to an intersubjectively shared scheme of description. Where he adopts scholastic usage in referring to categories as concepts, he does not regard them as highest genera, but interprets them as rules of connection, thereby providing a logical framework suitable for functional, rather than essentialist explanation. Finally, while retaining in his transcendental psychology the conception of mental activity derivative of the older empirical psychology, Kant still manages to distinguish successfully the previously conflated questions of the causal origins vs. the grounds of justification of knowledge. Consideration of subsequent developments in regard to these issues in the light of Kant's work not only lends a certain amount of support to pragmatic conceptions of the nature of knowledge and its justification, but also suggests some promising directions for future epistemological investigation along evolutionary lines. (shrink)

In his response to the question about the conditions of the possibility of dependable cognition Kant first points to the faculties of the cognitive powers and subsequently lists the criteria and normative foundations of knowledge—a system of forms, concepts and principles. Kant primarily seeks the possibilities of experience-independent cognition, the logical criteria governing the possibility of cognition as such. The paper outlines the creation of the systemic union of the primal concepts and principles of pure reason, which is (...) necessary for the creation of knowledge. In other words, it follows the constitution phases of the cognition system: apperception, experience, self-consciousness and the principles of reason. The principles of reason ultimately give systemic unity to humancognitive powers—and, in effect, the human world of experience and cognition. It is this systemic unity which makes cognition science—or, in other words, pure reason—as it constitutes a specific system and is able to create science understood as the systemic unity of specific fields. (shrink)

This course on logic and theory of knowledge fell exactly midway between the publication of the Logical Investigations in 1900-01 and Ideas I in 1913. It constitutes a summation and consolidation of Husserl’s logico-scientific, epistemological, and epistemo-phenomenological investigations of the preceding years and an important step in the journey from the descriptivo-psychological elucidation of pure logic in the Logical Investigations to the transcendental phenomenology of the absolute consciousness of the objective correlates constituting themselves in its acts (...) in Ideas I. In this course Husserl began developing his transcendental phenomenology as the genuine realization of what had only been realized in fragmentary form in the Logical Investigations. Husserl considered that in the courses that he gave at the University of Göttingen he had progressed well beyond the insights of the Logical Investigations. Once he exposed the objective theoretical scaffolding needed to keep philosophers from falling into the quagmires of psychologism and skepticism, he set out on his voyage of discovery of the world of the intentional consciousness and to introduce the phenomenological analyses of knowledge that were to yield the general concepts of knowledge needed to solve the most recalcitrant problems of theory of knowledge understood as the investigation of the thorny problems involving the relationship of the subjectivity of the knower to the objectivity of what is known. This translation appears at a time when philosophers in English-speaking countries have heartily embraced the thoughts of Husserl’s German contemporary Gottlob Frege and his concerns. It is replete with insights into matters that many philosophers have been primed to appreciate out of enthusiasm for Frege’s ideas. Among these are: anti-psychologism, meaning, the foundations of mathematics, logic, science, and knowledge, his questions about sets and classes, intensions, identity, calculating with concepts, perspicuity, and even his idealism. (shrink)

In this paper, I provide an account of what Kant means by “intuition” [Anschauung] in the Critique of Pure Reason. The issue is whether “intuition” should be understood in terms of (1) singularity (e.g., singular concepts, singular representation, etc.), or (2) immediacy in knowledge. By considering issues intemal to the Critique, such as the nature of transcendental logic, the type of intuition God exhibits, and Kant’s use of the term “Anschauung,” I argue that the most fundamental way (...) to view intuition is in terms of immediacy. More specifically, “immediacy” means that intuition is that through which the existence of an object, or the matter that goes into making an object, is given to the mind. (shrink)

In this paper, I provide an account of what Kant means by “intuition” [Anschauung] in the Critique of Pure Reason. The issue is whether “intuition” should be understood in terms of (1) singularity (e.g., singular concepts, singular representation, etc.), or (2) immediacy in knowledge. By considering issues intemal to the Critique, such as the nature of transcendental logic, the type of intuition God exhibits, and Kant’s use of the term “Anschauung,” I argue that the most fundamental way (...) to view intuition is in terms of immediacy. More specifically, “immediacy” means that intuition is that through which the existence of an object, or the matter that goes into making an object, is given to the mind. (shrink)

While discussing his notion of objective knowledge Popper introduces the idea of dispensability of knowing subjects, the autonomy of knowledge and the argumentative function of language. The main claim of our paper is that, on our view, objective knowledge produced by argumentative interaction is not achieved by dispensing knowing subjects but by differentiating between the play and the strategic levels of argumentation, where a distinction should be drawn between a particular concrete knowing subject engaged in that interaction, (...) say Karl, and an arbitrary one. Moreover, the theory of meaning deployed at the level of plays, the so-called local meaning, provides already some kind of objective knowledge, since it is player-independent and it does not reduce to the purely logical one of the strategy level. In fact, despite our criticism we think that Popper's discussion of the notion objective knowledge still deserves to be reflected on, particularly so in view of new results concerning the formalization of Brouwer’s Creating Subject and the dialogical interpretation of the notion of epistemic assumption. (shrink)

We show the faithful embedding of common knowledge logic CKL into game logic GL, that is, CKL is embedded into GL and GL is a conservative extension of the fragment obtained by this embedding. Then many results in GL are available in CKL, and vice versa. For example, an epistemic consideration of Nash equilibrium for a game with pure strategies in GL is carried over to CKL. Another important application is to obtain a Gentzen-style sequent calculus (...) formulation of CKL and its cut-elimination. The faithful embedding theorem is proved for the KD4-type propositional CKL and GL, but it holds for some variants of them. (shrink)

This classic text, written by philosopher and mathematician William Thomson, presents a systematic exposition of the laws of thought and their role in science, logic, and philosophy. The book is still widely used in philosophy and mathematics courses today. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other (...) nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

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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The thirteenth-century logician Lambert of Auxerre was well known for his Summa Lamberti, or simply Logica, written in the mid-1250s, which became an authoritative textbook on logic in the Western tradition. Our knowledge of medieval logic comes in great part from Lambert's Logica and three other texts: William of Sherwood's Introductiones in logicam, Peter of Spain's Tractatus, and Roger Bacon's Summulae dialectics. Of the four, Lambert's work is the best example of question-summas that proceed principally by asking (...) and answering questions on the subject matter. Thomas S. Maloney's translation of Logica, the only complete translation of this work in any language, is a milestone in the study of medieval logic. More than simply a translation, Maloney's project is a critical, comprehensive study of Lambert's logic situated in the context of his contemporaries and predecessors. As such, it offers a wealth of annotation and commentary. The lengthy introduction and extensive notes to the text explain the origin, theoretical context, and intricacies of the text and its doctrines. Maloney also addresses the disputed issues of authorship, date, and place of publication of the Summa Lamberti and makes available to the English-only audience the French, German, and Italian secondary sources--all translated--that are needed to enter the discussion. "Thomas S. Maloney fully commands the primary and secondary sources necessary to elucidate Lambert's Logica. An expert on Roger Bacon's philosophy, he demonstrates a rare proficiency in medieval Latin and scholastic logic. His references to sources from the ancient (Aristotle and Boethius) and medieval worlds are apposite, perspicuous, and useful. The volume's presentation with an appropriate introduction and commentary in the endnotes will no doubt establish it as an indispensable resource for scholars in the twenty-first century." --Alan Perreiah, University of Kentucky. (shrink)

The First International Workshop brings together researchers from the theoretical ends of the logic programming and artificial intelligence communities to discuss their mutual interests. Logic programming deals with the use of models of mathematical logic as a way of programming computers, where theoretical AI deals with abstract issues in modeling and representing human knowledge and beliefs. One common ground is nonmonotonic reasoning, a family of logics that includes room for the kinds of variations that can be (...) found in human reasoning. Topics covered: Stable Semantics. Default Logic. AutoEpistemic Logic. Truth Maintenance Systems. Implementation Issues. Diagnosis. Applications. Inheritance Reasoning. Logics of Belief. Inconsistency and Non-Monotonicity. (shrink)

The problematic relation between logic and knowledge has given rise to some of the most important works in the history of philosophy, from Books VIVII of Platos Republic and Aristotles Prior and Posterior Analytics, to Kants Critique of Pure Reason and Mills A System of Logic, Ratiocinative and Inductive. It provides the title of an important collection of papers by Bertrand Russell. 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. (shrink)

The goal of this paper is to provide an account of the role played by logic in the context of what Husserl names the “crisis of European sciences.” Presupposing the analyses offered in the Krisis, I look at Formale und Transzendentale Logik to demonstrate that the crisis of logic stems from the deviation of its original meaning as a “theory of science” and from its restriction to a mere “theoretical technique.” Through a comparison between Aristotelian syllogistic and modern (...) logic, I show why the modern discovery of the purely formal dimension of knowledge which makes possible such a mathematical technization is a positive achievement that hinders at the same time the disclosure of the truly philosophical nature of logic. The correct appraisal of this ambiguous phenomenon will explain why the rise of modern logic represents a decisive challenge for the success of Husserl’s late phenomenological project. (shrink)

The knowledge norm of assertion is the subject of a lively debate on when someone is in a position to assert something. However, not much has been said about the logic that underlies such debate. In this paper, I propose a formalisation of the knowledge norm in a deontic logic that aims to be explanatory and conceptually sound. Afterwards, I investigate some problems that this formalisation makes visible. This reveals some significant limitations of the underlying (...) class='Hi'>logic: it can neither contain Axiom 4 nor Axiom C4. Moreover, sentences of the form p and I have not asserted that p appear to licence a violation of deontic rules. (shrink)

When one thinks—knows, believes, imagines—that something is the case, one’s thought has a topic: it is about something, towards which one’s mind is directed. What is the logic of thought, so understood? This book begins to explore the idea that, to answer the question, we should take topics seriously. It proposes a hyperintensional account of the propositional contents of thought, arguing that these are individuated not only by the set of possible worlds at which they are true, but also (...) by their topic: what they are about. The book then builds epistemic, doxastic, probabilistic, and conditional logics based on this view. It applies them to issues ranging from dogmatism, scepticism, and epistemic fallibilism, to imagination and suppositional reasoning, belief revision, framing effects, and the acceptability of indicative conditionals. (shrink)

In this paper I address the question 'How is knowledge of logical truths possible'. The sought-after explanation should be independent of what the true story about logical truth is. In particular, I try to account for the epistemic warrant that is conferred upon logical beliefs when they are neither inferred from other beliefs nor grounded on empirical evidence or testimony. The need for such an account is motivated by the apparent failure of the notions ofanalyticity on the one hand (...) and intuition on the other in addressing the relevant question. I end up defending an account according to which warranted logical beliefs can be grounded on pure reasoning: they can be inferentially formed on the basis of pieces of suppositional reasoning. (shrink)

Sarah Moss’ thesis that we have probabilistic knowledge is from some perspectives unsurprising and from other perspectives hard to make sense of. The thesis is potentially transformative, but not yet elaborated in sufficient detail for epistemologists. This paper interprets Mossean probabilistic knowledge in a suitably-modified Kripke framework, thus filling in key details. It argues that probabilistic knowledge looks natural and plausible when so interpreted, and shows how the most pressing challenges to the thesis can be overcome. Most (...) importantly, probabilistic knowledge can satisfy factivity in the framework, though we are not forced to accept a specific account of probabilistic “facts”. The framework also reflects Moss’ claim that old-fashioned propositional knowledge is just a limiting case of probabilistic knowledge, and all knowledge is fundamentally probabilistic. Finally, Moss endorses a failure of contraposition: for example, p implies probably p, but not probably p does not imply not p. The framework makes clear the sense in which the valid inferences regarding probably p are as Moss claims. (shrink)

A brief historical comment on scientific knowledge as Socratic ignorance -- Some critical comments on the text of this book, particularly on the theory of truth Exposition [1933] -- Problem of Induction (Experience and Hypothesis) -- Two Fundamental Problems of the Theory of Knowledge -- Formulation of the Problem -- The problem of induction and the problem of demarcation -- Deductivtsm and Inductivism -- Comments on how the solutions are reached and preliminary presentation of the solutions -- Rationalism (...) and empiricism-deductivism and inductivism -- The possibility of a deductivist psychology of knowledge -- The Problem of Induction -- The infinite regression (Hume's argument) --The inductivist positions -- The Normal-Statement Positions -- The normal-statement positions: naive inductivism, strict positivism and apriorism -- Critique of strict positivism - twofold transcendence of natural laws -- The transcendental method - presentation of apriorism -- Critique of apriorism -- Kant and Fries -- Supplement to the critique of apriorism. (Psychologism and transcendentalism in Kant and Fries.-On the question of the empirical basis.) -- Probability Positions -- The probability positions - subjective belief in probability -- Statements about the objective probability of events -- Probability as an objective degree of validity of universal empirical statements -- One way of more closely defining the concept of the probability of a hypothesis (primary and secondary probability of hypotheses). The concept of simplicity -- The concept of the corroboration of a hypothesis - positivist, pragmatist and probabilistic interpretations of the concept of corroboration -- The infinite regression of probability statements -- Pseudo-Statement Positions -- The pseudo-statement positions: new formulation of the problem -- Natural laws as "instructions for the formation of statements" -- "True - false" or "useful - useless"? Consistent pragmatism --Difficulties of consistent pragmatism -- Tool and schema as purely pragmatic constructs -- Natural laws as propositional functions -- Conventionalism -- The pseudo-statement positions will temporarily be put away: conventionalism -- The three interpretations of axiomatic systems. (The circle of problems surrounding conventionalism) -- Conventionalist implicit and explicit definitions Propositional function and propositional equation -- Conventionalist propositional equations as tautological general implications -- Can axiomatic-deductive systems also be understood as consequence classes of pure propositional functions (of pseudo-statements)? -- The coordinative definitions of empiricism: synthetic general implications -- Conventionalist and empiricist interpretations, illustrated by the example of applied geometry -- Strictly Universal Statements and Singular Statements -- Implication and general implication -- General implication and the distinction between strictly universal and singular statements -- Universal concept and individual concept-class and element -- Strictly universal statements-the problem of induction and the problem of universals -- Comments on the problem of universals -- Back to the Pseudo-Statement Positions -- Return to the discussion of the pseudo-statement positions -- Symmetry or asymmetry in the evaluation of natural laws? -- The negative evaluation of universal statements. Critique of the strictly symmetrical interpretation of pseudo-statements -- An infinite regression of pseudo-statements -- An apriorist pseudo-statement position -- Interpretation of the critique up to this point; comments on the unity of theory and practice -- A last chance for the pseudo-statement positions -- Pseudo-Statement Positions and the Concept of Meaning -- The concept of meaning and logical positivism -- The concept of meaning and the demarcation problem-the fundamental thesis of inductivism -- Critique of the inductivist dogma of meaning -- Fully decidable and partially decidable empirical statements-the antinomy of the knowability of the world. (Conclusion of the critique of the pseudo-statement positions.) -- The dialectical and the transcendental corroboration of the solution -- Is the problem of induction solved? (shrink)

A well-known problem with Hintikka-style logics of knowledge is that of logical omniscience. One knows too much. This breaks down into two subproblems: one knows all tautologies, and one’s knowledge is closed under consequence. A way of addressing the second of these is to move from knowledge simpliciter, to knowledge for a reason. Then, as consequences become ‘further away’ from one’s basic knowledge, reasons for them become more complex, thus providing a kind of resource measurement. (...) One kind of reason is a formal proof. Sergei Artemov has introduced a logic of explicit proofs, LP. I present a semantics for this, based on the idea that it is a logic of knowledge with explicit reasons. A number of fundamental facts about LP can be established using this semantics. But it is equally important to realize that it provides a natural logic of more general applicability than its original provenance, arithmetic provability. (shrink)

A logic of grounding where what is grounded can be a collection of truths is a “many-many” logic of ground. The idea that grounding might be irreducibly many-many has recently been suggested by Dasgupta. In this paper I present a range of novel philosophical and logical reasons for being interested in many-many logics of ground. I then show how Fine’s State-Space semantics for the Pure Logic of Ground can be extended to the many-many case, giving rise (...) to the Pure Logic of Many-Many Ground. In the second, more technical, part of the paper, I do two things. First, I present an alternative formalization of plg; this allows us to simplify Fine’s completeness proof for plg. Second, I formalize plmmg using an infinitary sequent calculus and prove that this formalization is sound and complete. (shrink)

Immanuel Kant was one of the leading lights of 18th-century philosophy; his work provided the foundations for later revolutionary thinkers such as Hegel and Marx. This work contains the keystone of his critical philosophy - the basis of human knowledge and truth.