Charles S. Peirce attempted to develop his semiotic theory of cognitive signs interpretation, which are originated in our basic perceptual operations that quasi-prove the truth of perceptual judgment representing reality. The essential problem was to explain how, by a cognitive interpretation of the sequence of perceptual signs, we can represent external physical reality and reflectively represent our cognitive mind’s operations of signs. With his phaneroscopy introspection, Peirce shows how, without going outside our cognitions, we can represent external reality. Hence (...) Peirce can avoid the Berkeleyian, Humean, and Kantian phenomenologies, as well as the modern analytic philosophy and hermeneutic phenomenology. Peirce showed that with the trio of semiotic interpretation – abductive logic of discovery of hypotheses, deductive logic of necessary inference, and inductive logic of evaluation – we can reach a complete proof of the true representation of reality. This semiotic logic of reasoning is the epistemic logic representing human confrontation in reality, with which we can achieve knowledge and conduct our behavior. However, Peirce did not complete his realistic revolution to eliminate previously accepted nominalistic and idealistic epistemologies of formal logic and pure mathematics. Here, I inquire why Peirce did not complete his historical realist epistemological revolution and following that inquiry I attempt to reconstruct it. (shrink)

The purpose of this article is to consider an answer to the question whether Searle’s idea of sentence in a literary text is still relevant. Understanding literary utterances as specific speech acts, pretended illocutions, is inherent in the process of considering the sentence in a literary text in broader terms. Accordingly, it appears necessary to outline it. Reference to other ideas formulated both in the theory of literature as a speech act [R. Ohmann, S. Levin] as well as in (...) class='Hi'>logic, ontology and the theory of literature [J. Pelc, H. Markiewicz, R. Ingarden] will render it possible to adequately place and assess Searle’s theory. Confronting Searle’s theory with the order in a literary work (the relation between the text and the literary work, the status of the presented world, the issue of reference and fiction) will in turn render it possible to determine how empirically adequate Searle’s theory is. (shrink)

In this collection of essays, which were first delivered as lectures at the International Academy of Philosophy in the Principality of Liechtenstein in 1998, distinguished philosopher Peter Geach confronts some of the most difficult issues in philosophy with the precision of a logician and the grace and wit of an accomplished stylist. These essays constitute a significant addition to Professor Geach's esteemed body of work in philosophy, as he addresses not only problems of logic and analytic philosophy, but also (...) of epistemology and ethics. Geach's engaging discussions of human nature, truth, goodness, and love provide probing insight into perennial themes in an appealing, highly readable style which is nevertheless forceful and exacting. Geach knows the subjectivity of his own experience and belief and is able to illuminate that experience and belief by submitting it to a rational and philosophical inquiry. His avowed Catholic perspective is neither a weapon nor a shield. It is an integral part of the sustained, systematic, and constructive approach to philosophy demonstrated in these essays. They will certainly provoke serious reflection even in those inclined to disagree with Geach's conclusions. (shrink)

The lay follower Citta’s debate with Mahāvīra in the _Nigaṇṭha Sutta_ reflects not just simple polemic, but a fundamental epistemological division between Early Jains and Buddhists. A close reading of the _Ācārāṅga Sūtra_ shows that the Jains see the truth as a property of the self-knowing purified soul that knows all things. For the Buddhists, consciousness is conditioned and dependent. If truth is a property or relation of consciousness, then it too is conditioned and dependent. In order to (...) maintain that truth is the end of the Buddha’s path, Buddhists sever the connection between consciousness and truth by formulating a negative definition of truth. Truth is that which lacks a deceptive nature and accordingly, Nirvāṇa is the ultimate truth. The Buddha’s path culminates in the discovery of truth through the elimination of deception by the annihilation of consciousness, which the Jains hold is impossible because knowledge is essential to the soul. (shrink)

Epistemic Logic is our basic universal science, the method of our cognitive confrontation in reality to prove the truth of our basic cognitions and theories. Hence, by proving their true representation of reality we can self-control ourselves in it, and thus refuting the Berkeleyian solipsism and Kantian a priorism. The conception of epistemic logic is that only by proving our true representation of reality we achieve our knowledge of it, and thus we can prove our cognitions to (...) be either true or rather false, and otherwise they are doubtful. Therefore, truth cannot be separated from being proved and we cannot hold anymore the principle of excluded middle, as it is with formal semantics of metaphysical realism. In distinction, the intuitionistic logic is based on subjective intellectual feeling of correctness in constructing proofs, and thus it is epistemologically encapsulated in the metaphysical subject. However, epistemic logic is our basic science which enable us to prove the truth of our cognitions, including the epistemic logic itself. (shrink)

In this article, I argue that pragmatism has something to gain from returning once more to the question of truth, and acknowledging the truth of the existence of Being and its elements. The practical relevance of this insight is shown by my proposition for a practical hermeneutic social scientific method which logically follows from the truth of Being. The method is compatible with the inevitability of subjective judgments in any kind of scientific research, as well as with (...) many pragmatist insights. It is my hope that pragmatists will be willing to follow their own adagium and conceive of this confrontation with difference as an opportunity to re-assess their views. (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)

A. J. Ayer’s Language, Truth, and Logic had been responsible for introducing the Vienna Circle’s ideas, developed within a Germanophone framework, to an Anglophone readership. Inevitably, this migration from one context to another resulted in the alteration of some of the concepts being transmitted. Such alterations have served to facilitate a number of false impressions of Logical Empiricism from which recent scholarship still tries to recover. In this paper, I will attempt to point to the ways in which (...) LTL has helped to foster the various mistaken stereotypes about Logical Empiricism which were combined into the received view. I will begin by examining Ayer’s all too brief presentation of an Anglocentric lineage for his ideas. This lineage, as we shall see, simply omits the major 19th century Germanophone influences on the rise of analytic philosophy. The Germanophone ideas he presents are selectively introduced into an Anglophone context, and directed towards various concerns that arose within that context. I will focus on the differences between Carnap’s version of the overcoming of metaphysics, and Ayer’s reconfiguration into what he calls the elimination of metaphysics. Having discussed the above, I will very briefly outline the consequences that Ayer’s radicalisation of the Vienna Circle’s doctrines had on the subsequent Anglophone reception of Logical Empiricism. (shrink)

This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive (...) notation facilitates proofs of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory. Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises. Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification. (shrink)

The aim of this paper is to provide a proof-theoretic characterization of relevant logics including fusion and fission connectives, as well as Ackermann’s truth constant. We achieve this by employing the well-established methodology of labelled sequent calculi. After having introduced several systems, we will conduct a detailed proof-theoretic analysis, show a cut-admissibility theorem, and establish soundness and completeness. The paper ends with a discussion that contextualizes our current work within the broader landscape of the proof theory of relevant logics.

This chapter contains sections titled: Abstract Introduction Logic and Confronting the Truth Avoiding Contradiction in Discourse Relativism Inside Logic: Ways of Avoiding Contradictions Avoiding Contradiction in the Setting of Agency Conclusion References.

As we all know, metaphysics and objective truth are basically antagonistic, while dialectical materialism and objective truth are uniform. This is the common sense of Marxist philosophy and needs no argument. What, then, is the relationship between formal logic as a science and objective truth? This involves the problem of the correctness of thought form and the truthfulness of thought content. As shown, this problem is still an unsettled dispute in philosophy and logic circles. There (...) are two opposite views: one view holds that formal logic should concern itself with the correctness of thought form and the truthfulness of thought content; the other holds that formal logic should concern itself only with the correctness of thought form, but not the truthfulness of thought content. The substance of the issue involves the problem of the relationship between formal logic and objective truth. We consider that the science of formal logic itself does not and cannot assume the task of solving objective truth, since it is basically distinguished from the philosophy of dialectical materialism. However, formal logic does not exclude objective truth. It differs basically from metaphysics in that formal logic is a science. Thus, there is no inherent and necessary link between formal logic and objective truth. Formal logic does not study the problem of objective truth. (shrink)

This chapter explores logical semantics, that is, the structural meaning of logical expressions like connectives, quantifiers, and modalities. It focuses on truth-theoretical semantics for formalized languages, a tradition emerging from Carnap's and Tarski's work in the first half of the last century that specifies the meaning of these expressions in terms of the truth-conditions of the sentences in which they occur. It considers Tarski-style definitions of the semantics of a given language in a stronger metalanguage, Tarski's impossibility results, (...) and attempts to overcome them in the post-Tarskian tradition. (shrink)

The author describes an interpreted modal language and produces some clear examples of logical and analytic truths that are not necessary. These examples: (a) are far simpler than the ones cited in the literature, (b) show that a popular conception of logical truth in modal languages is incorrect, and (c) show that there are contingent truths knowable ``a priori'' that do not depend on fixing the reference of a term.

In lieu of an abstract, here is a brief excerpt of the content:BOOK REVIEWS 697 however, that extreme caution is to be advised upon entering those waters? Fully respectful of this concern, Professor Stambaugh enjoins the reader to "reach his own conclusions about parallels and affinities" concerning "some strains of Nietzsche's thought that are most consonant with an Eastern temper of experience." DAVID B. ALLISON SUNY, Stony Brook W. J. Mander. An Introduction to Bradley's Metaphysics. New York: Oxford University Press, (...) 1994. Pp. viii + 175. Cloth, $39-95. T. L. S. Sprigge. James and Bradley: American Truth and British Reality. Chicago: Open Court, 1993. Pp. xiv + 63o. Cloth, $66.95. Paper, $29.95Until the appearance of Mander's book there had been no short general introduction to Bradley in print since Penguin dropped Wollheim's F. H. Bradley from their list. But in any case, as a result of the work of scholars since its last revision in 1969, Wollheim's account, despite its many virtues, is now known to be misleading in crucial places, for he remained to some extent in the grip of the dismissive caricature of Bradley bequeathed to analytic philosophers by Russell and Moore and stilloften just taken for granted. (See, e.g., almost any textbook which has a chapter on truth.) By drawing on this scholarship Mander offers us a philosopher strikingly different from this caricature. Mander's replacement portrayal is, in its broad outlines, accurate enough to be confidently recommended as giving a good general sketch of Bradley's views (excepting the ethics, which Woliheim managed to include), presenting them sympathetically but not completely uncritically in a way which should offer something of interest to both advanced undergraduates and their teachers. As Oxford has also recently published a selection from Bradley's works (Writings on Logic and Metaphysics, edited by James Allard and Guy Stock, with both general and topic-specific introductions), there is the added benefit that one who wishes to read him can now do so without being faced with wading through some intimidatingly large volumes of often meandering discussion in baffling prose. The two should make a good pair around which to structure classes concerning Bradley. I am not quite so confident about some of the detail of Mander's account, which is, moreover, sometimes explained in a way nearly as obscure as the original on which it is intended to cast light. This last is, of course, hard to avoid in expounding a writer whose whole cast of mind is opposed to the exact formulation of precise theses illustrated with clear examples, and is less misleading than artificial precisification; it also perhaps reduces the risk that students will use it as a substitute for, rather than a guide to, the primary texts themselves. And I want to stress that Mander's overall picture of Bradley's views seems to me reliable and as well situated historically as the book's ' G. M. C. Sprung, "Nietzsche's Interest in and Knowledge of Indian Thought," in The Great Yearof Zarathuara (188z-1981), ed. David Goicoechea (Lanham, MD.: University Press of America, x983), 166-8o. 698 JOURNAL OF THE HISTORY OF PHILOSOPHY 33:4 OCTOBER 1995 brevity allows. Its usefulness is enhanced by a very full bibliography which does include some coverage of the ethics. Sprigge's massive work is far more ambitious. His aim is "to provide a comparative exposition and personal evaluation of [Bradley's and James's] main views on truth and on the general nature of reality" (xiii). He gives several reasons for selecting these two philosophers for attention: they are the most important of their time; they are misunderstood and misrepresented; and their views have much in common that is largely correct while being the main alternative solutions to the problems they confront. Further, ajoint treatment makes sense because "it is toJames, rather than Russell, let alone Moore, that we must look for a serious critique of Bradley" (417). This is a labor of love, exhibiting reading of remarkable breadth and depth and the familiarity with its subject matter that is the product only of decades of exploration. Perhaps this very familiarity is part of the explanation of an occasional paucity of textual backup for the pictures Sprigge... (shrink)

'There is much food for thought in McGinn's discussions and each chapter is rich with a series of considerations for thinking that the currently received views on the various topics have some serious difficulties that need confronting... For those interested in metaphysics and the philosophy of logic, this book will stimulate much further thought' -Mind 'The sweep of the book is broad and the pace is brisk... There is much material here to provide the basis for many a (...) deep philosophical discussion' -Mind 'Lucid and provocative little book... clear, direct and well argued' -Times Higher Education SupplementIdentity, existence, predication, necessity, and truth are fundamental philosophical concerns. Colin McGinn treats them both philosophically and logically, aiming for maximum clarity and minimum pointless formalism. He contends that there are real logical properties that challenge naturalistic metaphysical outlooks. These concepts are not definable, though we can say a good deal about how they work. The aim of Logical Properties is to bring philosophy back to philosophical logic. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Diacritics 29.4 (1999) 150-177 [Access article in PDF] The Desire for the Sovereign and the Logic of Reciprocity in the Family of Nations Lydia H. Liu It may sound like a truism that the modern nation cannot imagine itself except in sovereign terms. But what is this truism saying or, rather, withholding from us? When Benedict Anderson wrote his influential study of nationalism in 1983, he circumscribed the (...) imagining of the nation as "both inherently limited and sovereign" and relied on this basic understanding to explain the global transformation of dynastic empires into nation-states [Imagined Communities 6]. That insight, however, has not drawn to itself as much attention or scrutiny as some of his other concepts, like "print capitalism" or "creole nationalisms." If one were to name a few of the blind spots in the contemporary discussions of nationalism, cosmopolitanism, and diaspora, one of them would be the place and placing of sovereignty and sovereign right. To those of us whose initial purpose has been to historicize the nation and nationalism, this blind spot cannot but raise some serious methodological and interpretive questions. Insofar as sovereignty articulates a major mode of exchange between nation and empire in recent history and moreover figures prominently in the realm of what Anderson calls "quotidian universals" [Spectre of Comparisons 33], the truism of its truth needs to be unpacked carefully.Hence, I would like to raise some tentative questions about desire and sovereignty, not in terms of legal studies, but in light of what we have learned about colonial exchange and its production of difference, fetishism, identity, and the logic of reciprocity. I am going to show that these intellectual and material developments have had significant bearings on the making of international law such that our inquiry into the latter can no longer be confined to the self-explanatory evolution of legal discourse. For sovereign thinking is one of those areas that must be reexamined, to borrow Edward Said's words, "according to a detailed logic governed not simply by empirical reality but by a battery of desires, repressions, investments, and projections" [18].In this essay, I begin with a critical analysis of Benedict Anderson's work, focusing on the interplay of the historical and the universal in his study of the nation. I am particularly interested in examining what Anderson chose to do, or not to do, with sovereignty in his theory of nationalism, and I raise some questions about his idea of the "modular," whereby the universal takes on the role of a migrant figure making histories [End Page 150] here and there. Section two introduces the subject of fetishism and desire into the discussion by linking the display of the thrones of the Emperor Qianlong in British museums to significant moments of sovereign thinking in the reign of Queen Victoria and the Empress Dowager of China at the turn of the century. In section three, I attempt a detailed discussion of the sovereignty complex of Ku Hung-ming, a diasporic subject who grew up in colonial Malaysia, was educated in Europe, and ended up serving China as his adopted sovereign country. My analysis centers on Ku's well-known defense of the Empress Dowager during the popular nationalist uprising of 1900 and his work as a translator and publicist in Anglo-Chinese military confrontations. Finally, I turn to the theories of international law itself and ask how nineteenth-century jurists revised the notion of sovereignty to arrive at a new constitutive theory of recognition in the heyday of imperialist expansion. I argue that any attempt to explain the rise of the modern nation-state must take full account of this significant revision in the early nineteenth century, because the revision signaled a paradigmatic shift from natural law to positivist jurisprudence to the effect that a constitutive understanding of sovereign right would eventually overcome and displace the natural law notion of universal sovereignty. Sovereign Thinking in Migrant Nationalisms In Imagined Communities, Anderson pointed to sovereignty as a necessary condition in thinking about the nation when, for example, he... (shrink)

After defining a standard modal language and semantics, we offer some clear examples of logical and analytic truths that are not necessary. These examples: (a) are far simpler than the ones cited in the literature, (b) show that a popular conception of logical truth in modal languages is incorrect, and (c) show that there are contingent truths knowable ``a priori'' that do not depend on fixing the reference of a term.

The claim to truth has been common to both positive science and philosophy. But at present there is no consensus concerning what this claim to truth can mean for philosophical inquiry. Can a given philosophical position be regarded as true or false? Is it still possible to say that philosophical inquiry aims at truth at all? I argue that philosophy must be seen as oriented toward the disclosure of truth if it is to retain that critical (...) dimension in which alone constructive disagreement is possible. At the same time, I argue that the concept of truth which regulates philosophical inquiry is not that of the traditional correspondence theory. Rightly interpreted, the correspondence theory describes the meaning of truth for the positive sciences, which are concerned with facts; but it is adequate for an understanding of philosophy, which as a reflective enterprise is concerned with the meaning of facts. The aim of the dissertation, then, is to demonstrate the reflective connection between truth and meaning by exploring the concept of truth as developed in transcendental logic--the enterprise which thematizes the conditions which make knowledge of objects possible. ;In light of this problem, it is possible to see Heidegger's concept of truth in Being and Time as an important contribution to our understanding of the meaning of truth for reflection. Heidegger's theory of truth is often misinterpreted as an attempt to subvert the critical theory of truth as correspondence. However, it is in fact an attempt to situate the concept of propositional truth within a wider notion of truth as the disclosure of meaning as such, a notion which is necessary in order to understand the possibility of propositional truth. ;To show this, the dissertation traces the origin of Heidegger's concept of truth to its source in problems arising from the tradition of transcendental logic. This involves an examination of Heidegger's works prior to Being and Time, as well as a discussion of those philosophers from whom these works derive their inspiration. Most important among them are Emil Lask, whose revision of Kant's doctrine of categories led to a reflective identification of the object as such with meaning; and Edmund Husserl, whose concept of intuition and evidence allows us to see how such "original" meaning is given. But both Lask and Husserl remain tied to a correspondence theory in their attempts to explicate the relation between meaning and truth. Having subscribed to this position in his early works, Heidegger's reflection on the origin of meaning leads finally to the recognition that truth is first of all the historical disclosure of an horizon of meaning or intelligibility, within which alone it is possible to understand how a statement can "correspond" to the entity as it is in itself. ;The dissertation thus aims at establishing two points: that Heidegger's theory of truth is meant to describe a concept of truth adequate to the claims of philosophical reflection; and that this concept of truth must be seen as an answer to specific problems which arise from the theory of truth developed in the tradition of transcendental logic. (shrink)

A principal aim of Chateaubriand’s Logical Forms II: Logic, Language, and Knowledge is to clarify and defend what Chateaubriand describes as the ontological conception of logic against the standard model-theoretic or “linguistic” view. Both sides to the debate accept that if logic is a science then there must be logically necessary facts that this science discovers, Chateaubriand arguing that because logic is a science, there must be logically necessary facts, and his opponent that because there are (...) no logically necessary facts, logic cannot be a science. I argue that we can go between the horns of this dilemma by showing that, although logic is a science, it does not follow, as Chateaubriand assumes, that there are logically necessary facts. There are truths of logic; there are no “logical truths”.Um dos objetivos principais de Logical Forms II: Logic, Language and Knowledge de Chateaubriand é clarificar e defender o que ele descreve como a concepção ontológica da lógica, contra a visão predominante, modelo-teórica ou “lingüística”. Os dois lados do debate aceitam que, se a lógica é uma ciência, então deve haver fatos logicamente necessários que esta ciência descobre; Chateaubriand argumenta que, porque a lógica é ciência, deve haver fatos necessários que ela descobre, enquanto seus oponentes argumentam que, porque não há fatos logicamente necessários, a lógica não pode ser uma ciência. Eu argumento que podemos tomar uma via intermediária entre estes dois lados do dilema mostrando que, ainda que a lógica seja uma ciência, não se segue, como Chateaubriand assume, que existem fatos logicamente necessários. Existem verdades da lógica; não existem “verdades lógicas”. (shrink)

This article informally presents a solution to the paradoxes of truth and shows how the solution solves classical paradoxes (such as the original Liar) as well as the paradoxes that were invented as counterarguments for various proposed solutions (“the revenge of the Liar”). This solution complements the classical procedure of determining the truth values of sentences by its own failure and, when the procedure fails, through an appropriate semantic shift allows us to express the failure in a classical (...) two-valued language. Formally speaking, the solution is a language with one meaning of symbols and two valuations of the truth values of sentences. The primary valuation is a classical valuation that is partial in the presence of the truth predicate. It enables us to determine the classical truth value of a sentence or leads to the failure of that determination. The language with the primary valuation is precisely the largest intrinsic fixed point of the strong Kleene three-valued semantics (LIFPSK3). The semantic shift that allows us to express the failure of the primary valuation is precisely the classical closure of LIFPSK3: it extends LIFPSK3 to a classical language in parts where LIFPSK3 is undetermined. Thus, this article provides an argumentation, which has not been present in contemporary debates so far, for the choice of LIFPSK3 and its classical closure as the right model for the truth predicate. In the end, an erroneous critique of Kripke-Feferman axiomatic theory of truth, which is present in contemporary literature, is pointed out. (shrink)

The view that contradictions cannot be true has been part of accepted philosophical theory since at least the time of Aristotle. In this regard, it is almost unique in the history of philosophy. Only in the last forty years has the view been systematically challenged with the advent of dialetheism. Since Graham Priest introduced dialetheism as a solution to certain self-referential paradoxes, the possibility of true contradictions has been a live issue in the philosophy of logic. Yet, despite the (...) arguments advanced by dialetheists, many logicians and philosophers still hold the opinion that contradictions cannot be true. -/- Rather than advocating the truth of certain contradictions, this thesis offers a different challenge to the classical logician. By showing that it can be philosophically coherent to propose that true contradictions are metaphysically possible, the thesis suggests that the classical logician must do more than she currently has to justify her confidence in the impossibility of true contradictions. Simply fighting off the dialetheist’s putative examples of true contradictions at the actual world isn’t enough to justify the classical logician’s conclusion that true contradictions are impossible. -/- To aid the thesis dialectically, we introduce a new position, absolutism, which hypothesises that it’s metaphysically possible for at least one contradiction to be true, contrasting with the dialetheic hypothesis that some contradictions are true in the actual world. We demonstrate that absolutism can be given a philosophically coherent interpretation, an appropriate logic, and that certain criticisms are completely toothless against absolutism. The challenge put to the classical logician is then: On what logical or philosophical grounds can we rule out the metaphysical possibility of true contradictions? (shrink)

To criticize a philosopher’s views properly a primary requirement is an accurate understanding of the questions he raises, the problems he acknowledges, and the procedures he follows. In the following study I attempt to identify the specific question of truth which Hegel addresses, the basis of the sort of skepticism posing a serious threat to its resolution, and finally a strategy he adopts. The specific question of truth for Hegel is a question of metaphysical truth or, in (...) the Cartesian terms which Hegel willingly employed, the question of the objectivity of thoughts. The sort of skepticism he has in mind is one which, based on certain purported conditions of human knowing, rejects the possibility of metaphysical truth. While Hegel’s strategy is to analyze those various conditions in an encyclopedic fashion, my concern in this paper is his analysis of the logical conditions of human knowing. (shrink)

To criticize a philosopher’s views properly a primary requirement is an accurate understanding of the questions he raises, the problems he acknowledges, and the procedures he follows. In the following study I attempt to identify the specific question of truth which Hegel addresses, the basis of the sort of skepticism posing a serious threat to its resolution, and finally a strategy he adopts. The specific question of truth for Hegel is a question of metaphysical truth or, in (...) the Cartesian terms which Hegel willingly employed, the question of the objectivity of thoughts. The sort of skepticism he has in mind is one which, based on certain purported conditions of human knowing, rejects the possibility of metaphysical truth. While Hegel’s strategy is to analyze those various conditions in an encyclopedic fashion, my concern in this paper is his analysis of the logical conditions of human knowing. (shrink)

This chapter offers a philosophical reflection on the truth of the medial and the state of exception. It begins with the notion that every single media carrier—be it “natural” or produced by technical means—basically allows for only two operations with signs: to save and to transfer. The entire medial economy that operates with signs makes use of these two operations. All signs have a meaningless, nonsemantic, purely formal, and simultaneously material side beyond all signification. When we confront the media, (...) we are constantly aware of the hidden presence of submedial space. Yet we are structurally incapable of seeing through it as long as we are busy looking at the medial surface. This chapter argues that the media-ontological suspicion is “objective” in the phenomenological sense, because it necessarily appears during the act of observing the medial surface. It also examines the truth of media-ontology as well as the truth of the state of exception in relation to the media-ontological suspicion that defines our perception of the medial surface. (shrink)

This paper aims to explain how the Tractatus attempts to unify logic by deriving the truth-functionality of logical necessity from the thesis that a proposition shows its sense. I first interpret the Tractarian notion of showing as the displaying of what is intrinsic to an expression (or a symbol). Then I argue that, according to the Tractatus, the thesis that a proposition shows its sense implies the determinacy of sense, the possibility of the complete elimination of non-primitive symbols, (...) the analyticity thesis and the strong analyticity thesis. The picture theory emerges as what provides the only acceptable account of an elementary proposition, subject to the constraint that a proposition must show its sense. The picture theory and the analyticity thesis then entail the contingency thesis (that an elementary proposition is contingent) and the independence thesis (that elementary propositions are mutually logically independent) which, together with the strong analyticity thesis, imply that all logical propositions are tautologies. (shrink)

This book tackles the issues that arise in connection with intensional logic -- a formal system for representing and explaining the apparent failures of certain important principles of inference such as the substitution of identicals and existential generalization -- and intentional states --mental states such as beliefs, hopes, and desires that are directed towards the world. The theory offers a unified explanation of the various kinds of inferential failures associated with intensional logic but also unifies the study of (...) intensional contexts and intentional states by grounding the explanation of both phenomena in a single theory. When an axiomatized realm of abstract entities is added to the metaphysical structure of the world, we can use them to identify and individuate the contents of directed mental states. The special abstract entities can be viewed as the objectified contents of mental files, and they play a crucial role in the analysis of truth conditions of the sentences involved in inferential failures. (shrink)

Developing a suggestion of Wittgenstein, I provide an account of truth tables as formulas of a formal language. I define the syntax and semantics of TPL (the language of Tabular Propositional Logic), and develop its proof theory. Single formulas of TPL, and finite groups of formulas with the same top row and TF matrix (depiction of possible valuations), are able to serve as their own proofs with respect to metalogical properties of interest. The situation is different, however, for (...) groups of formulas whose top rows differ. For them I provide (i) a tree-style system of ‘row tree proofs’, which is shown to be sound and complete, and (ii) an alternative, re-writing strategy. (shrink)

Conservativeness has been proposed as an important requirement for deflationary truth theories. This in turn gave rise to the so-called ‘conservativeness argument’ against deflationism: a theory of truth which is conservative over its base theory S cannot be adequate, because it cannot prove that all theorems of S are true. In this paper we show that the problems confronting the deflationist are in fact more basic: even the observation that logic is true is beyond his reach. (...) This seems to conflict with the deflationary characterization of the role of the truth predicate in proving generalizations. However, in the final section we propose a way out for the deflationist — a solution that permits him to accept a strong theory, having important truth-theoretical generalizations as its theorems. (shrink)

The first chapter explores the theory developed in Kripke's "Outline of a Theory of Truth." A tension in Kripke's account of the concept of truth is revealed--a conflict between two intuitions. The first intuition, called the "fixed point conception of truth," is that the whole meaning of the truth predicate is given by the formula "we may assert of a sentence that it is true iff we may assert that sentence." The second intuition, called the "thesis (...) of the supervenience of semantics," is that the interpretation of the truth predicate is determined by the interpretations of all the other non-logical constants of the language. I show that these two intuitions cannot be reconciled within the context of Kripke's theory, and I argue for the choice of the fixed point conception of truth over the principle of the supervenience of semantics. Chief among the considerations that I advance is the fact that the fixed point conception of truth yields a natural logic of truth. In the second chapter I present that logic of truth in the form of a cut-free sequent calculus. I then turn, in chapter three, to a discussion of the significance of such cut-free sequent calculi. I argue that we may view the sequent calculus introduction rules for a logical constant as giving the meaning of that constant, under certain conditions. In particular, we can see our logic of truth as providing an explication of our intuitive concept of truth which complements Kripke's original model-theoretic explication. The fourth chapter takes up some criticisms of Kripke's theory which center on the logic of truth. In addition, the general ideas developed in the first three chapters are applied in a discussion of the various schemes of three-valued logic which can be used in the development of Kripke's approach. Finally, in the last chapter, it is shown that Kripke's technical concepts, and the logical ideas developed in the second and third chapters, can be used to provide a unified account of many contexts in which paradox arises. (shrink)

Though my ultimate concern is with issues in epistemology and metaphysics, let me phrase the central question I will pursue in terms evocative of philosophy of religion: What are the implications of our logic-in particular, of Cantor and G6del-for the possibility of omniscience?

It is usually held that what distinguishes a good inference from a bad one is that a good inference is truth-preserving. Against this view, this paper argues that a logical inference is good or bad depending not on whether it is truth-preserving or not, but whether it belongs to a logical system the addition of which makes a deductively conservative extension of the derivation relations among the atomic statements. To so argue, the paper first contends that the meaning (...) of the logical operators of classical logic is determined not by their connections to truth, but by their inferential roles. It is claimed in conclusion that there is no genuine issue over which logic, classical or intuitionistic, is the correct logic, for they are both conservative in the relevant sense. (shrink)

It is usually held that what distinguishes a good inference from a bad one is that a good inference is truth-preserving. Against this view, this paper argues that a logical inference is good or bad depending not on whether it is truth-preserving or not, but whether it belongs to a logical system the addition of which makes a deductively conservative extension of the derivation relations among the atomic statements. To so argue, the paper first contends that the meaning (...) of the logical operators of classical logic is determined not by their connections to truth, but by their inferential roles. It is claimed in conclusion that there is no genuine issue over which logic, classical or intuitionistic, is the correct logic, for they are both conservative in the relevant sense. (shrink)

In the Logic of Being: Realism, Truth, and Time, the influential philosopher Paul M. Livingston explores and illuminates truth, time, and their relationship by employing methods from both Continental and analytic philosophy.

Overgeneralization -- Vague definition -- Post hoc, propter hoc -- False analogy -- Partial selection of the evidence -- Groupthink -- Scams, deceptions, ruses, swindles, hoaxes and gaslights -- Begging the question -- The logic of Alice.

Abstract This paper discusses some recent work on the notion of possibility in Wittgenstein's Tractatus assessed by means of an interpretation of the notion put forward in Cerezo 2005. It argues that the proper way to understand the notion of possibility in the Tractatus must pay equal attention both to the picture theory and the truth-functions theory. From this perspective, through an examination of Peach's proposal (2007) it shows that the role played by the notion of logical space in (...) the determination of sense needs to be emphasized. In addition, the paper considers some consequences of the Tractarian notion of possibility, namely, the strong contingency of the world that it involves, which is revealed by the thinkability of logical space as empty envisaged by Wittgenstein in T 2.013, and also discusses the recent debate between Reinhardt (2005) and Geach (2006) on this issue. (shrink)

In this sequel to "The logic and meaning of plurals. Part I", I continue to present an account of logic and language that acknowledges limitations of singular constructions of natural languages and recognizes plural constructions as their peers. To this end, I present a non-reductive account of plural constructions that results from the conception of plurals as devices for talking about the many. In this paper, I give an informal semantics of plurals, formulate a formal characterization of (...) class='Hi'>truth for the regimented languages that results from augmenting elementary languages with refinements of basic plural constructions of natural languages, and account for the logic of plural constructions by characterizing the logic of those regimented languages. (shrink)

Logical reasoning is not only a component of religious faith (cf., for instance, the "Golden rule"), but, in addition, the religious faith itself can be conceived as a logical pragmatic function applied to sentences and their meanings. Pragmatic role of religious faith is shown on the examples of the analogy of seed and spoken word (e.g., Mt 13:3-23) and on the degrees of faith described in the episode about Nicodemus (John 3). Pragmatics adds (different grades of) perseverance to the correctness (...) of reasoning and to the truth-preservation of the consequence relation. Correspondingly, religious faith is described by formally defined model and satisfaction relation, which are applied to and examined on the text of John 3. (shrink)

It is explained what it is for a statement to be logically true and it is thereby explained what it is for a statement to be formally true. It is also explained how logical truth differs from formal truth. Further, it is explained what a system of logic is. Finally, the nature of entailment is explained and, in particular, it is explained how formal entailment differs from analytic entailment.

The volume contains twenty essays devoted to the philosophy of mathematics and the history of logic. They have been divided into four parts: general philosophical problems of mathematics, Hilbert's program vs. the incompleteness phenomenon, philosophy of mathematics in Poland, mathematical logic in Poland. Among considered problems are: epistemology of mathematics, the meaning of the axiomatic method, existence of mathematical objects, distinction between proof and truth, undefinability of truth, Goedel's theorems and computer science, philosophy of mathematics in (...) Polish mathematical and logical schools, beginnings of mathematical logic in Poland, contribution of Polish logicians to recursion theory. (shrink)

In this paper we show that first-order languages extended with partially ordered connectives and partially ordered quantifiers define, under a certain interpretation, their own truth-predicate. The interpretation in question is in terms of games of imperfect information. This result is compared with those of Kripke and Feferman.