Logic in Philosophy

Analyzing the position of two philosophers whose views are recognizably divergent, W. O. Quine and M. Dummett, we intend to support a striking point of agreement between them: the idea that our logical principles constitute our principles about what there is, and therefore, that logic is metaphysics.

The principle of universal instantiation plays a pivotal role both in the derivation of intensional paradoxes such as Prior’s paradox and Kaplan’s paradox and the debate between necessitism and contingentism. We outline a distinctively free logical approach to the intensional paradoxes and note how the free logical outlook allows one to distinguish two different, though allied themes in higher-order necessitism. We examine the costs of this solution and compare it with the more familiar ramificationist approaches to higher-order logic. Our assessment (...) of both approaches is largely pessimistic, and we remain reluctantly inclined to take Prior’s and Kaplan’s derivations at face value. (shrink)

A RELATIVISTIC THEORY OF PHENOMENOLOCICAL CONSTITUTION: A SELF-REFERENTIAL, TRANSCENDENTAL APPROACH TO CONCEPTUAL PATHOLOGY. (Vol. I: French; Vol. II: English) -/- Steven James Bartlett -/- Doctoral dissertation director: Paul Ricoeur, Université de Paris Other doctoral committee members: Jean Ladrière and Alphonse de Waehlens, Université Catholique de Louvain Defended publically at the Université Catholique de Louvain, January, 1971. -/- Universite de Paris X (France), 1971. 797pp. -/- The principal objective of the work is to construct an analytically precise methodology which can serve (...) to identify, eliminate, and avoid a certain widespread _conceptual fault_ or _misconstruction_, called a "projective misconstruction" or "projection" by the author. It is argued that this variety of error in our thinking (i) infects a great number of our everyday, scientific, and philosophical concepts, claims, and theories, (ii) has largely been undetected, and (iii), when remedied, leads to a less controversial and more rigorous elucidation of the transcendental preconditions of human knowledge than has traditionally been possible. The dissertation identifies, perhaps for the first time, a _projective_ variety of self-referential inconsistency, and proposes an innovative, self-reflexive approach to transcendental argument in a logical and phenomenological context. The strength of the approach lies, it is claimed, in the fact that a rejection of the approach is possible only on pain of self-referential inconsistency. The argument is developed in the following stages: A general introduction identifies the central theme of the work, defines the scope of applicability of the results reached, and sketches the direction of the studies that follow. The preliminary discussion culminates in a recognition of the need for a _critique of impure reason_. The body of the work is divided into two parts: Section I seeks to develop a methodology, on a purely formal basis, which is, on the one hand, capable of being used to study the transcendental foundations of the special sciences, including its own proper transcendental foundation. On the other hand, the methodology proposed is intended as a diagnostic and therapeutic tool for dealing with _projective_ uses of concepts. The approach initiates an analysis of concepts from a perspective which views _knowledge as coordination_. Section I describes formal structures that possess the status of preconditions in such a coordinative account of knowledge. Special attention is given to the preconditions of _identifying reference_ to logical particulars. The first section attempts, then, to provide a self-referential, transcendental methodology which is essentially revisionary in that it is motivated by a concern for conceptual error-elimination. Phenomenology, considered in its unique capacity as a self-referential, transcendental discipline, is of special relevance to the study. Section II accordingly examines a group of concepts which come into question in connection with the central theme of _phenomenological constitution_. The "_de-projective methodology_" developed in Section I is applied to these concepts that have a foundational importance in transcendental phenomenology. A translation is, in effect, proposed from the language of consciousness to a language in which preconditions of referring are investigated. The result achieved is the elimination of self-defeating, projective concepts from a rigorous, phenomenological study of the constitutive foundations of science. The dissertation was presented in a two volume, double-language format for the convenience of French and English researchers. Each volume contains an analytical index. (shrink)

This is Vol. I in French. Vol. II in English is available separately from this website. -/- The principal objective of the work is to construct an analytically precise methodology which can serve to identify, eliminate, and avoid a certain widespread conceptual fault or misconstruction, called a "projective misconstruction" or "projection" by the author. -/- It is argued that this variety of error in our thinking (i) infects a great number of our everyday, scientific, and philosophical concepts, claims, and theories, (...) (ii) has largely been undetected, and (iii), when remedied, leads to a less controversial and more rigorous elucidation of the transcendental preconditions of human knowledge than has traditionally been possible. -/- The dissertation identifies, perhaps for the first time, a projective variety of self-referential inconsistency, and proposes an innovative, self-reflexive approach to transcendental argument in a logical and phenomenological context. The strength of the approach lies, it is claimed, in the fact that a rejection of the approach is possible only on pain of self-referential inconsistency. The argument is developed in the following stages: -/- A general introduction identifies the central theme of the work, defines the scope of applicability of the results reached, and sketches the direction of the studies that follow. The preliminary discussion culminates in a recognition of the need for a critique of impure reason. -/- The body of the work is divided into two parts: Section I seeks to develop a methodology, on a purely formal basis, which is, on the one hand, capable of being used to study the transcendental foundations of the special sciences, including its own proper transcendental foundation. On the other hand, the methodology proposed is intended as a diagnostic and therapeutic tool for dealing with projective uses of concepts. -/- The approach initiates an analysis of concepts from a perspective which views knowledge as coordination. Section I describes formal structures that possess the status of preconditions in such a coordinative account of knowledge. Special attention is given to the preconditions of identifying reference to logical particulars. The first section attempts, then, to provide a self-referential, transcendental methodology which is essentially revisionary in that it is motivated by a concern for conceptual error-elimination. -/- Phenomenology, considered in its unique capacity as a self-referential, transcendental discipline, is of special relevance to the study. Section II accordingly examines a group of concepts which come into question in connection with the central theme of phenomenological constitution. The "de-projective methodology" developed in Section I is applied to these concepts that have a foundational importance in transcendental phenomenology. A translation is, in effect, proposed from the language of consciousness to a language in which preconditions of referring are investigated. The result achieved is the elimination of self-defeating, projective concepts from a rigorous, phenomenological study of the constitutive foundations of science. -/- The dissertation was presented in a two volume, double-language format for the convenience of French and English researchers. Each volume contains an analytical index. (shrink)

According to a prevalent view among philosophers formal logic is the philosopher’s main tool to assess the validity of arguments, i.e. the philosopher’s ars iudicandi. By drawing on a famous dispute between Russell and Strawson over the validity of a certain kind of argument – of arguments whose premises feature definite descriptions – this paper casts doubt on the accuracy of the ars iudicandi conception. Rather than settling the question whether the contentious arguments are valid or not, Russell and Strawson, (...) upon discussing the proper logical analysis of definite descriptions, merely contrast converse informal validity assessments rendered explicit by nonequivalent logical for-malizations. (shrink)

The present book discusses all aspects of paraconsistent logic, including the latest findings, and its various systems. It includes papers by leading international researchers, which address the subject in many different ways: development of abstract paraconsistent systems and new theorems about them; studies of the connections between these systems and other non-classical logics, such as non-monotonic, many-valued, relevant, paracomplete and fuzzy logics; philosophical interpretations of these constructions; and applications to other sciences, in particular quantum physics and mathematics. Reasoning with contradictions (...) is the challenge of paraconsistent logic. The book will be of interest to graduate students and researchers working in mathematical logic, computer science, philosophical logic, linguistics and physics. (shrink)

A collection of papers from Paul Hertz to Dov Gabbay - through Tarski, Gödel, Kripke - giving a general perspective about logical systems. These papers discuss questions such as the relativity and nature of logic, present tools such as consequence operators and combinations of logics, prove theorems such as translations between logics, investigate the domain of validity and application of fundamental results such as compactness and completeness. Each of these papers is presented by a specialist explaining its context, import and (...) influence. (shrink)

This work, the first book-length study of its topic, is an important contribution to the literature of philosophical logic and philosophy of language, with implications for other branches of philosophy, including philosophy of mathematics. However, five of the book's ten chapters , including many of the author's most original contributions, are devoted to issues about natural language, and lie pretty well outside the scope of this journal, not to mention that of the reviewer's competence. For this reason I will here (...) largely confine my attention to the other half of the book, and so will be far from doing full justice to the book as a whole; indeed, there is such a wealth of detail in the book that I will be unable to do full justice even to the five chapters selected for comment.Non-distributive predicates.To begin with some points that have often been remarked, formulas in classical first-order logic are built up from predicates by means of a limited range of logical operators . Natural language involves many other such operators, beginning with temporal and modal operators, that are of great philosophical interest, but these are ignored by classical first-order logic. The reasons why it ignores them are surely that classical first-order logic was developed primarily for analyzing mathematical arguments, and that such grammatical categories as tense and mood play no significant role in mathematics.It has been less often remarked that the range of predicates considered in classical first-order logic is also limited. From Frege onwards, predicates have been taken to be essentially sentences with one or more gaps or places suitable to be filled in by singular noun phrases. Natural language involves also plural predicates, as well as mixed predicates with some …. (shrink)

John Dewey is celebrated for his work in the philosophy of education and acknowledged as a leading proponent of American pragmatism. His philosophy of logic, on the other hand, is largely unheard of. In Dewey's New Logic, Burke analyzes portions of the debate between Dewey and Bertrand Russell that followed the 1938 publication of Dewey's Logic: The Theory of Inquiry. Burke shows how Russell failed to understand Dewey, and how Dewey's philosophy of logic is centrally relevant to contemporary developments in (...) philosophy and cognitive science. Burke demonstrates that Russell misunderstood crucial aspects of Dewey's theory and contends that logic today, having progressed well beyond Russell's early views, is approaching Dewey's broader perspective. -/- "[This] book should be of substantial interest not only to Dewey scholars and other historians of twentieth-century philosophy, but also to devotees of situation theory, formal semantics, philosophy of mind, cognitive science, and Artificial Intelligence."--Georges Dicker, Transactions of the C.S. Peirce Society "No scholar, thus far, has offered such a sophisticated and detailed version of central themes and contentions in Dewey's Logic . This is a pathbreaking study."--John J. McDermott, editor of The Philosophy of John Dewey. (shrink)

A conceptual theory of the referential and predicable concepts used in basic speech and mental acts is described in which singular and general, complex and simple, and pronominal and nonpronominal, referential concepts are given a uniform account. The theory includes an intensional realism in which the intensional contents of predicable and referential concepts are represented through nominalized forms of the predicate and quantifier phrases that stand for those concepts. A central part of the theory distinguishes between active and deactivated referential (...) concepts, where the latter are represented by nominalized quantifier phrases that occur as parts of complex predicates. Peter Geach's arguments against theories of general reference in Reference and Generality are used as a foil to test the adequacy of the theory. Geach's arguments are shown to either beg the question of general as opposed to singular reference or to be inapplicable because of the distinction between active and deactivated referential concepts. (shrink)

A Inseparabilidade entre Lógica e a Ética. Philósophos. 18 (2013) 245–259. Portuguese translation by Décio Krause and Pedro Merlussi: The Inseparability of Logic and Ethics, Free Inquiry, Spring 1989, 37–40. This essay takes logic and ethics in broad senses: logic as the science of evidence; ethics as the science of justice. One of its main conclusions is that neither science can be fruitfully pursued without the virtues fostered by the other: logic is pointless without fairness and compassion; ethics is pointless (...) without rigor and objectivity. The logician’s advice to be dispassionate is in resonance and harmony with the ethicist’s advice to be compassionate. (shrink)

A universal proposition is shown false by a known counterexample. A premise-conclusion argument is shown invalid by a known counterargument. The failure to distinguish counterexample from counterargument is like the failure to distinguish falsehood from invalidity.

The logical form of a discourse—such as a proposition, a set of propositions, an argument, or an argumentation—is obtained by abstracting from the subject-matter of its content terms or by regarding the content terms as mere place-holders or blanks in a form. In a logically perfect language the logical form of a proposition, a set of propositions, an argument, or an argumentation is determined by the grammatical form of the sentence, the set of sentences, the argument-text, or the argumentation-text expressing (...) it. Two such discourse-texts are said to have the same grammatical form, in this sense, if a uniform one-one substitution of content words transforms the one exactly into the other. The sentence ‘Abe properly respects every agent who respects himself’ may be regarded as having the same grammatical form as the sentence ‘Ben generously assists every patient who assists himself’. (shrink)

Peter H. Hare (1935-2008) developed informed, original views about the proposition: some published (Hare 1969 and Hare-Madden 1975); some expressed in conversations at scores of meetings of the Buffalo Logic Colloquium and at dinners following. The published views were expository and critical responses to publications by Curt J. Ducasse (1881-1969), a well-known presence in American logic, a founder of the Association for Symbolic Logic and its President for one term.1Hare was already prominent in the University of Buffalo's Philosophy Department in (...) 1969 when I was appointed. Soon after, he became Chair. As his Associate Chair from 1971to 1975, I spent many hours with him in Buffalo and on professional trips .. (shrink)

This essay takes logic and ethics in broad senses: logic as the science of evidence; ethics as the science justice. One of its main conclusions is that neither science can be fruitfully pursued without the virtues fostered by the other: logic is pointless without fairness and compassion; ethics is pointless without rigor and objectivity. The logician urging us to be dispassionate is in resonance and harmony with the ethicist urging us to be compassionate.

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

This interesting and imaginative monograph is based on the author’s PhD dissertation supervised by Saul Kripke. It is dedicated to Timothy Smiley, whose interpretation of PRIOR ANALYTICS informs its approach. As suggested by its title, this short work demonstrates conclusively that Aristotle’s syllogistic is a suitable vehicle for fruitful discussion of contemporary issues in logical theory. Aristotle’s syllogistic is represented by Corcoran’s 1972 reconstruction. The review studies Lear’s treatment of Aristotle’s logic, his appreciation of the Corcoran-Smiley paradigm, and his understanding (...) of modern logical theory. In the process Corcoran and Scanlan present new, previously unpublished results. Corcoran regards this review as an important contribution to contemporary study of PRIOR ANALYTICS: both the book and the review deserve to be better known. (shrink)

I saggi che compongono questo libro intendono presentare in maniera organica e interdisciplinare, anche se da una prospettiva fondazionale logico-filosofica, il ruolo che il concetto di prova svolge in differenti ambiti del sapere. L’elemento innovativo e caratterizzante del volume è quello di stabilire e formulare quali sono le condizioni di adeguatezza materiale e formale per una corretta esplicazione del concetto di prova nelle sue differenti applicazioni. Si cercherà, inoltre, di cogliere cosa ha qualificato storicamente e qualifica tuttora il concetto di (...) prova tentando di individuarne, da un lato, le caratteristiche persistenti o invarianti e, dall’altro, le differenze specifiche che esso assume in molteplici settori della ricerca. Vengono così presentati sette saggi che spaziano sui seguenti temi: dalle procedure logiche di prova medievali (Alfredo Di Giorgio), si va alla nozione di prova da Frege a Wittgenstein (Carlo Penco), al problema delle verità delle proposizioni gödeliane (Sergio Galvan), alla fondazione delle leggi logiche (Ciro De Florio), ai fondamenti del linguaggio pragmatico (Antonio Negro e Davide Sergio), alla relazione tra conoscibilità e prova (Massimiliano Carrara e Daniele Chiffi), fino all’analisi del paradosso del buon samaritano (Andrea Favaro e Silvia Gaio). (shrink)

Following the development of the selectionist theory of the immune system, there was an attempt to characterize many biological mechanisms as being "selectionist" as juxtaposed to "instructionist." But this broad definition would group Darwinian evolution, the immune system, embryonic development, and Chomsky's language-acquisition mechanism as all being "selectionist." Yet Chomsky's mechanism (and embryonic development) are significantly different from the selectionist mechanisms of biological evolution or the immune system. Surprisingly, there is a very abstract way using two dual mathematical logics to (...) make the distinction between genuinely selectionist mechanisms and what are better called "generative" mechanisms. This note outlines that distinction. (shrink)

Some commentators, such as Jürgen Habermas, think Martin Heidegger is guilty of a performative contradiction, because he uses judgments to situate judgments in a non-judicative context. This paper defends Heidegger by distinguishing two senses of judgment in his thought. Temporality enables two different directions of inquiry and hence two kinds of judgment. Scientific judgments arise when we turn from the temporal horizon toward entities alone; phenomenological judgments arise when we return to the temporal horizon in which such entities are accessible. (...) Consequently, using phenomenological judgments to show the condition for the possibility of scientific judgments is not contradictory. (shrink)

Research in multi-agent systems typically assumes a regulative model of social practice. This model starts with agents who are already capable of acting autonomously to further their individual ends. A social practice, according to this view, is a way of achieving coordination between multiple agents by restricting the set of actions available. For example, in a world containing cars but no driving regulations, agents are free to drive on either side of the road. To prevent collisions, we introduce driving regulations, (...) insisting that everyone drives on the left hand side of the road. We accept this limitation on our freedom because it lowers the probability of a collision. -/- This paper describes AI systems that are based on the constitutive view of social practice. According to this alternative view, there are certain actions that are only available to the agent because he is participating in a practice of a certain sort. For example, you can swing a peculiarly shaped piece of wood without participating in any particular practice - but this action will only constitute a strike if you are participating in a game of baseball. I can raise my hand whenever I like, but this only counts as voting for the motion within the institution of voting. But not all the examples are from frivolous, optional or institutional activities. Sellars and Brandom argue that even the fundamental act of assertion is only possible within the context of a particular social practice: the Game of Giving and Asking for Reasons. -/- The constitutive view, which is familiar to philosophers, is relatively unknown within the AI community. -/- The central aim of this paper is to show how the constitutive view of practice can be put to use in AI applications. (shrink)

In this article, I consider the possibility of interpreting Hegel’s dialectic as dialetheism. After a first basic recapitulation about the meaning of the words ‘dialetheism’ and ‘dialectic’ and a consideration of Priest’s own account of the relation between dialectical and dialetheic logic in 1989, I discuss some controversial issues, not directly considered by Priest. As a matter of fact, the reflection on paraconsistent logics and dialetheism has enormously grown in recent years. In addition, the reception of Hegel’s logic and metaphysics (...) has also impressively improved. So I suggest that the discussion about the binomial dialectic/dialetheism should be reopened, on these new bases. (shrink)

We discuss the interplay between the axiomatic and the semantic approach to truth. Often, semantic constructions have guided the development of axiomatic theories and certain axiomatic theories have been claimed to capture a semantic construction. We ask under which conditions an axiomatic theory captures a semantic construction. After discussing some potential criteria, we focus on the criterion of ℕ-categoricity and discuss its usefulness and limits.

One of the central tasks of Badiou’s Being and Event is to elaborate a theory of the subject in the wake of an axiomatic identification of ontology with mathematics, or, to be precise, with classical Zermelo-Fraenkel set theory. The subject, for Badiou, is essentially a free project that originates in an event, and subtracts itself from both being qua being, as well as the linguistic and epistemic apparatuses that govern the situation. The subjective project is, itself, conceived as the temporal (...) unfolding of a ‘truth’. originating in an event and unfolding in time, the subject cannot, for Badiou, be adequately understood in strictly ontological, i.e. set-theoretical, terms, insofar as neither the event nor time have any place in classical set theory. Badiou nevertheless seeks to articulate the ontological infrastructure of the subject within set theory, and for this he fastens onto Cohen’s concepts of genericity and forcing: the former gives us the set-theoretic structure of the truth to which the subject aspires, the latter gives us the immanent logic of the subjective procedure, the ‘law of the subject’. Through the forcing operation, the subject is capable of deriving veridical statements from the local status of the truth that it pursues. Between these set-theoretic structures, and a doctrine of the event and temporality, badiou envisions the subject as an irreducibly diachronic unfolding of a truth subtracted from language, a subject which expresses a logic quite distinct from that which governs the axiomatic deployment of his classical ontology. This vision of the subject is not unique to Badiou’s work. we find a strikingly similar conception in the thought of L.E.J. Brouwer, the founder of intuitionist mathematics. Brouwer, too, insists on the necessary subtraction of truth from language, and on its irreducibly temporal genesis. This genesis, in turn, is entirely concentrated in the autonomous activity of the subject. Moreover, this activity, through which the field of intuitionistic mathematics is generated, expresses a logical structure that, in 1963, Saul Kripke showed to be isomorphic with the forcing relation. In this essay, I take up an enquiry into the structure of these two theories of the subject, and seek to elucidate both their points of divergence and their strange congruencies; the former, we will see, primarily concern the position of the subject, while the latter concern its form. The paper ends with an examination of the consequences that this study implies for Badiou’s resolutely classical approach to ontology, and his identification of ontology as a truth procedure. (shrink)

I point out some logical errors and infelicities in Hájek’s discussion of philosophical heuristics.

Strawson offers three accounts of singular predication: a grammatical, a category and a mediating account. I argue that the grammatical and mediating accounts are refuted by a host of counter-examples and that the latter is worse than useless. In later works Strawson defends only the category account. This account entails that singular terms cannot be predicates; it excludes non-denoting singular terms from being logical subjects, except by means of an ad hoc analogy; it depends upon a notion of identification that (...) is too vague; and it is unnecessarily complicated, relying on analogies where a more uniform explanation should be possible. But I show how the account can be corrected to avoid all these difficulties and to provide an accurate account of singular predication. (shrink)

The approach to the question of philosophical practice has been dominated by a subordination of practice to theory corresponding in general to a representational conception of philosophy. Methods of diagrammatic reasoning developed within philosophical semiotics provide a more effective approach. Inparticular, Peirce’s system of existential graphs exemplifies how diagrammatic reasoning is able formally to express the processes through which philosophical dialogue and cooperation actually take place and to link such processes to the methods and practices arising in other disciplines and (...) traditions, including those of science, politics, art, religion and technological production. (shrink)

Pour des raisons essentiellement liées à la vocation des textes où la notion de présupposition a fait son apparition, c’est la présupposition d’existence qui s’est imposée la première à l’attention des philosophes du langage. Elle a également déterminé l’orientation des débats en les focalisant sur quelques problèmes traditionnels, au premier chef desquels le problème de l’absence de référence de certaines expressions et celui des imperfections du langage naturel. Contrairement aux noms propres et aux descriptions définies, les termes qui signifient des (...) universaux ont joué un rôle très marginal dans la discussion de ce qui est présupposé par les énoncés que nous échangeons. Ce sont pourtant les noms d’espèces et de genres qui ont été associés les tout premiers à des phénomènes qui relèvent de la présupposition. Afin de montrer que cette association n’a rien perdu de son intérêt, nous avons étudié le traitement qu’Aristote réserve à la famille de paralogismes qui exploitent la similarité morphologique entre noms propres et noms communs pour rattacher la même présupposition d’existence aux uns et aux autres, alors même que cette présupposition est légitime dans un cas (celui des expressions qui désignent des choses particulières), abusive dans l’autre cas (celui des expressions qui signifient des universaux). (shrink)

Die Reflexion der Grundlagen der Wissenschaft mit ihren eigenen Mitteln, wie die gedankliche Vermessung des Messprozesses, die in die Begründung der Quantenphysik eingeht, und die logische Analyse der Logik im Rahmen der mathematischen Entscheidungstheorie zeigt schließlich prinzipielle Grenzen des möglichen Wissens auf. Eine Theorie des Leib-Seele-Zusammenhangs läuft auf das Bewusstsein von Bewusstsein hinaus und ist damit von dem gleichen Typ des Selbstbezugs, der auf prinzipielle Grenzen der Erkenntnis verweist. Die moderne Naturwissenschaft ist offen für damit verbundene philosophische Fragestellungen, und das (...) Deutungsspektrum ist weit. Nicht zuletzt besteht Deutungsfreiheit auch in Bezug auf Kontingenz, auf unverfügbare, nicht voraussehbare, nicht ableitbare Einzelereignisse, die unser Leben wesentlich bestimmen. Eine Weltanschauung der Sinnleugnung oder des Sinnverzichts ist logisch möglich, naturwissenschaftlich zwingend ist sie nicht, und Kriterien der Lebenskunst würde sie kaum gerecht werden. Der Volltext ist lesbar in der Digitalisierung der DFG, S. 151-167 unter http://digi20.digitale-sammlungen.de/de/fs2/object/display/bsb00042852_00001.html . (shrink)

We show that there are continuum many different non-Fregean sentential logics that have adequate models. The proof is based on the construction of a special class of models of the power of the continuum.

Part of rethinking philosophy today, the author believes, is to rethink our logical concepts. The author questions the ontological existence of the proposition as the content of sentential utterances—written or spoken—as it was originally proposed by John Searle. While a performative is an utterance where the speaker not only utters a sentential or illocutionary content such as a statement, but also performs the illocutionary force such as the act of stating, the author reasserts John Austin’s constative as the general label (...) (genus) of specific utterances (species) that can be rendered true or false such as a statement, assertion, description, and prediction. In the remainder of the paper, the author tries to show that it is a category mistake for someone to assert a statement or to state an assertion. (shrink)

We can introduce singular terms for ordered pairs by means of an abstraction principle. Doing so proves useful for a number of projects in the philosophy of mathematics. However there is a question whether we can appeal to the abstraction principle in good faith, since a version of the Caesar Problem can be generated, posing the worry that abstraction fails to introduce expressions which refer determinately to the requisite sort of object. In this short paper I will pose the difficulty, (...) and then propose a solution. (shrink)

I LOGIC IN PHILOSOPHY— PHILOSOPHY OF LOGIC i. On the relation of logic to philosophy I n this book, the consequences of certain logical insights for ...

Strong reasoning skills are an important aspect to cultivate in life, as they directly impact decision making on a daily basis. By examining the different ways the world views logic and order, new methods and techniques can be employed to help expand on this skill further in the future. -/- Philosophical Perceptions on Logic and Order is a pivotal scholarly resource that discusses the evolution of logical reasoning and future applications for these types of processes. Highlighting relevant topics including logic (...) patterns, deductive logic, and inductive logic, this publication is an ideal reference source for academicians, students, and researchers that would like to expand their understanding of how society currently employs the use of logical reasoning techniques. (shrink)

A three dimensional hypercube representing all of the 4,096 dyadic computations in a standard bivalent system has been created. It has been constructed from the 16 functions arrayed in a table of functional completeness that can compute a dyadic relationship. Each component of the dyad is an operator as well as a function, such as “implication” being a result, as well as an operation. Every function in the hypercube has been color keyed to enhance the display of emerging patterns. At (...) the minimum, the hypercube is a “multiplication table” of dyadic computations and produces values in a way that shortens the time to do operations that normally would take longer using conventional truth table methods. It also can serve as a theorem prover and creator. With the hypercube comes a deductive system without the need for axioms. The main significance of the 3-D hypercube at this point is that it is the most fundamental way of displaying all dyadic computations in binary space, thus serving as a way of normalizing the rendition of uninterpreted, or raw, binary space. The hypercube is a dimensionless entity, a standard by which in binary spaces can be measured and classified, analogous to a meter stick. (shrink)

A common assumption among philosophers is that every language has at most denumerably many expressions. This assumption plays a prominent role in many philosophical arguments. Recently formal systems with indenumerably many elements have been developed. These systems are similar to the more familiar denumerable first-order languages. This similarity makes it appear that the assumption is false. We argue that the assumption is true.

This paper claims that there is no such thing as the correct answer to the question of what is logical form: two significantly different notions of logical form are needed to fulfil two major theoretical roles that pertain respectively to logic and semantics. The first part of the paper outlines the thesis that a unique notion of logical form fulfils both roles, and argues that the alleged best candidate for making it true is unsuited for one of the two roles. (...) The second part spells out a considerably different notion which is free from that problem, although it does not fit the other role. As it will be suggested, each of the two notions suits at most one role, so the uniqueness thesis is ungrounded. (shrink)

This paper outlines a truth-conditional view of logical form, that is, a view according to which logical form is essentially a matter of truth-conditions. Section 1 provides some preliminary clarifications. Section 2 shows that the main motivation for the view is the fact that fundamental logical relations such as entailment or contradiction can formally be explained only if truth-conditions are formally represented. Sections 3 and 4 articulate the view and dwell on its affinity with a conception of logical form that (...) has been defended in the past. Sections 5-7 draw attention to its impact on three major issues that concern, respectively, the extension of the domain of formal explanation, the semantics of tensed discourse, and the analysis of quantification.Este artículo esboza una concepción veritativo-condicional de la forma lógica, es decir, una concepción de acuerdo con la cual la forma lógica es esencialmente una cuestión de condiciones de verdad. La sección 1 proporciona algunas clarificaciones preliminares. La sección 2 muestra que la principal motivación para esta concepción es el hecho de que hay relaciones lógicas fundamentales, como la implicación o la contradicción, que sólo pueden explicarse formalmente si las condiciones de verdad se representan formalmente. Las secciones 3 y 4 articulan dicha concepción y profundizan en su afinidad con una concepción de la forma lógica que ha sido defendida en el pasado. Las secciones 5 a 7 destacan su impacto sobre tres asuntos principales que conciernen, respectivamente, a la extensión del dominio de las explicaciones formales, la semántica del discurso temporalizado, y el análisis de la cuantificación. (shrink)

One of the most common strategies in philosophical dispute is that of accusing the opponent of begging the question, that is, of assuming or presupposing what is to be proved. Thus, it happens quite often that the credibility of a philosophical argument is infected by the suspicion of begging the question. In many cases it is an open question whether the suspicion is grounded, and the answer lurks somewhere in the dark of what the proponent of the argument does not (...) say. This is why it may take years, or even centuries, before the begging of the question is brought to light. But few philosophers would deny that once it is established that a certain argument begs the question, that argument has to be rejected without hesitation: question-begging arguments are bad arguments, hence one should not appeal to them. Logicians traditionally classify begging the question as a fallacy, that is, as a bad reasoning that seems good at first sight. The fallacy is known under the name of petitio principii. This paper originated in our dissatisfaction with definitions of petitio principii found here and there in logic textbooks. Although it is uncontroversial that there is something wrong with begging the question, it is not clear from those definitions what is wrong. (shrink)

This paper proposes a possible reconstruction and philosophical-logical clarification of Gödel's idea of causality as the philosophical fundamental concept. The results are based on Gödel's published and non-published texts (including Max Phil notebooks), and are established on the ground of interconnections of Gödel's dispersed remarks on causality, as well as on the ground of his general philosophical views. The paper is logically informal but is connected with already achieved results in the formalization of a causal account of Gödel's onto-theological theory. (...) Gödel's main causal concepts are analysed (will, force, enjoyment, God, time and space, life, form, matter). Special attention is paid to a possible causal account of some of Gödel's logical concepts (assertion, privation, affirmation, negation, whole, part, general, particular, subject, predicate, necessary, possible, implication), as well as of logical antinomies. The problem of mechanical and non-mechanical procedures in the work with and on concepts is addressed in terms of Gödel's causal view. (shrink)

We want to show that Aristotle’s general conception of syllogism includes as its essential part the logical concept of necessity, which can be understood in a causal way. This logical conception of causality is more general then the conception of the causality in the Aristotelian theory of proof (“demonstrative syllogism”), which contains the causal account of knowledge and science outside formal logic. Aristotle’s syllogistic is described in a purely intensional way, without recourse to a set-theoretical formal semantics. It is shown (...) that the conclusion of a syllogism is justified by the accumulation of logical causes applied during the reasoning process. It is also indicated that logical principles as well as the logical concept of causality have a fundamental ontological role in Aristotle’s “first philosophy”. (shrink)

After introductory reminder of and comments on Gödel’s ontological proof, we discuss the collapse of modalities, which is provable in Gödel’s ontological system GO. We argue that Gödel’s texts confirm modal collapse as intended consequence of his ontological system. Further, we aim to show that modal collapse properly fits into Gödel’s philosophical views, especially into his ontology of separation and union of force and fact, as well as into his cosmological theory of the nonobjectivity of the lapse of time. As (...) a result, modal collapse should not be conceived in Gödel so much as a deficit, but rather as a kind of the rise of modalities to the “perfect” being. We further show that, in accordance with Gödel’s ontology, the concepts of modality and time should be derived in terms of the “fundamental philosophical concept” of cause. To give an example of how a formalization of such causative Gödelian ontology and ontological proof might look, we propose the transformation of GO into a kind of causally re-interpreted justification logic. (shrink)

Quine rejects intensional Platonism and, with it, also rejects attributes (properties) as designations of predicates. He pragmatically accepts extensional Platonism, but conceives of classes as merely auxiliary entities needed to express some laws of set theory. At the elementary logical level, Quine develops an “ontologically innocent” logic of predicates. What in standard quantification theory is the work of variables is in the logic of predicates the work of a few functors that operate on predicates themselves: variables are eliminated. This “predicate (...) functor logic” may be conceived as a peculiar sort of Platonism - ontologically neutral, reduced to schematized linguistic forms. (shrink)

A brief but rigorous description of the logical structure of mathematical truth.