What Would a Phenomenology of Logic Look Like?

Mind ◽  
2019 ◽  
Vol 129 (516) ◽  
pp. 1009-1031
Author(s):  
James Kinkaid
Keyword(s):  
Logical Consequence ◽  
Philosophy Of Logic ◽  
Contemporary Philosophy ◽  
Consequence Relations ◽  
Consequence Relation ◽  
If Logic ◽  
Pure Logic ◽  
Logical Investigations ◽  
Normative Status ◽  
Selection Of

Abstract The phenomenological movement begins in the Prolegomena to Husserl’s Logical Investigations as a philosophy of logic. Despite this, remarkably little attention has been paid to Husserl’s arguments in the Prolegomena in the contemporary philosophy of logic. In particular, the literature spawned by Gilbert Harman’s work on the normative status of logic is almost silent on Husserl’s contribution to this topic. I begin by raising a worry for Husserl’s conception of ‘pure logic’ similar to Harman’s challenge to explain the connection between logic and reasoning. If logic is the study of the forms of all possible theories, it will include the study of many logical consequence relations; by what criteria, then, should we select one (or a distinguished few) consequence relation(s) as correct? I consider how Husserl might respond to this worry by looking to his late account of the ‘genealogy of logic’ in connection with Gurwitsch’s claim that ‘[i]t is to prepredicative perceptual experience … that one must return for a radical clarification and for the definitive justification of logic’. Drawing also on Sartre and Heidegger, I consider how prepredicative experience might constrain or guide our selection of a logical consequence relation and our understanding of connectives like implication and negation.

Logical consequence relations in logics of monotone predicates and logics of antitone predicates

2017 ◽  
pp. 021-029
Author(s):  
O.S. Shkilniak ◽  
Keyword(s):  
Logical Consequence ◽  
Consequence Relations ◽  
Consequence Relation ◽  
First Order ◽  
Different Types ◽  
Composition Algebras

Logical consequence is one of the fundamental concepts in logic. In this paper we study logical consequence relations for program-oriented logical formalisms: pure first-order composition nominative logics of quasiary predicates. In our research we are giving special attention to different types of logical consequence relations in various semantics of logics of monotone predicates and logics of antitone predicates. For pure first-order logics of quasiary predicates we specify composition algebras of predicates, languages, interpretation classes (sematics) and logical consequence relations. We obtain the pairwise distinct relations: irrefutability consequence P |= IR , consequence on truth P |= T , consequence on falsity P |= F, strong consequence P |= TF in P-sеmantics of partial singlevalued predicates and strong consequence R |= TF in R-sеmantics of partial multi-valued predicates. Of the total of 20 of defined logical consequence relations in logics of monotone predicates and of antitone predicates, the following ones are pairwise distinct: PE |= IR, PE |= T, PE |= F, PE |= TF, RM |= T, RM |= F, RM |= TF. A number of examples showing the differences between various types of logical consequence relations is given. We summarize the results concerning the existence of a particular logical consequence relation for certain sets of formulas in a table and determine interrelations between different types of logical consequence relations.

Kant and the Science of Logic

2018 ◽  
Author(s):  
Huaping Lu-Adler
Keyword(s):  
History Of Philosophy ◽  
Logical Pluralism ◽  
Philosophy Of Logic ◽  
Science Of Logic ◽  
Transcendental Logic ◽  
If Logic ◽  
General Logic ◽  
Two Factors ◽  
History Of ◽  
Philosophical Debates

This book is both a history of philosophy of logic told from the Kantian viewpoint and a reconstruction of Kant’s theory of logic from a historical perspective. Kant’s theory represents a turning point in a history of philosophical debates over the following questions: (1) Is logic a science, instrument, standard of assessment, or mixture of these? (2) If logic is a science, what is the subject matter that differentiates it from other sciences, particularly metaphysics? (3) If logic is a necessary instrument to all philosophical inquiries, how is it so entitled? (4) If logic is both a science and an instrument, how are these two roles related? Kant’s answer to these questions centers on three distinctions: general versus particular logic, pure versus applied logic, pure general logic versus transcendental logic. The true meaning and significance of each distinction becomes clear, this book argues, only if we consider two factors. First, Kant was mindful of various historical views on how logic relates to other branches of philosophy (viz. metaphysics and physics) and to the workings of common human understanding. Second, he first coined “transcendental logic” while struggling to secure metaphysics as a proper “science,” and this conceptual innovation would in turn have profound implications for his mature theory of logic. Against this backdrop, the book reassesses the place of Kant’s theory in the history of philosophy of logic and highlights certain issues that are still debated today, such as normativity of logic and the challenges posed by logical pluralism.

Edmund Husserl, Logical Investigations. Volume I. Prolegomena to Pure Logic

2016 ◽  
Vol 32 (2) ◽  
pp. 165-166
Author(s):  
Maria Cherba ◽  
Frédéric Tremblay
Keyword(s):  
Edmund Husserl ◽  
Pure Logic ◽  
Logical Investigations

scholarly journals THE CONCEPT OF KUNSTLEHRE IN THE HUSSERL’S PHENOMENOLOGY

2021 ◽  
pp. 16-26
Author(s):  
Svetlana Berdaus
Keyword(s):  
Transcendental Phenomenology ◽  
Research Literature ◽  
Scientific Study ◽  
Main Task ◽  
Theoretical Level ◽  
Study Program ◽  
Important Place ◽  
Pure Logic ◽  
Logical Investigations ◽  
Practical Level

The article proposes a reconstruction of the Kunstlehre concept, which occupies an important place in the structural and disciplinary section of Husserl's phenomenology. The key point of the presented reconstruction is its separation from the traditional interpretation of Kunstlehre criticized by Husserl and the advancement of a new project that coordinates three levels – theoretical, normative and practical. The theoretical level (pure logic), being complementary to the normative level (pure norms of reason), forms the basis of the disciplines represented by the program of science of knowledge (Wissenschaftslehre). The scientific study program falls on the period of the so- called logicism of Husserl, regarding which there is an opinion in the research literature that it was interrupted by the founder of phenomenology immediately after the writing of the first volume of “Logical Investigations”. However, on the basis of textual arguments, we show that this program was extended by Husserl up to his last works. The nature of this expansion is related to the practical level of Kunstlehre (transcendental phenomenology). The main task of this level was to provide science and scientists with noetic conditions, i.e. skills of transcendental criticism of consciousness. It is suggested that the presented reconstruction of Kunstlehre shows the permanent development of the program of logicism by Husserl, and also demonstrates the connection of this program with transcendental phenomenology.

scholarly journals Power Matrices and Dunn--Belnap Semantics: Reflections on a Remark of Graham Priest

2014 ◽  
Vol 11 (1) ◽  
Author(s):  
Lloyd Humberstone
Keyword(s):  
Equational Logic ◽  
Consequence Relations ◽  
Consequence Relation ◽  
Power Matrix ◽  
Matrix Construction ◽  
The Given ◽  
The Universe ◽  
Power Algebras ◽  
Graham Priest ◽  
Natural Way

The plurivalent logics considered in Graham Priest's recent paper of that name can be thought of as logics determined by matrices (in the `logical matrix' sense) whose underlying algebras are power algebras (a.k.a. complex algebras, or `globals'), where the power algebra of a given algebra has as elements \textit{subsets} of the universe of the given algebra, and the power matrix of a given matrix has has the power algebra of the latter's algebra as its underlying algebra, with its designated elements being selected in a natural way on the basis of those of the given matrix. The present discussion stresses the continuity of Priest's work on the question of which matrices determine consequence relations (for propositional logics) which remain unaffected on passage to the consequence relation determined by the power matrix of the given matrix with the corresponding (long-settled) question in equational logic as to which identities holding in an algebra continue to hold in its power algebra. Both questions are sensitive to a decision as to whether or not to include the empty set as an element of the power algebra, and our main focus will be on the contrast, when it is included, between the power matrix semantics (derived from the two-element Boolean matrix) and the four-valued Dunn--Belnap semantics for first-degree entailment a la Anderson and Belnap) in terms of sets of classical values (subsets of {T, F}, that is), in which the empty set figures in a somewhat different way, as Priest had remarked his 1984 study, `Hyper-contradictions', in which what we are calling the power matrix construction first appeared.

Selecting laser eye protectors – a helping hand

2015 ◽  
Vol 4 (5-6) ◽  
Author(s):  
Catherine Gappenach ◽  
Jörg Krüger ◽  
Friedrich Offenhäuser ◽  
Sabine Pintaske ◽  
Hans-Joachim Krauß
Keyword(s):  
Laser Safety ◽  
Safety Standards ◽  
Know How ◽  
Normative Status ◽  
Selection Of

AbstractThe European laser safety standards EN 207, EN 208, and EN 12254 each contain an annex B, which serves as a guidance for the selection of products. These annexes are informative only and are therefore not binding. As there are a variety of hazard scenarios, it is not recommended to change these annexes to a normative status, through which they would become mandatory. Instead, it is recommended to allow users to apply their own skills and know-how in selecting appropriate products, justifying where and why they deviate from the guidance in the standards. This paper explains the background on which the guidance for selection in the annexes of the standards is based and shows physically meaningful leeway.

Aesthetics and the New Ethics: Theorizing the Novel in the Twenty-First Century

PMLA ◽  
2009 ◽  
Vol 124 (3) ◽  
pp. 896-905 ◽  
Author(s):  
Dorothy J. Hale
Keyword(s):  
Political Theory ◽  
Emmanuel Levinas ◽  
First Century ◽  
The Novel ◽  
Contemporary Philosophy ◽  
Special Issue ◽  
Giorgio Agamben ◽  
The One ◽  
Anglophone World ◽  
Selection Of

In the introduction to a 2002 special issue of diacritics on ethics and interdisciplinarity, mark sanders asks us to consider, “What points of contact, if any, are there between the current investment in ethics in literary theory, and the elaboration of ethics in contemporary philosophy?” (3). Yet the question behind this question—the one that motivates his selection of essays for the issue—is why literary critics and theorists have drawn their ideas about ethics from Emmanuel Levinas, Jacques Derrida, Michel Foucault, Giorgio Agamben, and Alain Badiou but have felt little or no need to consult past or present moral philosophers. As Sanders goes on to note, while “in North America and the Anglophone world generally, the tendency in ethics has been to bring moral reflection to bear on questions in political theory,” there “has been relatively little attention among literary theorists to developments in disciplinary philosophy” (4).

The Actual and the Possible

2017 ◽  
Keyword(s):  
Twentieth Century ◽  
Immanuel Kant ◽  
Early Modern ◽  
Bertrand Russell ◽  
Contemporary Philosophy ◽  
Baruch Spinoza ◽  
Christian Wolff ◽  
History Of ◽  
Historical Range ◽  
Selection Of

This volume offers a selection of essays by leading specialists on modality and the metaphysics of modality in the history of modern philosophy, from the seventeenth to the twentieth centuries. It revisits key moments in the history of modern modal doctrines, and illuminates lesser-known moments of that history. With this historical approach, the book aims to contextualize and even to offer alternatives to dominant positions within the contemporary philosophy of modality. Hence the volume contains not only new scholarship on the early-modern doctrines of Baruch Spinoza, G. W. Leibniz, Christian Wolff, and Immanuel Kant, but also work relating to less familiar nineteenth-century thinkers such as Alexius Meinong and Jan Łukasiewicz, together with essays on celebrated nineteenth- and twentieth-century thinkers such as G. W. F. Hegel, Martin Heidegger, and Bertrand Russell, whose modal doctrines have not previously garnered the attention they deserve. The volume thus covers a variety of traditions, and its historical range extends to the end of the twentieth century, since it addresses the legacy of Willard Van Orman Quine’s critique of modality within recent analytic philosophy.

Intuitionism Reconsidered

2009 ◽  
Author(s):  
Roy Cook
Keyword(s):  
Intuitionistic Logic ◽  
Algebraic Structure ◽  
Subject Matter ◽  
Logical Consequence ◽  
Consequence Relation ◽  
Mathematical Structures

The debate between intuitionists and classical logicians is fought on two fronts. First, there is the battle over subject matter—the disputants disagree regarding which mathematical structures are legitimate domains of inquiry. Second, there is the battle over logic—they disagree over which algebraic structure correctly codifies logical consequence. In this article the emphasis is on the latter issue—it focuses on what the correct (formal) account of correct inference might look like, and, given such an account, how we should understand disagreements regarding the extension of the logical consequence relation. In the next two sections of the article, two typical sorts of arguments for intuitionistic logic are examined. The article then examines exactly what is at stake when one provides a logic as an account of logical consequence.

The Oxford Handbook of Philosophy of Mathematics and Logic

2009 ◽  
Keyword(s):  
Philosophy Of Mathematics ◽  
Philosophy Of Logic ◽  
Scholarly Work ◽  
Contemporary Philosophy ◽  
Philosophical System ◽  
A Priority ◽  
Correct Reasoning

The Oxford Handbook of Philosophy of Math and Logic is a reference about the philosophy of mathematics and the philosophy of logic. Mathematics and logic have been central topics of concern since the dawn of philosophy. Since logic is the study of correct reasoning, it is a fundamental branch of epistemology and a priority in any philosophical system. Philosophers have focused on mathematics as a case study for general philosophical issues and for its role in overall knowledge-gathering. Today, philosophy of mathematics and logic remain central disciplines in contemporary philosophy, as evidenced by the regular appearance of articles on these topics in the best mainstream philosophical journals; in fact, the last decade has seen an explosion of scholarly work in these areas. This volume covers these disciplines, giving the reader an overview of the major problems, positions, and battle lines. The twenty-six articles are by established experts in the field, and these articles contain both exposition and criticism as well as substantial development of their own positions.

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