This book is a study in the logic of questions (sometimes called erotetic logic). The central topics in erotetic logic have been the structure of questions and the question-answer relationship. This book doesn't neglect these problems, but much of it is focussed on other issues. The main subject is the logical analysis of certain relations between questions and the contexts of their appearance. And our aim is to elaborate the conceptual apparatus of the inferential approach to (...) the logic of questions. Questions are asked for many reasons and for different purposes. Yet, before a question is asked or posed, a questioner must arrive at it. In many cases arriving at a question resembles coming to a conclusion: there are some premises involved and some inferential thought processes take place. If we agree that a conclusion need not be "conclusive", we may say that sometimes questions can play the role of conclusions. But questions can also perform the role of premises: we often pass from some "initial" question to another question. In other words, there are inferential thought processes - we shall call them erotetic inferences - in which questions play the roles of conclusions or conclusions and premises. The inferential approach to the logic of questions focusses its attention on the analysis of erotetic inferences. This book consists of eight chapters. (shrink)

Twisted Logic: Navigating Life's Puzzles, Paradoxes, and Big Questions draws upon an array of popular and novel puzzles and paradoxes to help us understand and navigate our everyday world, as well as engaging with the big questions beyond. It will appeal to all those interested in learning about twisted logic and the ways in which intuition and common sense can sometimes lead us astray. The book is designed for everyone and is accessible to the layman and student alike. (...) No prior mathematical skill or technical knowledge is required. (shrink)

Throughout history, a believer did not need logical proof to believe in Almighty God. This is because the spiritual proof was always enough to admit the existence of Almighty God and to submit to Him. Finding Almighty God is not a mathematical equation that needs to be proven. Rather, it is a spiritual feeling due to a call from inside a human being. The relationship between Almighty God and humans is spiritual rather logical.However, with the advances in science and technology, (...) this spiritual relationship decreases. Nowadays, modern man is looking for logic and scientific answers to many questions relating to Almighty God and religions. In fact, nonbelievers or atheists are not the only ones looking for answers to these types of questions; believers also want to increase their faith and remove doubts from their hearts. The main objective of this book is to provide logical answers to questions relating to belief in Almighty God, creations and Islam as the last heavenly religion. These questions are grouped under several topics, namely: 1) Almighty God, 2) the creation, 3) the soul, 4) the hereafter, 5) the destiny and freedom in choices, 6) the holy Quran and 7) the Islam.0The main feature of this book is that the author provides logic flowcharts with each presented question relating to the different topics. Each logic flowchart has three phases: a start, a process and an end.0Prof. Dr. Magd Abdel Wahab is a full-time Professor of Applied Mechanics in the Faculty of Engineering and Architecture at Ghent University, Belgium.Beside his interest in engineering, Prof. Wahab has a strong interest in research in Islamic religion. During the last 15 years, he has served as an Associate Imam, and has delivered Friday ceremony speeches and Islamic talks in several mosques in the UK and Belgium. This book, Logic and Islam, summarises his experiences and provides logical answers to questions related to Almighty God, creations and Islam. (shrink)

Under the influence of Quine’s famous manifesto, many philosophers have thought that logical theories are scientific theories that can be ‘adopted’ and tested as scientific theories. Here we argue that this idea is untenable. We discuss it with special reference to Putnam’s proposal to ‘adopt’ a particular non-classical logic to solve the foundational problems of quantum mechanics in his famous paper ‘Is Logic Empirical?’ (1968), which we argue was not really coherent.

This paper argues for the idea that the logic of questions should focus its attention on the analysis of arguments in which questions play the role of conclusions. The relevant concepts of validity are discussed and the concept of the logic of questions of a semantically interpreted formalized language is introduced.

In recent years, the logic of questions and dependencies has been investigated in the closely related frameworks of inquisitive logic and dependence logic. These investigations have assumed classical logic as the background logic of statements, and added formulas expressing questions and dependencies to this classical core. In this paper, we broaden the scope of these investigations by studying questions and dependency in the context of intuitionistic logic. We propose an intuitionistic team semantics, where teams (...) are embedded within intuitionistic Kripke models. The associated logic is a conservative extension of intuitionistic logic with questions and dependence formulas. We establish a number of results about this logic, including a normal form result, a completeness result, and translations to classical inquisitive logic and modal dependence logic. (shrink)

First published in German in 1984 as volume 45 of Martin Heidegger’s collected works, this book is the first English translation of a lecture course he presented at the University of Freiburg in 1937–1938. Heidegger’s task here is to reassert the question of the essence of truth, not as a "problem" or as a matter of "logic," but precisely as a genuine philosophical question, in fact the one basic question of philosophy. Thus, this course is about (...) the essence of truth and the essence of philosophy. On both sides Heidegger draws extensively upon the ancient Greeks, on their understanding of truth as aletheia and their determination of the beginning of philosophy as the disposition of wonder. In addition, these lectures were presented at the time that Heidegger was composing his second magnum opus, Beiträge zur Philosophie, and provide the single best introduction to that complex and crucial text. (shrink)

Hence, this book's provocative claim: today's so-called logical empiricism owes much more to Kant's notion of science than to Hume's.

Since Kripke, philosophers have distinguished a priori true statements from necessarily true ones. A statement is a priori true if its truth can be established before experience, and necessarily true if it could not have been false according to logical or metaphysical laws. This distinction can be captured formally using two-dimensional semantics. There is a natural way to extend the notions of apriority and necessity so they can also apply to questions. Questions either can or cannot be resolved before experience, (...) and either are or are not about necessary facts. Classical two-dimensionalism has no account of question meanings, so it has to be combined with a framework for question semantics in order to capture these observations. It is shown in [14] how two-dimensional semantics can be combined with inquisitive semantics, in which questions are analyzed in terms of information. The present paper investigates the logic of two-dimensional inquisitive semantics, and provides a complete proof system. (shrink)

This essay is part of larger project in which I attempt to show that Western formal logic, from its inception in Aristotle onward, has both been partially constituted by, and partially constitutive of, what has become known as racism. More specifically, (a) racist/quasi-racist/proto-racist political forces were part of the impetus for logic’s attempt to classify the world into mutually exclusive, hierarchically-valued categories in the first place; and (b) these classifications, in turn, have been deployed throughout history to justify (...) and empower racism/quasi-racism/proto-racism. In other words, (a) an important part of the chaos and messiness that so troubles logic has been the natural bio-cultural diversity of human beings as described by concepts such as race and ethnicity; and (b) once these concepts were historically in place, taken for granted, buttressed with pseudo-science, and had their origins forgotten, they became tools for the oppression of diverse human groups. The central thesis of this essay is that close readings of a variety of Leibniz’s writings (including several essays and one letter) will reveal a pattern of mutual dependency and creation in regard to logic and racism in Leibniz. My conclusion will be that there is a meaningful connection between logic and racism (or at least between logic and politics in general) in Leibniz such that one should be skeptical of his logic’s claim to offer transparent and neutral descriptions of the world as well as imperatives for action. Put differently, I want to ask the following specific question: how do Leibniz’s own racially-informed political goals, along with the emergence of race-centric European colonialism, both invest and disguise themselves within Leibniz’s mathematizing of logic? (shrink)

Philosophers and scientists are concerned with the why and the how of things. Questions like the following are so much grist for the philosopher’s and scientist’s mill: How can we be free and yet live in a deterministic universe?, How do neural processes give rise to conscious experience?, Why does conscious experience accompany certain physiological events at all?, How is a three-dimensional perception of depth generated by a pair of two-dimensional retinal images?. Since Belnap and Steel’s pioneering work on the (...) logic of questions, Van Fraassen has managed to apply their approach in constructing an account of the logic of why-questions. Comparatively little, by contrast, has been written on the logic of how-questions despite the apparent centrality of questions such as How is it possible for us to be both free and determined? to philosophical enterprise.1 In what follows I develop a logic for how-questions of various sorts including how-questions of cognitive resolution, how-questions of manner, how-questions of method, of means, and of mechanism. (shrink)

Many of the earliest books, particularly those dating back to the 1900s and before, are now extremely scarce and increasingly expensive. We are republishing these classic works in affordable, high quality, modern editions, using the original text and artwork.

A logic of questions and answers exists within the logic of statements, if we make the following identifications (roughly): "Whether" questions are identified with true exclusive disjunctions, and "which" questions are identified with true existential quantifications. The question-and-answer process is interpreted as an information-matching game. The question mark is not needed except as a device of abbreviation. Complete and partial answers can be distinguished and various relations of relevance, independence, and resolution defined.

The thesis that all learning has the character of enquiry is advanced and its implications are explored. R. G. Collingwood's account of ‘the logical priority of the question’ is explained and Hans-Georg Gadamer's hermeneutical justification and development, particularly the rejection of the re-enactment thesis, is discussed. Educators are encouraged to consider the following implications of the character of the question implied in all learning: (i) that it is a question that is constituted in the event rather than (...) prepared or given in advance, and that this leads to a necessary tension between learning and the curriculum or scheme, (ii) that it is a question that concerns some subject matter or issue that is at stake for both the student and the object of study, which draws our attention to the ‘intentionality’ of learning, and (iii) that it is a question that operates on the level of being—students are ‘called into question’, and thus transformed, by the object of study. (shrink)

Traditional logical theories are concerned with the characterization of valid reasoning. For such logical theories, the main object of investigation is the notion of entailment, a notion that is construed as a relation between two or more declarative statements, dictating when one of them can be legitimately inferred from the others. In the course of the previous century, however, and especially since the 1970s, the scope of logical theories has become much broader. In particular, logic is no longer only (...) concerned with declarative statements, but also with questions. Accordingly, the field is no longer focusing exclusively on the entailment relation that may hold between two or more statements, but also aims to characterize fundamental relations that may hold between questions, or between questions and statements. For instance, when does a statement resolve a given question? When does a statement evoke a certain question? And when does the resolution of one question depend on the resolu .. (shrink)

Questions are triggers for explicit events of ‘issue management’. We give a complete logic in dynamic-epistemic style for events of raising, refining, and resolving an issue, all in the presence of information flow through observation or communication. We explore extensions of the framework to multi-agent scenarios and long-term temporal protocols. We sketch a comparison with some alternative accounts.

Aims to transform logic into a reflection on the nature of language.

This study proposes a double thesis. The first concerns the Logische Untersuchungen itself. We will attempt to show that its statements about the nature of being are inconsistent and that this inconsis tency is responsible for the failure of this work. The second con cerns the Logische Untersuchungen's relation to the Ideen. The latter, we propose, is a response to the failure of the Logische Untersuchungen's ontology. It can thus be understood in terms of a shift in the ontology of (...) the Logische Untersuchungen, a shift motivated by the attempt to overcome the contradictory assertions of the Logische Untersuchungen. In this sense our thesis is that, in the technical meaning that Husserl gives the term, the Logische Untersuchungen and the Ideen can be linked via a "motivated path. " We can, by way of an introduction, clarify our theses by regard ing three elements. The first is the relation of epistemology to ontology. The second is the notion of motivation as Husserl conceives the term. The third is the fundamental distinctions that are to be explained via the notion of motivation. 1. We should begin by remarking that the goal of the Logische Untersuchungen is explicitly epistemological; it is that of answer ing "the cardinal question of epistemology, the question concerning the objectivity of knowledge" (LU, Tub. ed. , I, 8; F. , p. 56V For Husserl, his other questions - i. e. (shrink)

This work is central to Heidegger's overall project of reinterpreting Western thought in terms of time and truth.

This article is part of a larger project in which I attempt to show that Western formal logic, from its inception in Aristotle onward, has both been partially constituted by, and partially constitutive of, what has become known as racism. In contrast to this trend, the present article concerns the major philosopher whose contribution to logic has been perhaps the most derided and marginalized, and yet whose character and politics are, from a contemporary perspective, drastically superior—John Stuart Mill. (...) My approach to my core concern will be one of narrowing concentric circles. I will begin with Mill’s occasional political writings that bear on the issue of racism, including “The Negro Question.” From there, the core of the article will explore the political dimensions of Mill’s A System of Logic. (shrink)

In his book Knowledge and Belief, Jaakko Hintikka uses a model-theoretic approach of modal semantics as a theoretical basis for investigating the principles of epistemic logic. I shall first summarize the main points of Hintikka’s classic work and then address the most disputed themes raised by it in the 60s and later, such as logical omniscience and the KK-thesis, as well as Hintikka’s modifying his views on the basis of criticism. The last part of the book treats quantified epistemic (...) logic, particularly quantifying into “intensional” or “referentially opaque” epistemic contexts defended against Quine’s objections. I deal with this topic in Sect. 17.3 and add some relevant comparisons with John Buridan’s medieval approach in Sect. 17.4. A survey of Hintikka’s later theory of modelling knowledge acquisition is presented in Sect. 17.5; this includes the semantics of questions and inquiry in terms of game-theoretical semantics and their application to the logic of epistemology and scientific reasoning in the interrogative model of inquiry. Combining these results with the theory of independence friendly logic provides, Hintikka argues, a promising improvement of general epistemology which he calls a second-generation epistemic logic. The subject of the last section is “knowing who” in the sense of a basic epistemic attitude associated with identification which is the key notion in Hintikka’s epistemic theory of questions and answers, reference, and quantification. A central issue in this context is Hintikka’s discovery of the duality of cross-identification methods, the public or descriptive and the perspective ones. (shrink)

We reflect on lessons that the lottery and preface paradoxes provide for the logic of uncertain inference. One of these lessons is the unreliability of the rule of conjunction of conclusions in such contexts, whether the inferences are probabilistic or qualitative; this leads us to an examination of consequence relations without that rule, the study of other rules that may nevertheless be satisfied in its absence, and a partial rehabilitation of conjunction as a ‘lossy’ rule. A second lesson is (...) the possibility of rational inconsistent belief; this leads us to formulate criteria for deciding when an inconsistent set of beliefs may reasonably be retained. (shrink)

Epistemic Logic: 5 Questions is a collection of short interviews based on 5 questions presented to some of the most influential and prominent scholars in the field. We hear their views on the field, the aim, the scopes, the future direction of research and how their work fits in these respects.

_Aims to transform logic into a reflection on the nature of language._.

This chapter begins with a discussion of Herbart's theory of the structures of thought. It then discusses Drobisch's formal philosophy, Hegel's dialectical logic, Trendelenburg's logical investigations, and Herbartian and Hegelian reactions to the criticism.

_Questions of Form _was first published in 1989. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions. In _Questions on Form_, Joelle Proust traces the concept of the analytic proposition from Kant's development of the notion down to its place in the work of Rudolf Carnap, a founder of logical empiricism and a key figure in contemporary analytic philosophy. Using a method known in France (...) as _topique comparative_,she provides a rigorous exposition of analyticity, situating it within four major philosophical systems—those of Kant, Bolzano, Frege, and Carnap—and clearly delineating its development from one system to the next. Proust takes as her point of departure Kant's distinction between analytic and synthetic judgments. Though she makes clear that Kant drew on Locke, Hume, and Leibniz, she argues that his notion of analyticity was innovative, not simply an elaboration of something already found in their work. She shows that the analytic proposition unexpectedly came to play an important part in efforts to convert problems considered "transcendental" into questions of belonging to formal logic. Ultimately, her comparison of their systems reveals that the concept of the analytic, however specific its rile in each, remains linked to a foundationalist strategy—in effect, to the transcendentalist questions Kant used when he reinterpreted the findings of his empiricist predecessors. Hence, this book's provocative claim: today's so-called logical empiricism owes much more to Kant's notion of science than to Hume's. (shrink)

Danielle Macbeth's purpose in Macbeth 2005 is threefold. Her monograph proposes "to provide a logical justification for all aspects of Frege's peculiar notation, to motivate and explain the developments in Frege's views over the course of his intellectual life, and to explicate his most developed, critically reflective conception of his Begriffschrift, his formula language of pure thought" (p. vii). I shall focus here on a few selected aspects of the first and third points and leave on the side the discussion (...) of the historical development of Frege's views on logic, semantics and mathematics. The book's underlying claim is that although Frege's logical language, "can of course be read as a language of quantificational logic, [it] can also be read very differently" (p. vii), so much so, as a matter of fact, that although Frege's logic is usually thought of as a "notational variant of standard quantificational logic", it is nevertheless "unknown to us" (p. 1). This naturally prompts three questions : "What is Frege's logic?", "What is quantificational logic?", and given the way we understand formal languages for first and higher order predicate logic, most notably the notions of argument 2 place (for a predicate symbol), of scope and of binding (of variables - either individual or predicate of first or higher order): "How come Frege's logic says nothing about such notions, or something so different from what we say?". (shrink)

"Ces "questiones" sont particulièrement reprèsentatives de la logique italienne au XIVe siècle.

This new and revised edition of Peter Kreeft's Socratic Logic is updated, adding new exercises and more complete examples, all with Kreeft's characteristic clarity and wit. Since its introduction in the spring of 2004, Socratic Logic has proven to be a different type of logic text: This is the only complete system of classical Aristotelian logic in print. The "old logic" is still the natural logic of the four language arts. Symbolic, or "mathematical," (...) class='Hi'>logic is not for the humanities. This book is simple and user-friendly. It is highly interactive, with a plethora of exercises and a light, engaging style. It is practical. It is designed for do-it-yourselfers as well as classrooms. It emphasizes topics in proportion to probable student use: e.g., interpreting ordinary language, not only analyzing but also constructing effective arguments, smoking out hidden assumptions, making "argument maps," and using Socratic method in various circumstances. It is philosophical. Its exercises expose students to many classical quotations, and additional chapters introduce philosophical issues in a Socratic manner and from a commonsense, realistic point of view. It prepares students for reading Great Books rather than Dick and Jane, and models Socrates as the beginner's ideal teacher and philosopher. (shrink)

This paper provides a reconstruction and analysis of Marx’s early engagements with logic, and especially his studies of Hegel’s logic, on the one hand, and Hegel’s great if often overlooked critic Adolf Trendelenburg, on the other. It itemises the archival evidence that Marx read and planned to compose a Hegelian response to Trendelenburg’s devastating attack on dialectics in his 1840 Logische Untersuchungen – the work that arguably did more than any other single text to destroy the influence of (...) Hegelianism among German intellectuals at the time. It argues that the young Marx was a more sophisticated reader of Hegel and of philosophy in general than is typically acknowledged. Against the backdrop of these claims, it then proposes a new reading of Marx’s work from 1839 to 1842 – one that takes the emphasis off the familiar distinction between materialism and idealism, which was as much an invention of Engels’s later interpretations of the early Marx as it was an invention of Marx himself, and places it instead on what early nineteenth-century thinkers would have understood to be the more comprehensive question of logic. (shrink)

This article discusses various dangers that accompany the supposedly benign methods in behavioral evoltutionary biology and evolutionary psychology that fall under the framework of "methodological adaptationism." A "Logic of Research Questions" is proposed that aids in clarifying the reasoning problems that arise due to the framework under critique. The live, and widely practiced, " evolutionary factors" framework is offered as the key comparison and alternative. The article goes beyond the traditional critique of Stephen Jay Gould and Richard C. Lewontin, (...) to present problems such as the disappearance of evidence, the mishandling of the null hypothesis, and failures in scientific reasoning, exemplified by a case from human behavioral ecology. In conclusion the paper shows that "methodological adaptationism" does not deserve its benign reputation. (shrink)

A complete system of classical Aristotelian logic intended for honors high school and college.

There were in the past, just as there are in the present, several diverse attempts to establish a unique theory capable of identifying in all natural languages a similar, invariable basic structure of a logical nature. If such a theory exists, then there must be principles that rule the functioning of these languages and they must have a logical origin. Based on a work by the French linguist, Oswald Ducrot, entitled D’un mauvais usage de la logique , this paper aims (...) to present in a concise manner two of the above mentioned attempts. They were elaborated in diverse epochs and different arguments were put forward to support them. The first attempt was in XVII century France and its theoretic basis was the renowned ‘Port-Royal Logic’. The second attempt is recent and its theoretic support comes from Contemporary Logic. DOI: 10.5007/1808-1711.2011v15n1p111. (shrink)

This new and revised edition of Peter Kreeft's Socratic Logic is updated, adding new exercises and more complete examples, all with Kreeft's characteristic clarity and wit. Since its introduction in the spring of 2004, Socratic Logic has proven to be a different type of logic text: This is the only complete system of classical Aristotelian logic in print. The "old logic" is still the natural logic of the four language arts. Symbolic, or "mathematical," (...) class='Hi'>logic is not for the humanities. This book is simple and user-friendly. It is highly interactive, with a plethora of exercises and a light, engaging style. It is practical. It is designed for do-it-yourselfers as well as classrooms. It emphasizes topics in proportion to probable student use: e.g., interpreting ordinary language, not only analyzing but also constructing effective arguments, smoking out hidden assumptions, making "argument maps," and using Socratic method in various circumstances. It is philosophical. Its exercises expose students to many classical quotations, and additional chapters introduce philosophical issues in a Socratic manner and from a commonsense, realistic point of view. It prepares students for reading Great Books rather than Dick and Jane, and models Socrates as the beginner's ideal teacher and philosopher. (shrink)

Quentin Skinner has enduringly insisted that a past text cannot be ‘understood’ without the reader knowing something about its historical and linguistic context. But since the 1970s he has been attacked on this central point of all his work by authors maintaining that the text itself is the fundamental guide to the author’s intention, and that a separate study of the context cannot tell the historian anything that the text itself could not. Mark Bevir has spent much of the last (...) 20 years repeating a similar counter-argument. Although ‘study the linguistic context’ might be a useful heuristic maxim, Bevir says, it does not express a necessary or sufficient condition for understanding. But Skinner is right, and one of the figures he has consistently identified as a formative inspiration, R. G. Collingwood, has already (in his work of the 1930s) shown why. What Collingwood calls his ‘logic of question and answer’ explains why the historian cannot answer his characteristic ‘intention’ question about past texts without knowing the context of problems to which authors think they are offering solutions. The study of context is neither ‘prior’ (as Bevir incorrectly supposes) nor ‘separate’ (as Skinner inaccurately says), but it is, as Skinner maintains, nevertheless impossible to grasp an author’s intention without it. This ‘logic of question and answer’ also explains why, in history, dismissing the study of context is in fact a pre-judgement of evidence yet unseen. (shrink)

The book is a collection of lectures given during the spring colloquia between 2011 and 2019 at the Sorbonne. During these colloquia, a total of ten questions, such as ‘Should Logic be Mathematical...