This fresh look at the philosophy of language focuses on the interface between a theory of literal meaning and pragmatics--a philosophical examination of the relationship between meaning and language use and its contexts. Here, Atlas develops the contrast between verbal ambiguity and verbal generality, works out a detailed theory of conversational inference using the work of Paul Grice on Implicature as a starting point, and gives an account of their interface as an example of the relationship between Chomsky's Internalist Semantics (...) and Language Performance. Atlas then discusses consequences of his theory of the Interface for the distinction between metaphorical and literal language, for Grice's account of meaning, for the Analytic/Synthetic distinction, for Meaning Holism, and for Formal Semantics of Natural Language. This book makes an important contribution to the philosophy of language and will appeal to philosophers, linguists, and cognitive scientists. (shrink)

Logic and African Philosophy: Seminal Essays on African Systems of Thought aims to put African intellectual history in perspective, with focus on the subjects of racism, logic, language, and psychology. The volume seeks to fill in the gaps left by the exclusion of African thinkers that are frequent in the curricula of African schools concerning history, sociology, philosophy, and cultural studies. The book is divided into four parts that are preceded by an introduction to link up the essays and emphasize (...) their sociological implications. Part one is comprised of essays that opened the controversy of whether logic can be found in traditional African cultures as well as other matters like the nature of the mind and behavior of African peoples. The essays in part two are centered on the following question: are the laws of thought present in African languages and cultures? Part three brings together essays that sparkle the debate on whether there can be such a thing as African logic, which stems from the discussions in part two. Part four is concerned on the theme of system-building in logic; contributions are written by members of the budding African philosophy movement called the 'Conversational School of Philosophy' based at the University of Calabar, and the main objective of their papers is to formulate systems of African logic. (shrink)

Conversational thinking has emerged in recent years out of the scholarly philosophical work centered in Calabar Nigeria and spread throughout Africa and elsewhere. I have previously had the pleasure of discussing some of the finer points of conversationalism with Jonathan O. Chimakonam in the journal Confluence and the journal’s relaunch as the Journal of World Philosophies.. Our discussion there centered on questions I raised earlier about the nature and limits of dialogue, as well as my work on philosophy and place (...) in an African context. Our conversation, in other words, has a history, and I expect it will also have a future. It is a conversation that comes from different places. I am not an African, and I lay no claim to be able to represent African life. Therefore, the approach to philosophy I take is one of examining the conditions for the possibility of philosophy, and the barriers to being able to enact those conditions. This is why I write about place so much. The conditions for thinking in a place and abouta place differ in different places, but also have some commonalities. And the barriers to thinking in and about place can be fairly clearly outlined. This is of relevance, I argue, in thinking Africa, not as a set of identities or a history but as a space of thought. (shrink)

This fresh look at the philosophy of language focuses on the interface between a theory of literal meaning and pragmatics--a philosophical examination of the relationship between meaning and language use and its contexts. Here, Atlas develops the contrast between verbal ambiguity and verbal generality, works out a detailed theory of conversational inference using the work of Paul Grice on Implicature as a starting point, and gives an account of their interface as an example of the relationship between Chomsky's Internalist Semantics (...) and Language Performance. Atlas then discusses consequences of his theory of the Interface for the distinction between metaphorical and literal language, for Grice's account of meaning, for the Analytic/Synthetic distinction, for Meaning Holism, and for Formal Semantics of Natural Language. This book makes an important contribution to the philosophy of language and will appeal to philosophers, linguists, and cognitive scientists. (shrink)

We provide a simple translation of the satisfiability problem for regular grammar logics with converse into GF2, which is the intersection of the guarded fragment and the 2-variable fragment of first-order logic. The translation is theoretically interesting because it translates modal logics with certain frame conditions into first-order logic, without explicitly expressing the frame conditions. It is practically relevant because it makes it possible to use a decision procedure for the guarded fragment in order to decide regular grammar logics with (...) converse. The class of regular grammar logics includes numerous logics from various application domains. A consequence of the translation is that the general satisfiability problem for every regular grammar logics with converse is in EXPTIME. This extends a previous result of the first author for grammar logics without converse. Other logics that can be translated into GF2 include nominal tense logics and intuitionistic logic. In our view, the results in this paper show that the natural first-order fragment corresponding to regular grammar logics is simply GF2 without extra machinery such as fixed-point operators. (shrink)

This paper contributes to the principled construction of tableau-based decision procedures for hybrid logic with global, difference, and converse modalities. We also consider reflexive and transitive relations. For converse-free formulas we present a terminating control that does not rely on the usual chain-based blocking scheme. Our tableau systems are based on a new model existence theorem.

We provide a simple translation of the satisfiability problem for regular grammar logics with converse into GF2, which is the intersection of the guarded fragment and the 2-variable fragment of first-order logic. The translation is theoretically interesting because it translates modal logics with certain frame conditions into first-order logic, without explicitly expressing the frame conditions. It is practically relevant because it makes it possible to use a decision procedure for the guarded fragment in order to decide regular grammar logics with (...) converse. The class of regular grammar logics includes numerous logics from various application domains. A consequence of the translation is that the general satisfiability problem for every regular grammar logics with converse is in EXPTIME. This extends a previous result of the first author for grammar logics without converse. Other logics that can be translated into GF2 include nominal tense logics and intuitionistic logic. In our view, the results in this paper show that the natural first-order fragment corresponding to regular grammar logics is simply GF2 without extra machinery such as fixed-point operators. (shrink)

Questions whether the logic of language underlying Habermas's theory of communicative action is in fact the defining feature of conversational practice.

What justifies one interlocutor to challenge the conversational expectations of the other? Paul Grice approaches conversation as one instance of joint action that, like all such action, is governed by the Cooperative Principle. He thinks the expectations of the interlocutors must align, although he acknowledges that expectations can and do shift in the course of a conversation through a process he finds strange. Martin Heidegger analyzes discourse as governed by the normativity of care for self and for another. It is (...) the structure of care that warrants disrupting the presumed cooperative horizon of a conversation in order to occasion some new insight. The chapter expands Heidegger’s ontological conception of care to make sense of the exigencies of conversation. Conversation requires taking cognizance of (1) the human good, (2) the specifics of the conversational context, and (3) one’s responsibilities for the other. This threefold understanding can provide directives for subverting the interlocutor’s expectation for the purposes of a given conversation. (shrink)

The chapters in this timely volume aim to answer the growing interest in Arthur Schopenhauer’s logic, mathematics, and philosophy of language by comprehensively exploring his work on mathematical evidence, logic diagrams, and problems of semantics. Thus, this work addresses the lack of research on these subjects in the context of Schopenhauer’s oeuvre by exposing their links to modern research areas, such as the “proof without words” movement, analytic philosophy and diagrammatic reasoning, demonstrating its continued relevance to current discourse on logic. (...) -/- Beginning with Schopenhauer’s philosophy of language, the chapters examine the individual aspects of his semantics, semiotics, translation theory, language criticism, and communication theory. Additionally, Schopenhauer’s anticipation of modern contextualism is analyzed. The second section then addresses his logic, examining proof theory, metalogic, system of natural deduction, conversion theory, logical geometry, and the history of logic. Special focus is given to the role of the Euler diagrams used frequently in his lectures and their significance to broader context of his logic. In the final section, chapters discuss Schopenhauer’s philosophy of mathematics while synthesizing all topics from the previous sections, emphasizing the relationship between intuition and concept. -/- Aimed at a variety of academics, including researchers of Schopenhauer, philosophers, historians, logicians, mathematicians, and linguists, this title serves as a unique and vital resource for those interested in expanding their knowledge of Schopenhauer’s work as it relates to modern mathematical and logical study. (shrink)

This paper discusses how to update one’s credences based on evidence that has initial probability 0. I advance a diachronic norm, Kolmogorov Conditionalization, that governs credal reallocation in many such learning scenarios. The norm is based upon Kolmogorov’s theory of conditional probability. I prove a Dutch book theorem and converse Dutch book theorem for Kolmogorov Conditionalization. The two theorems establish Kolmogorov Conditionalization as the unique credal reallocation rule that avoids a sure loss in the relevant learning scenarios.

Experimental procedures routinely violate the cooperative principle of conversational conduct by presenting irrelevant information in a way that implies its relevance to the task at hand. This contributes to an overestimation of the prevalence of judgment errors relative to natural contexts. When research participants are aware that the usual norms of conversational conduct do not apply, the emerging errors are attenuated or eliminated.

An inviting alternative to traditional texts in introductory logic, The Art of Reasoning is widely acclaimed for its conversational tone and accessible exposition of rigorous logical concepts.

Rips, in The Psychology of Proof, argues that, through the processes of evolution, logic (e.g., modus ponens) has become established in the human mind as the basis for thinking, and that production systems rest on this foundation. In this paper we defend the converse argument that, through evolution, a production system architecture has become the basis for human thinking, and that formal logics rest on this production system and the accompanying mechanisms for recognition and search. It is through the “automaticity” (...) of the execution of productions that we experience the compellingness of deductive arguments. (shrink)

In this paper we study language use and language organisation by making use of Lewisean signalling games. Standard game theoretical approaches are contrasted with evolutionary ones to analyze conventional meaning and conversational interpretation strategies. It is argued that analyzing successful communication in terms of standard game theory requires agents to be very rational and fully informed. The main goal of the paper is to show that in terms of evolutionary game theory we can motivate the emergence and self-sustaining force of (...) (i) conventional meaning and (ii) some conversational interpretation strategies in terms of weaker and, perhaps, more plausible assumptions. (shrink)

Grammar logics were introduced by Fariñas del Cerro and Penttonen in 1988 and have been widely studied. In this paper we consider regular grammar logics with converse ( REG c logics) and present sound and complete tableau calculi for the general satisfiability problem of REG c logics and the problem of checking consistency of an ABox w.r.t. a TBox in a REG c logic. Using our calculi we develop ExpTime (optimal) tableau decision procedures for the mentioned problems, to which various (...) optimization techniques can be applied. We also prove a new result that the data complexity of the instance checking problem in REG c logics is coNP-complete. (shrink)

We study satisfiability and infinite-state model checking in ICPDL, which extends Propositional Dynamic Logic (PDL) with intersection and converse operators on programs. The two main results of this paper are that (i) satisfiability is in 2EXPTIME, thus 2EXPTIME-complete by an existing lower bound, and (ii) infinite-state model checking of basic process algebras and pushdown systems is also 2EXPTIME-complete. Both upper bounds are obtained by polynomial time computable reductions to ω-regular tree satisfiability in ICPDL, a reasoning problem that we introduce specifically (...) for this purpose. This problem is then reduced to the emptiness problem for alternating two-way automata on infinite trees. Our approach to (i) also provides a shorter and more elegant proof of Danecki's difficult result that satisfiability in IPDL is in 2EXPTIME. We prove the lower bound(s) for infinite-state model checking using an encoding of alternating Turing machines. (shrink)

We provide a direct method for proving Craig interpolation for a range of modal and intuitionistic logics, including those containing a "converse" modality. We demonstrate this method for classical tense logic, its extensions with path axioms, and for bi-intuitionistic logic. These logics do not have straightforward formalisations in the traditional Gentzen-style sequent calculus, but have all been shown to have cut-free nested sequent calculi. The proof of the interpolation theorem uses these calculi and is purely syntactic, without resorting to embeddings, (...) semantic arguments, or interpreted connectives external to the underlying logical language. A novel feature of our proof includes an orthogonality condition for defining duality between interpolants. (shrink)

The problem of the logic of understanding history is discussed. We propose a model of understanding history as a conversation, which the person thinking about history has with interlocutors (sources) of previous epochs. The epoch is interpreted as a special way of problematizing human's understanding of him (her) self and the world around. At the same time, three gifts — attention, recognition and name — underlie the connection of the historian in conversation with interlocutors (sources) from other eras. They are (...) not given in advance but are results of a struggle for the recognition. In choosing his (her) interlocutor (source), the historian chooses him (her) self. By giving this interlocutor (the source) the opportunity to be heard, the historian, at the same time, receives a gift from the source — the opportunity to express what would otherwise remain unspoken in the historian's own mind. The logic of conversation, designated as transduction, is not the connection through the identification of the beginning and the end of the discourse, which is appropriate and necessary within the speech of each of the conversationalists, but the connection of the beginnings of these discordant discourses among themselves. (shrink)

A range of formal models of human reasoning have been proposed in a number of fields such as philosophy, logic, artificial intelligence, computer science, psychology, cognitive science, etc.: various logics, probabilistic systems, belief revision systems, neural networks, among others. Now, it seems reasonable to require that formal models of human reasoning be empirically adequate if they are to be viewed as models of the phenomena in question. How are formal models of human reasoning typically put to empirical test? One way (...) to do so is to isolate a number of key principles of the system, and design experiments to gauge the extent to which participants do or do not follow them in reasoning tasks. Another way is to take relevant existing results and check whether a particular formal model predicts these results. The present investigation provides an illustration of the second kind of empirical testing by comparing two formal models for reasoning – namely the non-monotonic logic known as preferential logic; and a particular version of belief revision theories, screened belief revision – against the reasoning phenomenon known as belief bias in the psychology of reasoning literature: human reasoners typically seek to maintain the beliefs they already hold, and conversely to reject contradicting incoming information. The conclusion of our analysis will be that screened belief revision is more empirically adequate with respect to belief bias than preferential logic and non-monotonic logics in general, as what participants seem to be doing is above all a form of belief management on the basis of background knowledge. The upshot is thus that, while it may offer valuable insights into the nature of human reasoning, preferential logic is ultimately inadequate as a formal model of the phenomena in question. (shrink)

A range of formal models of human reasoning have been proposed in a number of fields such as philosophy, logic, artificial intelligence, computer science, psychology, cognitive science, etc.: various logics, probabilistic systems, belief revision systems, neural networks, among others. Now, it seems reasonable to require that formal models of human reasoning be empirically adequate if they are to be viewed as models of the phenomena in question. How are formal models of human reasoning typically put to empirical test? One way (...) to do so is to isolate a number of key principles of the system, and design experiments to gauge the extent to which participants do or do not follow them in reasoning tasks. Another way is to take relevant existing results and check whether a particular formal model predicts these results. The present investigation provides an illustration of the second kind of empirical testing by comparing two formal models for reasoning – namely the non-monotonic logic known as preferential logic; and a particular version of belief revision theories, screened belief revision – against the reasoning phenomenon known as belief bias in the psychology of reasoning literature: human reasoners typically seek to maintain the beliefs they already hold, and conversely to reject contradicting incoming information. The conclusion of our analysis will be that screened belief revision is more empirically adequate with respect to belief bias than preferential logic and non-monotonic logics in general, as what participants seem to be doing is above all a form of belief management on the basis of background knowledge. The upshot is thus that, while it may offer valuable insights into the nature of human reasoning, preferential logic is ultimately inadequate as a formal model of the phenomena in question. (shrink)

The paper uses the theory of generalized quantifiers to discuss existential import and its implications for Aristotelian logic, namely the square of opposition, conversions and the assertoric syllogistic, as well as for more recent generalizations to intermediate quantifiers like “most”. While this is a systematic discussion of the semantic background one should assume in order to obtain the inferences and oppositions Aristotle proposed, it also sheds some light on the interpretation of his writings. Moreover by applying tools from modern formal (...) semantics to the investigation of classical Aristotelian logic and its extensions, we combine different approaches to the logic of quantification. We will present variants of quantifiers that are associated to the four corners of the square of opposition with and without existential import and discuss their role for the logical square, conversions and the syllogistic. It will turn out that there is no way to ascribe existential import that validates all inferences and relations which one is willing to hold in Aristotelian logic. Two options, however, provide reasonable results. Existential import should either be ascribed only to affirmative statements or only be ascribed to universal quantification. The former option is preferable for a mere reconstruction of the classical Aristotelian logic while the latter option is more attractive if Aristotelian logic is generalized to intermediate quantifiers. (shrink)

Although first-order Kripke semantics has become a well established branch of modal logic, very little - almost nothing - is written about logics with a weaker modal fragment. We try to help the situation by isolating principles determining the interaction between quantifiers and modalities in minimal semantics. First, we let the standard-model properties of monotonic and anti-monotonic domains clue us in on how to do this – i. e. we try to articulate, in terms of the inclusiveness of the domains (...) of a certain set of worlds, a set of semantical restrictions that will validate the Barcan and converse Barcan formulae respectively. As it turns out, this can indeed by done, but only by adding assumptions strong enough to make the models virtually normal. Since the whole point of switching to a minimal framework would be to generalise the logic, we therefore abandon the worlds-objects thinking altogether, and switch to a much simpler and more direct validation strategy in which the propositions we are after are simply picked out as such. (shrink)

A textbook for undergraduate, introductory logic and critical thinking courses, Principles of Logic and Reasoning: Including LSAT, GRE, and Writing Skills by Christine A. James meets a specific set of student needs. The text is engaging and readable, but also includes detailed terms, definitions, section headings, and short exercises that build a specific set of foundational logic and argumentation skills. Each key term is carefully indexed in the back of the text so that students can review easily. The text includes (...) chapters that show how logic and reasoning can be used in planning major research papers, and how logic and argumentation connects with legal reasoning and preparing for graduate level examinations that have analytic reasoning sections such as the GRE and LSAT. Often logic textbooks do not include sections on issues like these that show the relevance of logic for the average college student. This textbook is unique because it leaves students with a clear understanding that they can and will use logic to their advantage beyond their first logic course. Another advantage of this text for students is the low cost, some logic textbooks are triple the cost of this textbook. -/- For faculty members, this text has advantages as well. Each section has an exercise that is clear, concise, and adaptable to online course platforms and frequently used lecture tools like PowerPoint and Prezi. With seven chapters, the book is suited for courses that are taught in sessions of varying weeks. Many schools now offer classes in formats of 8 weeks, 10 weeks, or 16 weeks. This text is arranged with a number of chapters that can be covered in any weekly format, with sections that can be included or not included at the discretion of the instructor. Written by a faculty member at a regional state university with an emphasis on accessible undergraduate teaching, the text is written in a relaxed, conversational style so that students from diverse backgrounds will feel comfortable with the examples used. The book welcomes students to continue studying Logic in other more advanced courses. Topics covered include essential approaches to critical thinking, informal logic, fallacies, categorical logic, Venn diagrams, formal symbolic logic, first order rules of inference and replacement, as well as logic in writing and preparing for graduate school and law school. (shrink)

We present the paradigm of categories-as-syntax. We briefly recall the even stronger paradigm categories-as-machine-language which led from -calculus to categorical combinators viewed as basic instructions of the Categorical Abstract Machine. We extend the categorical combinators so as to describe the proof theory of first order logic and higher order logic. We do not prove new results: the use of indexed categories and the description of quantifiers as adjoints goes back to Lawvere and has been developed in detail in works of (...) R. Seely. We rather propose a syntactic, equational presentation of those ideas. We sketch the (quasi-equational) categorical structures for dependent types, following ideas of J. Cartmell (contextual categories). All these theories of categorical combinators, together with the translations from -calculi into them, are introduced smoothly, thanks to the systematic use of– - an abstract variable-free notation for -calculus, going back to N. De Bruijn, – - a sequent formulation of the natural deduction. (shrink)

During the academic year 1940-1941, several giants of analytic philosophy congregated at Harvard, holding regular private meetings, with Carnap, Tarski, and Quine. Carnap, Tarski, and Quine at Harvard allows the reader to act as a fly on the wall for their conversations. Carnap took detailed notes during his year at Harvard. This book includes both a German transcription of these shorthand notes and an English translation in the appendix section. Carnap’s notes cover a wide range of topics, but surprisingly, the (...) most prominent question is: If the number of physical items in the universe is finite, what form should scientific discourse take? This question is closely connected to an abiding philosophical problem: What is the relationship between the logico-mathematical realm and the material realm? Carnap, Tarski, and Quine’s attempts to answer this question involve issues central to philosophy today.This book focuses on three such issues: nominalism, the unity of science, and analyticity. In short, the book reconstructs the lines of argument represented in these Harvard discussions, discusses their historical significance (especially Quine’s break from Carnap), and relates them when possible to contemporary treatments of these issues. (shrink)

Avicenna (d. 1037) and Tūsī (d. 1274) have different doctrines on the contradiction and conversion of the absolute proposition. Following Avicenna's presentation of the doctrine in Pointers and reminders, and comparing it with what is given in Tūsī's commentary, allow us to pinpoint a major reason why Avicenna and Tūsī have different treatments of the modal syllogistic. Further comparison shows that the syllogistic system Rescher described in his research on Arabic logic more nearly fits Tūsī than Avicenna. This in turn (...) has consequences for analysing Avicenna's logic, and for writing the history of a fascinating period of change and diversity in the discipline in the medieval Islamic world. (shrink)

Aristotle founds his modal syllogistic, like his plain syllogistic, on a small set of ?perfect? or obviously valid sylligisms. The rest he reduces to those, usually by means of modal conversion principles. These principles are open to more than one reading, however, and they are in fact invalid on one traditional reading (de re), valid on the other (de dicto). It is argued here that this way of framing the contrast is not Aristotelian, and that an interpretation involving modal copulae (...) allows us to see how these principles, and the modal system as a whole, are to be understood in light of close and precise connections to Aristotle's essentialist metaphysics. (shrink)