The paper examines the interplays between logic and politics in the Polish School of Logic starting from 1914. The Polish School of Logic flourished between 1920 and 1939. Philosophically, it was influenced by Kazimierz Twardowski (1866–1938). For Twardowski logic is fundamental for every kind of human activity, professional and private and this means that every argument should be formulated and proceed by correct inferential rules. These rules involve semiotics, formal logic and methodology of science. The paper shows how this position (...) was shared by Twardowski’s students, including Jan Łukasiewicz, Stanisław Leśniewski, Kazimierz Ajdukiewicz and Tadeusz Kotrabiński, as well as by the next generation of logicians and philosophers and especially by Alfred Tarski. These authors considered logic, philosophy and science as completely neutral with respect to politics and ideology but they also considered logical skills as indispensable in political activities. (shrink)

This chapter contains sections titled: Introduction Relevant Logic Paraconsistent Logic Dialetheism Boolean Negation The Logical Choice Conclusion.

One of the most influential logicians of the day has assembled and in part rewritten a number of his essays on important questions of logical theory. 1 The result is a most impressive book, at once powerful and graceful, and breathing a certain intellectual hauteur r which accords well with its conspicuous property of being intellectually first rate. These are not humble analytical gropings, undertaken by the dim light of an author’s sense of the sensible; but a series of (...) campaigns in abstract metaphysics, directed from the firm ground of mastery of a rigorous and exacting technique. “Those of us who have a taste for desert landscapes” is a phrase of the author’s. With a Roman ruthlessness he makes a solitude in which he can quantify peacefully over lumps of rock. (shrink)

Among the subject matters which logicians like at times to investigate are the forms of postulation that other branches of inquiry employ. Rarely, however, do they examine the postulates under which they themselves proceed. It long contented them to offer something they called a “definition” for logic, and let it go at that. They might announce that logic dealt with the “laws of thought,” or with “judgment,” or that it was “the general science of order“; More recently they are (...) apt to connect it in one or another obscure way with linguistic ordering. (shrink)

One of the most influential logicians of the day has assembled and in part rewritten a number of his essays on important questions of logical theory. 1 The result is a most impressive book, at once powerful and graceful, and breathing a certain intellectual hauteur r which accords well with its conspicuous property of being intellectually first rate. These are not humble analytical gropings, undertaken by the dim light of an author’s sense of the sensible; but a series of (...) campaigns in abstract metaphysics, directed from the firm ground of mastery of a rigorous and exacting technique. “Those of us who have a taste for desert landscapes” is a phrase of the author’s. With a Roman ruthlessness he makes a solitude in which he can quantify peacefully over lumps of rock. (shrink)

The Polish School of Logic flourished in the period 1920-1939. Philosophically, it was influenced by Kazimierz Twardowski, professor at the University of Lwow (now Lviv in Ukraine), who established the Lwow-Warsaw School, to which the mentioned logical group belonged. Twardowski claimed that logic is very important in every kind of human activity, professional as well as private. Hence, every argument should be clearly formulated and proceed by correct inferential rules. These postulates involved semiotics, formal logic, and methodology of science — (...) that is, logica sensu largo. This position was accepted by Twardowski’s most distinguished students, such as Jan Łukasiewicz, Stanisław Leśniewski, Kazimierz Ajdukiewicz, and Tadeusz Kotarbiński, who graduated before 1914, as well as the next generation of logicians and philosophers, particularly by Alfred Tarski. Although all these people considered logic, philosophy, and science as completely neutral with respect to politics and ideology, they treated logical skills as indispensable in political activities. In philosophical specialized terminology, Polish logicians regarded logic as a weapon against irrationalism. This position was also represented by Polish logicians who did not belong to the group of Twardowski’s students. (shrink)

Studies Plato's approach to argumentation, exploring his role as logician, rhetorician, and dialectician in a way that sees these three aspects working together.

Non‐classical logicians do not typically reject classically valid logical principles across the board. In fact, they sometimes suggest that their preferred logic recovers classical reasoning in most circumstances. This idea has come to be known in the literature as ‘classical recapture’. Recently, classical logicians have raised various doubts about it. The main problem is said to be that no rigorous explanation has been given of how is it exactly that classical logic can be recovered. The goal of the (...) paper is to address this problem. First, I discuss a number of different ways to characterize the idea of classical recapture and I examine how far it can be pushed. Secondly, I argue that a palatable form of classical recapture is given by the thought that classical logic can be retained for statements that are grounded (in Kripke’s sense). To substantiate this view I provide a formal fixed‐point semantics for a language containing a predicate standing for the concept of groundedness and I address a couple of objections that have been deployed against the claim that classical recapture can aid the non‐classical logician’s cause. (shrink)

Sextus Empiricus' Against the Logicians is by far the most detailed surviving examination by any ancient Greek sceptic of the areas of epistemology and logic. It critically examines the pretensions of non-sceptical philosophers to have discovered methods for determining the truth, either through direct observation or by inference from the observed to the unobserved. It is therefore a fine example of the Pyrrhonist sceptical method at work. It also provides a mine of information about the ideas of other Greek (...) thinkers, ideas that are in many cases poorly preserved in other sources. This volume presents Against the Logicians in a new and accurate translation, together with a detailed introduction that sets the work in its philosophical context. (shrink)

Graph polynomials are graph parameters invariant under graph isomorphisms which take values in a polynomial ring with a fixed finite number of indeterminates. We study graph polynomials from a model theoretic point of view. In this paper we distinguish between the graph theoretic (semantic) and the algebraic (syntactic) meaning of graph polynomials. Graph polynomials appear in the literature either as generating functions, as generalized chromatic polynomials, or as polynomials derived via determinants of adjacency or Laplacian matrices. We show that these (...) forms are mutually incomparable, and propose a unified framework based on definability in Second Order Logic. We show that this comprises virtually all examples of graph polynomials with a fixed finite set of indeterminates. Finally we show that the location of zeros and stability of graph polynomials is not a semantic property. The paper emphasizes a model theoretic view. It gives a unified exposition of classical results in algebraic combinatorics together with new and some of our previously obtained results scattered in the graph theoretic literature. (shrink)

In recent years, commentators have begun to re-examine the proximity of Frantz Fanon's and Jacques Lacan's work — a proximity which has traditionally been underappreciated. This article adds to these voices, demonstrating the reciprocal intellectual relationship between these two figures. It develops five interrelated arguments to chart this proximity. First, it emphasizes Lacan's and Fanon's connections through their ontological perspectives on madness. Second, it arbitrates the two theorists’ criticisms of the limits of Western psychoanalysis. Third, it shows the importance placed (...) by both on social structures in determining mental illnesses. Next, it demonstrates the centrality of their common understanding of psychosis. Finally, it argues that Lacan's argument in The Sinthome concerning the colonizer's power is inherited from Fanon's Black Skin, White Masks — itself influenced by Lacan's early theory of language. The article does not attempt to cast Fanon as an apprentice Lacanian but rather to argue that reciprocity helped shape both oeuvres. (shrink)

The combination of quantifiers with a semantics for epistemic operators in a modal framework is one of the major contributions of Hintikka in intensional logic. Hintikka’s starting point is his diagnosis of the failure of existential generalization and the substitution of identicals in terms of referential multiplicity. In this paper, I introduce Hintikka as a free logician. Indeed, Hintikka’s first-order epistemic logic is grounded on a logic free of ontological presuppositions with respect to singular terms. It is also a logic (...) free of presuppositions of uniqueness of reference. After having focused on the use of quantifiers and singular terms in Hintikka’s epistemic logic, I discuss some consequences from a semantico-logical perspective, but also from a philosophical one. By arguing against the so-called contingent a priori truths defended by Kripke, I conclude with a proposal in favour of Hintikka’s non-rigid interpretation of proper names. (shrink)

Classical logic yields counterintuitive results for numerous propositional argument forms. The usual alternatives (modal logic, relevance logic, etc.) generate counterintuitive results of their own. The counterintuitive results create problems—especially pedagogical problems—for informal logicians who wish to use formal logic to analyze ordinary argumentation. This paper presents a system, PL– (propositional logic minus the funny business), based on the idea that paradigmatic valid argument forms arise from justificatory or explanatory discourse. PL– avoids the pedagogical difficulties without sacrificing insight into argument.

Poincaré was a persistent critic of logicism. Unlike most critics of logicism, however, he did not focus his attention on the basic laws of the logicists or the question of their genuinely logical status. Instead, he directed his remarks against the place accorded to logical inference in the logicist's conception of mathematical proof. Following Leibniz, traditional logicist dogma (and this is explicit in Frege) has held that reasoning or inference is everywhere the same — that there are no principles of (...) inference specific to a given local topic. Poincaré, a Kantian, disagreed with this. Indeed, he believed that the use of non-logical reasoning was essential to genuinely mathematical reasoning (proof). In this essay, I try to isolate and clarify this idea and to describe the mathematical epistemology which underlies it. Central to this epistemology (which is basically Kantian in orientation, and closely similar to that advocated by Brouwer) is a principle of epistemic conservation which says that knowledge of a given type cannot be extended by means of an inference unless that inference itself constitutes knowledge belonging to the given type. (shrink)

Most work on the semantic paradoxes within classical logic has centered around what this essay calls “linguistic” accounts of the paradoxes: they attribute to sentences or utterances of sentences some property that is supposed to explain their paradoxical or nonparadoxical status. “No proposition” views are paradigm examples of linguistic theories, although practically all accounts of the paradoxes subscribe to some kind of linguistic theory. This essay shows that linguistic accounts of the paradoxes endorsing classical logic are subject to a particularly (...) acute form of the revenge paradox: that there is no exhaustive classification of sentences into “good” and “bad” such that the T-schema holds when restricted to the “good” sentences unless it is also possible to prove some “bad” sentences. The foundations for an alternative classical nonlinguistic approach is outlined that is not subject to the same kinds of problems. Although revenge paradoxes of different strengths can be formulated, they are found to be indeterminate at higher orders and not inconsistent. (shrink)

Find out what connects logic and humor in this alternative guide to logical reasoning. Combining jokes, stories, and ironic situations, Stan Baronett shows how it is possible to always ground the formal, symbolic language of logic in everyday experience. Each chapter introduces a basic logical reasoning concept through a plausible premise based on happenings in daily life. Using jokes as his examples, Baronett reveals the inner workings of logic. After all an effective joke often relies on an unanticipated assumption that (...) leads to an unexpected result. The assumption changes the normal context of an everyday situation, so we are surprised by the ending. A complex mind that learns from experience, and builds a storehouse of regularly recurring patterns, is a great survival tool. But for a joke to work, the punch line has to be something our minds don't logically anticipate. The ending jolts our minds for a split second while we grasp the absurdity of the situation. This is how logic works: one part of your mind determines whether the information you are receiving is true or false, while another part of your mind deals with logical consequences of fact. These ideas are explained and illustrated by showing how an effective joke may rely on an unanticipated assumption that leads to an unexpected result. Injecting a sense of humor into logical language, Baronett helps us understand how to analyze basic causal reasoning and provides light relief for anyone daunted by the complex world of logic. (shrink)

By far the most detailed surviving examination by any ancient Greek sceptic of epistemology and logic, this work critically reviews the pretensions of non-sceptical philosophers, to have discovered methods for determining the truth, either through direct observation or by inference from the observed to the unobserved. A fine example of the Pyrrhonist sceptical method at work, it also provides extensive information about the ideas of other Greek thinkers, which in many instances, are poorly preserved in other sources.

In the thirteenth century, the influential logician Afḍal al-Dīn al-Khūnajī departed from the Avicennan view that the subject matter of logic is “second intentions”. For al-Khūnajī, the subject matter of logic is “the objects of conception and assent”. His departure elicited intense and sometimes abstruse discussions in the course of subsequent centuries. Prominent supporters of Khūnajī's view on the subject matter of logic included Kātibī, Ibn Wāṣil and Taftāzānī. Defenders of Avicenna's view included Ṭūsī, Samarqandī and Quṭb al-Dīn al-Rāzī. This (...) article presents the outline of the development of this discussion down to the end of the fourteenth century and attempts to reconstruct the major arguments of both sides.Au xiiie siècle, l'influent logicien, Afḍal al-Dīn al-Khūnajī, se démarque du point de vue avicennien d'après lequel ce sont les “intentions secondes” qui forment le sujet de la logique. Pour al-Khūnajī, le sujet de la logique, ce sont “les objets des conceptions et des assentiments”. Cet écart par rapport à la formulation avicennienne va susciter, au cours des siècles suivants, d'intenses et parfois abstruses discussions. Dans le camp de ceux qui adhèrent au point de vue d'al-Khūnajī, on trouve des auteurs tels que Kātibī, Ibn Wāṣil et Taftāzānī. En revanche, Ṭūsī, Samarqandī et Quṭb al-Dīn al-Rāzī se rangent dans le camp des défenseurs du point de vue d'Avicenne. Cet article présente les grandes lignes qui marquent le développement de cette discussion jusqu'à la fin du xive siècle et tente de reconstruire les arguments des deux partis.Send article to KindleTo send this article to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle. Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply. Find out more about the Kindle Personal Document Service.POST-AVICENNAN LOGICIANS ON THE SUBJECT MATTER OF LOGIC: SOME THIRTEENTH- AND FOURTEENTH-CENTURY DISCUSSIONSVolume 22, Issue 1Khaled El-Rouayheb DOI: https://doi.org/10.1017/S0957423911000105Your Kindle email address Please provide your Kindle [email protected]@kindle.com Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Dropbox To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox. POST-AVICENNAN LOGICIANS ON THE SUBJECT MATTER OF LOGIC: SOME THIRTEENTH- AND FOURTEENTH-CENTURY DISCUSSIONSVolume 22, Issue 1Khaled El-Rouayheb DOI: https://doi.org/10.1017/S0957423911000105Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Google Drive To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive. POST-AVICENNAN LOGICIANS ON THE SUBJECT MATTER OF LOGIC: SOME THIRTEENTH- AND FOURTEENTH-CENTURY DISCUSSIONSVolume 22, Issue 1Khaled El-Rouayheb DOI: https://doi.org/10.1017/S0957423911000105Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Export citation Request permission. (shrink)

Logic as a subject has existed for a long time. Aristotle and the Stoics identified some of its principles, as did Indian logicians. And this ancient logic underwent an extraordinary mathematical development in the last hundred and fifty years. So logic certainly exists, at least as a branch of mathematics. The question is whether it is anything more than that.

A review of Sextus Empiricus, Against the Logicians, translated and edited by Richard Bett, Cambridge University Press, Cambridge, 2005.

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Against the Greek LogiciansCharles E. ButterworthIbn Taimiyya. Against the Greek Logicians. Translated with an introduction and notes by Wael B. Hallaq. Oxford: Clarendon Press, 1993. Pp. lviii + 204. $55.00.Wael Hallaq's most readable translation of Ibn Taimiyya's famous work is complemented by a masterful introduction and intelligent, relevant footnotes. In addition, he has taken care to help the reader in many ways, adding, for example, a list (...) of the emendations he has made to the Arabic text as well as a table that details the correspondence between the paragraphs of his translation and the pages and lines within the more standard Arabic texts.The editor-translator's introduction sets forth Ibn Taimiyya's teaching in a clear and well-argued manner, something that is necessary given the repetitiveness and confusing arguments that characterize the original. Though Hallaq tends to reveal himself to be something of a partisan of Ibn Taimiyya's doctrines and thus to overstate the case for his author, this is a minor flaw. The strength of the Introduction is such that the student of logic or philosophy is compelled to indicate the problems in Hallaq's presentation, that is, to identify the reasons for not being persuaded by his exposition. [End Page 273] To do so, however, is merely a means of carrying the argument a step further and thus a compliment of sorts to Hallaq.As I see it, there are five areas where one might take issue with the editor-translator's presentation of Ibn Taimiyya's teaching. First, because he follows his author too closely, Hallaq relies too much on Avicenna and on Avicenna's commentators to present the position of the philosophers. He seems to ignore that the teaching of Avicenna—he whom Averroes would identify only as "that man"-—is problematic even for the philosophers. Second, Hallaq relies too much on secondary literature in order to present the history of philosophy. He would have been far better advised to trace the history of philosophy for himself, especially the history of medieval Islamic philosophy. By relying on others, especially those whose interpretations are open to major objections, he weakens his own presentation. This tendency becomes especially evident in what I take as a third point of criticism, namely, Hallaq's too ready conflation of the history of philosophy and consequent willingness to blame ancient and medieval philosophers for the folly of modern philosophers (see xxx, n. 98 and xviii:17-18). Worse, Hallaq eventually becomes so carried away with the desire to refute the ancient and medieval philosophers that he no longer cares about the evil consequences of modern philosophy (see xviii:8-xlix:20, esp. xlviii:8-29). Indeed, and this is the fourth criticism, so intent is Hallaq on confirming that Ibn Taimiyya has refuted the philosophers that he is content to call anyone a philosopher, even al-Suhrawardī, al-Baghdādī, al-Tūsī, and, wonder of wonders, Fakhr al-Dīn al-Rāzī (see xliv:4). Though he has good guidance for this from Ibn Taimiyya, one would hope for more objectivity from the critical scholar than from the engaged defender of the faith. Finally, Hallaq actually introduces Ibn Taimiyya's wider teaching rather than the argument of this book, thereby neglecting the primary function of an introduction to a book. Thus, of 91 notes in the Introduction that refer to Ibn Taimiyya's works, only slightly more than half (52) cite this work. The other 39 are to Ibn Taimiyya's other writings. Moreover, many of the 52 notes to this work also refer to other writings by Ibn Taimiyya.Thankful as we must be to Hallaq for this translation, it is most unfortunate that he chose not to be consistent in his translation of Arabic terms. Apparently, he thought he could make more sense of Ibn Taimiyya's argument by translating terms in accordance with what he took to be the sense of what Ibn Taimiyya wished to say rather than in accordance with what he actually says. Consequently, tasdīq (a term I would translate as "assent") is rendered as "judgment"; but so is hukm (see ¶¶ 5 and... (shrink)

The purpose of this paper is to present a thought experiment and argument that spells trouble for “radical” deflationism concerning meaning and truth such as that advocated by the staunch nominalist Hartry Field. The thought experiment does not sit well with any view that limits a truth predicate to sentences understood by a given speaker or to sentences in (or translatable into) a given language, unless that language is universal. The scenario in question concerns sentences that are not understood but (...) are known to be logical consequences of known and understood sentences. Ultimately, the issue turns on the notion of logical consequence that is available to various versions of deflationism. (shrink)

In a chapter of - so to speak - an intellectual autobiography I sketch the reasons and ways I became a practitioning Meinongian logician. The way is a chain of transgressions, e.g., the transgression of extensionalism or of the law of excluded middle, and a struggle against widespread misinterpretations of Meinong's Gegenstandstheorie. Although the opposition towards Meinong's theory of objects persists in analytic philosophy, its main insights - that thought is intentional and that logic must be ontologically neutral - haven't (...) lost their attraction. Moreover: there is no substantive criticism to show that we cannot refer and truely predicate properties of intended objects regardless of their ontic status. (shrink)

Logic as a subject has existed for a long time. Aristotle and the Stoics identified some of its principles, as did Indian logicians. And this ancient logic underwent an extraordinary mathematical development in the last hundred and fifty years. So logic certainly exists, at least as a branch of mathematics. The question is whether it is anything more than that.

The logical rule of contraposition as applied to a particular affirmative proposition (I-contraposition), despite its rejection in the medieval Latin logic, had a different history in the medieval Arabic logic, varying from common acknowledgement to total dismissal (it was accepted by Avicenna and by all of his followers in the eleventh and twelfth centuries and rejected by all of Arabic logicians in the late thirteenth century onwards). This paper is a narrative of the fate of I-contraposition in the early (...) Arabic logic. I will study Avicenna’s, al-Suhrawardī’s, al-Rāzī’s, al-Kashshī’s, and al-Khūnajī’s views on this rule. Although Avicenna explicitly acknowledged I-contraposition in a brief note, and in an apparently Meinongian language, the other four figures found I-contraposition problematic and listed some counterexamples to it. Nonetheless, they all attempted to justify Avicenna’s acceptance of the rule by restricting its application conditions. These efforts led to interesting syntactic and semantic analyses but gathered little attention from later medieval logicians. Finally, in the middle Arabic logic, the revised versions of I-contraposition were also declared invalid. (shrink)

The author distinguishes a "term logic," where terms are the fundamental units, and a "sentential logic," where sentences are the fundamental units. Although this technical distinction is presented by Englebretsen as a war-like opposition throughout the entire history of logic, he reassures us that "no blood has been spilled". In recent times, the term-logic party has been eclipsed by the sentential-logic band; term logic is nowadays "almost mute". Only F. Sommers appears to proclaim the truth of term logic in the (...) twentieth century. The author's main goal is to "recount the history" of term logic through an examination of its three champions: Aristotle, Leibniz, and Sommers. The chronological sequence of these three logicians is a sequence towards perfection as well. The shortcomings of Aristotle's achievement are partially corrected by Leibniz and then fully repaired by Sommers, who finally extends the Aristotelian syllogistic into a "universal logic". Englebretsen himself has added "certain emendations and extensions in a modest way". (shrink)

I examine the treatment of metaphor by medieval logicians and how it stemmed from their reception of classical texts in logic, grammar, and rhetoric. I consider the relation of the word 'metaphor' to the notions of translatio and transumptio, and show that it is not always synonymous with these. I also show that in the context of commentaries on the Sophistical Refutations metaphor was subsumed under equivocation. In turn, it was linked with the notion of analogy not so much (...) in the Greek sense of a similarity between two proportions or relations as in the new medieval sense of being said secundum prius et posterius. Whether or not analogy could be reduced to metaphor, or the reverse, depended on the controversial issue of the number of acts of imposition needed to produce an equivocal term. A spectrum of views is canvassed, including those found in the logic commentaries of John Duns Scotus. (shrink)

InThe Many Faces of Realism and elsewhere, Hilary Putnam has presented an argument for the conclusion that there is no fact of the matter as to how many objects there are. In brief: Carnap says that a certain imaginary world contains three objects, ×1, ×2, and ×3. The Polish logician says that this same world must contain four other objects (×1 + ×2, ×1 + ×2 + ×3, etc.). Putnam maintains that there can be no fact of the matter as (...) to whether the imaginary world contains three or seven objects. I examine Putnam’s argument and find it, at bottom, unintelligible. (shrink)

What do you get when you cross a fallacy with a good argument? A fugu, that is, a valid argument that tempts you to reach its conclusion invalidly. You have yielded to the temptation more than you realize. If you are a teacher, you may have served many fugus. They arise systematically through several mechanisms. Fugus are interesting intermediate cases that shed light on the following issues: bare evidentialism, false pleasure, philosophy of education, and the ethics of argument. Normally, a (...) fugu will not yield knowledge from known premises. But if the reasoning is only slightly fallacious, they do yield knowledge. These mild fugus show that we can gain knowledge by invalid reasoning. This is a conservative resource for historians. They want to credit discoveries to Euclid rather than those who made minor corrections to his proofs, such as David Hilbert. We also benefit from this practice of grandfathering in old standards of knowledge attribution. For we can compete spiritedly for priority. We do not need to worry that credit will instead go to future scholars who will make the minor amendments needed to raise present proofs to a future standard of demonstration. (shrink)

Although much technical and philosophical attention has been given to relevance logics, the notion of relevance itself is generally left at an intuitive level. It is difficult to find in the literature an explicit account of relevance in formal reasoning. In this article I offer a formal explication of the notion of relevance in deductive logic and argue that this notion has an interesting place in the study of classical logic. The main idea is that a premise is relevant to (...) an argument when it contributes to the validity of that argument. I then argue that the sequents which best embody this ideal of relevance are the so-called perfect sequents—that is, sequents which are valid but have no proper subsequents that are valid. Church’s theorem entails that there is no recursively axiomatizable proof-system that proves all and only the perfect sequents, so the project that emerges from studying perfection in classical logic is not one of finding a perfect subsystem of classical logic, but is rather a comparative study of classifying subsystems of classical logic according to how well they approximate the ideal of perfection. (shrink)

C.S. Peirce offered an evaluation of Bentham's philosophy to the effect that on some points Bentham's performance was of great value, but essentially, he was ‘a shallow logician’ confined to analysis of ‘lower motive’. This paper argues that Bentham's logic is deeply metaphysically based, multi‐levelled, and comprehensive. There are at least three constituent parts in his utilitarian logic: the first is his ontology, with its distinction between real and fictitious entities, and with pain and pleasure constituting the core real entities; (...) the second is his reductionism in, and analytical view of, simple and complex pleasures and pains; the third is the distinction between private ethics and public ethics. Bentham's logic is staunchly based on empiricism and truth and he developed a pragmatic utilitarian solution to overcome the potential impasse of Hume's scepticism through a mechanism of reflection. Even the doctrines of belief and abduction embraced and developed by Peirce are contained in Bentham's utilitarian logic. Bentham would certainly take Peirce's philosophy as ipse dixitism. Peirce was not in fact a serious reader of Bentham and failed to employ the distinction between argument and argumentation in his study of Bentham's logic. (shrink)

Let us call “tense logic” the programme of explaining tense in natural languages by means of a model theory similar in structure to possible worlds semantics for modality. This programme would make the following claims.