Johannes Steuchius’ disputatio uses Arabic logic to present an historical account of the development of philosophical thought in Arabia before and after the emergence of Islam. Steuchius first proposes that philosophy drew its origins from the East. His evidence for this claim is that many of the Greek philosophers, considered the forefathers of European philosophy, began cultivating their philosophical thinking as a result of exposure to ancient Eastern philosophy. After the introduction of Greek philosophy, it is agreed that (...) dialectic was among the first of the arts the Arabs practiced. (shrink)

Rozprawa podkreśla związek między językową argumentacją a logiką. Argumentacja językowa jest systemem językowym, który stosuje znaczenie wyrażeń ujętych w zdania do zarysowania pełnego znaczenia zdań, w nich bowiem konstytuują się zależności między wyrażeniami. Rzeczywiście, to powiązanie między wyrażeniami wzmacnia całościowe znaczenie począwszy od samych podstaw struktury zdania w logicznym powiązaniu idei. W nim znajduje się relacja między słowami a umysłem, zależna od logiki powiązanych ze sobą wypowiedzi. Aby podkreślić znaczenie przedstawionego wyżej sposobu myślenia, autorka zwraca się ku teorii wczesnej gramatyki (...) arabskiej, ogniskującej się raczej wokół analogii niż anomalii. Nastawienie w systemie na analogię opiera się na podstawowej teorii, która implikuje wspomnianą wyżej relację, choć niektóre współczesne ujęcia odrzucają tę interpretację. W podsumowaniu swojej analizy, autorka uwzględnia podobne teorie gramatyki łacińskiej, które wykazują nastawienie logiczne, będące następstwem powiązania językowej argumentacji z logiką. Konkludując, autorka stwierdza, iż powiązanie słów i logiki okazuje się pojęciem uniwersalnym. (shrink)

The passionate and staunch defence of logic of the controversial thinker Ibn Ḥazm, Abū Muḥammad ʿAlī b. Aḥmad b. Saʿīd of Córdoba (384-456/994-1064), had lasting consequences in the Islamic world. Indeed, his book Facilitating the Understanding of the Rules of Logic and Introduction Thereto, with Common Expressions and Juristic Examples (Kitāb al-Taqrīb li-ḥadd al-manṭiq wa-l-mudkhal ilayhi bi-l-alfāẓ al-ʿāmmiyya wa-l-amthila al-fiqhiyya), composed in 1025-1029, was well known and discussed during and after his time; and it paved the way for (...) the studies of his compatriots Ibn Bājjah (d. 1138), Ibn Ṭufayl (1185), and Ibn Rushd (1198), who each gave demonstrative reasoning a privileged place within the methods of attaining knowledge. Unfortunately, as too often in the history of science, Ibn Ḥazm’s innovative perspectives and contributions in logic have been overlooked or considered with an attitude of contempt. On the one hand, his work has been seen, at best, as promulgating the benefits of studying Aristotle’s logic, so that his contribution is assessed as more didactical than conceptual. And on the other hand, those who do examine his innovations often consider them to be mistaken. As indicated by Chejne (1984, p. 2) contempt towards the logical work of Ibn Ḥazm was also present in its reception by the Eastern philosophers who accused him of deviating from Aristotelian logic and of dabbling in things beyond his capability. However, a reassessment of his work on logic has since begun, by delving into the ways the thinker of Córdoba studied the links between deontic and modal qualification of propositions. In this context Lameer’s (2013) paper on the logical sources of Ibn Ḥazm is worth mentioning; the author (p. 417, footnote 1) observes that, although, strictly speaking, it was al-Fārābī who first drew the parallelism between deontic and modal concepts, it was Ibn Ḥazm who developed it and worked it out in a more precise manner. A primary aim of this paper is to help fill some of these gaps by stressing the role of the work of Ibn Ḥazm in developing a notion of deontic necessity deeply rooted in legal normativity, and in explicitly discussing the transference between deontic and modal concepts. According to our view; the basic units of Islamic deontic logic are what we might call, indulging in terminological anachronism, heteronomous imperatives. As it turns out, the heteronomy of imperatives within Islamic legal systems contrasts with those of the purely moral realm, which seem to be closer to an autonomous conception of moral law. There it concurs again with Leibniz’s proposal to define obligatory as “what is necessary for a good person to do”. In the present paper, we will focus on the heteronomous imperatives of legal systems rather than on the imperatives of the purely moral realm. In this context, the work of Ibn Ḥazm extends the parallelism between the necessity of events and that of human actions stressed by his predecessors. According to our understanding, Ibn Ḥazm’s parallelism can be rendered explicit formally by means of a conditional (or hypothetical) structure shared by both deontic and modal propositions. Moreover, this structure makes apparent that this parallelism displays an underlying system of “degrees”. Indeed, while in the domain of events, given some conditions, it makes sense to distinguish between an event that is more likely to happen than another. Ibn Ḥazm speaks of near and distant possibility (such as the higher degree of likelihood of rain, given the condensation of clouds in December, and its lower degree, when the condensation occurs in summer); and, in the domain of actions, the Islamic notion of weighting actions determines degrees of virtue (or of legal and moral value). So whereas the degree of virtue of performing a forbidden act as determined by the distribution of sanction and reward is 0, we obtain the same value by pondering the likelihood of an impossible event to take place. Furthermore, as discussed in section II.3.2, the system of values at work in the parallelism can be seen as opening the way to a more direct correspondence. Thus, while in the realm of nature, likelihood of occurrence of an event is dependent upon the conditions specific to the occurrence of that event; while, in the realm of jurisprudence, likelihood of performing an action is dependent upon the distribution of reward and sanction specific to that action (being that, given the choice to perform or not perform a given action, those that will be rewarded are more likely to be performed than those that are not). According to this perspective, the point of the parallelism is that both deontic and modal qualifications measure the degree of an action or event to become actual; that is – indulging once more in anachronism (but this time from the Leibnizian background) – the degree measures how feasible (facile) an action or event may be. This suggests that Ibn Ḥazm’s perspectives already herald the links to probability and possibility explored by Leibniz six centuries later – see for example Leibniz’s (1671, A VI, I, p. 424-26) use of probability in the context of conditional right. Nevertheless, it also shows a crucial difference to the approach developed in the Elementa Jura Naturalis: whereas Leibniz’s studies seek to define what is to be just or virtuous, the logical system of deontic imperatives within Islamic jurisprudence presupposes that what is to be virtuous has already been settled. Determining what is to be virtuous is not achieved by logical reasoning within the system of legal jurisprudence, but by delving into the higher objectives of the Sharīʿa. While developing our point, we will delve into the logical structure of the heteronomous imperatives. This distinguishes our contribution from the existing literature, such as the papers of Chejne (1984), Lameer (2014), and Guerrero (1997, 2010, 2014), which do not provide a logical analysis of the deontic concepts put into work by Ibn Ḥazm. The true antecedent to the present paper is the work of Farid Zidani (2007, 2015), who, so far as we know, was the first to undertake such a task. Some of our own developments and general epistemological thoughts go beyond Ibn Ḥazm’s framework and motivations; mainly those contained in sections II.3.2 and IV. However, according to our view, these reflections suggest that Ibn Ḥazm’s approach has the substance for a broader and deeper exploration of the logic of norms. The paper is structured as follows:I.Ibn Ḥazm’s Logic of Heteronomous Imperatives. After presenting some extracts of the relevant text, we proceed by providing a formal reconstruction of the five forms of deontic modalities. II. A Landmark in the History of the Logical Analysis of Norms. Duties and Modalities. In this section, we study the transferences from deontic to modal necessity and possibility. We briefly compare the deontic system of Islamic Jurisprudence with that of Leibniz.III. Leibniz and Hypothetical Imperatives in Law.IV. Beyond Ibn Ḥazm: Conclusions and the Work Ahead. We will conclude the paper by discussing briefly some conceptual points that distinguish the logic of heteronomous imperatives from contemporary deontic logic. Our final words will discuss deontic-modal parallelism in the context of Ibn Ḥazm’s rejection of reasoning by conjecture and what we call “the internalization of nature.”. (shrink)

Like lynching and other mass hysterias, xenophobia exemplifies a contagious, collective wave of energy and hedonic quality that can point toward a troubling unpredictability at the core of political and social systems. While earlier studies of mass hysteria and popular discourse assume that cooler heads (aka rational individuals with their logic) could and should regain control over those emotions that are deemed irrational, and that boundaries are assumed healthy only when intact, affect studies pose individuals as nodes of biosocial (...) networks larger than themselves. Thus rather than suggesting that the individual can only prevent societal harm by gaining command and patrolling the borders of an autonomous self, we embrace the notion that affects can exert a positive and transformative force on a social reality that is resistant to top-down policy intervention and any straightforward moral or logical plea. (shrink)

We all know that problems of transportation and allocation appear frequently in practical life. We need to transfer materials from production centers to consumption centers to secure the areas’ need for the transported material or allocate machines or people to do a specific job at the lowest cost, or in the shortest time. We know that the cost factors Time is one of the most important factors that decision-makers care about because it plays an “important” role in many of the (...) practical and scientific issues that we face in our daily lives, and we need careful study to enable us to avoid losses. For this, the linear programming method was used, which is one of the research methods. Processes, where the problem data is converted into a linear mathematical model for which the optimal solution achieves the desired goal. Since these models are linear models, we can solve them using the direct simplex method and its modifications, but the specificity that these models enjoy has enabled scholars and researchers to find special methods that help us in obtaining the optimal solution. Whatever the method used, the goal is to determine the number of units transferred from any material from production centers to consumption centers, or to allocate a machine or person to do a job so that the cost or time is as short as possible. These issues were addressed according to classical logic, but the ideal solution was a specific value appropriate to the conditions in which the data was collected and does not take into account the changes that may occur in the work environment. In order to obtain results that are more accurate and enjoy a margin of freedom, we present in this book a study of transport issues and neutrosophic allocation issues and some methods for solving them. By neutrosophic issues we mean These are the problems in which the data are neutrosophic values, i.e. the required quantities and the available quantities. (shrink)

The philosophy is an important factor of education policy like the religion, heritage, culture and customs of the society .It concerns on the mind and its implication in our daily life. Philosophy focus on Logic, Science, Epistemology, Ethics and Esthetics which are important branches of human thoughts. During the human history, philosophy organizes education and the societies revert to philosophy to regulate education policy. In ancient time, Plato and Aristotle’s educational policy was established for Athens. For the Medieval, Al-Kindi, (...) Al-Farabi, Al-Razi, Ibn Sina, Ibn Tufail, and Ibn Rushd contributed to setting education policy in Arab culture. John Locke, Jean-Jacques Rousseau, Karl Marx and John Dewey elaborated philosophical theories of education. Philosophy contributes to: suggesting education goals, provide the learning outcome, classification of topics and learning activities in educational institutions , and proposes an educational curriculum. In this research, I will address these factors focusing on the fact that our present civilized societies need a philosophical dimension in organizing education policy. I will rely on philosophical theories, as well as contemporary studies that have been written on education policy in developed countries. (shrink)

The text is a drought outlining the development of logic in Bosnia and Herzegovina through several periods of history: period of Ottoman occupation and administration of the Empire, period of Austro-Hungarian occupation and administration of the Monarchy, period of Communist regime and administration of the Socialist Republic and period from the aftermath of the aggression against the Republic of Bosnia and Herzegovina to this day (the Dayton Bosnia and Herzegovina) and administration of the International Community. For each of the (...) aforementioned periods, the text treats the organization of education, the educational paradigm of the model, status of logic as a subject in the educational system of a period, as well as the central figures dealing with the issue of logic (as researchers, lecturers, authors) and the key works written in each of the periods, outlining their main ideas. Thework of aNeoplatonic philosopher Porphyry, “Introduction” (Greek: Eisagogee), Latin: Isagoge; Arabic: Īsāġūğī), can be seen, in all periods of education in Bosnia and Herzegovina, as the main text, the principal textbook, as a motivation for logical thinking. That gave me the right to introduce the syntagm Bosnia Porphyriana. (shrink)

Al-Taftāzānī introduces the Liar Paradox, in a commentary on al-Rāzī, in a short passage that is part of a polemic against the ethical rationalism of the Muʿtazila. In this essay, we consider his remarks and their place in the history of the Liar Paradox in Arabic Logic. In the passage, al-Taftāzānī introduces Liar Cycles into the tradition, gives the paradox a puzzling name—the fallacy of the “irrational root” —which became standard, and suggests a connection between the paradox and (...) what it tells us about truth and falsehood, and arguments for divine voluntarism and what they tell us about the nature of goodness and badness. On this last point, we also discuss a passage from al-Rāzī, which suggests similar connections. (shrink)

The article presents the chess composition as a logical art, with concrete examples. It began with Arabic mansuba, and later evolved to new-strategy designed by Italian Alberto Mari. The redefinition of mate (e.g. mate with a free field) or a theme to quasi-pseudo theme, opens the new space for combinations, and enables to connect it with other fields like computer science. The article was exhibited in Holland Park, W8 6LU, The Ice House between 18. Oct - 3. Nov. 2013.

In this fascinating book, Mehmet Karabela reveals the many roles assigned to Islam, Islamic history, the Ottoman Empire, Turks and Arabs by northern European Protestant intellectuals, mostly German Lutherans, from 1650 to 1800. The texts cover many topics that famously captivated European thinkers during a period which Karabela elects to call post-Reformation rather than Enlightenment. There are comparative studies of religion, philosophy, and literature. Karabela’s introduction provides a robust review of the historiography and offers context for patterns that emerge from (...) the texts. (shrink)

Early modern Protestant scholars closely engaged with Islamic thought in more ways than is usually recognized. Among Protestants, Lutheran scholars distinguished themselves as the most invested in the study of Islam and Muslim culture. Mehmet Karabela brings the neglected voices of post-Reformation theologians, primarily German Lutherans, into focus and reveals their rigorous engagement with Islamic thought. Inspired by a global history approach to religious thought, Islamic Thought Through Protestant Eyes offers new sources to broaden the conventional interpretation of the Reformation (...) beyond a solely European Christian phenomenon. -/- Based on previously unstudied dissertations, disputations, and academic works written in Latin in the seventeenth and eighteenth centuries, Karabela analyzes three themes: Islam as theology and religion; Islamic philosophy and liberal arts; and Muslim sects (Sunni and Shi‘a). This book provides analyses and translations of the Latin texts as well as brief biographies of the authors. -/- These texts offer insight into the Protestant perception of Islamic thought for scholars of religious studies and Islamic studies as well as for general readers. Examining the influence of Islamic thought on the construction of the Protestant identity after the Reformation helps us to understand the role of Islam in the evolution of Christianity. (shrink)

Dâwûd al-Qarisî (Dâvûd al-Karsî) was a versatile and prolific 18th century Ottoman scholar who studied in İstanbul and Egypt and then taught for long years in various centers of learning like Egypt, Cyprus, Karaman, and İstanbul. He held high esteem for Mehmed Efendi of Birgi (Imâm Birgivî/Birgili, d.1573), out of respect for whom, towards the end of his life, Karsî, like Birgivî, occupied himself with teaching in the town of Birgi, where he died in 1756 and was buried next to (...) Birgivî. Better known for his following works on Arabic language and rhetoric and on the prophetic traditions (hadith): Sharḥu uṣûli’l-ḥadîth li’l-Birgivî; Sharḥu’l-Ḳaṣîdati’n-nûniyya (two commentaries, in Arabic and Turkish); Şarḥu’l-Emsileti’l-mukhtalifa fi’ṣ-ṣarf (two commentaries, in Arabic and Turkish); Sharḥu’l-Binâʾ; Sharḥu’l-ʿAvâmil; and Sharḥu İzhâri’l-asrâr, Karsî has actually composed textbooks in quite different fields. Hence the hundreds of manuscript copies of his works in world libraries. Many of his works were also recurrently printed in the Ottoman period. One of the neglected aspects of Karsî is his identity as a logician. Although he authored ambitious and potent works in the field of logic, this aspect of him has not been subject to modern studies. Even his bibliography has not been established so far (with scattered manuscript copies of his works and incomplete catalogue entries). This article primarily and in a long research based on manuscript copies and bibliographic sources, identifies twelve works on logic that Karsî has authored. We have clarified the works that are frequently mistaken for each other, and, especially, have definitively established his authorship of a voluminous commentary on al-Kâtibî’s al-Shamsiyya, of which commentary a second manuscript copy has been identified and described together with the other copy. Next is handled his most famous work of logic, the Sharhu Îsâghûcî, which constitutes an important and assertive ring in the tradition of commentaries on Îsâghûcî. We describe in detail the nine manuscript copies of this work that have been identified in various libraries. The critical text of Karsî’s Sharhu Îsâghûcî, whose composition was finished on 5 March 1745, has been prepared based on the following four manuscripts: (1) MS Kayseri Raşid Efendi Kütüphanesi, No. 857, ff.1v-3v, dated 1746, that is, only one year after the composition of the work; (2) MS Bursa İnebey Yazma Eser Kütüphanesi, Genel, No.794B, ff.96v-114v, dated 1755; (3) MS Millet Kütüphanesi, Ali Emiri Efendi Arapça, No. 1752, ff.48v-58r, dated 1760; (4) MS Beyazıt Yazma Eser Kütüphanesi, Beyazıt, No. 3129, ff.41v-55v, dated 8 March 1772. While preparing the critical text, we have applied the Center for Islamic Studies (İslam Araştırmaları Merkezi, İSAM)’s method of optional text choice. The critical text is preceded by a content analysis. Karsî is well aware of the preceding tradition of commentary on Îsâghûcî, and has composed his own commentary as a ‘simile’ or alternative to the commentary by Mollâ Fanârî which was famous and current in his own day. Karsî’s statement “the commentary in one day and one night” is a reference to Mollâ Fanârî who had stated that he started writing his commentary in the morning and finished it by the evening. Karsî, who spent long years in the Egyptian scholarly and cultural basin, adopted the religious-sciences-centered ‘instrumentalist’ understanding of logic that was dominant in the Egypt-Maghrib region. Therefore, no matter how famous they were, he criticized those theoretical, long, and detailed works of logic which mingled with philosophy; and defended and favored authoring functional and cogent logic texts that were beneficial, in terms of religious sciences, to the seekers of knowledge and the scholars. Therefore, in a manner not frequently encountered in other texts of its kind, he refers to the writings and views of Muhammad b. Yûsuf al-Sanûsî (d.1490), the great representative of this logical school in the Egyptian-Maghrib region. Where there is divergence between the views of the ‘earlier scholars’ (mutaqaddimûn) like Ibn Sînâ and his followers and the ‘later scholars’ (muta’akhkhirûn), i.e., post-Fakhr al-dîn al-Râzî logicians, Karsî is careful to distance himself from partisanship, preferring sometimes the views of the earliers, other times those of the laters. For instance, on the eight conditions proposed for the realization of contradiction, he finds truth to be with al-Fârâbî, who proposed “unity in the predicative attribution” as the single condition for the realization of contradiction. Similarly, on the subject matter of Logic, he tried to reconcile the mutaqaddimûn’s notion of ‘second intelligibles’ with the muta’akhkhirûn’s notion of ‘apprehensional and declarational knowledge,’ suggesting that not much difference exists between the two, on the grounds that both notions are limited to the aspect of ‘known things that lead to the knowledge of unknown things.’ Karsî asserts that established and commonly used metaphors have, according to the verifying scholars, signification by correspondence (dalâlat al-mutâbaqah), adding also that it should not be ignored that such metaphors may change from society to society and from time to time. Karsî also endorses the earlier scholars’ position concerning the impossibility of quiddity (mâhiyya) being composed of two co-extensive parts, and emphasizes that credit should not be given to later scholars’ position who see it possible. According to the verifying scholars (muhaqqîqûn), it is possible to make definition (hadd) by mentioning only difference (fasl), in which case it becomes an imperfect definition (hadd nâqis). He is of the opinion that the definition of the proposition (qadiyya) in al-Taftâzânî’s Tahdhîb is clearer and more complete: “a proposition is an expression that bears the possibility of being true or false”. He states that in the division of proposition according to quantity what is taken into consideration is the subject (mawdû‘) in categorical propositions, and the temporal aspect of the antecedent (muqaddam) in hypothetical propositions. As for the unquantified, indefinite proposition (qadiyya muhmalah), Karsî assumes that if it is not about the problems of the sciences, then it is virtually/potentially a particular proposition (qadiyya juz’iyyah); but if it is about the problems of the sciences, then it is virtually/potentially a universal proposition (qadiyya kulliyyah). This being the general rule about the ambiguous (muhmal) propositions, he nevertheless contends that, because its subject (mawdû‘) is negated, it is preferable to consider a negative ambiguous (sâliba muhmalah) proposition like “human (insân) is not standing” to be a virtually/potentially universal negative (sâliba kulliyyâh) proposition. He states that a disjunctive hypothetical proposition (shartiyya al-munfasila) that is composed of more than two parts/units is only seemingly so, and that in reality it cannot be composed of more than two units. Syllogism (qiyâs), according to Karsî, is the ultimate purpose (al-maqsad al-aqsâ) and the most valuable subject-matter of the science of Logic. For him, the entire range of topics that are handled before this one are only prolegomena to it. This approach of Karsî clearly reveals how much the ‘demonstration (burhân)-centered’ approach of the founding figures of the Muslim tradition of logic like al-Fârâbî and Ibn Sînâ has changed. al-Abharî, in his Îsâghûjî makes no mention of ‘conversion by contradiction’ (‘aks al-naqîd). Therefore, Karsî, too, in his commentary, does not touch upon the issue. However, in his Îsâghûjî al-jadîd Karsî does handle the conversion by contradiction and its rules. Following the method of Îsâghûjî, in his commentary Karsî shortly touches on the four figures (shakl) of conjuctive syllogism (qiyâs iqtirânî) and their conditions, after which he passes to the first figure (shakl), which is considered ‘the balance of the sciences’ (mi‘yâr al-‘ulûm), explaining the four moods (darb) of it. In his Îsâghûjî al-jadîd, however, Karsî handles all the four figures (shakl) with all their related moods (darb), where he speaks of fife moods (darb) of the fourth figure (shakl). The topic of ‘modal propositions’ (al-muwajjahât) and of ‘modal syllogism’ (al-mukhtalitât), both of which do not take place in the Îsâghûjî, are not mentioned by Karsî as well, either in his commentary on Îsâghûjî or in his Îsâghûjî al-jadîd. Karsî proposes that the certainties (yaqîniyyât), of which demonstration (burhân) is made, have seven, not six, divisions. After mentioning (1) axioms/first principles (awwaliyyât), (2) observata/sensuals (mushâhadât), (3) experta/empiricals (mujarrabât), (4) acumenalia (hadthiyyât), (5) testata (mutawâtirât), and (6) instictives (fitriyyât), that is, all the ‘propositions accompanied by their demonstrations,’ Karsî states that these six divisions, which do not need research and reflection (nazar), are called badîhiyyât (self-evidents), and constitute the foundations (usûl) of certainties (yaqîniyyât). As the seventh division he mentions (7) the nazariyyât (theoreticals), which are known via the badîhiyyât, end up in them, and therefore convey certainty (yaqîn). For Karsî, the nazariyyât/theoreticals, which constitute the seventh division of yaqîniyyât/certainties, are too numerous, and constitute the branches (far‘) of yaqîniyyât. Every time the concept of ‘Mughâlata’ (sophistry) comes forth in the traditional sections on the five arts usually appended to logic works, Karsî often gives examples from what he sees as extreme sûfî sayings, lamenting that these expressions are so widespread and held in esteem. He sometimes criticizes these expressions. However, it is observed that he does not reject tasawwuf in toto, but excludes from his criticism the mystical views and approaches of the truth-abiding (ahl al-haqq), shârî‘â-observant (mutasharri‘) leading sufis who have reached to the highest level of karâmah. (shrink)

An essay on the philosophy of human nature in Islam, this article examines the views of contemporary Western thinkers to creatively rethink the concept of fiṭra, not only from a theological perspective but also a scientific perspective. Drawing upon Islamic scholarship and previous research on the subject that explore the wide spectrum of connotations couched in the Arabic term fiṭra in comparison with Western perspectives, this study offers a fresh look at, and approach to, the concept of human disposition (...) or primordial nature, giving special attention to the biological, epistemological, and ethical dimensions, while most studies of fiṭra focus mainly on the theological and spiritual sides. It is hoped that this conceptual analysis will serve as a stepping stone towards a more nuanced understanding of fiṭra not only as (i) a natural tendency to act or think in a particular way, but also as (ii) the religious instinct, (iii) the power of the mind to think and understand in a logical way, and (iv) the inner voice or conscience of what is right and wrong in one’s conduct or motives that drives the individual towards right action. (shrink)

The separation of Avicenna between Essence and Existence influenced logic and Arab and Muslim logicians in the Middle Ages among them Ibn al-Nafīs (1208-1288). Under this influence he contributed to the development of logic and especially the theory of the universal term. By means of the consequences of this analysis:-It has become possible to make a distinction between abstract concepts and formal concepts independent of any sensible reality, and hence the questioning of Aristotelian categories, that is to say (...) the ability to conceive for Ibn al-Nafīs like Avicenna, subjects and predicates which are not necessarily words expressing or belonging to one of the Aristotelian categories.-The analysis of the universal proposition as a conditional proposition, which made easier the distinction between absolute proposition which has no existential implication, and the other which differ from the first by an affirmation of explicit existence. (shrink)

With regard to the new directions in the Humanities, here I am going to consider and examine the approach of al-Farabi as a medieval thinker in introducing a new outlook to “language” in difference with the other views. Thereby, I will explore his challenges in the frame of “philosophical humanism” as a term given by Arkoun (1970) and Kraemer (1984) to the humanism of the Islamic philosophers and their circles, mainly in the tenth and eleventh centuries. Al-Farabi’s conception of philosophical (...) humanism, in which philosophy is thick and religion is thin, makes its agony with the other versions of humanism and also orthodox Islam. It means that his introduction of a humanistic understanding of language should be placed in such a multi-level contested environment. According to al-Farabi, language as a universal category has relation with reason that logic should function as its proper instrument. As a result, there is no specific privileged predetermined language, but the position of any language is shaped by its relation with human reason and formal logic that is something human-made. And such a conception means language in human terms. Key Terms: Al-Farabi; Language; Philosophical Humanism; Arabic: Greek . (shrink)

Science and mathematics continually change in their tools, methods, and concepts. Many of these changes are not just modifications but progress---steps to be admired. But what constitutes progress? This dissertation addresses one central source of intellectual advancement in both disciplines: reformulating a problem-solving plan into a new, logically compatible one. For short, I call these cases of compatible problem-solving plans "reformulations." Two aspects of reformulations are puzzling. First, reformulating is often unnecessary. Given that we could already solve a problem using (...) an older formulation, what do we gain by reformulating? Second, some reformulations are genuinely trivial or insignificant. Merely replacing one symbol with another does not lead to intellectual progress. What distinguishes significant reformulations from trivial ones? According to what I call "conceptualism" (or "conceptual empiricism"), reformulations are intellectually significant when they provide a different plan for solving problems. Significant reformulations provide inferentially different routes to the same solution. In contrast, trivial reformulations provide exactly the same problem-solving plans, and hence they do not change our understanding. This answers the second question about what distinguishes trivial from significant reformulations. However, the first question remains: what makes a new way of solving an old problem valuable? Here, a bevy of practical considerations come to mind: one formulation might be faster, less complicated, or use more familiar concepts. According to "instrumentalism," these practical benefits are all there is to reformulating. Some reformulations are simply more instrumentally valuable for meeting the aims of science than others. At another extreme, "fundamentalism" contends that a reformulation is valuable when it provides a more fundamental description of reality. According to this view, some reformulations directly contribute to the metaphysical aim of carving reality at its joints. Conceptualism develops a middle ground between instrumentalism and fundamentalism, preserving their benefits without their costs. I argue that the epistemic value of significant reformulations does not reduce to either practical or metaphysical value. Reformulations are valuable because they are a constitutive part of problem-solving. Both science and mathematics aim at solving all possible problems within their respective domains. Meeting this aim requires being able to plan for any possible problem-solving context, and this requires reformulating. By reformulating, we clarify what we need to know to solve problems. Still, one might wonder whether the value of reformulations requires underlying differences in explanatory power. According to "explanationism," a reformulation is valuable only when it provides a better explanation. Explanationism stands as a rival middle ground position to my own. However, it faces numerous counterexamples. In many cases, two reformulations provide the same explanation while nonetheless providing different ways of understanding a phenomenon. Hence, reformulating can be valuable even when neither formulation is more explanatory. Methodologically, I draw on a variety of case studies to support my account of reformulation. These range from classical mechanics to quantum chemistry, along with examples from mathematics. Symmetry arguments provide a paradigmatic example: the mathematics of symmetry groups radically recasts quantum mechanics and quantum chemistry. Nevertheless, elementary approaches exist that eschew this additional mathematical apparatus, solving problems in a more tedious but less mathematically-demanding manner. Further examples include reformulations of quantum field theory, Arabic vs. Roman numerals, and Fermat's little theorem in number theory. In each case, my account identifies how reformulations change and improve our understanding of science and mathematics. (shrink)

“Neutrosophics Knowledge” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc. The submitted papers should be professional, in good English and Arabic, containing a brief review of a problem and obtained results. Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as (...) well as their interactions with different ideational spectra. (shrink)

This chapter explores the cultural varieties of same-sex relationships that have long been constituent of traditional African life. A recent study shows that roughly 10% of the global population identify as homosexuals. This number consistently and equitably cuts across all cultures of the world despite variations in attitude towards homosexuality. If this is true of the contemporary world, then it extends to the ancient and by that traditional Africa. Accordingly, this research using phenomenological and historico-descriptive tools of enquiry together with (...) ethnographical accounts of anthropologists retraces homosexuality to its African roots ranging from the practices of Hausas of West Africa, Zanzibars of East Africa, Ovagandjeras of Central Africa to those of the Herero, Ovambo, and Ovahimba peoples of Southern Africa. Consequently, this research avers that current attitude towards homosexuality in Africa is as a result of Western hegemony and the revolutionary changes effected by Euro-Christian and Arab-Islamic movements in their first and earlier contact with the continent. Hence, a fair disposition towards historical facts will deflate the current homophobic agitation, stripping it of any moral, historical or logical justification. (shrink)

Once upon a time, logical conventionalism was the most popular philosophical theory of logic. It was heavily favored by empiricists, logical positivists, and naturalists. According to logical conventionalism, linguistic conventions explain logical truth, validity, and modality. And conventions themselves are merely syntactic rules of language use, including inference rules. Logical conventionalism promised to eliminate mystery from the philosophy of logic by showing that both the metaphysics and epistemology of logic fit into a scientific picture of reality. For (...) naturalists of all stripes, this was paradise. Alas, paradise was lost. By the end of the twentieth century, logical conventionalism had been almost universally abandoned. But more recently, it has been revitalized. This chapter provides an overview of logical conventionalism and its history, clears away misunderstandings, and briefly responds to both the canonical objections to conventionalism (from Quine, Dummett, Boghossian, and many others) as well as new objections (from Field and Golan). From paradise lost, to paradise regained: logical conventionalism is back. (shrink)

The aim of the paper is to argue that all—or almost all—logical rules have exceptions. In particular, it is argued that this is a moral that we should draw from the semantic paradoxes. The idea that we should respond to the paradoxes by revising logic in some way is familiar. But previous proposals advocate the replacement of classical logic with some alternative logic. That is, some alternative system of rules, where it is taken for granted that these (...) hold without exception. The present proposal is quite different. According to this, there is no such alternative logic. Rather, classical logic retains the status of the ‘one true logic’, but this status must be reconceived so as to be compatible with (almost) all of its rules admitting of exceptions. This would seem to have significant repercussions for a range of widely held views about logic: e.g. that it is a priori, or that it is necessary. Indeed, if the arguments of the paper succeed, then such views must be given up. (shrink)

Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as Hilbert developed systems of logic to formalize mathematics. These systems were meant to serve either as themselves foundational, or at least as formal analogs of mathematical reasoning amenable to mathematical study, e.g., in Hilbert’s consistency program. Similar efforts continue, (...) but have been expanded by the development of sophisticated methods to study the properties of such systems using proof and model theory. In parallel with this evolution of logical formalisms as tools for articulating mathematical theories (broadly speaking), much progress has been made in the quest for a mechanization of logical inference and the investigation of its theoretical limits, culminating recently in the development of new foundational frameworks for mathematics with sophisticated computer-assisted proof systems. In addition, logical formalisms developed by logicians in mathematical and philosophical contexts have proved immensely useful in describing theories and systems of interest to computer scientists, and to some degree, vice versa. Three examples of the influence of logic in computer science are automated reasoning, computer verification, and type systems for programming languages. (shrink)

We study logical reduction (factorization) of relations into relations of lower arity by Boolean or relative products that come from applying conjunctions and existential quantifiers to predicates, i.e. by primitive positive formulas of predicate calculus. Our algebraic framework unifies natural joins and data dependencies of database theory and relational algebra of clone theory with the bond algebra of C.S. Peirce. We also offer new constructions of reductions, systematically study irreducible relations and reductions to them and introduce a new characteristic of (...) relations, ternarity, that measures their ‘complexity of relating’ and allows to refine reduction results. In particular, we refine Peirce’s controversial reduction thesis, and show that reducibility behaviour is dramatically different on finite and infinite domains. (shrink)

This paper develops a new class of justification logic, the logic of epistemic entitlement. The logic of epistemic entitlement invokes the notion of epistemic entitlement in epistemology, and interprets a justification formula in the form of???? ∶???? as follows: the warrant???? entitles the agent to believe????. In the logic of epistemic entitlement, the formula???? ∶???? is true if and only if???? is true in all possible worlds entitled to be conceived by????. In contrast to the standard (...) epistemic semantics of justification logic, the formula???? ∶???? in Fitting’s model is true if and only if???? is true in all possible worlds that can be conceived of and satisfies the evidential condition: the epistemic state???? ∈ ℰ(????,????) that the epistemic agent is in. Thus, if???? is not a dead point in the model, the point model of???? cannot satisfy both formulas of the form???? ∶???? and????′∶ ¬????. Thus standard justification logic cannot characterize the conflicting beliefs of agents for different warrants. Instead, the logic of epistemic entitlement solves this problem by entitling agents to believe???? and ¬???? on two disjoint sets of possible worlds on????,???? and????′, respectively. ℳ,???? ⊩???? ∶???? if and only if ℳ,???? ⊩???? for every???? ∈????????????(????,????) with????????????. Such an epistemic entitlement in the paper is axiomatized into the logic J_???????????? and the validity of its axioms is verified. And a canonical model of J_???????????? is established to prove its completeness. Finally, extensions of J_???????????? are attempted to explore the logic of entitlement of belief J_EntD4 and logic of entitlement of knowledge J_EntT4. (shrink)

This paper introduces and discusses three models of future: a determinist model, a stochastic model, and the model of True Prophetic Knowledge. All three models coexist in natural languages and are represented both in their grammatical systems and in the text-building discourse strategies speakers and authors apply to.

GLOBALIZATION, ARAB SPRING AND THE CHANGING SOCIAL VALUES By Socrates Ebo, PhD -/- ABSTRACT -/- The tumultuous and eponymous events that set-off socio-political changes in the Maghreb from November 2010 were a confirmation or, better still, manifestation of a lager process which had gradually but steadily emerged a major factor in the socio-economic formation of the globe. This factor is no other than the process of globalization; a process that was heightened by the revolutions in Information and Communication Technology (ICT) (...) and the emergence of the New Media. Until the days of the social media, strong men who held authoritarian sway in the Maghreb carried on without any qualms as to the security of their political formation. But the New Media revolution changed all that. This work captures the role of globalization in the revolutions that swept through the Maghreb which have come to be known as the Arab Spring. -/- . (shrink)

Understanding Arab public opinion is central to the search for sustainable po- litical solutions in the Middle East. The way Westerners think about Arab public opinion may be affected by how it is referred to in their news media. Here, we show that Arab public opinion is rarely referred to as such in the US media. Instead, it is usually referred to as the Arab street, a metaphor that casts Arab public opinion as irrational and volatile. We trace the origins (...) of this metaphor to similar expressions in both English and Arabic, and note similarities and impor- tant differences between the English and Arabic usages. Ultimately, we argue that the Arab street metaphor misrepresents the Arab public, and invites dismissal of rather than engagement with Arab public opinion. (shrink)

Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about distinctions, differences and distinguishability and is formalized using the distinctions of a partition. All the definitions of simple, joint, conditional and mutual entropy of Shannon information theory are derived by a uniform transformation from the corresponding definitions at the logical level. The purpose of (...) this paper is to give the direct generalization to quantum logical information theory that similarly focuses on the pairs of eigenstates distinguished by an observable, i.e., qudits of an observable. The fundamental theorem for quantum logical entropy and measurement establishes a direct quantitative connection between the increase in quantum logical entropy due to a projective measurement and the eigenstates that are distinguished by the measurement. Both the classical and quantum versions of logical entropy have simple interpretations as “two-draw” probabilities for distinctions. The conclusion is that quantum logical entropy is the simple and natural notion of information for quantum information theory focusing on the distinguishing of quantum states. (shrink)

The purpose of the present article is two-fold. First, the article examines the reasons as to why Arab countries do not actively participate in WTO dispute settlement proceedings.17 Trade volume, lack of technical expertise, financial strains, political relations, enforcement, and language problems eachplay a role in Arab countries under-participation and are discussed herein. Second, the article provides possible avenues through which Arab countries can enhance their presence in the WTO dispute settlement process. In the process of examining these issues, the (...) article highlights the case(s) in which Arab countries participated in the WTO dispute settlement system. However, before addressing these issues, the article will briefly discuss the development of the WTO dispute settlement mechanism. (shrink)

Logical positivism is often characterized as a set of naive doctrines on meaning, method, and metaphysics. In recent decades, however, historians have dismissed this view as a gross misinterpretation. This new scholarship raises a number of questions. When did the standard reading emerge? Why did it become so popular? And how could commentators have been so wrong? This essay reconstructs the history of a “caricature” and rejects the hypothesis that it was developed by ill-informed Anglophone scholars who failed to appreciate (...) the subtleties of European scientific philosophy. It argues that the received view has a more complicated history and was frequently promoted by the European positivists themselves. The essay shows that the view has roots in both American and European scientific philosophy and emerged as a result of the complex interplay between the two communities in the years before the intellectual migration. (shrink)

According to certain normative theories in epistemology, rationality requires us to be logically omniscient. Yet this prescription clashes with our ordinary judgments of rationality. How should we resolve this tension? In this paper, I focus particularly on the logical omniscience requirement in Bayesian epistemology. Building on a key insight by Hacking :311–325, 1967), I develop a version of Bayesianism that permits logical ignorance. This includes: an account of the synchronic norms that govern a logically ignorant individual at any given time; (...) an account of how we reduce our logical ignorance by learning logical facts and how we should update our credences in response to such evidence; and an account of when logical ignorance is irrational and when it isn’t. At the end, I explain why the requirement of logical omniscience remains true of ideal agents with no computational, processing, or storage limitations. (shrink)

[[[ (Here only the chapters 3 – 8, see *** ) First I argue that the prohibition of linguistic self-reference as a solution to the antinomy problem contains a pragmatic contradiction and is thus not only too restrictive, but just inconsistent (chap.1). Furthermore, the possibilities of non-restrictive strategies for antinomy avoidance are discussed, whereby the explicit inclusion of the – pragmatically presuposed – consistency requirement proves to be the optimal strategy (chap.2). ]]] The central question here is that about the (...) actual reason for antinomic structures. It turns out to be a form of negative self-conditioning (chap.3). This makes it necessary to clarify the status of negative concepts (chap.4). The generalization of these considerations (chap.5) leads to the actual analysis of the antinomic basic structure (chap.6): Decisively for the pragmatics of the concept is that it positively owns a meaning, so that positivity is always constituted by the concept qua concept. Thus a negative concept is characterized by a fundamental ambivalence: From a semantic point of view it has negative character, in its pragmatic status as a concept, however, it has positive character. If the meaning is especially that of a negative self-reference, the ambivalence leads to the antinomic constellation of a negative self-condition – that is the crux of the matter here! The concept thus possesses the property defined by it exactly when it does not possess it and vice versa. A closer analysis shows that the function of reflective structures for the occurrence of antinomies has to be judged much more differentiated than previous opinions suggest. Not only are four forms of reflectivity to be distinguished in this context – ontic, semantic, pragmatic reflectivity, and especially the form of negative self-condition; but it is also apparent that these are intertwined with each other in a way that is difficult to be understood. The astonishing variety of relationships associated with this makes the irritation that has always emanated from the antinomy problem appear more comprehensible. In the developed pragmatic perspective furtheron parallels to the structure of self-consciousness become visible (chap.7). I conclude with considerations about the significance of the antinomic structure for the problem of dialectics, especially for the synthesis formation of mutually exclusive terms (chap.8). (shrink)

Overview of fundamental work in deontic logic.

Many philosophers take purportedly logical cases of ground ) to be obvious cases, and indeed such cases have been used to motivate the existence of and importance of ground. I argue against this. I do so by motivating two kinds of semantic determination relations. Intuitions of logical ground track these semantic relations. Moreover, our knowledge of semantics for first order logic can explain why we have such intuitions. And, I argue, neither semantic relation can be a species of ground (...) even on a quite broad conception of what ground is. Hence, without a positive argument for taking so-called ‘logical ground’ to be something distinct from a semantic determination relation, we should cease treating logical cases as cases of ground. (shrink)

Although the two worlds, Arabic and Byzantine, were in proximity for many centuries, the influence of Arabic philosophy on the Byzantine intellectual tradition has not been studied thoroughly. Recent studies have substantiated the influence of the Arabic and Persian thought over Byzantine science. However, in the field of philosophy, research is still at an early stage and the impact of Arabic thought on Byzantine and vice versa has not been examined widely and in depth. Direct references (...) to philosophers in the Islamic world are rare and, apart from occasional studies, there is not an organised, in-depth account of the influence the Arabic philosophy exercised on Byzantine scholars. The present study is a wider, complete, and renewed presentation of the initial conclusions of my research, which aims to bring out and evaluate the perception of Arabic philosophy by the Byzantine intelligentsia during the 14th and 15th centuries. As exemplary cases Ι have chosen Georgios Gemistos Pletho (c.1360-1454) and Georgios Scholarios (c.1400-1472), whose rivalry defined Byzantine philosophy of the 15th century to a considerable degree. (shrink)

The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof theory of finite-valued first (...) order logics in a general way, and to present some of the more important results in this area. In Systems covered are the resolution calculus, sequent calculus, tableaux, and natural deduction. This report is actually a template, from which all results can be specialized to particular logics. (shrink)

In this paper we present an overview, with historical and critical remarks, of two articles by S. Jaśkowski ([20, 21] 1948 and [22, 23] 1949), which contain the oldest known formulation of a paraconsistent logic. Jaśkowski has built the logic – he termed discussive (D2) – by defining two new connectives and by introducing a modal translation map from D2 systems into Lewis’ modal logic S5. Discussive systems, for their formal details and their original philosophical justification, have (...) attracted discrete attention among experts. Indeed, in what follows, after having introduced Jaśkowski methodology of building D2 and his main philosophical motivations for providing such a system, we will explore some of the main contributions to the development of D2. (shrink)

Logic and psychology overlap in judgment, inference and proof. The problems raised by this commonality are notoriously difficult, both from a historical and from a philosophical point of view. Sundholm has for a long time addressed these issues. His beautiful piece of work [A Century of Inference: 1837-1936] begins by summarizing the main difficulty in the usual provocative manner of the author: one can start, he says, by the act of knowledge to go to the object, as the Idealist (...) does; one can also start by the object to go to the act, in the Realist mood; never the two shall meet. He is himself inclined to accept the first perspective as the right one and he has eventually developed an original version of antirealism which starts, not from considerations about the publicity of meaning, in the manner of Dummett, but from an epistemic standpoint, trying to search in a non-Fregean tradition of analysis of judgement and cognate notions a way of founding constructivist semantics. The present paper ploughes the same field. We concentrate on the significance, for Sundholm’s program, of the perspective that has been opened by Twardowski in his important essay on acts and products (1912. (shrink)

The Symbolic Logic Study Guide is designed to accompany the widely used symbolic logic textbook Language, Proof and Logic (LPL), by Jon Barwise and John Etchemendy (CSLI Publications 2003). The guide has two parts. The first part contains condensed, essential lecture notes, which streamline and systematize the first fourteen chapters of the book into seven teaching sections, and thus provide a clear, well-designed roadmap for the understanding of the text. The second part consists of twelve sample quizzes (...) and solutions. The Symbolic Logic Study Guide is essential for all instructors and students who use LPL in their symbolic logic classes. (shrink)

This chapter considers the ways in which whiteness as a skin color and ideology becomes a dominant level that sets the background against which all things, people and relations appear. Drawing on Merleau-Ponty's phenomenology, it takes up a series of films by Bruce Nauman and Marlon Riggs to consider ways in which this level is phenomenally challenged providing insights into the embodiment of racialization.

In the *Science of Logic*, Hegel states unequivocally that the category of “life” is a strictly logical, or pure, form of thinking. His treatment of actual life – i.e., that which empirically constitutes nature – arises first in his *Philosophy of Nature* when the logic is applied under the conditions of space and time. Nevertheless, many commentators find Hegel’s development of this category as a purely logical one especially difficult to accept. Indeed, they find this development only comprehensible (...) as long as one simultaneously assumes that Hegel breaks his promise to let the logic do the leading. However, if Hegel were to in fact allow the logical development to be led by biological analogies at this point, problems would ensue. Not only would it contradict his own speculative method, which should secure the necessity of the categories, but it would also endanger the ontological generality of the category of life itself. Beyond undermining his method and the logical integrity of the category, however, I will argue that such a reading makes the transition to the next category of “cognition” unintelligible and problematic. My aim in the first part of this paper is to argue how logical life can be read as a pure category. I then argue in the second part how my reconstruction makes the transition to cognition intelligible without resorting to profane or supernatural interpretations. (shrink)

The result of combining classical quantificational logic with modal logic proves necessitism – the claim that necessarily everything is necessarily identical to something. This problem is reflected in the purely quantificational theory by theorems such as ∃x t=x; it is a theorem, for example, that something is identical to Timothy Williamson. The standard way to avoid these consequences is to weaken the theory of quantification to a certain kind of free logic. However, it has often been noted (...) that in order to specify the truth conditions of certain sentences involving constants or variables that don’t denote, one has to apparently quantify over things that are not identical to anything. In this paper I defend a contingentist, non-Meinongian metaphysics within a positive free logic. I argue that although certain names and free variables do not actually refer to anything, in each case there might have been something they actually refer to, allowing one to interpret the contingentist claims without quantifying over mere possibilia. (shrink)

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

I argue against inferentialism about logic. First, I argue against an analogy between logic and chess, before considering a more basic objection to stipulating inference rules as a way of establishing the meaning of logical constants. The objectionthe Mushroom Omelette Objectionis that stipulative acts are partly constituted by logical notions, and therefore cannot be used to explain logical thought. I then argue that the same problem also attaches to following existing conventional rules, since either those rules have logical (...) contents, or following those conventional rules is done for logical reasons. Lastly, I compare this argument with other arguments found in Quine’s early work, and consider two attempts to reply to Quine. (shrink)

A system of logic usually comprises a language for which a model-theory and a proof-theory are defined. The model-theory defines the semantic notion of model-theoretic logical consequence (⊨), while the proof-theory defines the proof- theoretic notion of logical consequence (or logical derivability, ⊢). If the system in question is sound and complete, then the two notions of logical consequence are extensionally equivalent. The concept of full formalization is a more restrictive one and requires in addition the preservation of the (...) standard meanings of the logical terms in all the admissible interpretations of the logical calculus, as it is proof-theoretically defined. Although classical first-order logic is sound and complete, its standard formalizations fall short to be full formalizations since they allow non-intended interpretations. This fact poses a challenge for the logical inferentialism program, whose main tenet is that the meanings of the logical terms are uniquely determined by the formal axioms or rules of inference that govern their use in a logical calculus, i.e., logical inferentialism requires a categorical calculus. This paper is the first part of a more elaborated study which will analyze the categoricity problem from its beginning until the most recent approaches. I will first start by describing the problem of a full formalization in the general framework in which Carnap (1934/1937, 1943) formulated it for classical logic. Then, in sections IV and V, I shall discuss the way in which the mathematicians B.A. Bernstein (1932) and E.V. Huntington (1933) have previously formulated and analyzed it in algebraic terms for propositional logic and, finally, I shall discuss some critical reactions Nagel (1943), Hempel (1943), Fitch (1944), and Church (1944) formulated to these approaches. (shrink)

A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems (...) to change this situation. The book includes almost every major author currently working in the field. The papers are on the cutting edge of the literature some of which discuss current debates and others present important new ideas. The editors have avoided papers about technical details of paraconsistent logic, but instead concentrated upon works that discuss more 'big picture' ideas. Different treatments of paradoxes takes centre stage in many of the papers, but also there are several papers on how to interpret paraconistent logic and some on how it can be applied to philosophy of mathematics, the philosophy of language, and metaphysics. (shrink)

Connexive logics are based on two ideas: that no statement entails or is entailed by its own negation (this is Aristotle’s thesis) and that no statement entails both something and the negation of this very thing (this is Boethius' thesis). Usually, connexive logics are contra-classical. In this note, I introduce a reading of the connexive theses that makes them compatible with classical logic. According to this reading, the theses in question do not talk about validity alone; rather, they talk (...) in part about (a property related to) the soundness of arguments. (shrink)

Usually thoughts are not in isolation but in varing degrees have interrelations with each other. With regard to this historical fact as a classist want to explore the reception of a few medieval Arabic texts and writers of Socrates available teachings about politics.

In some recent works, Crupi and Iacona have outlined an analysis of ‘if’ based on Chrysippus’ idea that a conditional holds whenever the negation of its consequent is incompatible with its antecedent. This paper presents a sound and complete system of conditional logic that accommodates their analysis. The soundness and completeness proofs that will be provided rely on a general method elaborated by Raidl, which applies to a wide range of systems of conditional logic.