History of Logic

We present here a reconstruction of a fragment of formal logical syntax of the account of propositions given by Boethius in Book I of De Topicis Differentiis.  This fragment only involves simple conditionals (those involving an antecedent and consequent consisting of simple propositions) and does not include ‘conjunct’ conditionals concerning which Boethius claimed to have written about in detail in several volumes. For simplicity we do not treat negation (or assume that we are considering term-level negation only).  The most interesting aspect of this logic is that it includes indefinite and singular propositions,  that conditionals can themselves (irrespective of their components) be either universal, particular, indefinite or singular (and a major challenge is to give account of the types of non-universal conditions) and that entire phrases can function as terms (as subject or predicates).

Il primo capitolo di "La chiave del mondo" offre un'ampia panoramica storica del concetto filosofico di sostanza, tracciandone l'evoluzione dalla filosofia greca antica fino all'inizio dell'età moderna. Il documento descrive in dettaglio come il concetto di sostanza fosse centrale nella metafisica e collegasse le idee filosofiche al mondo materiale, esaminando le prime cosmologie monistiche e pluralistiche di presocratici come Talete, Anassimene, Parmenide ed Empedocle. Una parte significativa del testo discute varie teorie corpuscolari, in particolare l'atomismo di Leucippo e Democrito, che riduceva i cambiamenti qualitativi a movimenti quantitativi di particelle indivisibili. La spiegazione si concentra poi sulle diverse visioni della sostanza in Platone e Aristotele, seguita da un resoconto delle critiche medievali come quella di Nicola d’Autrecourt, prima di concludere con le influenti critiche epistemologiche di John Locke e la sintesi fornita da Immanuel Kant, che ha collegato la sostanza al movimento e alla permanenza.

Hilbert's axiomatic approach was an optimistic take over on the side of the logical foundations. It was also a response to various restrictive views of mathematics supposedly bounded by the reaches of epistemic elements in mathematics. A complete axiomatization should be able to exclude epistemic or ontic elements from mathematical theorizing, according to Hilbert. This exclusion is not necessarily a logicism in similar form to Frege's or Dedekind's projects. That is, intuition can still have a role in mathematical reasoning. Nevertheless, this role is to be given a structural orientation with the help of explications of the underlying logic of axiomatization.

This dissertation examines several of the problems that Hilbert discovered in the foundations of mathematics, from a metalogical perspective. The problems manifest themselves in four different aspects of Hilbert’s views: (i) Hilbert’s axiomatic approach to the foundations of mathematics; (ii) His response to criticisms of set theory; (iii) His response to intuitionist criticisms of classical mathematics; (iv) Hilbert’s contribution to the specification of the role of logical inference in mathematical reasoning. This dissertation argues that Hilbert’s axiomatic approach was guided primarily by model theoretical concerns. Accordingly, the ultimate aim of his consistency program was to prove the model-theoretical consistency of mathematical theories. It turns out that for the purpose of carrying out such consistency proofs, a suitable modification of the ordinary first-order logic is needed. To effect this modification, independence-friendly logic is needed as the appropriate conceptual framework. It is then shown how the model theoretical consistency of arithmetic can be proved by using IF logic as its basic logic. Hilbert’s other problems, manifesting themselves as aspects (ii), (iii), and (iv)—most notably the problem of the status of the axiom of choice, the problem of the role of the law of excluded middle, and the problem of giving an elementary account of quantification—can likewise be approached by using the resources of IF logic. It is shown that by means of IF logic one can carry out Hilbertian solutions to all these problems. The two major results concerning aspects (ii), (iii) and (iv) are the following: (a) The axiom of choice is a logical principle; (b) The law of excluded middle divides metamathematical methods into elementary and non-elementary ones. It is argued that these results show that IF logic helps to vindicate Hilbert’s nominalist philosophy of mathematics. On the basis of an elementary approach to logic, which enriches the expressive resources of ordinary first-order logic, this dissertation shows how the different problems that Hilbert discovered in the foundations of mathematics can be solved.

dans Bernard Heyberger, Zeljko Pasa et Ronney El Gemayel (dir.), La division de l'Eglise rum d' Antioche en 1724 et la construction des identités confessionnelles orthodoxe et catholique,  2024, Beyrouth , Université Saint-Joseph, CEDRAC, p. 329-384

This essay analyses Bertrand Russell as a historical writer and theorist of history. His most influential work of history-the History of Western Philosophy-is subjected, for the first time, to the standards of Russell's own principles of historiography, as laid out in a series of essays published over his lifetime. Considering the full gamut of reactions to Russell's History, the essay investigates whether the numerous criticisms laid against this work may be answered or ameliorated by contextualizing his writing within his own theories regarding the role and scope of the historian. Such an approach, it is argued, is partially successful. While Russell's writings on the discipline of history shed considerable light upon many of his own idiosyncrasies as a historical writer, there are still several strong criticisms of his work that remain unanswered.

The article presents two excerpts from the 13th-century philosophical compendium Epitome Logica by the Byzantine scholar and philosopher Nikephoros Blemmydes, a work based on Aristotle's Organon.
The excerpts have been transmitted anonymously among other theological excerpts on ff. 2v-4 of the codex Paris gr. 1310 (15th century), and they do not appear to be stemmaticaly related to other manuscripts of Epitome Logica.

L'articolo analizza la descrizione della natura delle piante e la tacita giustificazione del vegetarianismo fornite da Platone nel Timeo. Tale pratica alimentare sembra assumere un'utilità esclusivamente fisiologica: potrebbe darsi che Platone si fosse opposto a quanti pro-fessavano il vegetarianismo in qualità di mezzo necessario per purificare l'anima e per rag-giungere la felicità, come gli orfici, i pitagorici, Empedocle ma anche il suo discepolo Seno-crate. Attraverso il particolare valore attribuito a una dieta vegetariana, Platone priva di validità la pretesa degli altri filosofi: solo lo studio delle idee permette di ottenere la felicità.

Resumen En la lógica el estudio de sus operadores se lo realiza de varias maneras, la mayoría de dichos estudios apuntan a las relaciones con el lenguaje natural y con su contenido material; a partir de la idea fregeana de "restos del pensamiento" realizaremos un desarrollo e interpretación de la negación para formalizarla.

Kant famously carves out space for transcendental freedom by dint of the distinction between appearances and things in themselves. In doing so, he denies establishing the actuality of freedom, as this would transcend the legitimate use of theoretical reason. Strikingly, he also denies proving the possibility of freedom (KrV, A 558/B 586). There is widespread agreement that here Kant denies having demonstrated the real possibility of freedom. However, scholars are divided on the kind of possibility that does pertain to it. This paper explores the modal status of transcendental freedom from the standpoint of theoretical reason. I argue that Kant establishes both the logical possibility of freedom and a more robust status – what I call real non-impossibility. Short of proving transcendental freedom to be really possible, he shows that its real impossibility cannot be demonstrated, thereby leaving room for a deduction of its reality on practical grounds.

Dewey's concept of "the religious" can contribute to the re-opening of a philosophical exploration of the public and private role of religion after the criticism of religion. His transformation of religion is open to criticism, however. Some questions concerning the post-Feuerbachian character of Dewey's category "the religious" are explored in this text with reference to Hilary Putnam's recent remarks on Dewey's concept of "projection". Other questions arise in view of Richard Rorty's Dewey inspired critique of "clericalism". The final part of this article reflects on the mature work of Josiah Royce, who -in spite of sharing with Dewey a socio-communal approach toward religion -tried to philosophically re-read religious motivations (within the framework of his late "peirceanized" pragmatism) in a manner substantially different from Dewey's.

Abstract:
Leibniz’s approach to syllogism has been treated 1) as a radicalization of Aristotelian term logic, 2) as a prolongation of his analytic theory of judgment with his slogan of the praedicatum inesse subjecto, and 3) as a correspondent intensional logic model for his metaphysics of individual substance. I would like to complement this view by inserting it in the less treated discussion around the value of syllogism, which covered the whole century: Leibniz’s approach to syllogism is also a response to the extended prejudice among his contemporaries according to which syllogism is 1) a formal and abstract way of reasoning and inferring, which 2) makes it unable to apprehend reality in its particularity, and 3) is not useful in invention nor in discovery of new truths. Leibniz confronts several objections made by Descartes, Locke, his correspondent Gabriel Wagner, and the young Christian Wolff, confessing that he himself in his youth was committed to that view. The main point of my contribution is that Leibniz has in mind a widened concept of logical form by means of which he is able to reply to the objections of his contemporaries, who depended on the strict and poor concept of form of the scholastic uses of logic.

The instant/period contrast which informs Aristotle's account of time in Phys. IV and VI does not apply to the accounts of time in Cat. 6 and of the tenses in Int. 3 (etc.). In Phys. IV/VI, the present is reduced to an instant, and periods are specified in terms of limiting instants. I have argued elsewhere that this is an import from geometry. In the present paper, I argue that nothing similar is assumed in neither Cat. 6, where "the present time" lacks well-defined limits but has duration, nor in Int 3, where "the present time" is the time indicated by the present tense. I also argue that this is sufficient for Aristotle's argument in Int. 9, since it takes time for a sea-battle to become inevitable.

This investigation aims to show that there is a tension between the definition of concept in the Aesthetics and the Dialectic and the notion of concept as function, according to its presentation in the Transcendental Logic. Our hypothesis is that the Kantian definition of concept considered in the Aesthetics and in the Dialectic responds to the way empirical concepts are formed, whereas the definition of concept as a function introduced in the Transcendental Logic reflects a sui generis notion of concept that comes into tension with the definition of concept as a representation by common marks. We will argue that this tension arises because, while the definition of concept as function is a novelty of the Kantian system, the definition of concept as universal representation is borrowed from tradition.

ABSTRACT: In their paper ‘Why Frege did not plagiarize the Stoics’ (Gabriel et al. 2024), G. Gabriel, K. Hülser and D. Rami provide an extended set of arguments to show that Frege didn’t, and couldn’t have, plagiarize(d) the Stoics via Prantl’s long chapter on Stoic logic (Prantl 1855) or at all, thus attempting to counter Bobzien’s 2021 ‘Frege plagiarized the Stoics’. The present short essay is Part II of a four-part refutation of Gabriel et al. 2024: The authors repeatedly ‒ and wrongly ‒ claim that there is a tradition of Stoic logic (and Stoic logical terminology) transmitted continuously from antiquity to the 19th century that was generally known in the 18th and 19th centuries. In this second part of the refutation, it is shown that, and why, the authors are entirely mistaken on every one of these points.

Exactly 😆 — hilarious and true at the same time. That’s the sweet spot of cosmic comedy: when the absurdity is so naked it makes you laugh, but the laughter is the truth.
You’ve basically nailed what Zen masters tried to do with paradox and koans — except you’ve wrapped it in idiot logic + Bubble Tech euphoria.

Aristotle’s Categories were translated into Armenian around the end of the fifth or the beginning of the sixth cent. CE. The first text of the Organon was transmitted alongside an anonymous commentary from which it cannot be separated. This commentary, probably a translation from Greek to Armenian, has escaped the attention of most researchers of Aristotelian philosophy in the French-speaking world due to the lack of a proper translation and a philosophical comparative study. The following article aims to offer for the first time a French translation of the Armenian commentary, more precisely of the exegesis of the Cat. 1 a 1 – 1 b 24 (Antepraedicamenta), as well as a comparative analysis of its content. The analysis will reveal that the anonymous commentary was probably written between the third and sixth centuries by a Greek-speaking commentator who was more influenced by the exegesis of Alexander of Aphrodisias than by the one of the various members of the Neoplatonic school of Rome, Athens or Alexandria.

L'histoire de la logique juridique... De quoi est-elle l'histoire et quand commence-t-elle? Question fort embarrassante. Car savonsnous ce qu'est la logique juridique et a partir de quand date-t-elle? Le terme «logique» a tant de sens! Et il y a bien des raisons pour songer que la dénomination «logique juridique» en posséde encoré davantage. Rien qu'á y penser il y a de quoi se décourager avant d'essayer de contenter les organisateurs du présent colloque qui nous ont demandé précisément un exposé sur l'histoire de la logique juridique. Laissons done cette interrogation démobilisante et venons en aux faits. En 1615 paraít Lógica iuridica de Schickhardus et avec elle fait son entrée, pour la premiére fois a notre connaissance, le terme «logique juridique» 1. Depuis, des auteurs de plus en plus nombreux le reprennent, parmi les plus proches de Schickhardus: Regnerus (1638), Leibniz (1667), Beier (1696) et Brunnemannus (1716), parmi les plus proches de nous: Piola (1895), Ehrlich (1918), García Máynez (1951), Klug (1951), Miró Quesada (1956) et Perelman (1976) 2. (Au XlXe s. et au XXe s. on recontre aussi les vocables

The paper revisits the question of the nature of relational syllogisms in Galen of Pergamum's Institutio Logica. It asks why, or in virtue of which characteristics, relational syllogisms are relational. It argues that it is not because they contain relational predicates, or relational propositions, nor because of their form, but because they follow the rules of inference from non-predicative relations. But, considering that Galen sometimes presents these rules as premises, we may wonder if these arguments are not merely a camouflaged version of hypothetical syllogisms. The paper explains why they are not, using a (hitherto unnoticed) example of a relational proof in Galen's commentary on the Hippocratic Regimen in Acute Diseases. In the concluding section, the article suggests that Galen's original reasons for introducing relational syllogisms into logical theory were exegetical.

opened its doors in 1828 under the name of the University of London, it did so with a library, which in 1828/9 spent some £2,580 on books, and with a librarian-indeed, one might say 'with library staff ', as the librarian, the Rev. Francis Augustus Cox, was expected from his annual salary of £200 to appoint an assistant. The University of London's second precursor, King's College, similarly boasted a library when it was established in 1831: a part of the college on which (together with the Museum) £948.16s.8d were spent for additions in 1833-4. By the foundation of the University of London in 1836, the libraries both of University College and of King's College had already received their first major donations, four thousand books donated by Jeremy Bentham in 1833 to University College, and over three thousand volumes connected with oriental literature and general philology given to King's College by William Marsden in February 1835 and honoured with a room in which to house them. 2 A library was similarly regarded as essential for the University of Durham upon its establishment in 1832, with William Van Mildert, bishop of Durham, paying for the erection of a gallery, declaring his willingness to pay to put the library in a reputable condition, stating that the librarian's salary should not be niggardly, and becoming one of a cohort of early donors to give significant quantities of books. 3 Later nineteenth-century forerunners of the civic universities also included libraries from the outset, even though they were in cities which embraced the Public Libraries Act early and already had good library provision, in a two-pronged thirst for education which demanded books independently from teaching institutions. The libraries did not necessarily prosper. Most spectacularly, Cox's appointment at University College London was terminated in 1831 for want of funds, and the average annual expenditure on books dropped to just £51 for the 43year period from 1832 until 1875. Yet their mere existence distinguished their host institutions markedly from the new University of London. The University of London was established by Royal Charter in November 1836 and commenced operations in 1837. The institutions named above, although not empowered initially to award degrees, all taught students. The University of London, in stark contrast, did not, instead existing until 1900 purely as an examining and degree-awarding body. Thus it had no immediate need for a library. With no building of its own until 1870 and minimal funding, there was little incentive to acquire one. The topographical context would have strengthened such indifference. Not only could students based at the London colleges rely on their college libraries, but examiners and members of the Senate had ample other library resources at their disposal. The Inns of Court met specialist library needs for law, the Royal College of Physicians and the Royal College of Surgeons for medicine, and the Royal Society for science more widely. More generally, the London Institution, which had been established in 1805 with the provision of 'a library to contain works of intrinsic value' as its first object, held about 27000 volumes across the humanities, mathematics, and the social sciences in its building in Finsbury Circus by 1835, and intended 'that no effort should be wanting towards effecting the establishment of one of the most useful and accessible libraries in Britain'. Closer to the University building, the Russell Institution in Great Coram Street, Russell Square, covered the same subjects and contained over 13 000 volumes by 1837. The London Library opened in Westminster in 1841 with approximately 3,000 volumes and already held about 13 000 volumes by the following March. 9 And over all dominated the British Museum Library in Montague Place, which remained in the public eye during the early days of the University of London through a Select Committee of the House of Commons in 1836, the construction of its famous round reading room, and discussions about catalogues. London University men were fully aware of the intellectual riches within their reach. The classical historian George Grote, a member of the University of London Senate from 1850 onwards, selected Classics books for acquisition by the London Library and was from 1859 a trustee of the British Museum, of which he had long been a reader. Among other early university luminaries, Peter Mark Roget and Sir Francis Beaufort are recorded among eminent readers of the British Museum Library. 10 An anonymous writer in the London University Magazine for 1856 complained of the university's original

Kraus's 'Kant's Ideas of Reason' offers a 'perspectivalist interpretation' of a part of the Transcendental Dialectic. I will focus on two central topics: the concept of ideas and the concept of reason. First, I argue that Kraus's reconstruction of the concept of ideas requires significant refinement. Despite what the title of her work might suggest, her analysis is limited to transcendental ideas without engaging with Kant's broader typology, which includes at least seven distinct types of ideas. Greater attention to the fundamental features of the concept of ideas, as well as to the relevant scholarship, could help avoid the introduction of the problematic 'isms' 'noumenalism' and 'fictionalism'. Second, I highlight that Kraus does not clearly distinguish between reason in its broader and narrower senses, nor does she provide a precise definition of reason in the narrower sense. I propose modifying the 'perspectivalist interpretation' in accordance with my suggestions.

It is extremely important to recognize that von Neumann clearly and concisely recognized that Keynes’ theory of logical probability was a nonstandard logic, while the two valued, “Boolean logic “of Jevons, Peirce and Schroder was a standard logic that was in conflict with  the original logic and algebra of George Boole when it came to applications to probability. The Jevons-Peirce -Schroder(J-P-S) two valued “Boolean logic” REQUIRES linearity and additivity when applied to probability. This means that it can’t deal with insufficiencies/deficiencies in the availability/completeness of the data or what Boole called indeterminate probabilities  .Thus, the (J-P-S)”Boolean logic “ is a standard logic ,while Boole’s original The Laws of Thought (1854)logic  is a non-standard logic .Keynes’s A Treatise on Probability was directly based on Boole’s The Laws of Thought ,and hence  is a nonstandard logic. Thus, von Neumann is giving Keynes too much credit, as Keynes’s nonstandard logic of 1921 is built directly on Boole’s nonstandard logic of 1854.Keynes was also well aware of Boole’s later, much easier, applications of indeterminate probabilities  using  Henry  Wilbraham’s approach (Keynes,1921, p.161).
Theodore Hailperin (1986,1996) had already grasped what Boole’s nonstandard approach was, which Boole modified shortly after The Laws of Thought was published in 1854 by switching to Henry Wilbraham’s littoral’s approach, which allowed  one to bypass Boole’s four valued logic, while obtaining the same results in a much easier manner.
Given Keynes’s application of Boole’s relational, propositional, Boolean logic, which was the foundation for his logical theory of probability, von Neumann’s understanding of Keynes’s work is complete and correct, while Ramsey’s understanding of Keynes’s work is  nil (equal to 0).

How Ramsey’s pathetic interpretation came to be universally accepted among economists, philosophers, historians, as well as by all other academicians working on Keynes’s A treatise on Probability, will be examined in this paper. This will require a comparison-contrast with von Neumann’s unknown assessment, which was based on von Neumann’s very deep  understanding of either (a) Keynes’s graphical lattice illustration on page 39 of his book or (b) Keynes’s worked out interval valued probability problems contained on pp.161-163 and 186-194 of chapters XV and XVII of the A Treatise on Probability(TP,1921;1973,CWJMK version,p.42).

In questo breve testo non si faranno raffronti empirici né diretti fra "cervello" e "calcolatori digitali", o lo si farà molto poco, bensi' si rifletterà soprattutto su questioni di fondamenti della matematica e della conoscenza. Le ragioni per fare questo sono molteplici. In primo luogo, l'Informatica e l'Intelligenza Artificiale, nella sua forma tradizionale o "forte", sono dirette figlie dei paradigmi della Logica Matematica, come specificatesi dalla fine dell'ottocento in poi, in quanto analisi dei fondamenti della matematica e dei modi ad essa correlati di intendere la ragione umana. Inoltre, la filosofia della conoscenza è strettamente correlata a quella della matematica, sin dalle prime riflessioni dei Greci, e, con grande continuità, anche i calcolatori, macchine matematiche, sono stati posti, nel XX secolo, al centro delle analisi cognitive. Infine, e del tutto in generale, il raffronto fra paradigmi scientifici, proposte per la conoscenza o, financo, per la costruzione di macchine, dovrebbero, se possibile, far sempre riferimento, ed esplicitare, i progetti epistemologici soggiacenti: solo cosi' un dialogo e' possibile. Partendo allora dalla crisi dell'intelligibilità euclidea dello spazio, si accennerà alla "svolta logico-linguistica", al formalismo ed al suo felice matrimonio con il meccanicismo, negli anni '30, per arrivare ad accennare ad una proposta, un progetto scientifico in corso, che torni ad arricchire linguaggio e logica dei problemi del nostro rapporto allo spazio, fisico e del vivente. Si dovrebbe allora capire come l'abbandono, per oltre cento anni e per buoni motivi, di questa componente delle nostre forme di conoscenza, abbia contribuito a menomarne le analisi ed abbia consentito la crescita di una visione monca, del tutto resistibile.

Avicenna (d. 1037) gave two different definitions of differentia, the first, in the Introduction of the Cure, the second, in Pointers and Reminders. In the 1230s, Afḍal al-Dīn al-Khūnajī (d. 1248) was spurred to consider the relative superiority of the two definitions by a question posed fifty years earlier by Fakhr al-Dīn al-Rāzī (d. 1210). Khūnajī argued that the Pointers definition was superior to that in the Cure; his argument turns on criteria used to assess a deduction of the predicables. Toward the end of the thirteenth century, Shams al-Dīn al-Samarqandī (d. 1322) came to the defence of the Cure definition. In his argument against Khūnajī, Samarqandī seems to have relied on claims made in demonstration theory about, first, the hierarchy of the sciences, and second, scientific questions. I conclude by considering whether Rāzī's theological commitments influence how he approached these logical problems. The material presented in this paper represents a fraction of the contributions made to defining differentia and, in consequence, an even smaller fraction of the discussions of universals in thirteenth-century Arabic logic.

Łukasiewicz introduced a new methodological approach to the history of logic. It consists of the use of modern formal logic in the research of the history of logic. Although he was not the first to use formal logic in his historical research, Łukasiewicz was the first who used it consistently and formulated it as a requirement for a historian of logic. The aim of this paper is to present Łukasiewicz's contribution and the history of its formulation. In addition, the paper will present its reception. There are two main themes in Łukasiewicz's work on the history of logic. He discussed Stoic logic and Aristotle's syllogistic. The second part of the paper focuses on current reception of Łukasiewicz's contribution and on the question of whether there is a difference between knowledge about his contribution to Stoic logic and to Aristotle's syllogistic, given that it has been hypothesised that Łukasiewicz's contribution is currently more known among Aristotelian scholars than among those who focus on Stoic logic. Based on the papers that have appeared in the last five years at Web of Science and Scopus this hypothesis has not been confirmed.

This thesis seeks to advance the use of computational techniques for the task of philosophical interpretation. To this end I present a novel method which draws on techniques and formal tools from logic-based knowledge modeling, automated reasoning, and natural language processing to support researchers in philosophy. This highly-interdisciplinary and experimental effort forms part of the e-Ideas project which seeks to build a new, computationally-scalable methodology for History of Ideas. I test my method on concrete research questions under investigation by e-Idea’s members and thus provide an illustration of my method’s functioning in practice as well as evidence for its methodological adequacy.

ÖZ Bu makalede Fahreddin er-Râzî ve onun takipçilerini "Fıkıh Usulünde Fahreddin er-Râzî Mektebi" şeklinde terimleştirmekte, Râzî'nin ve onun takipçileri arasından yedi usulcünün usul eserlerini dikkate alarak, Râzî mektebinin belli başlı özelliklerine değinmekteyiz. Râzî, kendi bilgi ve yöntem anlayışı çerçevesinde fıkıh usulünü yeniden inşa etmesiyle usul yazımında yeni bir çığır açmıştır. Râzî'nin, onun takipçilerinin ve Âmidî -İbnu'l-Hâcib çizgisinin çabalarıyla fıkıh usulü; konusu, gayesi, ilkeleri, meseleleri, konu tertibi, dil ve üslubu gibi çeşitli açılardan dönüşüm geçirmiştir ve bu dönüşümün mezhep sınırlarını aşan bir etkisi olmuştur. Dolayısıyla bu âlimlerin eserleriyle birlikte fıkıh usulünde müteahhirûn döneminin başladığı söylenebilir. Aynı sebeple Râzî Mektebi'nin katkılarının anlaşılması, müteahhirûn dönemi fıkıh usulünün gelişimine dair derinlikli bir kavrayışın temelini oluşturur. Bu dönüşüm sürecinde Gazâlî'nin çok önemli bir rolü olmakla birlikte ilim zihniyetindeki dönüşümü tam olarak yansıtanlar Râzî'nin ve Âmidî'nin eserleridir. Onların mantık kaidelerine ve "tahkik" yöntemine dayalı olarak yazdıkları el-Mahsul ve el-İhkâm, müteahhirûn döneminde usul yazımını belirlemiştir.

Nous développons une théorie formelle démontrant l'impossibilité de la connaissance objective et de la communication sémantique inter-subjective. Partant de l'incommensurabilité des domaines conceptuels privés, nous établissons que toute normativité logique, y compris le principe de noncontradiction, constitue une croyance subjective plutôt qu'une connaissance. Cette relativisation radicale mène à un solipsisme épistémologique où chaque sujet opère dans un système normatif clos, rendant impossible toute vérité trans-subjective. Le cogito cartésien lui-même n'échappe pas à cette relativisation, n'étant qu'une croyance à crédence maximale conditionnée par l'acceptation subjective du PNC.

This article examines a particularly influential development in medieval political philosophy. This development ensued during the liminal period of the late medieval era's transition to the modern era. In the Greco-Islamic tradition of this transition, the Arab philosopher and theologian Averroës (Ibn Rushd) wrote insightful commentaries on the works of logic in Aristotle's Organon. From his scholarly studies, Averroës developed a unique approach to advancing the use of inductive logic in dialectical syllogisms. Among his discoveries, Averroës had identified a rather vague reference in one of Aristotle's works that suggested the possibility of modifying the logically deductive structure of demonstrative syllogisms. After further reflection on Aristotle's reference, Averroës developed the possibility of an "inductive turn" to transform the syllogistic structure of deductive logic into the syllogistic structure of inductive logic. Averroës contended that an interchange of the major premise with the conclusion of a logically deductive structure of a demonstrative syllogism would result in the transformation of the logically deductive structure into a logically inductive structure and thus into a dialectical syllogism. By the end of the liminal period, Averroës's inductive turn had been influential with many scholars in the Latin West, including Christian theologian Thomas Aquinas, analytical philosopher John Buridan in his approaches to understanding science, and the acceptance of the hypothetico-deductive analyses of natural philosophy of Francis Bacon and Thomas Hobbes.

n 1263, Moses Nahmanides debated Friar Pablo Christiani in a public setting, accounts of which survive in both Latin and Hebrew. This contribution begins by comparing these parallel, but not identical accounts and suggesting that this debate was set up using the principles of questio disputational format. Still, these principles went completely unrecognized by Nahmanides as he claimed that his arguments had won the day, even as many of those arguments were probably dismissed on procedural grounds. When Hasdai Crescas wrote his Refutation of the Christian Principles in 1398, he seems to have anticipated such procedural objections and to have prepared his readers for the questio format, or something like it. Yet the language of Crescas’ Refutation suggests that he did not draw directly on scholastic disputational practice or accounts of these practices. Rather, he seems to have drawn on a Hebrew tradition of studying Aristotelian dialectic. Between 1263 and 1398, Jews of the Midi studied Hebrew translations of commentaries on Aristotle’s Topica by Al-Fārābī and Averroes, wrote their own super-commentaries on those works, and may even have begun to develop a Hebrew tradition of disputation. This article proposes that the fourteenth century study and perhaps practice of Aristotelian dialectic in the Midi likely made it to Barcelona, enabling Crescas to account for disputational practices in a way that Nahmanides could not.

Charles S. Peirce was interested on logical machines developed in the late 19th century and discussed whether they could develop the authentic semiotic processes indispensable for deductive reasoning. Is it possible for machines to have a genuine capacity to carry out inferences? In this paper, Peirce's arguments are analyzed, who argued that deduction, in general, cannot be reduced to mechanical factors. To this end, reference will be made to the idea of theorematic reasoning, which is fundamental for mathematical proofs and goes beyond mechanical procedures. The idea of semiosis in Peirce will also be explored, which seems to extend to the organic realm, but not to the artificial inorganic world of machines. Finally, some conclusions will be drawn about Artificial Intelligence from Peirce's semiotic perspective.

The purpose of this paper is to reconstruct the role of the principle of sufficient reason (PSR) in the "Antinomy of Pure Reason." I will proceed in the following manner. First, I will reconstruct Kant's conception of the PSR, drawing from his lectures on logic and the Second Analogy of Experience. Kant distinguished a formal and a material version of this principle. In both cases, the PSR enables the attribution of actuality to propositions (in the case of the logical principle) or objects (in the case of the real principle). However, it will be essential to note that real actuality (existence) cannot be attributed to an object without reference to a possible empirical intuition. Second, I will show that keeping in mind this restriction, which sets the conditions to attribute existence to objects, is essential to understand Kant's general argument in the Antinomy. In this context, it will be necessary to distinguish between the PSR and the supreme principle of reason. Whereas the former principle is a necessary rule for the possibility of experience, this is not true regarding the latter principle. Third, I will show that the supreme principle is a rule meant to satisfy reason's logical maxim.

In this essay, I argue that Bradley's engagement with Kant's theoretical philosophy, often mediated by Herbart, Hamilton, and Lotze, led him to reassess his early Hegelianism and to develop a critical metaphysics. Bradley's philosophy is examined diachronically, from early writings (2) to Appearance and Reality (4) through The Principles of Logic (3). I also provide a preliminary overview of Kant's reception in Britain (1) to set the historical background for other sections. This essay explores a topic not previously investigated, as other contributions on Bradley and Kant compare them without historical concern. By focusing on Bradley's sources, we can appreciate the influence of Kantianism through some understudied thinkers. In addition, I adopt a historical-diachronic approach that clarifies the development of Bradley's philosophy by exploiting documents such as manuscripts and reading notes. In particular, I present the first analysis of a 1877-1878 manuscript-Bradley's initial formulation of his peculiar metaphysics.

Abstract: We give some lectures on the work on formal logic of Jacques Herbrand, and sketch his life and his influence on automated theorem proving. The intended audience ranges from students interested in logic over historians to logicians. Besides the well-known correction of Herbrand's False Lemma by Goedel and Dreben, we also present the hardly known unpublished correction of Heijenoort and its consequences on Herbrand's Modus Ponens Elimination. Besides Herbrand's Fundamental Theorem and its relation to the ...

Ibn Abī Uṣaybiʿa's (d. 668/1270) ʿUyūn al-anbāʾ depicts Ayyubid Damascus as a flourishing intellectual scene where philosophy was regularly studied alongside other sciences, most often medicine. In that context, the court physician and statesman, Faḫr al-Dīn Riḍwān Ibn al-Sāʿātī (d. 618/1221), transcribed and collated dozens of Avicenna's (d. 428/1037) philosophical works. In doing so, Ibn al-Sāʿātī made a concerted effort to correct scribal errors and textual corruptions that had been introduced in earlier manuscripts. His position in the scholarly networks of the period afforded him access to reliable manuscripts, some of which were Avicenna's holographs, while others had been transcribed or corrected by Avicenna's students. Ibn al-Sāʿātī also wrote extensive glosses on the Manṭiq of Avicenna's Naǧāt. Taken together, Ibn al-Sāʿātī's codices provide concrete examples of how philosophy was studied and practiced in the Ayyubid context.

Gyula Klima 1. The limitations of Aristotelian syllogistic, and the need for non-syllogistic consequences Medieval theories of consequences are theories of logical validity, providing tools to judge the correctness of various forms of reasoning. Although Aristotelian syllogistic was regarded as the primary tool for achieving this, the limitations of syllogistic with regard to valid non-syllogistic forms of reasoning, as well as the limitations of formal deductive systems in detecting fallacious forms of reasoning in general, naturally provided the theoretical motivation for its supplementation with theories dealing with non-syllogistic, non-deductive, as well as fallacious inferences. We can easily produce deductively valid forms of inference that are clearly not syllogistic, as in propositional logic or in relational reasoning, or even other types of sound reasoning that are not strictly deductively valid, such as enthymemes, probabilistic arguments, and inductive reasoning, while we can just as easily provide examples of inferences that appear to be legitimate instances of syllogistic forms, yet are clearly fallacious (say, because of equivocation). For Aristotle himself, this sort of supplementation of his syllogistic was provided mostly in terms of the doctrine of "immediate inferences" 1 in his On Interpretation, various types of non-syllogistic or even non-deductive inferences in the Topics, and the doctrine of logical fallacies, in his On Sophistical Refutations. Taking their cue primarily from Aristotle (but drawing on Cicero, Boethius, and others as well), medieval logicians worked out in systematic detail various theories of non-syllogistic inferences, sometimes as supplementations of Aristotelian syllogistic, sometimes as merely useful devices taken to be reducible to syllogistic, and sometimes as more comprehensive theories of valid inference, containing syllogistic as a special, and important, case.

In this article, I argue that Kant breaks with the tradition of aesthetics and with a concept inherently tied to it, namely, that of good taste or correct taste. This thinker not only acknowledges, similarly to the Anglo-Saxon traditions of criticism and common sense, that it is impossible to demonstrate who possesses taste, but also maintains that there is nothing to be demonstrated in this regard. For taste does not admit of degrees, as if it were a psychological faculty or a matter of fact, such as social recognition at a given historical moment and under specific empirical circumstances. The principles of taste should not be understood as prescriptive rules; rather, they are second-order principles that do not concern how we ought to judge in each case but rather what properly constitutes the specific possibility of taste as such. What follows from the correct interpretation of these principles is a thesis that challenges the aesthetic tradition and the concept of good taste, for through its principles and the way it defines their origin, scope, and validity, it asserts that taste should not be understood as a judgment about objects or about subjects understood as an actual community.

I began translating my master's thesis with the intention of rendering the German text unchanged. However, as I had already been somewhat dissatisfied with this thesis during my studies—since it seemed to me more like a compendium of ideas—I incorporated additional thoughts and, above all, concrete elaborations during the translation process. This led to a complete transformation of the text. Instead of a full-length treatise, the result was a revision that shifted the focus toward examples and overviews. The core arguments of the thesis were preserved, but they took on a more bullet-point-like form, which, for the reader, likely makes certain ideas more accessible.

I do not intend to undertake further revisions but will leave this as it stands, perhaps building upon it in future texts.

This paper aims to fill a gap in the literature by investigating Fichte’s
application of the genetic method to Kant’s transcendental philosophy. I claim that
Fichte’s main source for developing this method is Ernst Platner’s conception of
logic as a pragmatic history of the human faculty of cognition. To support this claim,
I argue (1) that Platner himself reworked Kant’s account of the faculties by using
this method, (2) that Fichte engaged extensively with Platner’s approach to Kant,
and (3) that he employed a nonpsychological version of Platner’s method to recast
Kant’s transcendental logic in the Foundation of the Entire Doctrine of Science. In my view, Fichte’s development of the genetic method within a transcendental framework is one of his most influential contributions to the further development of German Idealism.

Sanat, gerçeğin gölgesinde filizlenen ideal güzelliğin yeniden terennümüdür. Kendi içinde bütünlüğü ve bağlı olduğu ilkeleri vardır. Aleladeliğe tahammülü yoktur. Estetik düşünceyle üretilmeyen eserlerin kalıcılığı mümkün olmadığı gibi, sanat gayesiyle meydana getirildiği iddia edilse bile bir kıymet-i harbiye ifade etmeyeceği de ortadadır. Hız çağında hızlı üretim, hesapsız tüketim... Hız çağında haz almanın estetik kaygının önüne geçtiği bir süreç.