History of Logic

"From the 1930 Reiser edition (emended second impression) of the Ars logica, itself comprising the first two parts of the five part Cursus philosophicus of 1631-1635, by the same author.".

Gödel’s ontological proof is by now well known based on the 1970 version, written in Gödel’s own hand, and Scott’s version of the proof. In this article new manuscript sources found in Gödel’s Nachlass are presented. Three versions of Gödel’s ontological proof have been transcribed, and completed from context as true to Gödel’s notes as possible. The discussion in this article is based on these new sources and reveals Gödel’s early intentions of a liberal comprehension principle for the higher order (...) modal logic, an explicit use of second-order Barcan schemas, as well as seemingly defining a rigidity condition for the system. None of these aspects occurs explicitly in the later 1970 version, and therefore they have long been in focus of the debate on Gödel’s ontological proof. (shrink)

Aristotle counts as the founder of formal logic. The logic he develops dominated until Frege and others introduced a new logic. This new logic is taken to be more powerful and better capable of capturing inference patterns. The new logic differs from Aristotelian logic in significant respects. It has been argued by Fred Sommers and Hanoch Ben-Yami that the new logic is not well equipped as a logic of natural language, and that a logic closer to Aristotle's is better suited (...) for this task. Each of them developed their own formalism - Sommers in form of term logic, Ben-Yami in form of his Quantified Argument Calculus (QUARC). I discuss Aristotle's logic - a term logic - and attempt a comparison between Aristotelian logic and (i) the new logic, (ii) Sommers' term logic, and (iii) Ben-Yami's QUARC. I consider differences between the systems, and show how they are related to and diverge from the new logic. (shrink)

The systematic account of deductive reasoning and the development of a formal logic to reveal the principles of such reasoning began with Aristotle's syllogistic. It was a term logic, a logic that dominated the field until the rise of modern predicate logic at the end of the Nineteenth century. That system quickly supplanted the old logic of terms. However, in the middle of the Twentieth century Fred Sommers took up the challenge to build a revised and strengthened term logic, one (...) fit to challenge the hegemony of predicate logic. The aim was to devise a formal logic that could better serve as the logic of natural language. -/- In recent years a new group of logicians have taken this version of term logic into many new directions. This book presents here for the first time some of the best examples of their work with new essays by philosophers, logicians, mathematicians, computational theorists, and historians of logic. The topics addressed include relative terms, logical copulation, Aristotelian diagrams, modality, truth, semantics, epistemic term logic, non-classical quantifiers, and more. (shrink)

In this paper, I outline a pragmatist epistemology of logic inspired by later work of Charles S. Peirce that shares many features with an anti-exceptionalism about logic but, I argue, can better respond to a key problem that plagues the anti-exceptionalist. I first lay out what I take to be the tenets of anti-exceptionalism, discussing some difficulties in formulating the position that make it difficult to definitively label the position discussed here. I then analyze a key problem for the anti-exceptionalist, (...) the background logic problem, and suggest that when framed as a problem for certain types of inquiry, it shares a presupposition about the priority of logic with other problems in the epistemology of logic. Turning to a discussion of Peirce from the 1903 Lowell Lectures, I then outline a pragmatism about logic that rejects the priority claims underlying the problems for inquiry in logic and, I argue, can resolve the background logic problem. (shrink)

We develop some of Williamson’s ideas regarding how propositional calculus aids in comprehending Aristotelian logic. Specifically, we enhance the utilisation of truth tables to examine the structure of opposition diagrams. Using ‘conditioned truth tables’, we establish logical dependency relationships between the truth values of different propositions. This approach proves effective in interpreting various texts of the Organon concerning the doctrine of opposition.

In this paper I provide an analysis of an anonymous text which appeared at Sondershausen and Mühlhausen in 1687: Initiatio philosophi sive Dubitatio Cartesiana, ad indubiam philosophiam viam monstrans, iuxta mentem Renati des Cartes, Nobilis Galli, utraque methodo explicata, titled after Johannes Clauberg’s homonymous 1655 treatise. It consisted of (1) an abridgement of his Paraphrasis in Renati Des Cartes Meditationes (1658), and (2) a demonstration more geometrico of the necessity of methodical doubt as the beginning of philosophy, partially based on (...) Clauberg’s own 1655 Initiatio. I place the publication of the 1687 text in the context of the attacks on Cartesianism taking place in German areas especially after 1677 and the appearance of Spinoza’s texts, focusing on the ways in which Clauberg’s philosophy was adapted to the rebuking of such attacks and to the re-establishment of a Cartesian presence in Germany. (shrink)

Justification of theorems plays a vital role in any rational human activity. It is indispensable in science. The deductive method of justifying theorems is used in all sciences and it is the only method of justifying theorems in deductive disciplines. It is based on the notion of proof, thus it is a method of proving theorems. In the Warsaw School of Logic (WSL) – the famous branch of the Lvov-Warsaw School (LWS) – two types of the method: axiomatic deduction method (...) and natural deduction method were developed and practiced. In this paper, both of these methods are briefly discussed with an emphasis on their historical, groundbreaking significance for logic. The axiomatic method by means of rejection (proposed by Jan Łukasiewicz – a co-creator of the WSL), which is the method of the so-called rejection proof (rejection/refutation method) in logical systems and the proving method of generalized natural deduction, which is a hybrid deduction–refutation method of proving theorems, are also outlined in the paper. The author discusses their historical significance. This paper also contains a brief mention of the most significant results which the application of the discussed methods introduced into contemporary scientific research, not only logical one. (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 was revered in the thirteenth century, perhaps more highly than it has been revered before or since. In the Muslim East, logic was an integral part of the syllabus of schools and found to be especially helpful for legal studies. It was at this time that The Canons of Logic was composed by Najm al-Din al-Katibi, a scholar of the Shafi'i school of law. The Rules of Logic is the most widely read introduction to logic in the Arabic-speaking world. (...) It has probably enjoyed a longer shelf-life than any other logic textbook ever written, having been in use by madrasa students from the early fourteenth century up until the present day. Building on the theories of Avicenna, al-Razi, and other pioneers of logic, al-Katibi discusses the many pitfalls of building arguments and setting out unambiguous claims in natural language. The enduring nature of the text is a testament to al-Katibi and his impact on concepts of formal discourse and argument. This new translation of The Canons of Logic provides new life to an influential text that has shaped the work of scholars of logic for centuries. (shrink)

Najm al-Din al-Katibi's al-Risalah al-Shamsiyyah is a scholarly edition and translation of The Canons of Logic, with additional commentary and notes. Composed by Najm al-Din al-Katibi, a scholar of the Shafi'i school of law, al-Risalah al-Shamsiyyah is the most widely read introduction to logic in the Arabic-speaking world. It has probably enjoyed a longer shelf-life than any other logic textbook ever written, having been in use by madrasa students from the early fourteenth century up until the present day. Building on (...) the theories of Avicenna, al-Razi, and other pioneers of logic, al-Katibi discusses the many pitfalls of building arguments and setting out unambiguous claims in natural language. The enduring nature of the text is a testament to al-Katibi and his impact on concepts of formal discourse and argument. (shrink)

Commentary on Quwaysinī's commentary on Akhḍarī's work titled the Sullam al-muawraq on logic.

‘Feminist logic’ may sound like an impossible, incoherent, or irrelevant project, but it is none of these. We begin by delineating three categories into which projects in feminist logic might fall: philosophical logic, philosophy of logic, and pedagogy. We then defuse two distinct objections to the very idea of feminist logic: the irrelevance argument and the independence argument. Having done so, we turn to a particular kind of project in feminist philosophy of logic: Valerie Plumwood's feminist argument for a relevance (...) logic. Plumwood's work serves as our primary case study as we turn to the project of considering three different ways we might understand her argument and revisionist arguments like it: as a priori theorizing, as ameliorative conceptual engineering, or as instances of anti-exceptionalist approaches to logic. After arguing that the anti-exceptionalist approach seems to provide the most promising means of understanding the kind of project undertaken in a feminist challenge to classical logic, we briefly address the consequences that this might have for logic instruction. Here, we argue for the perhaps unexpected conclusion that feminist programs ought to offer more, not less, instruction in logic for those who take interest. (shrink)

ALL THE MORE, by Avi Sion, Ph.D., comprises a merged list of 72 qal vachomer arguments in the Tanakh, i.e. of a fortiori arguments in the Hebrew Bible. This listing brings together lists proposed in past rabbinic literature and in more recent studies by the author. The literature research for it was carried out mainly by R. Yaakov Gabay, who looked into works in Hebrew by five rabbis who had proposed lists, namely: R. Shmuel Yaffe Ashkenazi (Yefeh Toar, 1597), R. (...) Zvi Hirsch Katzenellenbogen (Netivot Olam, 1822), R. Zeev Wolf Einhorn (Midrash Tannaim, 1839), R. Mattityahu Strashun (Mattat Yah, 1892), R. Chaim Hirschensohn (Berure HaMidot, 1928). The author of the present essay brought additional information from the Tanakh commentary of R. Shlomo Yitzchaki (Rashi, 11th Cent.) and an essay by R. Louis Jacobs (2005), as well as from his own past works (Judaic Logic, 1995, and A Fortiori Logic, 2013). The information thus gathered is here presented in a systematic manner, after careful evaluation by the author of each case with reference to narrative context, language used, and logical form. Efforts are made to identify which cases were known to each of the past authors, and to determine who found each case first and whether subsequent listings of the case (if any) were independent or derivative. (shrink)

U članku se promatraju osnovne karakteristike razvojne dinamike hrvatskoga logičkoga nazivlja od izlazka Pacelove Logike za gimnazije, prve sustavne logike na hrvatskome jeziku, 1868. godine, pa sve do Petrovićeve Logike, također za srednja učilišta, iz 1964., koja je još uviek u uporabi. Nazivlje je u tu svrhu razvrstano u nekoliko tipičih skupina. Općenito, uočava se porast zastupljenosti latinizama (i grecizama) na štetu hrvatskih naziva. U analizi nazivlja autor se ograničuje na knjige namienjene nastavi logike bilo na srednjim učilištima, bilo na (...) sveučilištu, i to na nazivlje tradicionalne logike. Mjestimice su pridodane i napomene o nazivlju moderne (matematičke) logike. (shrink)

Two commentaries by Kamalpaşazade and Birgivi Efendi on Samarqandī's Risālah fī ādāb al-baḥth which is also included.

To believe that logic has no history might at first seem peculiar today. But since the early 20th century, this position has been repeatedly conflated with logical monism of Kantian provenance. This logical monism asserts that only one logic is authoritative, thereby rendering all other research in the field marginal and negating the possibility of acknowledging a history of logic. In this paper, I will show how this and many related issues have developed, and that they are founded on only (...) one prominent statement by Kant. I will argue, however, that this statement takes on a very different meaning in a broader context of the history and philosophy of science, and that Kant and his supporters never advocated the logical monism that they are still said to hold today. (shrink)