Zapadna suvremena logika korištena je za unapređenje islamske filozofske teologije, koja je povijesno koristila aristotelovsko-avicenovsku logiku, na temelju toga što se logika shvaćala kao inherentno normativna. To je usprkos kontroverzama o statusu logike u islamskoj teološkoj tradiciji. Normativni autoritet logike znači da ona utječe na sadržaj onoga u što bismo trebali vjerovati i na to kako bismo trebali revidirati ta uvjerenja. Ovaj rad nastoji pokazati da je, bez obzira na nekompatibilne razlike između dvaju sustava, temeljna značajka zapadne suvremene logike i (...) aristotelovsko-avicenovske logike njihova normativnost. Zatim se tvrdi da je inherentna normativnost logike u islamskoj teološkoj/filozofskoj tradiciji nemotivirana. Umjesto toga, kao održivu alternativu rad predlaže ponovno uspostavljanje logike kao anti-ekscepcionalističke unutar islamske teološke/filozofske tradicije. (shrink)

This paper undertakes an in-depth examination of the intriguing argument for the existential import of negative propositions by the fifteenth-century Ottoman scholar Hatibzâde Mehmed (d. 1496) and the counterarguments by his disciple, Taşköprizâde Kâsım (d. 1513). It argues that this discussion is a significant example of Ottoman scholars engaging in long-standing disputes concerning the nature and ontological ground of negative propositions, which date back to Plato and Aristotle. It is also intended to underline the need for considering not only logic (...) texts but also works primarily associated with other disciplines in order to attain a comprehensive picture of logical discussions in the post-classical period of Islamic thought. (shrink)

This article examines the traditional and modern doctrines of categorical propositions and argues that both doctrines have serious problems. While the doctrines disagree about existential imports...

Contrary to received opinion, the Aristotelian Square of Opposition (square) is logically sound, differing from standard modern predicate logic (SMPL) only in that it restricts the universe U of cognitively constructible situations by banning null predicates, making it less unnatural than SMPL. U-restriction strengthens the logic without making it unsound. It also invites a cognitive approach to logic. Humans are endowed with a cognitive predicate logic (CPL), which checks the process of cognitive modelling (world construal) for consistency. The square is (...) considered a first approximation to CPL, with a cognitive set-theoretic semantics. Not being cognitively real, the null set Ø is eliminated from the semantics of CPL. Still rudimentary in Aristotle’s On Interpretation (Int), the square was implicitly completed in his Prior Analytics (PrAn), thereby introducing U-restriction. Abelard’s reconstruction of the logic of Int is logically and historically correct; the loca (Leaking O-Corner Analysis) interpretation of the square, defended by some modern logicians, is logically faulty and historically untenable. Generally, U-restriction, not redefining the universal quantifier, as in Abelard and loca, is the correct path to a reconstruction of CPL. Valuation Space modelling is used to compute the effects of U-restriction. (shrink)

In Baghdad in the mid twelfth century Abū al-Barakāt proposes a radical new procedure for finding the conclusions of premise-pairs in syllogistic logic, and for identifying those premise-pairs that have no conclusions. The procedure makes no use of features of the standard Aristotelian apparatus, such as conversions or syllogistic figures. In place of these al-Barakāt writes out pages of diagrams consisting of labelled horizontal lines. He gives no instructions and no proof that the procedure will yield correct results. So the (...) reader has to work out what his procedure is and whether it is correct. The procedure turns out to be insightful and entirely correct, but this paper may be the first study to give a full description of the procedure and a rigorous proof of its correctness. (shrink)

A number of medieval Arabic logicians discussed inferences that combine the principles of propositional and term logic, for example: Whenever H is Z then Every J is DNo D is AWhenever H is Z then S...

Bu makale, 19. yüzyılın başlarında Kuzey Hindistan’da ortaya çıkan ve günümüze kadar devam eden, ilahî kudret hakkında önemli bir kelâmî ihtilafı ele alan ilk mantık araştırmasıdır. İhtilaf, birbiriyle bağlantılı iki tez içermektedir. İlk tez "imkān-i naẓīr" olarak bilinir ve bu, Allah’ın Hz. Muhammed'in aynısını yaratabilmesidir. İkinci tez ise "ikmān-i kızb" olarak adlandırılır ve Allah’ın yalan söyleme veya gerçeğe aykırı şeyler söyleme olasılığını hakkındadır. Makale, iki güçlü düşünürün argümanlarını inceleyecektir. İlk olarak, tartışmayı başlatan Shah İsmail Dihlawi (ö. 1831), Allah’ın benzer bir (...) Muhammed'i yaratabilme ve yalan söyleyebilme olasılığını savunan argümanlar sunar. İkinci olarak, karşıt görüşteki ve baş rakibi Fazl-e Haqq Khayrabadi (ö. 1861), her iki olasılığı da kesin bir şekilde reddeder. Makale, argümanların yapısının ve öncüllerinin yanı sıra tartışmada deruhte edilen temel modal kavramların ayrıntılı mantıksal analizine odaklanmaktadır. (shrink)

The square of opposition has never been drawn by classical Arabic logicians, such as al-Fārābī and Avicenna. However, in some later writings, we do find squares, which their authors call rather ‘tables’ (sing. _lawḥ_). These authors are Shihāb al-Dīn al-Suhrawardī and Muhammed b. Yūsuf al-Sanūsī. They do not pertain to the same geographic area, but they both provide squares of opposition. The aim of this paper is to analyse these two squares, to compare them with each other and with the (...) traditional square of opposition drawn by Apuleius and Boethius, with regard to their particular structure and their vertices and to evaluate their validity. We will show that both squares are different from each other and from the traditional square both with regard to their vertices, and to the arrangements of the oppositional relations. In addition, while al-Suhrawardī uses the notion of matter modalities to define the oppositions, al-Sanūsī relies rather on al-Rāzī’s and al-Khūnajī’s distinctions. Both authors agree, however, on the fact that affirmatives have an import while negatives do not. For this reason, their squares are valid from a logical viewpoint. As diagrams, these squares are nevertheless entirely original, due to the particular arrangements of their oppositional relations. Our analysis shows also that the later author does not seem to know the square drawn by the earlier one and that both authors do not seem to know Apuleius’ or Boethius’ squares. (shrink)