Archives of Philosophy

SUBMITINFORMATION
EnglishTürkçe

Research Article


DOI :10.26650/arcp.1562928   IUP :10.26650/arcp.1562928    Full Text (PDF)

Truth Conditions of Hypothetical Propositions According to Fakhr al-Dīn al-Rāzī

Fatma Karaismail

This article examines the truth conditions of conditional (muttaṣil) and disjunctive conditional (munfaṣil) propositions in Fakhr al-Dīn al-Rāzī’s (d. 606/1210) logic system and whether these propositions can be classified under truth functional propositional logic. Accordingly, the work is structured in two main sections. The subject is discussed in the first section in the context of implicative (luzūmī) and coincidental (ittifāqī) conditional propositions, and in the second section within the framework of three types of disjunctive conditional propositions. This study concludes that the truth values of implicative conditional propositions depend not only on the truth values of their components but also on whether they contain the implication relation. Similarly, the truth values of disjunctive conditional propositions are based on whether they include the conflict (ʿinād) relation, as well as on the truth values of their components. As a result, it has been established that the implicative conditional and disjunctive conditional propositions in al-Rāzī’s system are not truth functional and these propositions do not overlap in meaning with truth functional compound propositions in propositional logic. In contrast, coincidental conditional propositions are considered truth functional due to the absence of any implication or conflict relationship between their components.

Keywords: Islamic Logic, Propositional Logic, Truth Functional Propositions, Hypothetical Propositions, Fakhr al-Dīn al-Rāzī
DOI :10.26650/arcp.1562928   IUP :10.26650/arcp.1562928    Full Text (PDF)

Fahreddin er-Râzî’ye Göre Şartlı Önermelerde Doğruluk

Fatma Karaismail

Bu makale, Fahreddin er-Râzî’nin (ö. 606/1210) mantık sisteminde yer alan bitişik ve ayrık şartlı önermelerin doğruluk kriterlerinin ne olduğu ve bu önermelerin doğruluk işlevli (truth functional) olup olmadıkları sorularını ele almaktadır. Bu doğrultuda çalışma iki ana bölüm olarak kurgulanmıştır. Birinci bölümde mesele, lüzûmî ve rastlantısal (ittifâkî) bitişik şartlı önermeler, ikinci bölümde ise ayrık şartlı önermelerin üç türü bağlamında tartışılmıştır. Bu tartışma neticesinde lüzûmî bitişik şartlı önermelerin doğruluğunun, bileşenlerinin doğruluk değerlerinin yanı sıra bu önermelerin içermeleri gereken lüzûm ilişkisine sahip olmalarına; ayrık şartlı önermelerin doğruluğunun ise bileşenlerinin doğruluk değerlerinin yanı sıra ifade etmeleri beklenen ayrıklık ilişkisini ifade ediyor olmalarına bağlı olduğu sonucuna varılmıştır. Bunun sonucu olarak, Râzî’nin sistemindeki lüzûmî bitişik şartlı ve ayrık şartlı önermelerin doğruluk işlevli olmadığı ve bu önermelerin, önermeler mantığındaki doğruluk işlevli bileşik önermelerle anlam açısından örtüşmediği belirlenmiştir. Rastlantısal bitişik şartlı önermeler ise bileşenleri arasında gerektirme veya ayrıklık ilişkisi bulunmaması nedeniyle doğruluk işlevli olarak değerlendirilmiştir.

Keywords: İslam Mantığı, Önermeler Mantığı, Doğruluk İşlevli Önermeler, Şartlı Önermeler, Fahreddin er-Râzî

EXTENDED ABSTRACT


This article analyzes the truth conditions of hypothetical propositions (qaḍiyya sharṭiyya) in Fakhr al-Dīn al-Rāzī’s logic system and whether these propositions are truth functional or not. Truth functional compound propositions contain truth functional logical connectives and their truth values are determined based on the truth values of their components. On the other hand, non-truth-functional compound propositions are propositions whose truth values are not determined according to the truth values of their components. al-Rāzī’s theory of hypothetical propositions falls under propositional logic, as it examines new propositions formed by combining others through logical connectives and analyzes the relations between their components. However, does this theory also belong to truth functional propositional logic, which is the most comprehensive branch of propositional logic? This question, which points to the purpose of the article, is addressed in the context of conditional propositions (qaḍiyya sharṭiyya muttasila) in the first section and disjunctive conditional propositions (qaḍiyya sharṭiyya munfaṣila) in the second section. In these two chapters, first, the types of conditional and disjunctive conditional propositions according to al-Rāzī are briefly explained, followed by al-Rāzī’s explanations of the truth conditions of each of these propositions. In the first section, the problem is examined in two sub-sections for implicative (luzūmiyya) and coincidental (ittifāqiyya) conditional propositions.

According to al-Rāzī, implicative conditional propositions may be either true or false when the truth values of their antecedents and consequents are true and true, false and false, or false and true, respectively. The fact that the truth value of implicative conditional propositions may also be false when their components have these truth values distinguishes implicative conditional propositions from material conditionals. This is because material conditionals are necessarily true when the components have these truth values. The reason of this difference between implicative conditional propositions and material conditionals is the relation of implication (luzūm) that must exist between the antecedent and consequent in implicative conditional propositions. In other words, according to al-Rāzī, implicative conditional propositions mean that the antecedent necessarily entails its consequent and as a result, an implicative conditional proposition cannot be true if the antecedent does not necessarily entail the consequent even if they are both true. According to al-Rāzī coincidental conditional propositions are truth functional because they do not carry the meaning of implication. However, they also do not have the meaning of material implication, as a coincidental conditional proposition with a false antecedent and a false consequent is false.

al-Rāzī categorizes disjunctive conditionals into three types: (i) Real disjunctive conditionals (ḥaqīqiyya): According to al-Rāzī, real disjunctive conditionals are propositions in which one component is contradiction of the other. Since it is impossible for two mutually contradictory propositions, such as p and not p, to be true at the same time, one of the components of real disjunctive conditional propositions must be true and the other false. (ii) Mani‘at al-jam‘ disjunctive conditionals are propositions in which one of the components has a narrower scope than the contradiction of the other. (iii) Mani‘at al-ḥuluv disjunctive conditionals are propositions in which one component has a broader scope than the contradiction of the other. In mani‘at al-jam‘ disjunctive conditionals, all components can be false but cannot all be true. Conversely, in mani‘at al-ḥuluv disjunctive conditionals, all components can be true but cannot all be false. In conclusion, according to al-Rāzī, the meanings of disjunctive conditional propositions are determined by the law of non-contradiction. Therefore, the truth values of the components of disjunctive conditional propositions are not the only condition for determining the truth values of these propositions. When determining the truth value of these propositions, we consider not only the truth values of the components but also whether the conflict (ʿinād) relationship mentioned by al-Rāzī exists between the components. This shows that the types of disjunctive conditional propositions are also not truth functional.


PDF View

References

  • Bobzien, Susanne. “Ancient Logic”. Stanford Encyclopedia of Philosophy. ed. Edward N. Zalta. Erisim 10 Aralık 2022. https://plato.stanford. edu/entries/logic- ancient/ google scholar
  • Chatti, Saloua. Arabic Logic from al-Fârâbî to Averroes. Cham: Birkhauser, 2019. google scholar
  • Chatti, Saloua. “On Some Ambiguities in Ibn Sîna’s Analysis of the Quantified Hypothetical Propositions”, Arabic Sciences and Philosophy, 32/1 (2022), 67-107. google scholar
  • Chatti, Saloua. “Syncategoremata in Arabic Logic, al-Fârabî and Avicenna”. History and Philosophy of Logic, 35/2 (2014), 167-197. google scholar
  • Çetres, İbrahim Halil. “Sıkı İçerme Sistemleri”. Felsefi Düşün, 7 (Ekim 2016), 21-31. google scholar
  • Egre, Paul - Rott, Hans. “The Logic of Conditionals”. Stanford Encyclopedia of Philosophy. ed. Edward N. Zalta. Erisim 12 Aralık 2022. https://plato.stanford.edu/entries/logic-conditionals/ google scholar
  • Fellâhî, Esedullah. “Şart-ı ittifâkî der mantık-ı cedîd”. Pejüheşha-yi Felsefî, 52/214 (1388 ş.), 105-133. google scholar
  • Fellâhî, Esedullah. “Şart-ı ittifâkî nezd-i mantık-dânân-ı Müselman”. Mutâlaât-ı İslâmî: Felsefe ve Kelâm, 43/ 87/2, (1390 ş.), 111-140. google scholar
  • Fellâhî, Esedullah. “Şart-ı lüzûm-i der mantık-ı cedîd”. Faslnâme-i Teemmülât-ı Felsefî, 1/1 (1388 ş.), 7-46. google scholar
  • Franks, Curtis. “Propositional Logic”. Stanford Encyclopedia of Philosophy. ed. Edward N. Zalta. Erisim 13 Aralık 2022. https://plato.stanford. edu/entries/logic-propositional google scholar
  • Goodman, Lenn E. Avicenna. London, New York: Routledge, 1992. google scholar
  • Grünberg, Teo, v.d. Mantık Terimleri Sözlüğü. Ankara: ODTÜ Geliştirme Vakfı Yayınları, 2003. google scholar
  • Halbach, Volker. The Logic Manual. Oxford: Oxford University Press, 2015. google scholar
  • İbn Sînâ. eş-Şifâ: el-Kıyâs. nşr. Saîd Zâyed. Kahire, el-Hey’etü’l-Âmme li Şuûni’l-Metâbi‘i’l-Emîriyye, 1965. google scholar
  • Jadaane, Fehmi. Stoacılığın İslam Düşüncesi Üzerindeki Etkisi. İstanbul: Albaraka Yayınları, 2020). google scholar
  • Karaismail, Fatma. Fahreddin er-Râzî’nin Önerme Anlayışı. İstanbul: İstanbul Üniversitesi, Sosyal Bilimler Enstitüsü, Doktora Tezi, 2022. google scholar
  • Karimullah, Kamran I. Avicenna (d. 1037), Logical Theory, and the Aristotelian Tradition. Montreal: McGill University, The Institute of Islamic Studies, Doktora tezi, 2014. google scholar
  • Kâtibî. el-Münassas. İstanbul: Süleymaniye Kütüphanesi, Şehid Ali Paşa, 1680. google scholar
  • Kâtibî. Şemsiyye Risâlesi. nşr. ve çev. Ferruh Özpilavcı. İstanbul: Litera Yayıncılık, 2017. google scholar
  • Kayar, Esma. “Megaralı Philon’da Koşullu Önerme Anlayışı ve Modern Mantıkta Maddi İçerme Kavramının Oluşumu”, Kaygı, 20/1 (2021), 325-345. google scholar
  • Kenny, Anthony. Batı Felsefesinin Yeni Tarihi: Antik Felsefe. çev. Serdar Uslu. İstanbul: Küre Yayınları, 2021. google scholar
  • Kuşlu, Harun. Nasîruddin Tûsî’de Önermeler Mantığı. İstanbul: Klasik Yayınları, 2017. google scholar
  • Lewis, C. Irving, Cooper H. Langford. Symbolic Logic. New York: Dover Publications, 1932. google scholar
  • Maroth, Miklos. Ibn Sîna Und Die Peripatetische „Aussagenlogik”. Almancaya çev. Johanna Till. Leiden, New York, K0benhavn, Köln: E. J. Brill, 1989. google scholar
  • Movahed, Zia. “A Critical Examination of Ibn-Sina’s Theory of the Conditional Syllogism”. Sophia Perennis, 1/1 (2009), 5-21. google scholar
  • Özel, Aytekin. İbn Sînâ’nın Birleşmeli Kıyas Teorisi ve Sembolik Yorumu. Bursa: Emin Yayınları, 2009. google scholar
  • Özlem, Doğan. Mantık. İstanbul: Notos Kitap, 2016. google scholar
  • Râzî, Fahreddîn. Mantıku’l-Mülahhas. nşr. Ahad Ferâmerz Karâmelekî - Âdîne Asgarînejad. Tahran, İntişârât-ı Dânişgâh-ı İmam Sâdık, 1381 ş. google scholar
  • Râzî, Fahreddîn. Şerhu’l-İşârât ve’t-tenbîhât. nşr. Ali Rızâ Necefzâde. 2 Cilt. Tahran: Encümen-i Âsâr, 1384 ş. google scholar
  • Rescher, Nicholas. “Avicenna on the Logic of “Conditional” Propositions”. Studies in the History of Arabic Logic içinde. Pittsburgh: University of Pittsburgh Press, 1963, 76-86. google scholar
  • Shehaby, Nabil. The Propositional Logic of Avicenna, A Translation from al-Shifa’: al-Qiyas with Introduction, Commentary and Glossary. Dordrecht-Holland: D. Reidel Publishing Company, 1973. google scholar
  • Street, Tony. “Ibn Sma und die peripatetische „Aussagenlogik”, Miklos Maroth”. Philosophy East and West, 45/2 (1995), 281-286. google scholar
  • Street, Tony. “Tusı on Avicenna’s Logical Connectives”. History and Philosophy of Logic, 16:2 (1995), 257-268. google scholar
  • Tûsî, Nasîruddin. Tercemetu Esâsi’l-iktibâs fi’l-mantık. nşr. Ferruh Özpilavcı. 2 Cilt. Arapçaya çev. Molla Hüsrev. Kuveyt: Dâru Fâris, 2023. google scholar
  • Yıldırım, Cemal. Mantık. Ankara: Fol Yayınevi, 2019. google scholar

Citations

Copy and paste a formatted citation or use one of the options to export in your chosen format


EXPORT



APA

Karaismail, F. (2024). Truth Conditions of Hypothetical Propositions According to Fakhr al-Dīn al-Rāzī. Archives of Philosophy, 0(61), 38-48. https://doi.org/10.26650/arcp.1562928


AMA

Karaismail F. Truth Conditions of Hypothetical Propositions According to Fakhr al-Dīn al-Rāzī. Archives of Philosophy. 2024;0(61):38-48. https://doi.org/10.26650/arcp.1562928


ABNT

Karaismail, F. Truth Conditions of Hypothetical Propositions According to Fakhr al-Dīn al-Rāzī. Archives of Philosophy, [Publisher Location], v. 0, n. 61, p. 38-48, 2024.


Chicago: Author-Date Style

Karaismail, Fatma,. 2024. “Truth Conditions of Hypothetical Propositions According to Fakhr al-Dīn al-Rāzī.” Archives of Philosophy 0, no. 61: 38-48. https://doi.org/10.26650/arcp.1562928


Chicago: Humanities Style

Karaismail, Fatma,. “Truth Conditions of Hypothetical Propositions According to Fakhr al-Dīn al-Rāzī.” Archives of Philosophy 0, no. 61 (Jan. 2025): 38-48. https://doi.org/10.26650/arcp.1562928


Harvard: Australian Style

Karaismail, F 2024, 'Truth Conditions of Hypothetical Propositions According to Fakhr al-Dīn al-Rāzī', Archives of Philosophy, vol. 0, no. 61, pp. 38-48, viewed 19 Jan. 2025, https://doi.org/10.26650/arcp.1562928


Harvard: Author-Date Style

Karaismail, F. (2024) ‘Truth Conditions of Hypothetical Propositions According to Fakhr al-Dīn al-Rāzī’, Archives of Philosophy, 0(61), pp. 38-48. https://doi.org/10.26650/arcp.1562928 (19 Jan. 2025).


MLA

Karaismail, Fatma,. “Truth Conditions of Hypothetical Propositions According to Fakhr al-Dīn al-Rāzī.” Archives of Philosophy, vol. 0, no. 61, 2024, pp. 38-48. [Database Container], https://doi.org/10.26650/arcp.1562928


Vancouver

Karaismail F. Truth Conditions of Hypothetical Propositions According to Fakhr al-Dīn al-Rāzī. Archives of Philosophy [Internet]. 19 Jan. 2025 [cited 19 Jan. 2025];0(61):38-48. Available from: https://doi.org/10.26650/arcp.1562928 doi: 10.26650/arcp.1562928


ISNAD

Karaismail, Fatma. “Truth Conditions of Hypothetical Propositions According to Fakhr al-Dīn al-Rāzī”. Archives of Philosophy 0/61 (Jan. 2025): 38-48. https://doi.org/10.26650/arcp.1562928



TIMELINE


Submitted07.10.2024
Accepted13.12.2024
Published Online31.12.2024

LICENCE


Attribution-NonCommercial (CC BY-NC)

This license lets others remix, tweak, and build upon your work non-commercially, and although their new works must also acknowledge you and be non-commercial, they don’t have to license their derivative works on the same terms.


SHARE




Istanbul University Press aims to contribute to the dissemination of ever growing scientific knowledge through publication of high quality scientific journals and books in accordance with the international publishing standards and ethics. Istanbul University Press follows an open access, non-commercial, scholarly publishing.