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52 Cards in this Set
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[From Khaled El-Rouayheb, "Relational Syllogisms and the History of Arabic Logic, 900-1900" (Leiden/Boston: Brill, 2010).] |
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قضيّة موجبة |
qaḍiyya mūjiba
affirmative proposition
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تصديق |
taṣdīq
assent
[The acceptance of a proposition. It was opposed "conception" (تصوّر), which is the comprehension of a concept. Both تصديق and تصوّر could be used both of the mental act and of the object of such a mental act. The exact relationship between "assent" (تصديق), "judgment" (حُكم), and "proposition" (قضيّة) was much debated in later centuries.] |
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بذاته |
bi-dhātihi
by itself
[This phrase would seem to play the same role in the definition of syllogism as Aristotle's τῷ ταῦτα εἶναι (An. Pr. 24b20), translated into English as "from there being so" (Jenkinson) or "from the fact that the assumptions are such" (Tredennick) or "because these things are so" (Smith). In the Arabic translation of Theodorus, an associate of the celebrated translator Ḥunayn b. Isḥāq (d. 877), Aristotle's τῷ ταῦτα εἶναι is translated as لِوُجُوْدِ تِلْكَ الأَشْيَاءِ المَوْضُوْعَةِ بِذَاتِهَا in the definition of the syllogism, but then merely as بِذَاتِهَا in Aristotle's immediately following explication of what he means by τῷ ταῦτα εἶναι (see ʿA. al-Badawī, ed., "Manṭiq Arisṭū" (Kuwait/Beirut: Wikālat al-maṭbūʿāt / Dār al-qalam, 1980 [reprint]), 1:142-43). Since the Arabic Aristotelians (following Aristotle) explicitly meant the condition to rule out elliptical arguments with suppressed premises, the translation of the Arabic بِذَاتِهَا as "by themselves" seems to me to be in order. Note that rendering the term into "by their essence" (as done in E.E. Calverley and J.W. Pollock, trans., "Nature, Man and God in Medieval Islam" [Brill: Leiden, 2002], 1:88-90) would suggest falsely that the subsequent mention of لَا بِالعَرَضِ in definitions of syllogism is a clarificatory reiteration. The Arabic Aristotelians did not consider it as such, but as an independent condition. It is also far from clear what the "essence" of two premises would be.] |
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بواسطة |
bi-wāsiṭa
by mediation
[A pair of premises that is not formally productive of a conclusion but becomes formally productive with the addition of a further premise is said to imply the conclusion "by the mediation" of that further premise, as opposed to implying the conclusion "by itself." The term was also used in slightly different contexts to modify other things than "implication" (لزوم). For example, some logicians distinguished the above-mentioned sense -- which they called "mediation in the obtaining of the implication" (الواسطة في الثبوت) -- from "mediation in proving the implication" (الواسطة في الإثبات). The latter is required in any syllogism that is not self-evidently productive but needs a proof. Logicians could also state that the judgment made in the major premise "transmits" to the minor term "by the mediation" of the middle-term. In the important discussion of relational inferences by Dawānī, it is said that in the true relational proposition "To the world there is a composer" the predicate "composer" is true of the subject "world" by the mediation of the preposition "to."] |
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حمليّ |
ḥamlī
categorical
[A categorical proposition asserts that a predicate belongs or does not belong to a subject. It is opposed to "hypothetical" propositions which have the form "Either ... or" or "If ... then." A categorical syllogism is a syllogism consisting of categorical premises.] |
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قياس اقترانيّ |
qiyās iqtirānī
combinatorial syllogism
[In a combinatorial syllogism, the parts of the conclusion have not been presented together in the premises, but are only brought together in the conclusion. This distinguishes it from so-called "reduplicative syllogisms" in which the conclusion or its negation has already appeared as part of the conditional or disjunctive premise. The category of "combinatorial syllogism" includes both (i) the combinatorial categorical syllogism (القياس الاقترانيّ الحمليّ), i.e. the standard Aristotelian syllogisms and (ii) the combinatorial hypothetical syllogism (القياس الاقترانيّ الشرطيّ), for example what Western logicians called the "purely hypothetical syllogism" such as "If P then Q & If Q then R, so If P then R". For the translation of اقتران as "combination," see J. Lameer, "Al-Fārābī and Aristotelian Syllogistics," 80-82. |
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تأليف |
taʾlīf
composition
[Often used interchangeably with "formation" (تركيب). Definitions of syllogism typically stated that it is a statement "composed" or "formed" of two propositions that "by itself" implies another statement.] |
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برهان |
burhān
demonstration
[A syllogism in which the premises are known with certainty to be true, being self-evident or proven. This is at least a minimal definition accepted by practically all logicians writing in Arabic. It was common, though, to add further divisions depending on the causal or epistemic relation between the three terms of the premise-pair.]
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نتيجة |
natīja
conclusion |
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الشرطيّة المتصلة |
ash-sharṭiyya al-muttaṣila
conditional
[A subdivision of the hypothetical proposition, covering propositions with the form "If ... then".] |
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رابطة |
rābiṭa
copula
[The third element in a statement, linking the subject-term and predicate-term. It indicates the "relation" (نسبة) between the subject and predicate in a proposition. Logicians writing in Arabic were faced with the problem that Arabic lacks the copulative "is," by contrast to Greek (esti) or Persian (ast). They tended to say that the copula is implicitly understood even when not expressed.] |
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مطلوب |
maṭlūb
desired conclusion |
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الشرطيّة المنفصلة |
ash-sharṭiyya al-munfaṣila
disjunction
[A subdivision of the hypothetical proposition, covering propositions with the form "Either ... or".] |
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مقدّمة خارجيّة |
muqaddima khārijiyya
extraneous premise
[A premise that is not explicitly mentioned but which needs to be added to a pair of premises before they imply a desired conclusion. Arabic logicians tended to use this term interchangeably with the term "imported premise" (مقدمة غريبة) or or one of its subdivisions: "extrinsic premise" (مقدمة أجنبية).
This use of خارجية should not be confused with خارجية as opposed to حقيقية. A خارجية premise in the latter sense is a categorical proposition with existential import, i.e. the subject term is held to include extra-mentally existing entities of which it is true. By contrast, a حقيقية proposition is a categorical proposition in which the subject-term includes entities of which it is true if they exist.] |
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طرف |
ṭaraf
extreme
[The two terms in a syllogism that are not the middle-term and that are brought together to form the conclusion.] |
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مقدمة أجنبيّة |
muqaddima ajnabiyya
extrinsic premise
[A premise that is not explicitly mentioned and which is not logically implied by any of the premises either. Classical handbooks on logic from the 13th and 14th century tended to present "extrinsic premise" as a subdivision of "imported premise" (مقدمة غريبة), being distinguished from other "imported premises" by the fact that it is not formally implied by either of the explicitly mentioned premises. This was a topic of contention, however. A number of logicians rejected the idea that a premise could count as "imported" even though it is not extrinsic but logically implied by one of the original premises. On this account, the distinction between the "extrinsic" and the "imported" premise collapses. Both terms were used interchangeably with "extraneous premise" (مقدمة خارجيّة). |
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شكل |
shakl
figure
[The figure of a standard Aristotelian syllogism is determined by the position of the middle-term (الأوسط) in the premises. If it is the predicate of the minor premise and the subject of the major premise, then the syllogism is in the first figure. If it is predicate of both premises, then the syllogism is in the second figure. If it is the subject in both premises, then the syllogism is in the third figure. If it is the subject of the minor premise and the predicate of the major premise then the syllogism is in the fourth figure. The fourth figure was not recognized by the early Arabic Aristotelians. One of the first to recognize it in the Arabic tradition was Ibn al-Sārī (d. 1153), and its common acceptance from the 13th century was due to its recognition by Fakhr ad-Dīn ar-Rāzī (d. 1210).] |
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صورة |
ṣūra
form
[The form of a syllogism is what remains after the uniform substitution of the terms (حدود) of the syllogism with schematic letters. Thus the argument "Every human is a mammal & Every mammal is an animal, so Every human is an animal" has the form "Every J is B & Every B is A, so Every J is A". Sometimes used interchangeably with "structure of the composition" (هيئة التأليف). Its opposing concept is that of "matter" (مادة).] |
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شرطيّ |
sharṭī
hypothetical
[A hypothetical proposition (قضيّة شرطيّة) is a disjunction or conditional, as opposed to a categorical (حمليّ) proposition. A hypothetical syllogism (قياس شرطيّ) is one of the Stoic schemata of propositional logic: modus ponens, modus tollens, and disjunctive syllogism. The latter expression tended to be replaced by "reduplicative syllogism" (قياس استثنائيّ) in the Avicennian and post-Avicennian tradition.] |
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لزوم |
luzūm
implication
[The following of one or more propositions from one or more other propositions. The relation was said to obtain between a proposition and for example its converse; between premises and conclusion in a valid argument; and between antecedent and consequent in a non-coincidentally true conditional (متصلة لزوميّة). Arabic-Islamic logicians distinguished between what implies (الملزوم) and what is implied (اللازم). Later Christian-Arabic logicians used الملزوم for what is implied, and اللازم of what implies.] |
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مقدمة غريبة |
muqaddima gharība
imported premise
[A premise that needs to be added to a pair of premises before they imply a desired conclusion. The classical Arabic handbooks of logic from the 13th and 14th centuries subdivided "imported premises" into (i) "extrinsic" (أجنبيّة), which is not implied by any of the original premises, and (ii) "non-extrinsic" (غير أجنبيّة), which is implied by the original premises but which does not have terms in common with them -- the latter would apply specifically to the case of proving a syllogism productive by contraposition of one of the premises. Some logicians expressed reservations about the idea that a proposition should be considered to be "imported" even though it is logically implied by one of the premises. This reservation would in effect annul the distinction between "imported" and "extrinsic." |
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اطّراد |
iṭṭirād
invariance
[Traditionally used in Islamic juridical discourse of the condition that a definition must be such that whenever it is satisfied then so is the definiendum. It was used by later logicians of formal syllogistic productivity. In a formally productive syllogism, the following of a conclusion is "invariant" (muṭṭarid مطّرد) in all matter, in the sense that there are no counter-examples with the same form in which the premises are true and the conclusion false.] |
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حُكم |
ḥukm
judgment |
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المقدمة الكبرى |
al-muqaddima al-kubrā
major premise
[The premise of a classic Aristotelian syllogism that includes the major term.] |
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الحدّ الأكبر |
al-ḥadd al-akbar
major term
[The predicate of the conclusion of a syllogism.] |
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الحدّ الأوسط |
al-ḥadd al-awsaṭ
middle term
[The term that repeats in both premises of a classic Aristotelian syllogism and that is left out of the conclusion.] |
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المقدمة الصغرى |
al-muqaddima aṣ-ṣughrā
minor premise
[The premise of a classic Aristotelian syllogism that includes the minor term.] |
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الحدّ الأصغر |
al-ḥadd al-aṣghar
minor term
[The subject of the conclusion of a syllogism.] |
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ضرب |
ḍarb
mood
[The mood of a figure of the syllogism is determined by the quality and quantity of the premises. If for example the premises of a first-figure syllogism are both universal and affirmative, then the first-figure syllogism is in the first mood.] |
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قضيّة طبيعيّة |
qaḍiyya ṭabīʿiyya
natural proposition
[A categorical proposition in which the subject-term stands for a "nature" rather than the particulars that fall under the subject-term, for example "Human is a species".] |
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قضيّة سالبة |
qaḍiyya sāliba
negative proposition |
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تخلّف |
takhalluf
non-following
[Opposed to "implication" (لزوم)] |
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قضيّة جزئيّة |
qaḍiyya juzʾiyya
particular proposition
[A proposition in which the subject-term is modified by a particular quantifier, for example "Some human is literate".] |
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محمول |
maḥmūl
predicate |
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مقدمة |
muqaddima
premise |
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إنتاج |
intāj
productivity
[A characteristic of syllogisms in which the conclusion is implied by the premises. It is a narrower concept than "implication" (لزوم), since it only applied to syllogisms. Its opposing concept is "sterility" (ʿuqm عقم).] |
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قضيّة |
qaḍiyya
proposition |
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دليل |
dalīl
proof
[In logic, the term دليل could be used in two related senses: (i) in the narrow sense of a step-by-step derivation of a proposition from other propositions -- in this sense it was used interchangeably with the term بيان ; (ii) a generic term covering syllogism (قياس), induction (استقراع) and analogy (تمثيل) -- in this sense it was used interchangeably with "argument" (حُجّة).] |
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قضيّة مسوّرة - قضيّة محصورة |
qaḍiyya musawwara or qaḍiyya maḥṣūra
quantified proposition
[A categorical proposition is quantified if it is indicated whether the judgment pertains to all or some of the particulars that fall under the universal subject-term -- for example "Every human is an animal" or "Some human is literate." The Avicennian tradition also used "quantifiers" (أسوار , the plural of سور) of hypothetical propositions, for example: "Always (دائمًا): If this is a human then it is an animal" or "It may be (قَدْ يَكُوْنُ): If this is an animal then it is a human".] |
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إرجاع |
irjāʿ
reduction
[Either the recasting of an argument into explicit syllogistic form, or the recasting of a syllogistic figure in a more evident figure by means of converting or reordering the premises. In the former sense, إرجاع is used interchangeably with تحليل , in the latter sense with رَدّ .] |
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استثنائيّ |
istithnāʾī
reduplicative
[A subdivision of syllogism, used of the Stoic schemata of propositional logic modus tollens, modus ponens, and disjunctive syllogism, and thus corresponding to what the early Arabic Aristotelians called "hypothetical syllogism" (قياس شرطيّ). The term "reduplicative" tended to be preferred by Avicennian and post-Avicennian logicians, since they recognized syllogisms involving hypothetical premises other than the Stoic schemata, for example a syllogism with the form: "If P then Q & If Q then R, so If P then R". On their account, the distinctive feature of "reduplicative" syllogisms is not that one of the premises is hypothetical, but rather that one of its premises is a conditional or disjunction and the other premise is an affirmation or denial of one of the parts of the conditional or disjunction. Arabic logicians themselves often assumed that such syllogisms were called استثنائيّ because the hypothetical premise is followed by a "particle of exception" (حرف استثناء) -- "but" (لكن) -- that introduces the categorical premise. It has been argued convincingly, however, that the term استثناء (translating the Greek πρόσφεσις) was originally intended to convey the idea that the categorical premise in such a syllogism is a "reduplication" (استثناء) of a part of the hypothetical premise (see K. Gyekye, "The Term Istithnāʾ in Arabic Logic," Journal of the American Oriental Society 92 (1972): 88-92).] |
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نسبة |
nisba
relation
[The term نسبة was standardly applied to the "relation" between subject and predicate in a categorical proposition. As such the نسبة was considered to be the third element in any categorical proposition, besides the subject and the predicate. It was held to be indicated linguistically by a "copula" ( رابطة ) in some languages (Greek and Persian) and implicitly understood in others (Arabic). In this sense, all categorical propositions express a نسبة . The term نسبة was also used of a relational property such as "owner of money" or "brother of a writer" or "equal to B." This latter meaning is presupposed, for example, in Samarqandī's using the term قياس النسبة of "relational syllogisms," and his explication of the validity of such syllogisms by invoking the principle that المُنْتَسِبُ إِلَى مُنْتَسِبٍ آخَرٍ بِنِسْبَةٍ مُنْتَسِبٌ إِلَى تِلْكَ النِّسْبَة . This implies that in a proposition such as "A is equal to B" there are two "relations": (1) the subject-predicate "relation" indicated by the copula, and (2) the "relation" indicated by the relational predicate. This analysis is also clear when Khūnajī, for example, wrote that in a proposition with predicates such as "owner of money" (ذو مال), a نسبة is the predicate. This again implies that in such propositions there is (i) a subject, (ii) a subject-predicate "relation," and (iii) a relational predicate. Both the second and third element would be referred to as نسبة . The term إضافة tended to be used of the Aristotelian category of "relation".] |
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متعلّق |
mutaʿalliq
semantic dependent
[A grammatical term that would include several types of modifiers of the subject or predicate of a sentence, for example: a prepositional phrase ("Zayd is going to the house"); an adjective or adverb ("Every human is a rational animal"); and the second part of a construction ("He is a writer's son"). From the 14th century and on, logicians writing in Arabic tended to invoke this grammatical term in their analysis of the premises of the "syllogism of equality." Instead of considering that the proposition "A is equal to B" has simple subject-predicate form with "A" as subject and "equal to B" as predicate, they tended to see "equal" as the predicate and "B" as the semantic dependent of the predicate. Though clearly influenced by the grammatical tradition, logicians considered "B" alone to be the semantic dependent, with the preposition serving as the link between semantic dependent and predicate. Some logicians used the term "semantic dependent" interchangeably with the term "qualifier" (qayd قيد).] |
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قضيّة شخصيّة |
qaḍiyya shakhṣiyya
singular proposition
[A categorical proposition in which the subject-term denotes a particular rather than a universal, for example "Zayd is human".] |
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قول |
qawl
statement |
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موضوع |
mawḍūʿ
subject |
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مقدمة مطويّة |
muqaddima maṭwiyya
suppressed premise
[Used interchangeably with muqaddima muḍmara ( مقدمة مضمرة ), i.e. a premise that is implicitly understood along with the explicitly stated premises.] |
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قياس |
qiyās
syllogism
[In logic, a pair of premises that implies formally or "by itself" another proposition. In the Arabic logical tradition, a syllogism is the premises that imply a conclusion; it is not the whole consisting of premises plus conclusion (the latter was the usual understanding in the Western logical tradition and among early-modern Catholic Arab scholars trained in the Latin tradition). It should be noted that قياس was used in the Islamic juridical tradition as "analogy," which was called تمثيل in the logical tradition.] |
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حدّ |
ḥadd
term
[The subject or predicate of a premise in a syllogism. A paradigmatic Aristotelian syllogism has three and only three terms, one of which -- the "middle term" -- recurs in both premises. Ḥadd حدّ was also the standard term for "definition".] |
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قضيّة كلّيّة |
qaḍiyya kulliyya
universal proposition
[A proposition in which the subject-term is modified by a universal quantifier, for example "Every human is an animal".] |
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قضيّة مهملة |
qaḍiyya muhmala
unquantified proposition
[A proposition in which the subject-term is a universal (as opposed to a singular term) and stands for the particulars falling under it (as opposed to the concept itself), but which lacks a quantifier, for example "Arabs are generous".] |
