Abstract
The Arabic logicians traditionally divide logic into two parts as witnessed by Tony Street in his article “Arabic and Islamic Philosophy of Language and Logic” ([139]).
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Notes
- 1.
Sībawayhī is considered as the founder of Arabic grammar. His distinction has been challenged by some other grammarians, but it resisted all the criticisms and seems to be still admitted nowadays by the contemporary grammarians.
- 2.
- 3.
See the whole classification and its analysis in [52].
- 4.
- 5.
- 6.
The vowels A, E, I, and O are not used by the Arabic logicians, who do not name the quantified propositions. We have introduced them only for convenience.
- 7.
I owe this reference (and many other ones) to Prof. Wilfrid Hodges. I thank him very much for his help and his fruitful and numerous suggestions and remarks which made me improve significantly my work.
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- 9.
- 10.
The root used by Ikhwān aṣ-ṣafā is “ṭāla” (see [150]), which evokes the ideas of length and of superiority. So maybe subalternation is what relates one “superior” proposition (the universal one) to its inferior dependent one (the particular).
- 11.
I thank Prof. Hodges for bringing my attention to this text and providing me with Gutas’ book.
- 12.
The usual translation of the Arabic adverb “dā’iman” is “always”. However, when one scrutinizes closely the text, one notes that what is meant by Avicenna when he says “dā’iman” is not “always” or “perpetually” (i.e., forever or for a long time), rather it is “permanently as long as the thing exists.” This is why one has to be careful when translating the adverb “dā’iman” (contained in some propositions) or the adjective “dā’im”, because 1. Avicenna calls “dā’im” the sentences containing “as long as it exists” and not another kind of sentences containing “always”, which would be different from them, despite the fact that the text is not always clear (I thank Prof. Hodges for bringing my attention to that particular point), and 2. this condition (as long as it exists) means “continuously” (or “permanently” where the permanence is understood just as the continuous link between the subject and the predicate, not the fact that the subject satisfies the predicate forever or for a very long time), since the idea stressed by Avicenna is not the length of the duration but the duration itself (even if it is in some cases short as when we talk about some insects which live only a few days and say “Some insects are invertebrate (as long as they exist)” (personal example), i.e., the fact that the link between the subject and the predicate is continuous and not discontinuous or present only at some specific periods (as for the eclipse of the moon, for instance).
- 13.
I thank Prof. Hodges for bringing my attention to this passage and other ones where the same idea is stressed by Avicenna.
- 14.
Of course, one could object that these snows are also conditioned by the very existence of the mountains. But the reason why they are called “perpetual” is not the existence of the mountains, rather it is the fact that they are always there, whether in winter or in summer. So people who live in these areas have always seen them in all seasons, given that these snows don’t disappear in the summer unlike the snow on the ground which is present only in the cold season(s). They thus stress the length of the duration by using the word “perpetual”. Note that in French, they are called “neiges éternelles” (i.e., eternal, not only perpetual).
- 15.
W. Hodges provides formalizations of these propositions which he calls two-dimensional propositions in his book Mathematical Background to the Logic of Ibn Sina (see [92], 157ff), where he uses time quantifiers and shows that the general absolutes containing “at some times” contradict the propositions containing the condition “as long as they exist,” provided they do not have the same quality nor the same quantity.
- 16.
In this treatise, these propositions are abandoned as shown in [60].
- 17.
The full formalizations of these temporal propositions can be found in W. Hodges ([92], 159ff).
- 18.
For instance, Saloua Chatti (see [53], 332–354) deals with modal oppositions and presents a dodecagon containing the whole set of propositions held by Avicenna and their relations. Tony Street (see [137]) gives the whole set of propositions held by Avicenna and their contradictories. All these propositions give rise to several squares of oppositions which are presented in [54], but Avicenna does not draw any figure at all.
- 19.
I am indebted to Dr. Lorenz Demey for having drawn my attention to that particular feature of the two negative special absolutes , which differ in this respect from the two affirmative ones. I thank him for his enlightening observation.
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- 21.
- 22.
I owe this remark to Prof. Wilfrid Hodges whom I thank for his comments and suggestions.
- 23.
Abderrahman Badawi, Manṭiq Arisṭu, volume 1, Dar al Kalam, Beirut 1980. The two volumes of this book contain the old Arabic translations of the main Aristotle’s treatises. Volume 1 contains 1. Al-Maqūlāt (Categories, translation Isḥāq ibn Ḥunayn, pp. 33–98), 2. Kitāb al-‘Ibāra (De Interpretatione, translation Isḥāq ibn Ḥunayn, pp. 99–136), 3. Kitāb al-Taḥlīlāt al-ʼŪlā (Prior Analytics, translation Tayadurus, corrected by Ḥunayn ibn Isḥāq, pp. 137–316), while the volume 2 contains 1. al-Taḥlīlāt al -Thāniya or Al-Burhān (Posterior Analytics, translation Ishaq ibn Hunayn from Greek to Syriac and Abu Bishr Mattā from Syriac to Arabic, pp. 329–485), 2. Kitāb al-Tupīqā (Topics, translation Abu Uthmān al-Dimishqi, pp. 489–595).
- 24.
The name Barbara as well as the other names of the syllogistic moods is not in al-Fārābī, since their origin is, as is well known, Latin. Note that neither of the logicians of the Arabic tradition gives names to the moods, they only enumerate them, by saying: the first mood of the first figure, the second mood of the first figure, etc. We use the usual names here only for convenience.
- 25.
“Dire que le prédicat A (ύπάρχει) appartient au sujet B, c’est évidemment s’exprimer intensivement, car en extension c’est au contraire B c’est-à-dire l’espèce, qui appartient à A, c’est-à-dire au genre, comme y étant incluse”.
- 26.
“Sans doute le schème de Barbara sera toujours le même, que l’on interprète l’inclusion des concepts en extension ou en compréhension”.
- 27.
As a matter of fact, although al-Fārābī does not say it and presumably is not aware of it, they apply only to Barbara, for even Darii may contain a minor whose extension is larger than its major, since its second premise is particular, for instance, in the following example: “every human is an animal, some living beings are human; therefore some living beings are animals,” where the extension of the minor “living being,” which includes plants apart from animals is larger than the extension of the major (animal) and of the middle (human), which both are parts of it. As to Celarent and Ferio, where some propositions are negative, the middle is not included in the major, as shown in the example illustrating Celarent below.
- 28.
Professor Hodges is talking about Avicenna’s ekthetic proof in his article and he justifies Avicenna’s use of it by saying what follows: “Ibn Sīnā violates this picture by introducing a step where the conclusion of the step is not a logical consequence of the premises of the step, but it doesn’t matter because the conclusion of the proof as a whole is a logical consequence of the premises of the proof” ([87], 17–18). However, according to him, this justification does not apply to al-Fārābī’s proof, which does not rely on the same conception of the logical deduction.
- 29.
On the notion of form, see [62].
- 30.
This author has been considered by some people as being Alexander of Aphrodisias, but Tony Street has shown in an article entitled “‘The eminent later scholar’ in Avicenna’s Book of the Syllogism”, Arabic Sciences and Philosophy ([135], 205–218) that he is in fact al-Fārābī, by providing convincing arguments.
- 31.
For more details about the formalizations of these propositions, see W. Hodges ([92], 159).
- 32.
There is an error here, for what is written in the text is “No C is D”, but this could not be so, first because Avicenna does not use in that second proof the letter D at all, second because “No C is D” is not deducible by Celarent from the two premises given, and it is not itself contradictory.
- 33.
As we will see below (Sect. 4.3.1.1), the two A propositions are named, respectively, Ap and As, the only difference between them being the conditions they contain. The same remark applies to I-conversion , which is expressed in two ways too, depending on the conditions contained in the initial I propositions.
- 34.
- 35.
Here too, there is an error in al-Qiyās, for what is written in that treatise is the word aḥsin (= the best) instead of akhass (= the least). This is why we also cite al-Najāt, where there is no error, and the right word is used.
- 36.
See for instance, ([62], 4), where it is said: “…But he (is right in) blaming Hospinianus for having identified the singula r propositions with the particulars, and he shows that they are, on the contrary, equivalent to the universals, given that the subject, in these propositions, is taken in the totality of its extension” (my translation).
- 37.
Arnault, Antoine & Nicole, Pierre ([25], 158) say: “although the singular proposition is different from the universal one in that its subject is not general, it is nevertheless closer to the universal than to the particular; because its subject, being individual, is for this very reason, necessarily taken in all its extension, which is the essence of a universal proposition and distinguishes it from the particular” ([25], my translation).
- 38.
In stating these examples, we have started with the minor premise , as Avicenna does.
- 39.
The commentary that we can find in the French Edition of Prior Analytics mentions many sources, where this extensionalist view is criticized. The editor says: “The modern logicians of the school of Lachelier, Rodier and Hamelin (Le système d’Aristote, pp. 178ff) blame Aristotle for having abandoned the comprehensivist point of view in favor of the extensionalist view.” ([21], note 1, p. 2, my translation)
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Chatti, S. (2019). Categorical Logic. In: Arabic Logic from al-Fārābī to Averroes . Studies in Universal Logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-27466-5_3
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