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Arabic and Mathematics

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1 Arabic and Mathematics on Wed Aug 05, 2009 3:59 pm

الماس

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السلام عليكم

I am sure the Mathematicians amongst us will be able to keep this topic alive as there is much to say about the factuality of logical inference and the light cast from it over grammatical structures in Arabic. Here is an interesting read about what Abu Nasr al-Farabi (870-950 CE) has to say...

Al-Farabi: On Logic vs. Grammar.

"When by ourselves we wish to verify the truth of a judgment, we think and inform ourselves, and set up in ourselves the matters and concepts that serve to verify that judgment. When we do this with someone else, we perform the speech though which such matters and concepts may be understood.

"It is not possible to verify any judgment we may come to using just any concepts we happen to have, nor can we disregard their number nor the condition, composition and order in which we find them. Rather, for every judgment we seek to verify, we need matters and concepts which are well-defined, known quantities, and determination of condition, composition and order. This requires that the state of the words that express these be in the same state as the words we submit to one another for verification. For this, we need rules concerning our concepts as well as our expressions for them, in order to protect us from error. These two things – I mean concepts and the words which express them – are what the ancients called logos and speech. 'Intelligibles' are what they called the internal speech and logos implanted in the soul, whose outward expression is spoken speech and logos. When he is by himself, the speech which a man uses in order to verify a judgment is that which is implanted in his soul. When he does it with someone else, he gives voice to outward speech. The kind of speech that creates analogies in order to verify judgments is called 'syllogism,' whether its terms are implanted in the soul or spoken aloud. And logic imposes the above-mentioned rules on both types of speech.

"Logic shares with grammar its function of giving rules for utterances, but insofar as grammar gives rules for the utterances of a given nation, the science of logic is different since its rules govern the utterances of every nation. Now words present certain aspects that are the same for all nations, such as whether they are simple or compound, whether they are nouns, verbs or particles, whether or not they are endowed with meter, etc. But language differs from language in many ways: its case endings and article usage are only two of many features by which Arabic is distinguished from other languages. Every language is distinguished in ways like these. The domain of grammar does include features common to the utterances of every nation, but those who practice it take them up as encountered in terms of the language in which they happen to be working."

"By contrast, when logic gives rules for the use of words it does so for the words of every nation, which it takes up in their common aspects, avoiding those which are specific to one nation in particular. When logic does take up an expression specific to a given language, however, it does so according to the grammatical authorities on that language.

"As for the rubric 'logic,' the totality of its meaning is clearly announced in that it is derived from logos, a word said by the ancients to mean three different things:

1. Outward speech, spoken aloud. Its expression is made possible by the tongue.
2. The speech that is implanted in the soul, made up of the intelligibles that words signify.
3. The spiritual faculty instilled in man, by which he is distinguished from the other animals, and through which the intelligibles arise for him, together with the sciences and the arts. It makes judgment possible, and moral distinctions between good and bad actions. All men have this -- even children, though in children it is trifling since it cannot yet carry out all its functions. In this it is like the child's leg not wholly fit for walking, or a fire of low intensity which cannot yet ignite the palm branch. Even drunks and crazy people have it, though in them its purview is narrowed, and in the sleeper it has gone out. For the sufferer of a petit mal it is as if a veil had come between him and it."

From: Catalogue of the Sciences, ch. 2

If you love Mathematics, keep posting!

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2 Article - From Arabic to Mathematics on Wed Aug 05, 2009 4:12 pm

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