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My only formal exposure to Logic is from an Arabic text book, where five methods for proving and/or convincing an opponent of your argument was described.

These methods are termed "the five crafts" and consist of:

  • demonstrative/proof
  • dialectic
  • rhetorical
  • poetic
  • sophistic/fallacy

I've looked in a few English text books, and while they may mention one or two of the methods above, I've not seen any reference to all five as a whole. Is there an equivalent phrase in English?

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    They date back to Aristotle but today formal logic is only demonstartive (+ fallacies), while rhetoric and poetic are not more part of "logical disciplines". – Mauro ALLEGRANZA Mar 14 '16 at 16:37
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    For the Western Medieval tradition, see Trivium: the part of the seven liberal arts composed of: grammar, logic, and rhetoric. – Mauro ALLEGRANZA Mar 14 '16 at 16:42
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    I would translate "لصناعات الخمس" as the "five crafts" not the "five arts". – Alexander S King Mar 14 '16 at 18:09
  • Just out of curiousity, what is the textbook you're using? This "five arts/crafts" sounds highly suspicious to me. I suspect it's a 19th century coinage. And if you can provide the Arabic terms that would be helpful. – user20153 Apr 30 '16 at 1:27
  • @mobileink The textbook is simply called "al-Mantiq" by Muhammad Ridha al-Muzhaffer, but commonly known as Mantiq al-Muzhaffer (منطق المظفر). It's the standard textbook for Logic used in Islamic seminaries across the middle-east. The terms (in the same order as above) are: البرهان، الجدل، الخطابة، الشعر، المغالطة – Adnan May 2 '16 at 15:25
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These appear to originate with Avicenna, and not to have been communicated to the West in a lasting way.

They may be a tuning and clarification of Cicero's Five Canons of Rhetoric: construction, arrangement, style, memorability, and performance.

Each of your listed arts, in turn, seems to be dominated by the corresponding canon of Cicero, with less emphasis on potential political deployments than educational ones.

It seems to me that:

  • The heart of proof is knowing your argument is well constructed.

  • The heart of dialectic is arranging your argument in a way that speaks to others.

  • The central art of rhetoric itself, as a domain separate from logic, is about style.

  • Poetry is deployed as a mnemonic device, not only for your own ability to stay on track, but so that your words remain with your listener when you are done.

  • And performance, applying charisma, is the part of the process where sophism has the most chance.

  • Quite an unconvincing attempt to appropriate Arabic thought by claiming it is based on a European precedent. – user8284 Mar 16 '16 at 10:41
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    @jwg: As ancient greek philosophy is known to us westeners mainly through arabic scholars, I find this rant to be quite amusing, trying to highlight an independence that seems hard to maintain looking at historical facts.. – Philip Klöcking Mar 16 '16 at 16:48
  • The "poetry" craft might also be analogous to how elegance is seen as important in mathematics - it's widely agreed that a beautiful and simple proof is "better" than a obfuscated and verbose one, even if both prove the same theorem to your full (logical) satisfaction. – Derek Janni Mar 16 '16 at 17:42
  • @jwg I am not dismissing what is original in Arabic thought, but it is not just Europeans who spent most of their time improving and refining Greek philosophy and its Roman offshoots. Avicenna was an expert on Aristotle, and a Neoplatonist. Cicero was an Academic, from the school descended from Plato. It does not seem unlikely that someone seeking an intermediate position between Plato and Aristotle would read Academic writers. – jobermark Mar 17 '16 at 14:35
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    @DerekJanni As something of a neo-Intuitionist, I think there is a firmer basis for the aesthetic end of mathematics, separate from its relationship to rhetoric: philosophy.stackexchange.com/a/32969/9166 -- Besides, I think the elegance you are talking about is actually part of 'arrangement' or dialectic. If there is 'poetry' in math it is in choosing names and in constructing notations that guide usage. – jobermark Mar 17 '16 at 14:38

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