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Ibn Sīnā on analysis: 1. Proof search. Or: Abstract State Machines as a tool for history of logic
"... and I have removed some personal references. The 11th century ArabicPersian logician Ibn Sīnā (Avicenna) in section 9.6 of his book Qiyās gives what appears to be a proof search algorithm for syllogisms. We confirm that it is indeed a proof search State Machine from Ibn Sīnā’s text. The paper also ..."
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and I have removed some personal references. The 11th century ArabicPersian logician Ibn Sīnā (Avicenna) in section 9.6 of his book Qiyās gives what appears to be a proof search algorithm for syllogisms. We confirm that it is indeed a proof search State Machine from Ibn Sīnā’s text. The paper also contains a translation of the passage from Ibn Sina’s Arabic, and some notes on the text and translation. 1
The grammar of meanings in Ibn Sīnā and
, 2013
"... This is not yet the paper; in fact it is barely more than a set of notes. But in submitting a precis of the paper to the journal AlMukhtabat I undertook to make the acknowledgements and references available here. It will turn into a proper paper covering all the required references as soon as I can ..."
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This is not yet the paper; in fact it is barely more than a set of notes. But in submitting a precis of the paper to the journal AlMukhtabat I undertook to make the acknowledgements and references available here. It will turn into a proper paper covering all the required references as soon as I can manage. The listing follows the sections of the precis. I thank Manuela Giolfo, Ahmad Hasnaoui, Amirouche Moktefi, Zia Movahed and Kees Versteegh for information, corrections and comments that relate directly to things discussed below. I should also thank Kais Dukes of the Arabic Language Computing group at Leeds University, who sent me some very useful information before going silent — I hope I didn’t make myself a nuisance to him. None of these people are responsible for any errors of fact or judgment below. 1 Ibn Sīnā and Frege as logicians Gottlob Frege’s books Begriffsschrift [8] and Grundgesetze der Arithmetik [13] mark the beginning and the end of his main involvement with giving formal proofs for arithmetical truths. Ibn Sīnā’s logical writings are in nearly all cases first sections of works covering other disciplines as well. Gutas ([20] Chapter 2) discusses and defends what is now the standard dating of these works. The earliest that I use is Kitāb alNajāt [37], or Najāt for short, which was written in around 1 1013 when Ibn Sīnā was around 33, but it was published a dozen or so years later, probably after some light editing. His major surviving work in logic is the first few volumes of his encyclopedic ˇSifā’, which take the form of commentaries on Aristotle’s Organon and were written in the early to mid 1020s. From this work we will use Madk al [29] (commentary on Porphyry’s
Ibn Sīnā on Logical Analysis
"... 1.2 Colleagues and students..................... 5 1.3 The commentary tradition.................... 5 ..."
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1.2 Colleagues and students..................... 5 1.3 The commentary tradition.................... 5
1 In memory of Maria Panteki How Boole broke through the top syntactic level
, 2010
"... 1984. In that year the college was closed down, and the assets and records of its Mathematics department were scattered around London University. Last year I was involved in an unsuccessful attempt to track some of them down. So I think it would be hopeless to try to dig out the official records on ..."
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1984. In that year the college was closed down, and the assets and records of its Mathematics department were scattered around London University. Last year I was involved in an unsuccessful attempt to track some of them down. So I think it would be hopeless to try to dig out the official records on Maria, and I have to rely on memory. She was a lively member of my Universal Algebra class. I'm told she had attended my Logic class before that, but it was a large class and I confess I don't remember. She was a close friend of my PhD student Cornelia Kalfa, and the two later became colleagues on the staff of the Aristotle University of Thessaloniki. To me as a logician it has been a particular point of pride that two logicians at the Aristotle University were students of mine. She moved on from Bedford College to work with Ivor GrattanGuinness on a group of mid nineteenthcentury British mathematicians, some but not all of whom were also logicians. Her work in this field has become well known and justly praised for its scholarship and its penetration. She was an eager correspondent, and over the
Ibn Sīnā on reductio ad absurdum
"... This paper studies the analysis of reductio ad absurdum by Ibn Sīnā (known to the Latin West as Avicenna), who was born in 980 in a village near the Bactrian town of Balkh on the Silk Road, and died in 1037 after a career spent moving around within the present boundaries of Iran. References to Ibn S ..."
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This paper studies the analysis of reductio ad absurdum by Ibn Sīnā (known to the Latin West as Avicenna), who was born in 980 in a village near the Bactrian town of Balkh on the Silk Road, and died in 1037 after a career spent moving around within the present boundaries of Iran. References to Ibn Sīnā’s writings are to his Arabic texts listed in the bibliography, and are given in the format page.line. References to the text translated from Qiyās [14] at the end of this paper are marked with an asterisk 1 The argument form in question We should start with what Ibn Sīnā calls the ‘usual ’ ( c āda) form of proof by reductio ad absurdum (Qiyās [14] 410.13?). He gives an example at (38) below: (1) Not not every C is a B Every C is a B Every B is an A Every C is an A (Not every C is an A) Not every C is a B Ibn Sīnā’s description omits the premise ‘Not every C is an A’. But we can see that it is needed in order to get a contradiction from ‘Every C is an A’, and in fact Ibn Sīnā does include the premise in his fuller analysis at (26). This is only one example. Ibn Sīnā was certainly well aware that reductio arguments can include many more steps than this. So it seems reasonable to assume that the syllogism from ‘Every C is a B ’ and ‘Every B is an 1 A ’ to ‘Every C is an A ’ is proxy for an arbitrarily complicated derivation, for example a derivation of from and a set of assumptions. Also Ibn Sīnā gives the form for proving a negated conclusion, and this allows him to remove a double negation at the top of the derivation. If the conclusion was not negated this step would be missing. So we have two general forms:
Ibn Sīnā’s view of the practice of logic
, 2010
"... In the last half century Ibrahim Madkour revolutionised the study of Arabic logic by making available a modern edition of the text of the Logic section of Ibn Sīnā’s ˇSifā’. Ibn Sīnā’s account of logic in the ˇSifā ’ is much fuller than any of his other surviving accounts; it runs to some two thousa ..."
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In the last half century Ibrahim Madkour revolutionised the study of Arabic logic by making available a modern edition of the text of the Logic section of Ibn Sīnā’s ˇSifā’. Ibn Sīnā’s account of logic in the ˇSifā ’ is much fuller than any of his other surviving accounts; it runs to some two thousand pages. It is also — in my view — more radical and more independent of Aristotle than his other accounts of logic, though the Logic section of his Maˇsriqiyyūn comes close. In this talk I want to take up some important aspects of logic that are discussed in several places in the ˇSifā ’ but hardly at all in Ibn Sīnā’s other known logical works. The basic question is this. Logic is a skill, and Ibn Sīnā means to teach this skill. But how does Ibn Sīnā expect his students to apply this skill in practice? What exactly are they supposed to be able to do after this teaching that they couldn’t do before? What is the aim of the exercise? A fundamental principle in history of science is that you can’t properly assess the work of a past scientist if you don’t know what questions that