Traditional Logic, Modern Logic and Natural Language

  title={Traditional Logic, Modern Logic and Natural Language},
  author={Wilfrid Hodges},
  journal={Journal of Philosophical Logic},
  • W. Hodges
  • Published 14 October 2009
  • Philosophy
  • Journal of Philosophical Logic
In a recent paper Johan van Benthem reviews earlier work done by himself and colleagues on ‘natural logic’. His paper makes a number of challenging comments on the relationships between traditional logic, modern logic and natural logic. I respond to his challenge, by drawing what I think are the most significant lines dividing traditional logic from modern. The leading difference is in the way logic is expected to be used for checking arguments. For traditionals the checking is local, i.e… 
Mill on logic
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Sı̄nā ’ s view of the practice of logic
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The 11th century Arabic-Persian logician Ibn Sīnā (Avicenna) in Section 9.6 of his book Qiyās gives what appears to be a proof search algorithm for syllogisms, which is confirmed by extracting all the essential ingredients of an abstract state machine from Ibn Sínā’s text.
Consequence is a, if not the, core subject matter of logic. Aristotle’s study of the syllogism instigated the task of categorising arguments into the logically good and the logically bad; the task
Ibn Sina on Analysis: 1. Proof Search. Or: Abstract State Machines as a Tool for History of Logic
  • W. Hodges
  • Computer Science, Philosophy
    Fields of Logic and Computation
  • 2010
The 11th century Arabic-Persian logician Ibn Sīnā (Avicenna) in Sect. 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
The Move from One to Two Quantifiers
Ibn Sīnā (Persian, 980–1037) made a dramatic extension to Aristotle’s syllogistic by adding quantifiers over times or situations, thus introducing multiple and mixed quantification. The extension is
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Proofs as Cognitive or Computational: Ibn Sı̄nā’s Innovations
We record the advances made by the eleventh century Persian logician Ibn Sina—known in the West as Avicenna—away from a purely cognitive view of proofs and towards a more computational view, and the
Formal Languages in Logic: A Philosophical and Cognitive Analysis
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