This number of newly comissioned essays through foreign members bargains a consultant assessment of an important advancements in modern philosophical logic.
•Presents controversies in philosophical implications and purposes of formal symbolic common sense.
•Surveys significant tendencies and gives unique insights.
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Extra info for A Companion to Philosophical Logic
C. 350? BCE) put together a treatise during Aristotle’s lifetime that incorporated work by a number of other prominent mathematicians, including Archytas (428–347 BCE), Eudoxus (400–347 BCE), Leodamas (fl. c. 380 BCE), Theaetetus (c. 415–c. 369 BCE), and Menaechmus (c. 350? BCE). Euclid’s Elements (c. 295 BCE) presupposes a certain overall structure for a mathematical system. At its basis are propositions which are not proved in the system; some of these are definitions, some are ‘common conceptions’ (koinai ennoiai), and some are ‘things asked for’ (aitemata: the customary translation is ‘postulates’).
At its basis are propositions which are not proved in the system; some of these are definitions, some are ‘common conceptions’ (koinai ennoiai), and some are ‘things asked for’ (aitemata: the customary translation is ‘postulates’). Further propositions are added to the system by logical deduction from these first propositions and any others already proved; these are called theorems. 3, and one of the main goals of the treatise is to argue for it. Specifically, Aristotle argues that any demonstrative system must contain first propositions which are not demonstrated, or even demonstrable, in that system.
If there are no such true premises, then ‘A belongs to every B,’ though true, is absolutely undeducible, and thus indemonstrable in a purely logical or semantic sense. Similar results hold for the other forms of sentence, though they are more complicated because there are multiple ways of deducing each of them. Aristotle calls such true but undeducible sentences ‘unmiddled’ (amesos: the standard translation ‘immediate,’ though etymologically correct, is highly misleading). Since an unmiddled proposition cannot be deduced from anything, it obviously cannot be the object of a demonstration.
A Companion to Philosophical Logic