Part of the book series:Synthese Library ((SYLI,volume 291))
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Abstract
It is one thing for a given proposition to follow or to not follow from a given set of propositions and it is quite another thing for it to beshown either that the given proposition follows or that it does not follow.* Using a formal deduction to show that a conclusionfollows and using a countermodel to show that a conclusiondoes not follow are both traditional practices recognized by Aristotle and used down through the history of logic. These practices presuppose, respectively, a criterion of validity and a criterion of invalidity each of which has been extended and refined by modern logicians: deductions are studied in formal syntax (proof theory) and coun-termodels are studied in formal semantics (model theory).
The mathematics we have to construct are the mathematics of the human intellect. —Boole, 1847
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State University of New York at Buffalo, Buffalo, New York, 14260, USA
John Corcoran & Susan Wood
- John Corcoran
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- Susan Wood
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University of Lausanne, Switzerland
James Gasser
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Corcoran, J., Wood, S. (2000). Boole’s Criteria for Validity and Invalidity. In: Gasser, J. (eds) A Boole Anthology. Synthese Library, vol 291. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9385-4_7
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