The square of opposition and the four fundamental choices

Logica Universalis 2 (1):127-141 (2008)
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Abstract

.  Each predicate of the Aristotelian square of opposition includes the word “is”. Through a twofold interpretation of this word the square includes both classical logic and non-classical logic. All theses embodied by the square of opposition are preserved by the new interpretation, except for contradictories, which are substituted by incommensurabilities. Indeed, the new interpretation of the square of opposition concerns the relationships among entire theories, each represented by means of a characteristic predicate. A generalization of the square of opposition is achieved by not adjoining, according to two Leibniz’ suggestions about human mind, one more choice about the kind of infinity; i.e., a choice which was unknown by Greek’s culture, but which played a decisive role for the birth and then the development of modern science. This essential innovation of modern scientific culture explains why in modern times the Aristotelian square of opposition was disregarded.

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Citations of this work

Leibniz and the Square: A Deontic Logic for the Vir Bonus.Chris Johns - 2014 - History and Philosophy of Logic 35 (4):369-376.

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References found in this work

The Traditional Square of Opposition.Terence Parsons - 2008 - Stanford Encyclopedia of Philosophy.
From the Closed World to the Infinite Universe.[author unknown] - 1958 - British Journal for the Philosophy of Science 9 (35):234-245.

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