Jean-Yves Beziau (Rio de Janeiro) gives a talk at the MCMP Colloquium (15 Dec, 2011) titled "The Power of the Hexagon". Abstract: In this lecture I will present and discuss the hexagon of opposition, an improvement of the square of opposition due to Robert Blanché. The hexagon of Blanché is made of a triangle of contrariety and a triangle of subcontrariety linked together by the relations of contradiction and subalternation. This hexagon includes the traditional square and can be extended to three dimensional objects giving a better understanding of modalities and negations. I will also show how this simple logical structure based on three  oppositions  can be applied to many different concepts ranging from logic
to music, through metalogic, economy and semiotics.

Jean-Yves Beziau (Rio de Janeiro) gives a talk at the MCMP Colloquium (15 Dec, 2011) titled "The Power of the Hexagon". Abstract: In this lecture I will present and discuss the hexagon of opposition, an improvement of the square of opposition due to Robert Blanché. The hexagon of Blanché is made of a triangle of contrariety and a triangle of subcontrariety linked together by the relations of contradiction and subalternation. This hexagon includes the traditional square and can be extended to three dimensional objects giving a better understanding of modalities and negations. I will also show how this simple logical structure based on three oppositions can be applied to many different concepts ranging from logic to music, through metalogic, economy and semiotics.

The Power of the Hexagon

Mathematical Philosophy - the application of logical and mathematical methods in philosophy - is about to experience a tremendous boom in various areas of philosophy. At the new Munich Center for Mathematical Philosophy, which is funded mostly by the German Alexander von Humboldt Foundation, philosophical research will be carried out mathematically, that is, by means of methods that are very close to those used by the scientists.
The purpose of doing philosophy in this way is not to reduce philosophy to mathematics or to natural science in any sense; rather mathematics is applied in order to derive philosophical conclusions from philosophical assumptions, just as in physics mathematical methods are used to derive physical predictions from physical laws.
Nor is the idea of mathematical philosophy to dismiss any of the ancient questions of philosophy as irrelevant or senseless: although modern mathematical philosophy owes a lot to the heritage of the Vienna and Berlin Circles of Logical Empiricism, unlike the Logical Empiricists most mathematical philosophers today are driven by the same traditional questions about truth, knowledge, rationality, the nature of objects, morality, and the like, which were driving the classical philosophers, and no area of traditional philosophy is taken to be intrinsically misguided or confused anymore. It is just that some of the traditional questions of philosophy can be made much clearer and much more precise in logical-mathematical terms, for some of these questions answers can be given by means of mathematical proofs or models, and on this basis new and more concrete philosophical questions emerge. This may then lead to philosophical progress, and ultimately that is the goal of the Center.

Mathematical Philosophy - the application of logical and mathematical methods in philosophy - is about to experience a tremendous boom in various areas of philosophy. At the new Munich Center for Mathematical Philosophy, which is funded mostly by the German Alexander von Humboldt Foundation, philosophical research will be carried out mathematically, that is, by means of methods that are very close to those used by the scientists. The purpose of doing philosophy in this way is not to reduce philosophy to mathematics or to natural science in any sense; rather mathematics is applied in order to derive philosophical conclusions from philosophical assumptions, just as in physics mathematical methods are used to derive physical predictions from physical laws. Nor is the idea of mathematical philosophy to dismiss any of the ancient questions of philosophy as irrelevant or senseless: although modern mathematical philosophy owes a lot to the heritage of the Vienna and Berlin Circles of Logical Empiricism, unlike the Logical Empiricists most mathematical philosophers today are driven by the same traditional questions about truth, knowledge, rationality, the nature of objects, morality, and the like, which were driving the classical philosophers, and no area of traditional philosophy is taken to be intrinsically misguided or confused anymore. It is just that some of the traditional questions of philosophy can be made much clearer and much more precise in logical-mathematical terms, for some of these questions answers can be given by means of mathematical proofs or models, and on this basis new and more concrete philosophical questions emerge. This may then lead to philosophical progress, and ultimately that is the goal of the Center.

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The Power of the Hexagon

The Power of the Hexagon

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