Saturday, November 6, 2010

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Bolzano / Philosophy and Mathematical


Bernard Placidus Johann Nepomuk Bolzano ( 5 October 1781 - December 18 1848) is a mathematician, logician, philosopher, bohemian German theologian, son of an Italian immigrant to Prague .

Bolzano For what is purely a priori is the concept and only him. Purely a priori knowledge are those qi proceed purely by concepts, that is to say primarily mathematics and philosophy, science discourse one Both. Kant believed that mathematical proceed by construction of concepts in intuition when philosophy it purely discursive is knowledge by concepts. Bolzano argues that mathematical philosophy and method have same and differ only in their subject . mathematics are also knowledge through concepts, whose intuition at the meaning of Bolzano, is excluded .. The identity of method is the search for reasons and consequences , the establishment day of the objective truths connection . This identity is so strong that sometimes Bolzano considers mathematics as a "branch of philosophy and way of thinking just practice," sometimes defines philosophy as a Reflection on and in every science, and on mathematics in particular. All science involves an element of philosophy, which consists both seek the reasons and consequences to reflect on this link . The difference between mathematics and philosophy that is only the first, to the fullest Generally, science is a priori forms of objects "possible" and when the latter seeks to deduce a priori the existence of "real" object like the freedom of individuals God or the immortality of the soul. By "forms , Bolzano means general laws governing necessarily the conditions of possibility of any object. The mathematical answer to the question: "what properties necessarily belong to the things that must be possible? " Science a priori forms of possible objects, a priori science laws" everything in general can be the object of our faculty representation , 'mathematics is a kind of formal ontology, as noted by Husserl.

Barbin Evelyne and Maurice Caveing " Philosophers and mathematics
" Bolzano and mathematics, "Hourya Sinaceur.

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