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Abstract:
It is necessary to distinguish the logic of certainty from the logic of prob-able. By fusing together the logic of certainty with the logic of probable by means of geometry we deepen probability concept in a philosophical way. Hence, we obtain some fundamental and original results of probability theory: we observe the two ex-treme aspects of the logic of certainty by identifying their corresponding structures into a linear space, we extend probability laws P formally admissible in terms of coherence to random quantities, we give a geometric representation of these laws P and of a coherent prevision-function P we previously defined in an original way. We are the first in the world to do this kind of work which is the philosophical foundation of our next and extensive study concerning the formulation of a geometric, well-organized and original theory of random quantities. For this reason we believe that it is sufficient that our references limit themselves to those pioneering and math-ematical works which do not keep the real and deep meaning of probability concept a secret.
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