Prof. Vladimir Drekalović
Conference of East European Network for Philosophy of Science
/Comenius University in Bratislava
(20-22/6/2018)
SEMINAR FOR GENERAL PROOF THEORY
/Mathematical Institute of the Serbian Academy of Sciences and Arts (3/4/2017)
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UPCOMING EVENTS
European Congress of Analytic Philosophy/LMU Munich, Germany (21-26/8/2017)
MY LATEST RESEARCH
This paper analyses two definitions of contingency. Both definitions have been widely accepted and used as to identify contingent events. One of them is primarily of a philosophical character, whereas the other is more commonly used in mathematics. Evidently, these two definitions do not describe the same set of phenomena, and neither of them determines the completely intuitive notion of contingency. Namely, carefully selected examples testify that the first definition is too narrow and the second too wide. These facts have certain epistemological consequences. They must, therefore, serve as a warning for using the definitions only in a restrictive and cautious way when detecting random beliefs – those we cannot identify as knowledge.
The sum of all objects of a science, the objects’ features and their mutual relations compose the reality described by that sense. The reality described by mathematics consists of objects such as sets, functions, algebraic structures, etc. Generally speaking, the use of terms reality and existence, in relation to describing various objects’ characteristics, usually implies an employment of physical and perceptible attributes. This is not the case in mathematics. Its reality and the existence of its objects, leaving aside its application, are completely virtual and yet clearly organized. This organization can be recognized in the creation of axioms or in the arrival at new theorems and definitions. It results either from a formalization of an intuitive idea or from a combinatorics that has not been guided by intuition. In all four possible cases – therefore, also in the two in which there is no intuitive “lead”, we can plausibly talk about a discovery of mathematical facts and thus support the Platonist view.