caa a22 4500 605475199 CHVBK 20210128100350.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s10516-014-9253-8 doi (NATIONALLICENCE)springer-10.1007/s10516-014-9253-8 Drekalović Vladimir Faculty of Philosophy, University of Montenegro, Filozofski fakultet, Danila Bojovića bb, 81400, Nikšić, Montenegro aut Some Aspects of Understanding Mathematical Reality: Existence, Platonism, Discovery [Elektronische Daten] [Vladimir Drekalović] 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. Springer Science+Business Media Dordrecht, 2014 Reality nationallicence Existence nationallicence Discovery nationallicence Proof nationallicence Platonism nationallicence Axiomathes Springer Netherlands 25/3(2015-09-01), 313-333 1122-1151 25:3<313 2015 25 10516 https://doi.org/10.1007/s10516-014-9253-8 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10516-014-9253-8 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Drekalović Vladimir Faculty of Philosophy, University of Montenegro, Filozofski fakultet, Danila Bojovića bb, 81400, Nikšić, Montenegro aut NATIONALLICENCE 773 0- Axiomathes Springer Netherlands 25/3(2015-09-01), 313-333 1122-1151 25:3<313 2015 25 10516