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SOURCE:   Historical, Philosophical, Political and Law Sciences, Culturology and Study of Art.
Issues of Theory and Practice
. Tambov: Gramota, 2013. № 10. Part 2. P. 38-42.
SCIENTIFIC AREA: Philosophical Sciences
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MODAL STRUCTURES OF MATHEMATICAL THINKING: ONTOLOGICAL ASPECT

Bukin Dmitrii Nikolaevich
Volgograd State University


Abstract. The article shows that in addition to the traditional ontological categories of quantity, space, measure, etc. the modal alethic characteristics of necessary, real and possible play an important role in fixing and describing the existence of the mathematical object. Mathematical regularities always, in the end, prove to be either modal necessary or modal possible. The ontological "dependence" of the mathematical object representation "as it is" indicates assertion modalities supporting role in mathematical thinking structuring.
Key words and phrases: модальные категории, бытие, математический объект, необходимое и случайное, действительное, возможное, доказательство, вероятность, modal categories, existence, mathematical object, necessary and accidental, real, possible, proving, probability.
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