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PL
Leibniz's idea of creation is best epitomized by a note written by him on the margin of his work entitled 'Dialogus'. The note reads:'When God thinks things through and calculates, the world is made'. Simple calculations are almost mechanical. The true mathematical thinking begins when one is confronted with a problem that has to be solved, when starting from the known mathematical structure one has to construct a new structure, to comprehend its intricacies, the ways of its functioning, and its connections with other mathematical structures. And when one successfully applies the new mathematical structure to a physical theory, the new world is made. This was Leibniz's experience when he was discovering calculus and tried to apply it to mechanical problems. Leibniz's doctrine that our world is the best of all possible words is often ridiculed, but this attitude is the result of a very superficial reading of Leibniz's texts. In fact, God's calculations to choose the best possible world are similar to solving the variational problem in mathematics. Leibniz claims that in mathematical reasoning if there is neither 'maximum' nor 'minimum' nothing can happen. Similarly, if there were no world better that other possible worlds, God's wisdom would have not been able to create anything. Some consequences of this doctrine, concerning the nature of space, time and causality, are also considered.
RU
Antithesis of juvenility and senility is examined in connection with grammatical presentation of redundant paradigm «years – times». In the context of understanding of the meaning of existence and the idea of being the thesis of not an existential nature of senility is formulated. In ontognoseological aspect the contraposition of concepts of «reality» and «actuality» becomes meaningful.
EN
In everyday experience mathematics rarely appears to us as a whole, and certainly never as a system in the sense of David Hilbert’s considerations from early 20th Century. Mathematical disciplines seem to be independent and autonomous. We do not see that specific deduction goes beyond particular convention applicable in given discipline. In the late 19th Century this view was shared by Felix Klein and Richard Dedekind. The latter’s work “What are numbers and what should they be?” (Was Was sind und was sollen die Zahlen?) was the inspiration for writing this article. This essay is an attempt to see mathematics not as a building, but as a living organism seeking its explanation.
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