Что значит для математики давать реальные определения своих понятий?
The article deals with the Malcolm’s version of the ontological argument and its variation proposed by Hartshorne. It also highlights some "eternal" problems which are to be faced by everyone who wish to consider the ontological argument as a purely logical proof.
Russian researchers polemics on Kants essay On a supposed right to tell lies from benevolent motives in which Kant argues that if a malefactor (a murderer) who is going to kill a persons friend asks that person where ones friend is, the morality requires to tell the truth. It is proved in the paper that though Kantians are usually considered as absolutists and their opponents - as relativists, the Kantians perform a large-scale relativization of maxim of truthfulness and exhibit more conformity to lie than the relativisits do. Paradoxes A Precious Friend and Kants Generalized Consequence for Many Friends showing inconsistency and contradictoriness of Kantians point of view are introduced. The confrontation of absolutists and relativists is interpreted as a fundamental opposition of reductionism and holism followers, with understanding that in this case the opposition is many times strengthened by confrontation of moral values.
The paper analyzes the general basis for analytic and synthetic judgments, expressed in terms of a priori representation of thoroughgoing determination of every thing, which was proposed in Kant’s concept of transcendental prototype. It is showed how existential predication, performed on the basis of concept «thing-in-itself», is connected to the possibility of real predication in judgments.
The three already traditional volumes of the WDS Proceedings you are holding in the hands are composed of the contributions which have been presented during the 21st Annual Conference of Doctoral Students that was held in Prague, at Charles University, Faculty of Mathematics and Physics from May 29 to June 1, 2012. In this year, 100 student manuscripts were submitted to publishing and 88 were accepted after the review process.
This article presents the results of a pilot study assessing the level of formation of a stochastic competence among teachers of mathematics. Besides, the indicators that reflect the competence of formation of stochastic students are identified and ranked in order of importance. Different instruments (questionnaires, tests, assignments) have been used to solve the problem under study.