With reference to certain ideas of Reuben Hersh, the paper attempts to present and confront two approaches concerning the essence of mathematics. On one hand mathematics is presented as an inflexible stronghold of truth in which what is established is considered final. However, on the other hand, as R. Hersh points, it does not differ from other forms of scientific research; it is burdened with uncertainty and it can be modified. Appreciating the importance of Hersh's social-mathematical observations, the author indicates that mathematics simply has two different facets. In one mathematics is a process of achieving the truth, in the other, it is a generally accepted way of presenting this truth.
The paper evaluates W. Sady's criterion of demarcation between science and non-science according to a metacriterion proposed by L. Laudan. The outcome of the examination is rejection of Sady's proposal. First, it is not-adequate, as it eliminates all discoveries not made in a systematic, planned way, even if they are of scientific importance and contribute to development of science. Secondly, it is not sufficiently precise, at it gives only the necessary condition of scientific status. Additionally, this short review points out some other flaws in Sady's theory.
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