Critical view of the nature of the unquestionable truth of mathematics - Lucas-Cabello, Adalberto (2019)
The research which is entitled critical view of the nature of unquestionable truth of mathematics, were like sub headings: philosophical meditations on the truth; pragmatic conception of truth, thesis on the truth in the phenomenological direction. Fecundity of the error in mathematical logic, which in turn contains: failure of the logización of mathematics in Gottlof Frege, Russell paradox: impossibility of completely formalized arithmetic and the axiomatic Hilbert and the failure of the ideal of rigorous formalization. Philosophical meaning of Kurt Gödel's theorem, which also has subtitles: Gödel's theorem philosophically understood as a principle a posteriori, relativity of absolute truth in mathematics according to the theorem of Gödel and inconsistency of the character of unquestionable truth of mathematics. Methods used were: the dialectical hermeneutic and phenomenological, their use led to the following results. 1) Los students acknowledged the indubitable of math truth relativity, because they came to rationally understand the theorem of Gödel's incompleteness, which provides as follows: any axiomatic system from which you can derive the basic arithmetic, it contains ambiguous propositions or undecidable; 2) Los student acknowledged the indubitable of math truth relativity, because they came to rationally understand the theorem of Gödel's incompleteness, which provides as follows: any axiomatic system from which you can derive the basic arithmetic, it contains ambiguous propositions or undecidable. We conclude that: can be is a criterion of absolute truth, because to do so, it would be necessary to resort to another criterion which justified. But to establish that second criterion of truth, at the same time would be necessary to resort to another and thus to infinity, in such a way that would never be a criterion of truth, specifically, in the so-called logización of mathematics. Que if there is a really true and complete knowledge of mathematics in general, then this knowledge would be irrevisable, it would be definitive, it contradicts the meaning of philosophy, which is that of problematize or not accept statements as definitely true.