Mathematics Presenting, Reflecting, Judging

To understand what it means to present, to reflect, and to discuss mathematics, mathematics shall in the first place be characterized in connection of Peirce's classification of the inquiring sciences. The threefold view of the universal categories of Peirce suggests to orientate the expositions - for presenting on the self-image of mathematics (as a First), - for reflecting on the relationship of mathematics to the real world (as a Second), and - for judging on the sense, meaning and connection of mathematics (as a Third). These expositions support the following basic thesis: sense and meaning of mathematics finally lie in the fact, that mathematics may effectively support the rational communication of human beings. Contents 1. Mathematics in the context of the inquiring sciences 2. Presenting Mathematics (as a First) 3. Reflecting Mathematics (as a Second) 4. Judging Mathematics (as a Third) 5. Mathematics for supporting rational communication.