@misc{Lexicon of Arguments, title = {Quotation from: Lexicon of Arguments – Concepts - Ed. Martin Schulz, 28 Mar 2024}, author = {Thiel,Christian}, subject = {Set Theory}, note = {Thiel I 308 Set Theory: Bourbaki never talks about logicism, only about set theory. Sets are genuinely mathematical objects, not reducible to others (logic: classes). The set concept is an essential tool for the unification of mathematics. >Unification, >Generalization, >Generality. I 308/309 Set Theory: as a fundamental discipline of mathematics: Basic concepts such as relation and function are traced back to the concept of set by explicit definition. Relation as symmetrical or asymmetrical pair formation. Two-digit relation. >Relations. Sometimes we need means to express the order. Ordered pairs. Def I 310. Functions: Def: right unambiguous relations. If one presupposes the traceability of all higher types of numbers to the natural numbers once, one can also win these still set-theoretically. >Reduction, >Reducibility, >Numbers, >Real numbers. I 311 The real question is a philosophical one and concerns the justification of the reductionist program behind everything. Thiel: whether even numbers as mathematical entities turn out to be sets still appears today to be one of the most important philosophical questions, despite all the logical dead ends into which the classical logizistic approach has fallen. >Mathematical entities, >Logic, >Ontology, >Platonism, cf. >Hartry Field.}, note = { T I Chr. Thiel Philosophie und Mathematik Darmstadt 1995 }, file = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=527056} url = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=527056} }