@misc{Lexicon of Arguments, title = {Quotation from: Lexicon of Arguments – Concepts - Ed. Martin Schulz, 29 Mar 2024}, author = {Waismann,Friedrich}, subject = {Ultimate Justification}, note = {I 50 Ultimate justification/foundation/Mathematics/Waismann: The question of the last anchorage has not been solved with these researches, but merely pushed back further. A justification is unsuitable with the help of arithmetic; we have already reached the last clues of the arithmetic deduction. But such a possibility seems to arise when one looks beyond arithmetic: this leads to the third standpoint. >Foundation. Arithmetic/Waismann: is based on logic. In doing so, one makes strong use of terms of the set theory, or the class calculus. The assertion that mathematics is only a >"part of logic" includes two theses, which are not always clearly separated: A) The basic concepts of arithmetic can be traced back to purely logical ones by definition B) The principles of arithmetic can be deduced from evidence from purely logical propositions. >Logic, >Proof, >Empiricism. I 51 It looks like the sets of logic are tautologies. (Wittgenstein in 1921 introduced the concept of tautology). >Tautology. WaismannVsFrege: Frege was completely lacking the insight that the whole logic becomes meaningless, because he did not understand the nature of logic at all. In Frege's opinion, logic should be a descriptive science, such as mechanics. And to the question of what it describes, he replied: the relations between ideal objects, such as "and", "or", "if", etc. Platonic conception of a realm of uncreated structures. >Platonism, >G. Frege.}, note = { Waismann I F. Waismann Einführung in das mathematische Denken Darmstadt 1996 Waismann II F. Waismann Logik, Sprache, Philosophie Stuttgart 1976 }, file = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=537984} url = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=537984} }