|Ultimate justification: here we are concerned with the search for a justification of ethical norms or of measurement methods, which are proven to be no longer traceable. These are intended to enable the development of systems which cannot be rebutted as a whole, but against which only objections with regard to the internal structure can be put forward. This is intended to encourage collective work to improve generally accepted systems._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. |
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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.
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.
It looks like the sets of logic are tautologies. (Wittgenstein in 1921 introduced the concept of tautology).
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._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution.
Einführung in das mathematische Denken Darmstadt 1996
Logik, Sprache, Philosophie Stuttgart 1976