Philosophy Dictionary of ArgumentsHome
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| Mathematics: Mathematics is the study of patterns and relationships. It encompasses arithmetic, algebra, calculus, geometry, trigonometry, topology, and others. Mathematics is used in science, engineering, business, and finance. See also Physics, Logic._____________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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Paul Lorenzen on Mathematics - Dictionary of Arguments
Thiel I 225 Arithmetic/Lorenzen: arithmetic is the theory in which the infinite appears in its simplest form; it is essentially nothing else but the theory of the infinite itself. >Infinity, >Numbers. Arithmetic as the theory of the set of characters (for example, tally) is universal in the sense that the properties and relations of every other infinite set of characters can always be "represented" in some way in it. The complexity of matter has led to the fact that a large portion of the secondary literature about Goedel has created a lot of nonsense on metaphors such as "reflection", "self-rejection", etc. I 224 The logical arithmetic full-formalism is denoted by F. It contains, inter alia, inductive definitions of the counting signs, the variables for them, the rules of quantifier logic, and the rules written as Dedekind-Peano's axioms. I 226 The derivability or un-derivability of a formula means nothing else but the existence or non-existence of a proof-figure or a genealogical tree with A as the final formula. >Derivation, >Derivability, >Syntax. Therefore the meta-mathematical statements "derivable" or "non-derivable" correspond unambigiously in each case reversible to a basic number which characterizes them. >Metamathematics._____________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. Translations: Dictionary of Arguments The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition. |
Lorn I P. Lorenzen Constructive Philosophy Cambridge 1987 T I Chr. Thiel Philosophie und Mathematik Darmstadt 1995 |
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> Counter arguments against Lorenzen
> Counter arguments in relation to Mathematics
Ed. Martin Schulz, access date 2024-04-18