Philosophy Lexicon of Arguments

Author Item Excerpt Meta data
Lorenzen, Paul
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Mathematics 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.
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.
Therefore the meta-mathematical statements "derivable" or "non-derivable" correspond unambigiously in each case reversible to a basic number which characterizes them.

Lorn I
P. Lorenzen
Constructive Philosophy Cambridge 1987

Chr. Thiel
Philosophie und Mathematik Darmstadt 1995

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Ed. Martin Schulz, access date 2017-04-29