|Substitution, philosophy: here we are concerned with replacing verbal elements or logical symbols within expressions or logical formulas by other linguistic elements or logical symbols that are able to form a meaningful statement at the same syntactic position. If the truth value (true or false) of the statement is preserved, one speaks of the substitutability of a term by another term in a certain context. See also equality, insertion, meaning, identity, co-reference._____________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. |
Christian Thiel on Substitution - Dictionary of Arguments
Thiel I 92
Substitution/Thiel: >Substitution rule: if you replace all equal letters with the same correct formula or another letter. >Separation rule: A,A > B >>B (?)
So "if, then" are introduced by simple rules, negation of a statement ..+... def "designated formula".... "allocation". I 95
Some of the formulas formed with the help of the newly added negation sign are not designated formulas.
For example, one of the assignments of the formula ~~p > p is the expression (~~1) >1. Its value is calculated according to the tables as (~~1) x 1 = (~2) x 1 = 0 x 1 = 1
The assignment also receives
0 > (~~0) of the formula p > ~~p the value
0 x (~~0) = 0 x (~1) = 0 x 2 = 1. If the value is different from 0, there is no designated formula regarding our table._____________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.
Philosophie und Mathematik Darmstadt 1995