Philosophy Dictionary of ArgumentsHome
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| Derivability: this is about the question which statements can be obtained according to the rules of a calculus. In logic, derivability refers to the ability to prove a statement from a set of premises using the rules of inference of a given logical system. A statement is said to be derivable if there is a proof of it in the system._____________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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Bernard Bolzano on Derivability - Dictionary of Arguments
Berka I 18/19 Derivability/Bolzano: exists, if certain ideas i, j, which make the premises A, B, C, true, also make the conclusions M, N, O... true. Namely the epitome (the totality) of the ideas is intended to make the entire conclusions and the whole premises true. ((s) >truthmaker). Comprise/include/Bolzano: Premises: are here the included, Conclusions: the comprehensive/including sentences. I 20 Derivability/Bolzano: Problem: sentences obtained through an arbitrary exchange of ideas from given true must not always be true. (s) Exchange of ideas: insert for variables. Bolzano: thus the relationship of derivability can also exist under false theorems. E.g. Follow-up relationship/Bolzano/(s): (content-related): if it is warmer in one place, a higher temperature is displayed in this place. In reality, higher temperature is displayed because it is warmer. The thermometer does not generate the temperature. That is, the follow-up relationship consists only in one direction: Heat > Temperature. Different in the derivability: E.g. derivability/Bolzano/(s): if the sentence "... higher temperature" is true, the sentence "it is warmer" is also true and vice versa. Reversible ratio of two true sentences. Content is not decisive. I 21 Follow-up relationshiop/Bolzano: is not already present when the corresponding sentences are all true. (1) 1. B. Bolzano, Wissenschaftslehre, Sulzbach 1837 (gekürzter Nachdruck aus Bd. II S. 113-115, S. 191 – 193; § 155; §162)_____________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. |
Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 |
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> Counter arguments against Bolzano
> Counter arguments in relation to Derivability
Ed. Martin Schulz, access date 2024-04-18