Philosophy Dictionary of ArgumentsHome
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| Conditional: A conditional in logic is a statement that asserts a relationship between two propositions, typically in an "if-then" format. It states that if the antecedent is true, then the consequent must also be true. In contrast to (purely formal) implication, the conditional refers to the content of the propositions. See also Implication._____________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 Conditional - Dictionary of Arguments
Berka I 8 Conditional/ relationship/Conclusion/Bolzano: for Bolzano follows M, N, O..from A, B, C... only if (1) each (semantic) model of A, B, C ... is also a model of M, N, O .... That is, if each of the final sentences M, N, O, can be deduced separately from the assumptions A, B, C. and (2) the premises are the (s) content-related) reason for the conclusion. Berka: that is a very strong conclusion concept. TarskiVsBolzano: it is enough for him if the first condition is fulfilled. GentzenVsBolzano: for Gentzen it is sufficient if at least one of the final sentences is derivable from the set of premisses. Special case: if the claim quantity contains only one final sentence, the Bolzano's and the Gentzen's inference system are identical. Conclusion/Bolzano: additional condition: one must be able to decide which concepts are logical concepts. --- Berka I 20 f E.g. Entailment/Bolzano: (content-wise): if it is warmer in a place, then there are higher temperatures at the location - in reality, higher temperatures are shown, because it's warmer - the thermometer does not generate the temperatures. I.e. the entailment only exists in one direction: heat > temperature.(1) - different to Deducibility/Bolzano/(s): if the sentence "... higher temperatures" is true, the sentence "it's warmer" is true, and vice versa. Reversible relation of two true sentences. Content is not decisive here - entailment: only in one direction - derivability: goes in both directions, regardless of truth - Entailment/Bolzano: for reason - Derivability/>Mates: formal. 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 Conditional
Ed. Martin Schulz, access date 2024-04-18