## Psychology Dictionary of ArgumentsHome | |||

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Deduction theorem: The deduction theorem is a metatheorem in logic that states that if a proposition B can be deduced from a proposition A, then the implication A → B is also deducible. In other words, if we can prove that B is true given that A is true, then we can also prove that A implies B.
The deduction theorem is a useful tool for proving theorems, as it allows us to break down complex proofs into smaller, more manageable steps._____________ 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. | |||

Author | Concept | Summary/Quotes | Sources |
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David Hilbert on Deduction Theorem - Dictionary of Arguments Berka I 112 Definition "Deduction Theorem"/Hilbert: if a formula B can be derived from a formula A in such a way that every free variable occurring in A is fixed, i.e. that it is neither used for an insertion, done for it, nor as a designated variable of a shemata (α), (β), then the formula A > B can be derived without using the formula A ((s) elimination of the premise). >Deduction, >Premises. I 116 Note: Rule of the back generalization/scheme (α)/Hilbert: A > B(a) A > (x) B(x) Rule of the front particularisation/scheme (β)/Hilbert: B(a) > A (Ex)B(x) > A >Particularization, >Existential Generalization, >Universal Generalization. 1. D. Hilbert & P. Bernays: Grundlagen der Mathematik, I, II, Berlin 1934-1939 (2. Aufl. 1968-1970). _____________ 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 |

> Counter arguments against **Hilbert**

> Counter arguments in relation to **Deduction Theorem**