Economics Dictionary of ArgumentsHome
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| One, number 1: in modern logic it is not possible to introduce the number one directly. It must be introduced indirectly, via existential quantification ("for at least one x ...") and universal quantification ("for all x ..."). In addition, identity is needed. See also definition, identity, logic, elementary logic, number theory, numbers._____________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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David Hilbert on One (Number 1) - Dictionary of Arguments
Berka I 121 Definition 1/one/number/logical form/Hilbert: 1(F) : (Ex)[F(x) & (y)(F(y) > ≡ (x,y)]. Hilbert: "There is an x for which F(x) exists, and every y for which F(y) exists is identical with this x". Definition 2/two/number/logical form/Hilbert: 2(F) :(Ex)(Ey) {~≡(x,y) & F(x) & F(y) & (z)[F(z) > ≡ (x,z) v ≡ (y,z)]}. I 122 "There are two different x and y to which F applies, and every z for which F(z) exists is identical with x or y"(1). >Numbers, >Equality, >Identity, >Equations. 1. D. Hilbert & W. Ackermann: Grundzüge der Theoretischen Logik, Berlin, 6. Aufl. Berlin/Göttingen/Heidelberg 1972, §§ 1, 2._____________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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Authors A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Concepts A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
