Economics Dictionary of ArgumentsHome
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| Law of the Excluded Middle: an assertion is either true or false. "There is no third possibility."See also bivalence, anti-realism, multivalued logic._____________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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Arend Heyting on Excluded Middle - Dictionary of Arguments
I 67 Sentence of the excluded middle/VsIntuitionism: one does not accuse the intuitionist of accepting too little, as the representative of classical mathematics thinks, the intuitionist rather accepts too much. >Intuitionism, >VsIntuitionism. E.g.: is the principle of the excluded middle as evident to most people as is the one of complete induction? Why does he reject the one and agrees on the other? Intuitionism: in fact, intuitionist claims must appear dogmatic to those who regard them as assertions about facts, but they are not meant like this. They consist of mental constructions. Mathematical ideas belong to my highly private world of thought. E.g. "I've added 2 and 3 and then 4 and i and have determined that this leads to the same result". >Constructivism. I 68 This does not convey any knowledge about the external world, but about my thoughts. One must distinguish between the mere practice of mathematics and its assessment. The value always depends on our philosophical ideas. >Mathematics, >Description levels. If science really tends to formalize language, then intuitionist mathematics does not belong to science in the sense of the word. Rather, it is a phenomenon of life, a natural activity of the human being. The meta-mathematical considerations may be useful, but they cannot be integrated into intuitionist mathematics. >Discoveries, >Meta-mathematics. I 69 The mathematics, from the intuitionist standpoint, is the study of certain functions of the human mind. >Science._____________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. |
Heyting I Arend Heyting "Disputation", in: Intuitionism, Amsterdam 1956 German Edition: Streitgespräch In Kursbuch 8/1967, H. M. Enzensberger, Frankfurt/M. 1967 Heyting II Arend Heyting Intuitionism: An Introduction (Study in Logic & Mathematics) 1971 |
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