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In logic, the law of excluded middle or the principle of excluded middle states that for every proposition, either this proposition or its negation is true. Symbolically expressed, the law is p ∨ ¬ p {\displaystyle p\lor \neg p} .
The analysis highlights History, Criticisms and Examples as prominent areas in the source structure around Law of excluded middle.
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The extracted context around Law of excluded middle shows recurring relationship patterns in the source. For example, Law of excluded middle → Arthur Prior, Curry's, Fraenkel, Furthermore, Liar's, Paradox, Russell's, Zermelo Another extracted example is Law of excluded middle → Buddhist, Greek, Indian, Many, Pyrrhonism, The Catuṣkoṭi. Use these groups to spot repeated connection types before inspecting the individual relationships.
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law excluded logic brouwer proof true principle negation either displaystyle russell false van heijenoort example reprinted infinite mathematical hilbert intuitionists
TTTA extracted 20 structured relationships around Law of excluded middle. Examples in this analysis include Law of excluded middle → is a → proof by cases such as follows and follows → instance of → must be true.An example of an argument that depends on the law of excluded middle is a proof by cases. The table shows each extracted connection, where it came from and its confidence.
| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| Law of excluded middle | is a | proof by cases such as follows | 0.90 | text |
| follows | instance of | must be true.An example of an argument that depends on the law of excluded middle is a proof by cases | 0.80 | text |
| Brouwer | instance of | but it is not built-in a priori into these systems.Mathematicians | 0.80 | text |
| Arend Heyting have also contested the usefulness of the law of excluded middle in the context of modern mathematics.In mathematical logicIn modern mathematical logic | instance of | but it is not built-in a priori into these systems.Mathematicians | 0.80 | text |
| the excluded middle has been argued to result in possible self-contradiction | instance of | but it is not built-in a priori into these systems.Mathematicians | 0.80 | text |
| ternary logic | instance of | Propositional calculus in which there are more than two truth values | 0.80 | text |
| Law of excluded middle | related to Criticisms | The Catuṣkoṭi | 0.60 | section |
| Law of excluded middle | related to Criticisms | Indian | 0.60 | section |
| Law of excluded middle | related to Criticisms | Buddhist | 0.60 | section |
| Law of excluded middle | related to Criticisms | Greek | 0.60 | section |
| Law of excluded middle | related to Criticisms | Pyrrhonism | 0.60 | section |
| Law of excluded middle | related to Criticisms | Many | 0.60 | section |
The concept neighborhoods around Law of excluded middle bring nearby vocabulary together. In this analysis, examples include Excluded, Law and True. Use the clusters to find adjacent concepts and terminology that may deserve separate research.
For Law of excluded middle, one of the stronger structural bridges in this analysis connects Law of excluded middle with History. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.
TTTA analyzes the structure around Law of excluded middle to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as History, Criticisms & Examples, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.
Source: Wikipedia — Law of excluded middle · EN edition · Analysis: TopicsToTalkAbout
