Math 2.0

Mathematical logic and foundations Constructive mathematics Concept

Constructivism

Builds on Constructive proofLaw of excluded middleProof by contradiction

Summary

Constructivism is the view in the philosophy of mathematics that a mathematical object exists only when one can construct it. To prove that something exists, one must give a method to find it, as in a constructive proof. As a result, constructive mathematics does not accept the law of excluded middle as a general principle. Its main schools are Brouwer's intuitionism, Markov's recursive constructive mathematics, and Bishop's constructive analysis.

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Proposition, concept, no evidence levelPropositionconceptConjunction, definition, no evidence levelConjunctiondefinitionDisjunction, definition, no evidence levelDisjunctiondefinitionImplication, definition, no evidence levelImplicationdefinitionNegation, definition, no evidence levelNegationdefinitionPredicate, definition, no evidence levelPredicatedefinitionBiconditional, definition, no evidence levelBiconditionaldefinitionTruth table, concept, no evidence levelTruth tableconceptLaw of excluded middle, statement, no evidence levelLaw of excluded middlestatementModus ponens, concept, no evidence levelModus ponensconceptExistential quantifier, definition, no evidence levelExistential quantifierdefinitionPropositional logic, concept, no evidence levelPropositional logicconceptMathematical proof, concept, no evidence levelMathematical proofconceptTautology, definition, no evidence levelTautologydefinitionConstructive proof, concept, no evidence levelConstructive proofconceptLogical equivalence, definition, no evidence levelLogical equivalencedefinitionDouble negation law, statement, no evidence levelDouble negation lawstatementProof by contradiction, concept, no evidence levelProof by contradictionconceptConstructivism, concept, no evidence levelConstructivismconcept
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Proposition concept
  2. Conjunction definition
  3. Disjunction definition
  4. Implication definition
  5. Negation definition
  6. Predicate definition
  7. Biconditional definition
  8. Truth table concept
  9. Law of excluded middle statement
  10. Modus ponens concept
  11. Existential quantifier definition
  12. Propositional logic concept
  13. Mathematical proof concept
  14. Tautology definition
  15. Constructive proof concept
  16. Logical equivalence definition
  17. Double negation law statement
  18. Proof by contradiction concept
  19. Constructivism concept

Where this leads

5 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Constructivism_(philosophy_of_mathematics)
About this page
TagG958EQ8CWW
URIm2://G958EQ8CWW
Kindconcept
WritingW0 stub
MSC03F65, 03F55, 00A30
UsesConstructive proof, Law of excluded middle, Proof by contradiction
Same as
Changed2 November 2026

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