{
  "id": "constructivism",
  "domain": "foundations-logic",
  "type": "Concept",
  "title": "Constructivism",
  "slug": "constructivism",
  "url": "/mathematics/foundations-logic/constructivism/",
  "summary": "Mathematical existence requires explicit construction. Rejects law of excluded middle. Brouwer intuitionism c.1907-1920s; Bishop 1967 constructive analysis; intuitionistic logic; Kleene realizability 1945; topos theory (Lawvere-Tierney 1960s-70s).",
  "added_to_codex": "2026-07-09",
  "last_verified": "2026-07-09",
  "sources": [
    {
      "tier": 1,
      "citation": "Bishop, E. (1967). Foundations of Constructive Analysis. McGraw-Hill."
    },
    {
      "tier": 1,
      "citation": "Troelstra, A.S. and van Dalen, D. (1988). Constructivism in Mathematics. 2 vols."
    },
    {
      "tier": 2,
      "citation": "Dummett, M. (2000). Elements of Intuitionism. 2nd ed."
    },
    {
      "tier": 3,
      "citation": "Bridges, D. and Richman, F. (1987). Varieties of Constructive Mathematics."
    }
  ],
  "entry_status": "live",
  "reading_levels_available": [
    "curious",
    "exploring",
    "deep_dive"
  ],
  "completeness": 1.0,
  "codex_version": "2.5"
}