Cognitive Scaffold

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MENTAL MODEL · M13250

Intuitionistic Logic

Intuitionistic Logic
StructureHigh supportLogic
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Updated 2026-09-10

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INTRODUCTION

English translation pending.

CORE DEFINITION

Intuitionistic logic is the system of reasoning principles that logicians abstracted from the intuitionistic mathematics developed by L. E. J. Brouwer from 1907 and 1908 onward. The same principles apply to Russian recursive mathematics and to the constructive analysis of the Bishop school, so it is regarded as the logical basis of constructive mathematics. Excluded middle and double negation elimination are not valid.

SCAFFOLDING EFFECT

psychology

Reduce cognitive load

- Demand construction: accept an existence claim only when a concrete witness can be given. - Check decidability: before asserting an instance of excluded middle, ask whether you can actually decide it. - Read proofs as programs: treat a proof as a set of executable construction steps rather than a ready-made truth.

anchor

Anchor fast decisions

Intuitionism reads truth as provability or constructibility: A or not A requires that we can decide A or decide not A, and that ability is not always available, so excluded middle fails. An existential claim requires a concrete witness, and negation and implication are defined by transformations between proofs, which is why double negation does not entail the proposition.

MINIMUM ACTION

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Source support: Explicit

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    plato.stanford.eduhttps://plato.stanford.edu/entries/logic-intuitionistic/ZH · Explicit
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