intuitionism
LowFormal, Academic, Technical
Definition
Meaning
A philosophical or mathematical doctrine that knowledge or truth is grasped by immediate apprehension or insight, rather than through rational or empirical processes.
In ethics, a theory that moral truths are self-evident through moral intuition. In mathematics, a foundational approach (associated with L.E.J. Brouwer) that mathematics is a mental construction, rejecting non-constructive proofs and the law of excluded middle for infinite sets.
Linguistics
Semantic Notes
The term is highly domain-specific, primarily used in philosophy (ethics, epistemology) and the foundations of mathematics. Its meaning shifts significantly between these contexts. It is not used in casual conversation about 'gut feelings'.
Dialectal Variation
British vs American Usage
Differences
No significant spelling or usage differences. Pronunciations may vary slightly as per IPA. The academic discourse is identical.
Connotations
Identical technical connotations in philosophical and mathematical contexts.
Frequency
Extremely low in general usage; frequency is confined to specialised academic texts in both regions.
Vocabulary
Collocations
Grammar
Valency Patterns
[Subject] advocates/rejects intuitionism.Intuitionism in [Domain, e.g., ethics/mathematics] holds that...The central tenet of intuitionism is...Vocabulary
Synonyms
Neutral
Weak
Vocabulary
Antonyms
Usage
Context Usage
Business
Virtually never used.
Academic
Primary context. Used in philosophy departments (ethics, epistemology) and mathematics departments (foundations, logic).
Everyday
Extremely rare and likely to be misunderstood. Not used for casual 'intuition'.
Technical
Core technical term in meta-ethics and mathematical logic.
Examples
By Part of Speech
verb
British English
- The philosopher did not seek to intuitionise moral principles.
- One cannot simply intuitionise a mathematical proof.
American English
- The philosopher did not seek to intuitionize moral principles.
- One cannot simply intuitionize a mathematical proof.
adverb
British English
- He argued intuitionistically, rejecting the use of indirect proof.
- The theorem is interpreted intuitionistically.
American English
- He argued intuitionistically, rejecting the use of indirect proof.
- The theorem is interpreted intuitionistically.
adjective
British English
- His intuitionist stance rejected the classical proof.
- An intuitionist approach to ethics prioritises self-evident principles.
American English
- His intuitionist stance rejected the classical proof.
- An intuitionist approach to ethics prioritizes self-evident principles.
Examples
By CEFR Level
- 'Intuitionism' is a difficult word from philosophy and maths.
- In moral philosophy, intuitionism suggests we know basic right and wrong through a kind of inner sense.
- The mathematician opposed formalism, favouring a version of intuitionism.
- Brouwer's intuitionism led him to reject non-constructive existence proofs, profoundly influencing modern logic.
- Moore's ethical intuitionism posited that 'good' is a simple, indefinable, non-natural property apprehended directly.
Learning
Memory Aids
Mnemonic
Think: 'IN TUITION' - it's about inner 'tuition' or teaching, a knowledge from within, not from external proof.
Conceptual Metaphor
KNOWLEDGE IS VISION (direct seeing/insight), MATHEMATICS IS A MENTAL CONSTRUCTION.
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Do not confuse with the common word 'интуиция' (intuition as a gut feeling). In academic contexts, 'интуиционизм' is the direct equivalent.
- Avoid using 'интуиция' to translate 'intuitionism' as it loses the '-ism' (doctrine) component.
Common Mistakes
- Using 'intuitionism' to mean simply 'relying on intuition'.
- Confusing mathematical intuitionism with philosophical intuitionism.
- Misspelling as 'intuisionism' or 'intuitonism'.
Practice
Quiz
In which field is intuitionism associated with the rejection of the law of excluded middle for infinite sets?
FAQ
Frequently Asked Questions
No. Intuitionism is a specific technical doctrine in philosophy and mathematics. Having 'intuition' is a general cognitive ability.
In ethics, it's about self-evident moral truths. In mathematics, it's about mathematics as a mental construction, requiring constructive proofs.
The Dutch mathematician L.E.J. Brouwer (1881–1966).
A proof that claims 'X either exists or does not exist' without providing a method to find or construct X. Intuitionism demands a constructive method.