transcendentals
Beyond polynomial solutions
In scholastic philosophy, the transcendentals are properties that belong to all beings regardless of category—traditionally unity, truth, goodness, and beauty.
They "transcend" the Aristotelian categories because they apply universally rather than to particular kinds of things.
In mathematics, transcendentals are numbers or functions that cannot be expressed as solutions to polynomial equations with rational coefficients—pi and e being the classic examples.
Existing as something
- existenceState of being real
- essenceFundamental nature of something
- substancePhysical material with mass
- universalsProperties holding across all
categories · properties · unity · Aristotle · Plato · Aquinas · Scholasticism · metaphysics
Conformity to fact
- authenticityQuality of being genuine
- certaintyTotal absence of doubt
- objectivityFreedom from personal bias
- validityQuality of being sound
reality · factuality · honesty · sincerity · genuineness · accuracy · fidelity · reliability
Theory of beauty
- sublimityExalted, awe-inspiring quality
- harmonyAgreement or musical blend
- symmetryInvariance under transformation
- eleganceRefined, graceful quality
proportion · splendor · radiance · majesty · grace · refinement · exquisiteness · form
Moral goodness or merit
- moralityRight and wrong principles
- benevolenceDisposition toward doing good
- righteousnessMoral correctness or virtue
- ethicsStudy of right conduct
charity · compassion · justice · integrity · kindness · altruism · nobility · mercy
being
Existing as something
- existenceState of being real
- essenceFundamental nature of something
- substancePhysical material with mass
universals · categories · properties · unity · Aristotle · Plato · Aquinas · Scholasticism · metaphysics · ontology
veracity
Conformity to fact
- authenticityQuality of being genuine
- certaintyTotal absence of doubt
- objectivityFreedom from personal bias
validity · reality · factuality · honesty · sincerity · genuineness · accuracy · fidelity · reliability · evidence
aesthetics
Theory of beauty
- sublimityExalted, awe-inspiring quality
- harmonyAgreement or musical blend
- symmetryInvariance under transformation
elegance · proportion · splendor · radiance · majesty · grace · refinement · exquisiteness · form · perfection
virtue
Moral goodness or merit
- moralityRight and wrong principles
- benevolenceDisposition toward doing good
- righteousnessMoral correctness or virtue
ethics · charity · compassion · justice · integrity · kindness · altruism · nobility · mercy · generosity
transcendentalsrational numbers
Integers' quotients, including terminating decimals
integers · rationals · whole numbers · natural numbers · fractions
- transcendental experienceAwareness surpassing ordinary perception
- Transcendental MeditationTrademarked silent mantra method
- transcendental beautyLoveliness exceeding physical reality