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The Curriculum

The seven liberal arts

The arts called liberal because they befit a free mind: studied for the sake of understanding, not for gain. Three serve the mind as it names, judges and expresses what it knows; four study quantity. Take them as a spiral, every art three times and each round deeper: learn from the Library and the labs, practise with spaced review, prove each art with a check and a task, and read the sources in seminar.

Begin Round 1How it works

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Philosophia GrammarLogicRhetoricArithmeticGeometryMusicAstronomy
The seven arts

What each art is about

ArtCentral concern
Trivium the arts of language
GrammarGrammatica Understanding language, its structure, and meaning Opens soon
Logic or dialecticDialectica Definitions, inference, arguments, and objections Round 1 open
RhetoricRhetorica Clear, effective expression suited to an audience Opens soon
Quadrivium the arts of number
ArithmeticArithmetica Number and its properties Round 1 open
GeometryGeometria Magnitude, spatial relationships, and demonstration Round 1 open
MusicMusica Numerical relationships and harmony Round 1 open
AstronomyAstronomia Mathematical order and celestial motion Opens soon
The order of the arts

Why these seven, in this order

The seven are not a list of school subjects. In the classical view each art has its own object and method, and together they follow the order of things. On a common later reading, the Trivium serves the mind as it first grasps and names things, then judges and reasons about them, then expresses what it knows. The Quadrivium studies quantity: what can be counted (multitude) and what can be measured (magnitude), each considered in itself or in relation, at rest or in motion. All seven prepare for philosophy, which is why Philosophia sits at the centre of the rose.

Philosophiathe study of being as being, for which the seven arts prepare

Trivium the arts of the mind: they serve the intellect as it knows and expresses things

  1. Grammarapprehending and naming
  2. Logicjudging and reasoning
  3. Rhetoricexpressing what is known

Quadrivium the sciences of quantity

The classical order. Quantity is discrete or continuous (Aristotle, Categories 6); taken in itself or in relation, at rest or in motion, it gives the four mathematical arts (Nicomachus, Introduction to Arithmetic I.3). Matching the three arts of language to three acts of the mind is a later scheme: in Aquinas, logic itself covers all three acts.

Read the full account in the Library →

How it works

Three rounds. Four moves. Five levels.

An art, in the old sense, is a settled habit of the mind, formed by practice: not a pile of facts and not a trick. The checks and tasks are how you find out whether the habit has formed.

Three rounds

  1. Round I · Foundations The first pass through all seven arts: the core idea of every strand, from founding texts and simple labs.
  2. Round II · Practice The same strands worked harder: classic problems, longer proofs and arguments, real tunings and measurements.
  3. Round III · Mastery The turning points and limits of each art, and tasks you could show anyone.

Four moves in every competency

  1. Learn from a Library page or a lab, chosen for this one skill.
  2. Practise with spaced-review cards that come back before you forget them.
  3. Prove it twice: an objective check (pass at 80%) and a performance task with a rubric.
  4. Discuss a primary text in seminar: the question, not a quiz.

Five levels

  1. Not started
  2. Attempted You have opened the lesson, tried some cards, or started the check or task.
  3. Familiar Half the practice cards recalled at least once, or 60% on a check.
  4. Proficient The mastery check passed (80%) and three-quarters of the cards recalled.
  5. Mastered Proficient, the task done against its rubric, and recall that lasts: most cards still recalled weeks later, or two passes a week apart.
Principles

What this curriculum is for

  1. Understanding first. Not information, novelty or a credential. Success is understanding, through your own reasoning, what you could otherwise only repeat.
  2. Go to the roots. Ask what a thing is, how you know it, and what your way of looking at it assumes.
  3. Tradition is an argument. The great texts answer, correct and overturn one another. Read them attentively and independently: neither dismiss them nor defer to them.
  4. Sources show thinking in motion. A textbook gives the finished result; the original shows the problem that made it necessary.
  5. Words and numbers together. Interpreting a sentence and demonstrating a theorem are two powers of one mind. The seven arts train both.
  6. Conversation is accountable. In seminar you listen, answer the person before you, and justify your reading from the text.
  7. Freedom needs capacities. A set course takes you past "I'm not a maths person". Independence comes from what you can do, not from a menu of options.
  8. Humility. Say what you don't know. That is where inquiry starts.
The map

Every competency

Grammar

  1. Name the parts of speech and parse a sentence
  2. Define a term by genus and difference
  3. Restate a passage and find its ambiguity
  4. Parse complex sentences and repair them
  5. Choose the right kind of definition
  6. Read scope, negation and quantifiers
  7. Analyse a hard sentence from a primary text
  8. Settle a verbal dispute and trace a change of meaning
  9. Read signs, sense and reference

Logic

  1. Reconstruct an argument
  2. Test a definition
  3. Grade a claim
  4. Test an argument's form
  5. Define and refine a concept
  6. Weigh rival explanations
  7. Prove it, and know the limits
  8. Cross-examine a contested concept
  9. Calibrate your confidence

Rhetoric

  1. Mark the three appeals in a short speech
  2. Say one idea plainly to one reader
  3. State the strongest objection to your own claim
  4. Make a case that uses all three appeals honestly
  5. Explain the same idea to two audiences
  6. Find the point at issue
  7. Tell persuasion from manipulation
  8. Keep the uncertainty when you cut
  9. Defend a thesis against its best objection in an essay

Arithmetic

  1. Primes and Euclid's proof
  2. Ratio and common measure
  3. Patterns, recurrence and induction
  4. Factoring, sieving and testing
  5. The Euclidean algorithm
  6. Induction in practice
  7. Primes at scale
  8. Magnitudes without fractions
  9. Induction and the foundations of number

Geometry

  1. What each step rests on
  2. Construct and justify
  3. Squares, diagonals and the incommensurable
  4. Dependencies in Book I
  5. Euclid's basic constructions
  6. Area and the Pythagorean theorem by areas
  7. Gaps, axiom systems and rival geometries
  8. What compass and straightedge cannot do
  9. Magnitudes without numbers

Music

  1. Intervals as ratios of string length
  2. Measuring intervals in cents and hearing beats
  3. Twelve fifths and seven octaves
  4. Building scales from ratios
  5. Cents in practice
  6. Comparing tuning systems
  7. Ratio, number and the irrational
  8. Consonance, beats and roughness
  9. Choosing a temperament

Astronomy

  1. Describe the daily and yearly motions of the sky
  2. Reproduce Eratosthenes' measurement of the Earth
  3. Compare the three arrangements of the heavens
  4. Locate and predict with sky coordinates
  5. Distances to the Moon and the Sun
  6. Kepler's laws and the tests the telescope made possible
  7. Long cycles: precession, eclipses and the calendar
  8. Stellar parallax and the scale of the universe
  9. From Kepler's laws to Newton's moon test

Greyed items are planned for later rounds.

Progress as a table
ArtRound 1: FoundationsRound 2: PracticeRound 3: Mastery
GrammarComingComingComing
Logic or dialecticNot startedComingComing
RhetoricComingComingComing
ArithmeticNot startedComingComing
GeometryNot startedComingComing
MusicNot startedComingComing
AstronomyComingComingComing

Seminars

Read the sources

Twenty-one seminars, one per art per round, on primary texts from Plato and Euclid to Kepler and Newton. Each has a question worth an evening.

Open the seminars

Studium

How to study here

Self-administered checks and self-assessed tasks: no credential is awarded. The design borrows from Khan Academy (mastery levels), WGU (competencies proved by assessment) and St. John's College (seminars on primary texts); this site is not affiliated with any of them. Your progress, export and import →