Reading and attention Levels 1 to 10
The bar: Say it back: restate it in your own words, define its key terms, ask one real question about it, and do the practice step with the book open.
Level 1
Reading one poem slowly
Grammar
- Practice
- Method: Copy the poem out by hand. Underline every word you could not explain to someone else and look each one up. Write down one question the poem raises. Then do the same with two more short poems.
- Acts
- Understand exactly, Examine the reasons
Pass when: Copy fragment 31 out by hand, underline every word you could not explain, and look each one up. Write the one question the poem raises, then repeat the whole routine on two more short poems of your choice. You pass when every underlined word has a note in your own words and you can read each poem aloud with no word left unexplained.
On the site: How to Read a Great Book: Levels, Modes and the Completion Standard
Level 2
Saying it in your own words
Grammar
- Practice
- Method: Restate the poem in plain prose without reusing any of its phrases. Compare your version with the original line by line and note what was lost.
- Acts
- Understand exactly, Express it truly
Pass when: Write a plain-prose version of fragment 1 that reuses no phrase of the poem, then set it beside the original line by line. List at least five things your version lost, such as sound, word order or tone. You pass when your version shares no phrase of three words or more with the poem and each loss on your list can be pointed to in a particular line when you reopen the poem.
On the site: English Expression Mastery: Words, Sentences, Paragraphs and Speech
Level 3
What education is for: Sayers
Grammar Logic
- Practice
- Method: Outline the essay's argument as numbered steps. Mark which steps are claims of fact and which are proposals.
- Acts
- Understand exactly, Examine the reasons
Pass when: Set out the essay's argument as about eight numbered steps and mark each as a claim of fact or a proposal. State in two sentences what Sayers says education is for, and ask one real question about her proposal. You pass when you can reopen the essay and find the passage behind every numbered step.
On the site: The Seven Liberal Arts: a spiral curriculum, Liberal Arts and Reasoning: Start Here
Level 4
Order and method in reading: Hugh
Grammar Rhetoric
- Practice
- Method: Write a reading plan for the next ten levels that follows Hugh's advice on order and method, and start a reading notebook: date, pages, one question per sitting.
- Acts
- Understand exactly, Express it truly
Pass when: Write a plan for how you will work through the next ten levels (when you read, in what order you take the reading, notes and practice step of each, and how you record your questions), with one sentence beside each choice saying which piece of Hugh's advice on order and method it follows. Begin the notebook with an entry for your first sitting: date, pages, one question. You pass when every plan choice can be traced to a passage in Book 3 when you reopen it and the first notebook entry is complete.
On the site: The Weekly Loop: Read, Reconstruct, Make, Defend, Log, How to Read a Great Book: Levels, Modes and the Completion Standard
Level 5
Asking what a thing is: Meno, part 1
Grammar Logic
- Practice
- Logic: List every definition of virtue that Meno offers and the objection that defeats each one.
- Acts
- Understand exactly, Examine the reasons
Pass when: Without the book, state each of Meno's definitions of virtue in one sentence with the objection that defeats it. Then write one definition of your own and the strongest objection to it. You pass when every definition and objection matches the text when you reopen it.
On the site: What Does It Take to Know Something?, The Academy: Proofs, Definitions and the Method of Reason
Level 6
Learning by finding: Meno, part 2
Geometry Logic
- Practice
- Mathematics: Draw a square of side two and try to double its area before reading the boy's answer. Then redraw the figure that solves it and explain why it works.
- Acts
- Understand exactly, Check it against evidence
Pass when: Draw a square of side two and try to double its area before you read the boy's answer, then redraw the figure that solves it. Explain the figure aloud step by step, saying why the new square has twice the area and what the boy's wrong guesses showed him. You pass when your figure has a square built on the diagonal and your explanation counts the triangles to show that its area is eight.
On the site: Multipliers and Limits: Doubling the Square Again, Squares, diagonals and the incommensurable: Geometry, Round 1
Level 7
Knowledge and true opinion: Meno, part 3
Grammar Logic
- Practice
- Writing and speaking: In 200 words, state the difference between knowledge and true opinion that the dialogue ends with, and give one example of each from ordinary life.
- Acts
- Understand exactly, Express it truly
Pass when: Write 200 words stating the difference between knowledge and true opinion that the dialogue ends with, with one everyday example of each. Add one sentence saying what your example of true opinion would need before it counted as knowledge. You pass when you can reopen the end of the dialogue and find the passage that each claim in your 200 words rests on.
On the site: What Does It Take to Know Something?
Level 8
Narration: telling it straight
Rhetoric Grammar
- Practice
- Writing and speaking: Retell a story you know well in 150 words: who, what, when, where and why. Then tell it aloud in one minute, and again after cutting every unnecessary word.
- Acts
- Understand exactly, Express it truly
Pass when: Retell a story you know well in 150 words that answer who, what, when, where and why. Tell it aloud in one minute with a timer running, then tell it again after cutting every unnecessary word. Name one piece of advice from the Book 1 selections about speaking or writing and say whether your retelling followed it. You pass when the second telling is shorter than the first by the clock and both tellings still answer all five questions.
On the site: English Expression Mastery: Words, Sentences, Paragraphs and Speech, Rhetoric: one of the seven liberal arts
Level 9
What is up to us: Epictetus
Grammar Logic
- Practice
- Practical judgment: Sort twenty ordinary situations into what is and is not within a person's control, and write one sentence on how each column should be met.
- Acts
- Understand exactly, Act and review
Pass when: Sort twenty ordinary situations into what is and is not within a person's control, and write one sentence on how each column should be met. Mark the three situations that were hardest to sort and say what made them hard. You pass when you can restate the Manual's opening distinction in your own words, matching the text when you reopen it, and every situation has a placed entry with a reason.
On the site: Reasoning for What Ends? Wisdom, Character and the Examined Life
Level 10
Stage check: the Apology
Grammar Logic Rhetoric
- Practice
- Writing and speaking: Reconstruct Socrates' defence as three claims with their reasons. Deliver it aloud in three minutes, then write down the strongest objection a juror could make.
- Acts
- Understand exactly, Examine the reasons, Express it truly
Pass when: Without the text, state Socrates' defence as three claims with a reason for each, then deliver it aloud in three minutes. Write down the strongest objection a juror could make to one of the claims. You pass when your three claims and reasons match the speech when you reopen it and a timer shows the talk ended within three minutes.
On the site: Reconstruct an argument: Logic, Round 1
Grammar: words, sentences, meanings Levels 11 to 20
The bar: Say it back: restate it in your own words, define its key terms, ask one real question about it, and do the practice step with the book open.
Grammar
- Practice
- Language: Name the part of speech of every word in ten sentences from the Apology.
- Acts
- Understand exactly, Examine the reasons
Pass when: Name the part of speech of every word in ten sentences from the Apology, then choose three sentences you have not yet marked and do it again with your first notes closed. Define grammar in your own words and ask one real question about it. You pass when a dictionary confirms each part of speech you gave for the three fresh sentences, or you can defend any difference from the sentence itself.
On the site: Grammar: one of the seven liberal arts
Level 12
Sentences: who does what
Grammar
- Practice
- Language: Parse every sentence in one sonnet into subject, verb, object and modifiers, and rewrite each sentence in plain prose order.
- Acts
- Understand exactly, Express it truly
Pass when: Parse every sentence of one sonnet into subject, verb, object and modifiers, and rewrite each in plain prose order. Say in one sentence what the longest sentence of the sonnet asserts. You pass when each prose sentence, read aloud, says what the original says and you can name the subject of every verb you marked.
On the site: Grammar: one of the seven liberal arts, English Expression Mastery: Words, Sentences, Paragraphs and Speech
Level 13
Words and their histories
Grammar
- Practice
- Language: For twenty words from the poems, record the dictionary sense the poem uses and the word's origin.
- Acts
- Understand exactly, Check it against evidence
Pass when: Write, for twenty words from the ten poems, the dictionary sense the poem uses and the word's origin, from a dictionary that gives origins. Choose two words whose older sense changes how you read the line and say how. You pass when each of the twenty entries gives a sense you can justify from the line it stands in.
On the site: English Expression Mastery: Words, Sentences, Paragraphs and Speech
Grammar
- Practice
- Language: Mark the parallel lines in two psalms and say whether each pair repeats, contrasts or extends the first line.
- Acts
- Understand exactly, Examine the reasons
Pass when: Mark the parallel lines in two of the psalms and label each pair as repeating, contrasting or extending the first line. Restate one psalm in plain prose, and ask one real question about a pair that was hard to label. You pass when, for every labelled pair, you can point to the words in the second line that repeat, contrast or extend the first.
On the site: How to Read a Great Book: Levels, Modes and the Completion Standard
Level 15
Words as signs: Augustine
Grammar Logic
- Practice
- Language: Classify thirty signs (words, gestures, symbols) as natural or given, and the given ones as literal or figurative, with one line of reason each.
- Acts
- Understand exactly, Examine the reasons
Pass when: Classify thirty signs, among them words, gestures and symbols, as natural or given, and classify the given ones as literal or figurative, with one line of reason each. Define 'sign' in your own words from Book 2. You pass when your definition sorts five new things into sign and not-sign without a doubtful case and the reasons for your classes agree with what Book 2 says when you reopen it.
On the site: Observe, Define, Represent: The First Three Moves
Level 16
Ambiguity and how to settle it
Grammar Logic
- Practice
- Language: Collect ten ambiguous sentences from books or newspapers. Show the two readings of each and what settles it: punctuation, context, or the author's other words.
- Acts
- Understand exactly, Examine the reasons
Pass when: Collect ten ambiguous sentences from books or newspapers and write both readings of each, with what settles the matter: punctuation, context or the author's other words. State in your own words what Book 3 advises when a passage is ambiguous. You pass when the two readings of each sentence are plainly different when you read them aloud and each choice has a written reason.
On the site: English Expression Mastery: Words, Sentences, Paragraphs and Speech
Level 17
Definition: kind and difference
Logic Grammar
- Practice
- Logic: Write definitions by kind and difference for fifteen common terms, then test each by finding something it wrongly includes or excludes.
- Acts
- Understand exactly, Examine the reasons
Pass when: Write a definition by kind and difference for each of fifteen common terms. Test each by looking for one thing it wrongly includes and one it wrongly excludes, and rewrite any that fail. You pass when every final definition has a recorded search for counterexamples and you can explain kind and difference in your own words with an example.
On the site: Test a definition: Logic, Round 1
Level 18
What translation loses
Grammar Rhetoric
- Practice
- Language: Compare two public-domain English translations of the Iliad's opening lines, such as Chapman's and Pope's. List what each keeps and what each changes.
- Acts
- Understand exactly, Examine the reasons
Pass when: Set Chapman's and Pope's versions of the Iliad's opening lines side by side and list what each keeps and what each changes in sound, word order, tone and meaning. Write 150 words on what Woolf says the reader without Greek is missing. You pass when each item on your list points to a particular word or phrase in one of the two translations and your 150 words match the essay when you reopen it.
On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond
Level 19
Stress and metre
Grammar Rhetoric
- Practice
- Language: Mark the stressed syllables in twenty lines and name the metre of each poem. Read them aloud with the stresses you marked.
- Acts
- Understand exactly, Check it against evidence
Pass when: Mark the stressed syllables in twenty lines and name the metre of each of the five poems. Read the lines aloud with your marks, and find two lines where the stress of natural speech pulls against the metre. You pass when a dictionary agrees with your stress on every word you were unsure of and your reading aloud follows your marks.
On the site: English Expression Mastery: Words, Sentences, Paragraphs and Speech
Level 20
Stage check: a close reading
Grammar Rhetoric
- Practice
- Writing and speaking: Write a 500-word close reading that answers one question about a sonnet with evidence from its words, sound and syntax. Read it aloud and revise one paragraph after hearing it.
- Acts
- Understand exactly, Examine the reasons, Express it truly
Pass when: Write a 500-word close reading that answers one question about a sonnet with evidence from its words, sound and syntax. Read it aloud, revise one paragraph after hearing it, and keep both versions. You pass when every claim in the essay is tied to words you can find in the sonnet and the revised paragraph reads more clearly aloud than the first.
On the site: English Expression Mastery: Words, Sentences, Paragraphs and Speech, Technical Writing as Reasoning
Logic: terms, statements, inference Levels 21 to 30
The bar: Say it back: restate it in your own words, define its key terms, ask one real question about it, and do the practice step with the book open.
Level 21
What can be said of a thing
Logic Grammar
- Practice
- Logic: Sort forty predicates ("is white", "is in the market", "is a horse") into Aristotle's categories and mark the hard cases.
- Acts
- Understand exactly, Examine the reasons
Pass when: Sort forty predicates into Aristotle's categories, mark the hard cases, and write a line on why each hard case is hard. Then write the categories from memory with an example of your own for each. You pass when your list of categories matches the chapters when you reopen them and every hard case has a stated reason.
On the site: Logic or dialectic: one of the seven liberal arts
Level 22
Affirming and denying
Logic
- Practice
- Logic: For ten universal statements ('every S is P' or 'no S is P'), write the contradictory and the contrary, and draw the square of opposition for one of them.
- Acts
- Understand exactly, Examine the reasons
Pass when: For ten universal statements of the form 'every S is P' or 'no S is P', write the contradictory and the contrary, then draw the square of opposition for one of them and label its corners. Say in your own words why contradictories cannot both be true and cannot both be false. You pass when each of your ten contradictories passes the test that exactly one of the pair must be true, and your contraries can both be false.
On the site: Logic or dialectic: one of the seven liberal arts
Level 23
Statements and their forms
Logic
- Practice
- Logic: Symbolise twenty English sentences in sentential logic and say which English words were hard to translate.
- Acts
- Understand exactly, Examine the reasons
Pass when: Symbolise twenty English sentences in sentential logic, with a key saying what each letter stands for. List the sentences where an English word was hard to translate and say what you chose. You pass when reading each formula back into English, using only your key, gives a sentence that means the original.
On the site: Reconstruct an argument: Logic, Round 1
Level 24
Validity and truth tables
Logic
- Practice
- Logic: Use truth tables to test ten arguments for validity. For each invalid one, describe the counterexample row in plain words.
- Acts
- Examine the reasons, Check it against evidence
Pass when: Test ten arguments for validity with truth tables. For each invalid one, point to the row with true premises and a false conclusion and describe it in plain words. You pass when you recheck every table row by row and your verdicts do not change.
On the site: Reconstruct an argument: Logic, Round 1
Level 25
Rebuilding an argument: Crito
Logic Grammar
- Practice
- Logic: Set out the speech of the Laws as numbered premises and a conclusion. Mark the premise you find weakest and say why.
- Acts
- Understand exactly, Examine the reasons
Pass when: Set out the speech of the Laws as numbered premises and a conclusion. Mark the premise you find weakest, state the strongest objection to it, and say whether the conclusion survives. You pass when each numbered premise can be found in the speech when you reopen the dialogue and the conclusion follows from the premises as you listed them.
On the site: Reconstruct an argument: Logic, Round 1
Logic
- Practice
- Logic: Judge twenty syllogisms valid or invalid, naming the rule each invalid one breaks.
- Acts
- Examine the reasons, Check it against evidence
Pass when: Judge twenty syllogisms valid or invalid, naming the rule broken by each invalid one. Write two valid syllogisms of your own and two invalid ones that look valid. You pass when you can state each rule from the chapter without notes and a second pass over the twenty gives the same verdicts.
On the site: Logic or dialectic: one of the seven liberal arts
Logic
- Practice
- Logic: Complete fifteen natural-deduction proofs, then write one of them out in ordinary English.
- Acts
- Examine the reasons, Check it against evidence
Pass when: Complete fifteen natural-deduction proofs, then write one of them out in ordinary English, one sentence for each line. You pass when every line of every proof cites a rule and the earlier lines it uses, and checking each line against its rule finds no error.
On the site: Logic or dialectic: one of the seven liberal arts
Level 28
Fallacies, old and new
Logic Rhetoric
- Practice
- Logic: Name the fallacy or trick in fifteen examples and rewrite three of them as honest arguments.
- Acts
- Examine the reasons, Express it truly
Pass when: Name the fallacy or trick in fifteen examples, and rewrite three of them as honest arguments that claim only what their evidence supports. You pass when each name is defined in one sentence from the readings and each rewritten argument can be set out as premises and a conclusion without the trick.
On the site: The Seven Liberal Arts, Hands-On: Logic, Proof and the Quadrivium, Real Finding or Hype?
Logic
- Practice
- Logic: Translate twenty sentences using "all", "some" and "no" into quantified form, and find two that ordinary English leaves ambiguous.
- Acts
- Understand exactly, Examine the reasons
Pass when: Translate twenty sentences using 'all', 'some' and 'no' into quantified form, with a key. Find two sentences that ordinary English leaves ambiguous and write a formula for each reading. You pass when each formula read back into English means the original and the two readings of each ambiguous sentence have different formulas.
On the site: Logic or dialectic: one of the seven liberal arts
Level 30
Stage check: the Declaration's argument
Logic Rhetoric
- Practice
- Logic: Reconstruct the Declaration's argument as premises and a conclusion, test its form, and write 400 words on which premise carries the most weight.
- Acts
- Understand exactly, Examine the reasons, Express it truly
Pass when: Reconstruct the Declaration's argument as numbered premises and a conclusion and test whether the conclusion follows. Write 400 words on which premise carries the most weight and what would happen to the conclusion if it failed. You pass when every premise is a claim you can find in the text when you reopen it and your 400 words answer what happens if the weightiest premise fails.
On the site: Reconstruct an argument: Logic, Round 1
Rhetoric: composition and speaking Levels 31 to 40
The bar: Rebuild it: set out the argument or construction step by step, and do the practice step without help.
Level 31
The orator's education: Cicero
Rhetoric Grammar
- Practice
- Writing and speaking: Paraphrase one paragraph three ways: plainer, more formal and shorter, keeping the sense each time.
- Acts
- Understand exactly, Express it truly
Pass when: Paraphrase one paragraph of the reading three ways: plainer, more formal and shorter, keeping the sense each time. Then write three sentences saying what Cicero's selections claim a speaker must learn. You pass when you can state the same point in one sentence from each of your three versions and the shortest is at most half the length of the original.
On the site: English Expression Mastery: Words, Sentences, Paragraphs and Speech
Level 32
Proof and refutation
Rhetoric Logic
- Practice
- Writing and speaking: Take a short claim from a fable, a proverb or a newspaper, and write a 250-word confirmation of it and a 250-word refutation.
- Acts
- Examine the reasons, Express it truly
Pass when: Take a short claim from a fable, a proverb or a newspaper and write a 250-word confirmation of it and a 250-word refutation. Name one point from the Book 2 selections that you followed in writing them. You pass when each piece gives its reasons in order, the refutation answers the best point of the confirmation, and you can say in a sentence which of the two is stronger and why.
On the site: Rhetoric: one of the seven liberal arts
Level 33
Three ways to persuade
Rhetoric Logic
- Practice
- Writing and speaking: Find each of Aristotle's three proofs (the speaker's character, the hearer's emotion, the argument itself) in two speeches, quoting the line that shows each.
- Acts
- Understand exactly, Examine the reasons
Pass when: Find each of Aristotle's three kinds of proof in two speeches and write out the line that shows each, six lines in all. Give a one-sentence reason with every line. You pass when each reason uses Aristotle's description of that kind of proof from Book 1 and the six lines are sorted the same way when you sort them again a day later.
On the site: Rhetoric: one of the seven liberal arts
Level 34
Imitation: learning from a model
Rhetoric Grammar
- Practice
- Writing and speaking: Write a speech of the same length for a different occasion that follows the Gettysburg Address sentence by sentence in structure.
- Acts
- Understand exactly, Express it truly
Pass when: Write a speech of the same length as the Gettysburg Address for a different occasion, following it sentence by sentence in structure. Set the two side by side and write beside each of your sentences what it does that its model sentence does. You pass when every sentence of yours is matched to one sentence of the original and the two speeches take about the same time to read aloud.
On the site: English Expression Mastery: Words, Sentences, Paragraphs and Speech, Rhetoric: one of the seven liberal arts
Level 35
Writing and revision
Rhetoric Grammar
- Practice
- Writing and speaking: Write 400 words on a question from the readings, then revise twice: first cut a quarter, then fix every sentence a listener could misread.
- Acts
- Express it truly, Check it against evidence
Pass when: Write 400 words on a question from the readings, then revise twice: first cut a quarter, then fix every sentence a listener could misread. Keep all three drafts and name one point from the Book 10 reading that you used in revising. You pass when the first revision is about 300 words, every cut has a reason written in the margin, and reading the second revision aloud leaves no sentence you stumble over.
On the site: Technical Writing as Reasoning, English Expression Mastery: Words, Sentences, Paragraphs and Speech
Level 36
Arrangement and memory
Rhetoric
- Practice
- Writing and speaking: Arrange a three-minute talk into introduction, statement, proof, refutation and conclusion. Memorise its outline by places (the method of loci) and give it without notes.
- Acts
- Express it truly, Check it against evidence
Pass when: Arrange a three-minute talk into introduction, statement, proof, refutation and conclusion. Fix its outline in memory by places, using the method of loci, and give the talk without notes. You pass when you give all five parts in order within three minutes with no notes in your hand and your written outline matches what you said.
On the site: Rhetoric: one of the seven liberal arts
Rhetoric Music
- Practice
- Writing and speaking: Record a three-minute talk, listen back for pace, pauses and emphasis, and record it again with three specific changes.
- Acts
- Express it truly, Check it against evidence
Pass when: Record a three-minute talk, listen back and note its pace, pauses and emphasis, then record it again with three specific changes written down beforehand, each taken from a point in the Book 11 reading. You pass when you can hear each of the three changes in the second recording and the second recording is clearer than the first on a fresh listen.
On the site: Rhetoric: one of the seven liberal arts
Level 38
Comparison and style
Rhetoric Grammar
- Practice
- Writing and speaking: Write a 400-word comparison of two characters or two arguments from the readings, then mark where you aimed at each of Cicero's virtues of style: correctness, clarity, ornament and fitness.
- Acts
- Understand exactly, Express it truly
Pass when: Write a 400-word comparison of two characters or two arguments from the readings. Mark in the margin where you aimed at each of Cicero's virtues of style: correctness, clarity, ornament and fitness. You pass when each virtue has at least one marked passage and a reading of the 400 words finds each marked passage doing what its virtue names.
On the site: English Expression Mastery: Words, Sentences, Paragraphs and Speech
Level 39
From topic to question
Rhetoric Logic
- Practice
- Evidence and inquiry: Turn three interests into research questions, and each question into a problem a reader would care about.
- Acts
- Understand exactly, Examine the reasons, Express it truly
Pass when: Turn three interests into research questions, then turn each question into a problem by stating why a reader would care about the answer. You pass when each problem is written as a topic, a question and a reason in three plain sentences, and each question is one that evidence could answer.
On the site: Principles Ledger and Question Arcs
Level 40
Stage check: the good speaker
Rhetoric Logic
- Practice
- Writing and speaking: Write a 600-word persuasive essay on a question from the stage, deliver it in four minutes, and answer two objections a listener raises.
- Acts
- Examine the reasons, Express it truly
Pass when: Write a 600-word persuasive essay on a question from the stage and deliver it in four minutes. Write down two objections a listener could raise and answer each aloud. You pass when you can state your thesis in one sentence, the delivery fits within four minutes by the clock, and each answer to an objection uses a reason from your essay.
On the site: Rhetoric: one of the seven liberal arts
Arithmetic and algebra Levels 41 to 50
The bar: Rebuild it: set out the argument or construction step by step, and do the practice step without help.
Level 41
Number in itself
Arithmetic
- Practice
- Mathematics: Classify the numbers 1 to 50 as even or odd, prime or composite, and perfect, deficient or abundant. Prove that the sum of two odd numbers is even.
- Acts
- Understand exactly, Check it against evidence
Pass when: Classify the numbers 1 to 50 in a table as even or odd, prime or composite, and perfect, deficient or abundant, marking 1 as neither prime nor composite. Prove in numbered steps that the sum of two odd numbers is even. You pass when you can recompute the divisor sums for five numbers of your choice and they agree with the table, which shows 6 and 28 as perfect.
On the site: Primes and Euclid's proof: Arithmetic, Round 1
Level 42
The oldest algorithm
Arithmetic
- Practice
- Mathematics: Find the greatest common measure of eight pairs of numbers by Euclid's repeated subtraction and then by division, and explain why the process must stop.
- Acts
- Understand exactly, Check it against evidence
Pass when: Find the greatest common measure of eight pairs of numbers by repeated subtraction and again by division, and write down why the process must stop. You pass when both methods agree on all eight pairs and your explanation uses the fact that a list of positive whole numbers cannot keep shrinking for ever.
On the site: Ratio and common measure: Arithmetic, Round 1
Arithmetic Music
- Practice
- Mathematics: Name the ratio of twenty pairs of numbers, covering every kind he names, in Nicomachus's terms (multiple, superparticular and the rest) and as fractions, and order them from least to greatest.
- Acts
- Understand exactly, Check it against evidence
Pass when: Name the ratio of twenty pairs of numbers, covering every kind the chapters name, in Nicomachus's terms and as fractions, then order the twenty from least to greatest. You pass when each name matches the definition in the chapters when you reopen them and your ordering is confirmed by turning each fraction into a decimal.
On the site: Ratio and common measure: Arithmetic, Round 1
Level 44
Algebra 1: letters for numbers
Arithmetic
- Practice
- Mathematics: Simplify forty polynomial expressions, collecting like terms and expanding products, and check each result by substituting a number.
- Acts
- Understand exactly, Check it against evidence
Pass when: Simplify forty polynomial expressions by collecting like terms and expanding products, and check each result by substituting a number. You pass when each result agrees with the original expression at two different numbers and you can redo five of them from a blank page and reach the same answers.
On the site: Algebra: The Skills That Carry Everything
Level 45
Algebra 2: exponents and factoring
Arithmetic
- Practice
- Mathematics: Work thirty problems on the laws of exponents and thirty on factoring, including the difference of two squares, and check each factorisation by multiplying back.
- Acts
- Understand exactly, Check it against evidence
Pass when: Work thirty problems on the laws of exponents and thirty on factoring, including the difference of two squares, and check each factorisation by multiplying back. You pass when every factorisation multiplies back to the original expression and you can state each law of exponents with an example of your own.
On the site: Algebra: The Skills That Carry Everything
Level 46
Algebra 3: algebraic fractions
Arithmetic
- Practice
- Mathematics: Simplify, add and divide thirty rational expressions, stating the values that must be excluded each time.
- Acts
- Understand exactly, Check it against evidence
Pass when: Simplify, add and divide thirty rational expressions, and list the values that must be excluded each time. You pass when each answer agrees with the original at two numbers you substitute and each exclusion list names the values that make a denominator or a divisor zero.
On the site: Algebra: The Skills That Carry Everything
Level 47
Algebra 4: two unknowns
Arithmetic Geometry
- Practice
- Mathematics: Solve twenty pairs of simultaneous equations by substitution and by elimination, and graph three pairs to see where the lines meet.
- Acts
- Understand exactly, Check it against evidence
Pass when: Solve twenty pairs of simultaneous equations by both substitution and elimination, and graph three pairs to see where the lines meet. You pass when each solution satisfies both original equations, the two methods agree, and each graphed pair meets at the point your algebra gave.
On the site: Algebra: The Skills That Carry Everything
Level 48
Algebra 5: the quadratic
Arithmetic Geometry
- Practice
- Mathematics: Solve twenty quadratic equations by factoring, by completing the square and by the formula, and draw one completion of the square as a figure.
- Acts
- Understand exactly, Check it against evidence
Pass when: Solve twenty quadratic equations by factoring, by completing the square and by the formula, and draw one completion of the square as a figure. You pass when every method you used on an equation gives the same roots and each root put back into the equation gives zero, or nearly zero at the decimal places you kept.
On the site: Algebra: The Skills That Carry Everything
Level 49
A proof you can carry
Arithmetic Logic
- Practice
- Mathematics: Prove that there are infinitely many primes, aloud and without the book, then write the proof for a reader who has never seen it.
- Acts
- Understand exactly, Examine the reasons, Express it truly
Pass when: Prove aloud and without the book that there are infinitely many primes, then write the proof for a reader who has never seen it. You pass when your spoken proof builds a new number from a list of primes, shows why no prime on the list can divide it, and matches the structure of the proposition when you reopen it.
On the site: Primes and Euclid's proof: Arithmetic, Round 1
Level 50
Stage check: number and equation
Arithmetic
- Practice
- Mathematics: Choose thirty problems from the exercises of Levels 41 to 49 and sit them under time, mark it, and write a one-page guide to the method you got wrong most often.
- Acts
- Understand exactly, Check it against evidence, Express it truly
Pass when: Choose thirty problems from the exercises of Levels 41 to 49, at least two from each level, and sit them as a test within a time limit you set beforehand, then check every answer by substitution or by working back. Write a one-page guide to the method you got wrong most often, or the one that took you longest if you made no errors. You pass when every answer you marked correct has been verified by checking back and the guide holds one worked example of that method, redone correctly.
On the site: Placement, Repair and Retention: Keeping Mathematics Alive
Geometry: Euclid's first book Levels 51 to 60
The bar: Rebuild it: set out the argument or construction step by step, and do the practice step without help.
Geometry Logic
- Practice
- Mathematics: Copy out the postulates and common notions. Say which statements are definitions and which are assumptions, and why Euclid needs both.
- Acts
- Understand exactly, Examine the reasons
Pass when: Copy out the postulates and common notions, then sort the starting points of Book 1 into definitions, postulates and common notions in a three-column table. Write one paragraph on why Euclid needs both definitions and assumptions. You pass when you can write the five postulates from memory in your own words and your table agrees with the book when you reopen it.
On the site: What each step rests on: Geometry, Round 1
Level 52
The first construction
Geometry
- Practice
- Mathematics: Do each construction with compass and straightedge, then demonstrate Proposition 1 aloud, naming the postulate or definition behind every step.
- Acts
- Understand exactly, Check it against evidence
Pass when: Carry out the constructions of Propositions 1 to 3 with compass and straightedge, then demonstrate Proposition 1 aloud, naming the postulate or definition behind every step. You pass when the three sides of your triangle measure equal with a ruler to within the width of your pencil line and you gave a reason for every step without the book.
On the site: Construct and justify: Geometry, Round 1
Geometry Logic
- Practice
- Mathematics: Demonstrate Propositions 4 and 5 without the book, and find the step in Proposition 4 that rests on something Euclid never states as a postulate.
- Acts
- Examine the reasons, Check it against evidence
Pass when: Demonstrate Propositions 4 and 5 without the book, then find the step in Proposition 4 that rests on something Euclid never states as a postulate. Write that assumption in a sentence. You pass when your demonstrations match the book step for step when you reopen it and you can say why the unstated step is needed.
On the site: What each step rests on: Geometry, Round 1
Level 54
Bisections and angles
Geometry
- Practice
- Mathematics: Bisect a given angle and a given straight line, and demonstrate that vertical angles are equal, with a diagram for each.
- Acts
- Understand exactly, Check it against evidence
Pass when: Bisect a given angle and a given straight line, and demonstrate that vertical angles are equal, drawing a diagram for each. You pass when your constructions measure into equal halves, with a protractor and ruler, to within the width of your pencil line and your proof of the vertical angles names the earlier results it relies on.
On the site: Construct and justify: Geometry, Round 1
Geometry
- Practice
- Mathematics: Demonstrate Propositions 16 and 20 aloud, then test Proposition 20 on three triangles you draw and measure.
- Acts
- Examine the reasons, Check it against evidence
Pass when: Demonstrate Propositions 16 and 20 aloud, then test Proposition 20 on three triangles you draw and measure. You pass when your demonstrations name the earlier result behind each step and, for all three triangles, any two measured sides added together are longer than the third.
On the site: What each step rests on: Geometry, Round 1
Level 56
Parallels and the fifth postulate
Geometry Logic
- Practice
- Mathematics: Find the first proposition that uses the fifth postulate and explain why the propositions before it do not need it.
- Acts
- Examine the reasons, Check it against evidence
Pass when: Find the first proposition in Book 1 that uses the fifth postulate and write a paragraph on why the propositions before it do not need it. You pass when you can point to the line in its proof where the postulate is invoked and you have checked that no proof before it invokes the postulate.
On the site: What each step rests on: Geometry, Round 1
Geometry
- Practice
- Mathematics: Construct a parallelogram equal to a given triangle in a given angle (Proposition 42) and explain how the earlier propositions make it possible.
- Acts
- Understand exactly, Check it against evidence
Pass when: Construct a parallelogram equal to a given triangle in a given angle, as Proposition 42 does, and explain which earlier propositions make the construction possible. You pass when your drawing has a parallelogram whose area equals the triangle's, tested by measuring base and height, and your explanation names each earlier proposition you used.
On the site: Construct and justify: Geometry, Round 1
Level 58
Pythagoras, Euclid's way
Geometry
- Practice
- Mathematics: Demonstrate Proposition 47 from the figure without the book, then explain how it differs from the proof by similar triangles.
- Acts
- Understand exactly, Examine the reasons, Check it against evidence
Pass when: Demonstrate Proposition 47 from the figure without the book, then write a paragraph on how it differs from the proof by similar triangles. You pass when your demonstration compares areas of squares step by step, matches the book when you reopen it, and you have checked the theorem by calculation on a right triangle with sides 3, 4 and 5 and on one more of your own.
On the site: Squares, diagonals and the incommensurable: Geometry, Round 1
Level 59
Geometric algebra
Geometry Arithmetic
- Practice
- Mathematics: Draw the figure for each proposition and write it as an algebraic identity, then say what the figures show that the symbols hide.
- Acts
- Understand exactly, Examine the reasons, Check it against evidence
Pass when: Draw the figure for each proposition and write it as an algebraic identity, then write a paragraph on what the figures show that the symbols hide. You pass when each identity holds when you substitute numbers and each figure's areas add up to the two sides of its identity.
On the site: Geometry, Euclid and Trigonometry
Level 60
Stage check: an oral demonstration
Geometry Logic
- Practice
- Mathematics: Demonstrate three linked propositions in order, book closed, to a listener who may ask "why?" at any step. Write one of them out in full.
- Acts
- Examine the reasons, Express it truly
Pass when: Demonstrate three linked propositions in order, book closed, aloud to a listener who may ask 'why?' at any step, or to a recording you question yourself. Write one of the three out in full. You pass when each step gives a reason from an earlier proposition, postulate or definition, and a comparison with the book finds no missing or wrong step.
On the site: What each step rests on: Geometry, Round 1
Music and astronomy Levels 61 to 70
The bar: Test it: check one claim against evidence or raise one objection, and answer it.
Level 61
Notation and the scale
Music Grammar
- Practice
- Music: Learn to read pitch and rhythm in standard notation and sing a major scale with note names, slowly, recording yourself.
- Acts
- Understand exactly, Check it against evidence
Pass when: Learn to read pitch and rhythm in standard notation and sing a major scale with note names, slowly, recording yourself. Choose one claim about pitch or the scale, from the selections or from the site's Tools page, that an instrument or a tuner can test, and test it. You pass when your recording matches a drone or tuner on the eight scale notes and you can state the claim, your test and its result in three sentences.
On the site: Music: one of the seven liberal arts, Guitar Tools: Tuner, Metronome, Drone, Fretboard
Level 62
Intervals as ratios
Music Arithmetic
- Practice
- Music: On a monochord (the site's Tools page has one), find the octave, fifth and fourth by string length, write each as a ratio, and sing each interval from a given note.
- Acts
- Understand exactly, Check it against evidence
Pass when: Find the octave, fifth and fourth by string length on a monochord and write each as a ratio. Sing each interval from a given note, and test one claim about string-length ratios, from the selections or from the site's Tools page, against your measurements. You pass when your measured lengths agree with the ratios you wrote to within an error you state and your sung intervals match the monochord's when played back.
On the site: Intervals as ratios of string length: Music, Round 1, Labs: proofs, sound and instruments
Level 63
The diatonic system and chant
Music
- Practice
- Music: Follow two chants in notation (square notation or a modern transcription) while listening and sing one of them. Name the interval between each pair of successive notes in one phrase.
- Acts
- Understand exactly, Check it against evidence
Pass when: Follow two chants in notation (square notation or a modern transcription) while listening, and sing one of them. Say which note each chant ends on and which note it keeps returning to, and what that suggests about the scale it uses. Name the interval between each pair of successive notes in one phrase. You pass when your statement about the final and the returning note agrees with a keyboard or tuner, your list of intervals, checked against a keyboard or tuner, contains no wrong name and your singing keeps to the chant's notes on a second hearing.
On the site: Music: one of the seven liberal arts
Level 64
Listening with a score
Music Grammar
- Practice
- Music: Listen three times with a score: first for the entries of each voice, then for where the words are heard clearly, then for the cadences. Mark all three.
- Acts
- Understand exactly, Examine the reasons, Check it against evidence
Pass when: Listen three times with a score: first for the entry of each voice, then for where the words are heard clearly, then for the cadences. Write 150 words testing one claim about this style, such as that the words are kept clear, against what you marked. You pass when your marks agree on a further listening and every point in your 150 words refers to a place you marked in the score.
On the site: Music: one of the seven liberal arts
Music
- Practice
- Music: Follow the subject through the Invention with the score, marking each entry, inversion and change of key you can hear.
- Acts
- Understand exactly, Check it against evidence
Pass when: Follow the subject through the Invention with the score and mark each entry, inversion and change of key you can hear, saying plainly if you hear no inversion. State one claim about the piece, such as that both voices take up the same subject, and test it against your marks. You pass when you can sing or hum the subject from memory, a second listening finds no entry missing or wrongly marked, and your marks support or refute the claim.
On the site: Music: one of the seven liberal arts
Level 66
The sun's daily path
Astronomy
- Practice
- Laboratory: Set up a gnomon (a straight stick upright on level ground) and mark the tip of its shadow every half hour for a day. Find local noon and the north-south line.
- Acts
- Check it against evidence, Understand exactly
Pass when: Set up a gnomon on level ground and mark the tip of its shadow every half hour for a day. Find local noon as the time of the shortest shadow and draw the north-south line through the base. You pass when your marks form a smooth curve and your north-south line agrees with a compass to within about ten degrees once you correct the compass for magnetic declination at your location (look up the local value).
On the site: The Sky as a Sphere: Days, Seasons and the Phases of the Moon, Explain the sky: days, seasons and phases: Astronomy, Round 1
Level 67
The moon's month
Astronomy
- Practice
- Laboratory: Record the moon's phase, position and time on as many evenings and mornings as you can over four weeks, and explain the phases with a lamp and a ball.
- Acts
- Check it against evidence, Understand exactly
Pass when: Record the moon's phase, position and time on as many evenings and mornings as you can over four weeks, drawing each, and explain the phases with a lamp and a ball. You pass when your record has at least ten observations and your lamp-and-ball model reproduces each phase you drew, including a prediction of one evening's phase that you wrote down in advance and then checked.
On the site: Explain the sky: days, seasons and phases: Astronomy, Round 1, The Sky as a Sphere: Days, Seasons and the Phases of the Moon
Level 68
Measuring the Earth
Astronomy Arithmetic
- Practice
- Laboratory: Rework Eratosthenes' measurement of the Earth with shadow data, and state which input carries the most uncertainty.
- Acts
- Understand exactly, Check it against evidence
Pass when: Rework Eratosthenes' measurement of the Earth with shadow data and state which input carries the most uncertainty. Recompute with that input changed by a plausible amount and report the range of results. You pass when your result and range are given in kilometres and your recomputation shows how much a small change in the most uncertain input moves the answer.
On the site: Eratosthenes Measures the Earth: Shadows, Angles and Stated Assumptions, Reproduce Eratosthenes' measurement of the Earth: Astronomy, Round 1
Level 69
Why the seasons happen
Astronomy Geometry
- Practice
- Laboratory: Explain the seasons by the tilt of the Earth's axis with a model, and give one piece of evidence against the common explanation by distance from the sun.
- Acts
- Understand exactly, Check it against evidence
Pass when: Explain the seasons with a model, such as a lamp and a tilted globe, and give one piece of evidence against explaining them by the Earth's distance from the sun. You pass when your model shows the sun higher and the days longer in the summer hemisphere and your evidence is stated in a sentence and tested against the distance explanation.
On the site: The Sky as a Sphere: Days, Seasons and the Phases of the Moon, Explain the sky: days, seasons and phases: Astronomy, Round 1
Level 70
Stage check: ratio heard and seen
Music Astronomy Arithmetic
- Practice
- Music: Sing the octave, fifth and fourth on request, explain one sky observation with a model, and write 400 words on ratio in music and in the heavens, saying where the link is fact and where it is analogy.
- Acts
- Check it against evidence, Express it truly
Pass when: Sing the octave, fifth and fourth on request, explain one sky observation with a model, and write 400 words on ratio in music and in the heavens, labelling each link between them as fact or analogy. You pass when your sung intervals agree with a reference instrument, the model reproduces the observation, and every link in the essay carries a label and a reason.
On the site: From a Vibrating String to a Proof, The Science of Music: Ratios, Beats, the Comma and String Physics
Inquiry: observation, measurement, probability Levels 71 to 80
The bar: Test it: check one claim against evidence or raise one objection, and answer it.
Level 71
Observation and inference
Grammar Logic
- Practice
- Laboratory: Observe one plant or animal for a week. Draw it, measure it, and keep two columns: what you saw and what you inferred.
- Acts
- Understand exactly, Check it against evidence
Pass when: Observe one plant or animal for a week, drawing and measuring it, and keep two columns: what you saw and what you inferred. You pass when every entry in the 'saw' column is something another observer looking at the same organism could check and each inference names the observation it rests on.
On the site: Observe, Define, Represent: The First Three Moves
Level 72
Measuring and its errors
Arithmetic
- Practice
- Laboratory: Measure the same object ten times with a ruler and with a kitchen scale. Find the mean and the spread, and name two sources of error.
- Acts
- Check it against evidence, Examine the reasons
Pass when: Measure the same object ten times with a ruler and ten times with a kitchen scale, and find the mean and spread of each set. Name two sources of error, and write down one claim from the first propositions of Archimedes that you could test by measurement and what you would measure. You pass when both sets are recorded to the instrument's resolution, the means and ranges are given, and the sources of error are specific to your instruments.
On the site: Quantitative Reasoning with Stated Assumptions
Level 73
Data and study design
Arithmetic Logic
- Practice
- Evidence and inquiry: Classify the variables in five published studies, say whether each was an experiment or an observational study, and what that allows it to conclude.
- Acts
- Examine the reasons, Check it against evidence
Pass when: Classify the variables in five published studies, say whether each was an experiment or an observational study, and state what that design allows it to conclude. You pass when you can point in each report to the sentence showing how subjects were assigned or observed and your conclusion claims no more than that design allows.
On the site: Reading Nutrition Evidence: What a Study Can and Cannot Show
Level 74
Probability and base rates
Arithmetic Logic
- Practice
- Evidence and inquiry: Solve ten conditional-probability problems, including a screening test for a rare condition, and explain the base-rate answer in words a friend would follow.
- Acts
- Understand exactly, Check it against evidence
Pass when: Solve ten conditional-probability problems, including a screening test for a rare condition, and explain the base-rate result in plain words. You pass when you have checked each answer by counting in a table of a thousand people and your explanation says why a positive result from a good test can still probably be false.
On the site: Judgment Under Uncertainty: Probability, Causation and Forecasting, Mathematics for Better Decisions
Level 75
Samples and populations
Arithmetic
- Practice
- Evidence and inquiry: Simulate sampling with dice or coins: draw thirty samples of size ten, plot the means, and describe how they spread.
- Acts
- Check it against evidence, Understand exactly
Pass when: Draw thirty samples of size ten with dice or coins, work out each sample mean, plot the thirty means and describe how they spread. You pass when your plot is centred near the value you would expect from the dice or coins, is narrower than the spread of single throws, and you have written both of these as findings.
On the site: Mathematics for Better Decisions
Level 76
Cause and effect
Logic Arithmetic
- Practice
- Evidence and inquiry: For five news claims that X causes Y, write the counterfactual question each implies and name one confounder that could explain the association.
- Acts
- Examine the reasons, Check it against evidence
Pass when: Take five news claims that X causes Y, write the counterfactual question each implies and name one confounder that could explain the association. Say what comparison would test each claim. You pass when each counterfactual question asks what would have happened to Y had X been different and each confounder is tied to both X and Y by a stated reason.
On the site: Real Finding or Hype?
Logic
- Practice
- Evidence and inquiry: State in two sentences the problem of induction, or Popper's answer to it, as the chapters give it. Then state three hypotheses, each with a prediction that could fail, and design the observation that would test it.
- Acts
- Examine the reasons, Check it against evidence
Pass when: State in two sentences the problem of induction, or Popper's answer to it, as the chapters give it. Then state three hypotheses, each with a prediction that could fail, and design the observation that would test each. You pass when each prediction says what result would count against its hypothesis and each designed observation could actually produce that result.
On the site: Hypotheses, Predictions and Tests
Level 78
Stocks, flows and feedback
Arithmetic Logic
- Practice
- Evidence and inquiry: Draw a stock-and-flow diagram of a simple system (a bathtub, a savings account, a reading habit) and mark one reinforcing and one balancing loop.
- Acts
- Understand exactly, Check it against evidence
Pass when: Draw a stock-and-flow diagram of a simple system and mark one reinforcing and one balancing loop. Test the diagram with numbers: choose a starting stock and the flows, and calculate the stock after five steps. You pass when your calculation moves in the direction the diagram predicts and each loop carries a note on how a change travels around it.
On the site: Systems Thinking: Feedback, Queues, Information and Dynamics
Arithmetic Rhetoric
- Practice
- Evidence and inquiry: Find two misleading graphs, explain what misleads in each, and redraw one honestly.
- Acts
- Examine the reasons, Check it against evidence
Pass when: Find two misleading graphs, explain what misleads in each, and redraw one honestly. You pass when your explanation names the device in each, such as a cut axis or an odd scale, and the numbers on your redrawn graph give an impression that matches the data.
On the site: Judgment Under Uncertainty: Probability, Causation and Forecasting
Level 80
Stage check: a small investigation
Arithmetic Logic Rhetoric
- Practice
- Evidence and inquiry: Pose one answerable question, collect data, analyse it with the stage's tools, and write an 800-word report that states its uncertainty and its strongest rival explanation.
- Acts
- Examine the reasons, Check it against evidence, Express it truly
Pass when: Pose one answerable question, collect data, analyse it with tools from this stage and write an 800-word report that states its uncertainty and its strongest rival explanation. You pass when another person could repeat your data collection from the report, every figure in it can be recomputed from your table, and it names a result that would have shown you wrong.
On the site: Hypotheses, Predictions and Tests, Real Finding or Hype?
Sources and judgment Levels 81 to 90
The bar: Test it: check one claim against evidence or raise one objection, and answer it.
Level 81
Reading laterally
Logic Grammar
- Practice
- Evidence and inquiry: Check five online claims by leaving the page and reading what others say about its source. Record what you found about each source and how long it took.
- Acts
- Examine the reasons, Check it against evidence
Pass when: Check five online claims by leaving the page and reading what others say about its source. Record for each claim what you found and how long it took. You pass when each record names the outside sources you read and gives a verdict, so that another person could follow it and reach the same place.
On the site: Real Finding or Hype?
Level 82
Tracing a claim to its origin
Logic Grammar
- Practice
- Evidence and inquiry: Trace three widely shared quotations to their earliest source and grade each as attested, reported, paraphrase or doubtful, the way the site's Canon does.
- Acts
- Examine the reasons, Check it against evidence
Pass when: Trace three widely shared quotations to their earliest source and grade each as attested, reported, paraphrase or doubtful, the way the site's Canon does. You pass when each grade rests on the earliest source you found, named with where you found it, and your record says what you could not find.
On the site: The Canon: Sourced Quotations on Reason, Number and Music
Level 83
Weighing testimony
Logic Grammar
- Practice
- Evidence and inquiry: Compare two accounts of the same event and judge which is more reliable on three points, giving the reason for each judgment.
- Acts
- Examine the reasons, Check it against evidence
Pass when: Compare two accounts of the same event and judge which is more reliable on three points, giving a reason for each. You pass when each judgment cites a feature of the accounts, such as who observed the event, when it was written or what the author stood to gain, and you name one point on which the less reliable account is still useful.
On the site: Stale Information and Dependable Reports
Level 84
Evidence and reports of evidence
Logic Grammar
- Practice
- Evidence and inquiry: Build an annotated list of five sources on one question, separating what each source observed from what it reports that others observed.
- Acts
- Understand exactly, Check it against evidence
Pass when: Build an annotated list of five sources on one question. For each, separate what it observed itself from what it reports that others observed. You pass when every annotation has those two labelled parts and you can say which statements, if the source were wrong, would change your answer to the question.
On the site: Real Finding or Hype?
Level 85
Saying how sure you are
Arithmetic Logic
- Practice
- Practical judgment: Make ten forecasts with probabilities about public, checkable events, each falling due within three weeks. Write down how you will score them, and score them when they fall due.
- Acts
- Check it against evidence, Act and review
Pass when: Make ten forecasts with probabilities about public, checkable events, each falling due within three weeks, and write down how you will score them. Score them when they fall due. You pass when each forecast has a probability, a date and a test of how it resolves, all written before the event, and all ten forecasts have been scored by your method.
On the site: Judgment Under Uncertainty: Probability, Causation and Forecasting
Level 86
Duty and advantage
Logic Grammar
- Practice
- Practical judgment: Analyse three cases where the honourable and the advantageous seem to conflict, as Cicero's third book frames the problem, and say what should be done and why.
- Acts
- Examine the reasons, Act and review
Pass when: Analyse three cases where the honourable and the advantageous seem to conflict, as Cicero's third book frames the problem, and say what should be done and why. You pass when each case states the apparent advantage, the honourable demand, your decision, and the strongest reason against it with your answer to that reason.
On the site: Reasoning for What Ends? Wisdom, Character and the Examined Life
Level 87
Friendship and its limits
Logic Grammar
- Practice
- Practical judgment: State the rule Laelius gives for what a friend may ask, and apply it to three cases from literature or history.
- Acts
- Understand exactly, Act and review
Pass when: State in your own words the rule Laelius gives for what a friend may ask, and apply it to three cases from literature or history. You pass when your statement of the rule matches the text when you reopen the dialogue and the verdict in each case follows from the rule as you stated it.
On the site: Reasoning for What Ends? Wisdom, Character and the Examined Life
Level 88
Philosophy as a way of life
Grammar Logic
- Practice
- Practical judgment: Practise one ancient exercise that Hadot describes, such as an exercise of daily self-examination if your selections describe one, for seven days, and write privately what changed in your attention.
- Acts
- Understand exactly, Act and review
Pass when: Practise one ancient exercise that Hadot describes, such as an exercise of daily self-examination if your selections describe one, for seven days, and write privately what changed in your attention; the private note is for you alone. You pass when your log marks seven days and you can state Hadot's account of the exercise in two sentences that match the text when you reopen it.
On the site: Reasoning for What Ends? Wisdom, Character and the Examined Life
Level 89
Habit and choice
Logic Grammar
- Practice
- Practical judgment: Choose one small habit, plan it with Aristotle's mean in view, practise it for a week, and review the result against what you predicted.
- Acts
- Act and review, Check it against evidence
Pass when: Choose one small habit, plan it with Aristotle's mean in view, practise it for a week, and review the result against what you predicted. Say in two sentences what Aristotle means by the mean in Book 2. You pass when your two sentences match Book 2 when you reopen it, your prediction was written before the week began, your log covers seven days, and the review says where the result differed from the prediction without changing the prediction.
On the site: Deliberate Practice for Learning and Mastery
Level 90
Stage check: judgment in action
Logic Rhetoric
- Practice
- Practical judgment: Write a decision memo on a public question: the options, your reasons, your forecast of the outcome, and how you would know you were wrong.
- Acts
- Examine the reasons, Express it truly, Act and review
Pass when: Write a decision memo on a public question: the options, your reasons, a forecast of the outcome with a probability and a date, and how you would know you were wrong. You pass when the memo names one observable result that would show your choice wrong and a reread finds that every reason supports the option you chose.
On the site: Judgment Under Uncertainty: Probability, Causation and Forecasting
Thresholds: Greek begins, the first essay Levels 91 to 100
The bar: Show it: a finished short essay and an oral examination on the tier's work.
Level 91
Wisdom first: Hugh
Grammar
- Practice
- Language: Learn the Greek alphabet: write each letter, say it, and read twenty Greek words aloud.
- Acts
- Understand exactly, Express it truly
Pass when: Learn the Greek alphabet by writing each letter and saying its name, and read twenty Greek words aloud. Summarise Book 1 of Hugh's work in 150 words. You pass when you can write all the letters in order from memory and check them against a printed chart, you read the twenty words aloud without checking, and your summary matches Book 1 when you reopen it.
On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond
Level 92
The map of knowledge: Hugh
Grammar
- Practice
- Language: Use a lexicon or word-lookup tool that gives dictionary forms to look up twenty words from the opening lines of the Iliad and note each one's dictionary form.
- Acts
- Understand exactly, Express it truly
Pass when: Using a lexicon or a word-lookup tool that gives the dictionary form of an inflected word, look up twenty words from the opening lines of the Iliad and note each dictionary form beside the form in the text. Redraw Hugh's map of knowledge from Book 2 without the book. You pass when each of the twenty entries shows both forms and your map matches Book 2 when you reopen it.
On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond
Level 93
The studies before dialectic: Plato
Grammar Logic
- Practice
- Language: Learn the Greek article and the first noun endings, and read five short Greek phrases with their endings explained.
- Acts
- Understand exactly, Express it truly
Pass when: Learn the Greek article and the first noun endings and read five short Greek phrases, explaining the endings in each. State in 200 words, in your own words, what Book 7 says about the studies that come before dialectic. You pass when you can write the article and the noun endings in a table from memory, every ending in the five phrases is explained, and your 200 words match Book 7 when you reopen it.
On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond
Level 94
Grammar, reason and eloquence together
Grammar Rhetoric
- Practice
- Language: Read and translate ten simple Greek sentences with a grammar's help. (On the optional Latin track, work through the first chapter of Ørberg's Familia Romana instead.)
- Acts
- Understand exactly, Examine the reasons, Express it truly
Pass when: Translate ten simple Greek sentences into English with a grammar's help, accounting for the form of each word. Write 150 words on how John of Salisbury joins grammar, reason and eloquence. (On the Latin option, read and summarise the first chapter of the Latin course and apply the same test.) You pass when each translation reads as correct English, every word is accounted for by its ending, and your 150 words match the selection when you reopen it.
On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond
Level 95
One art or three?
Grammar Logic Rhetoric
- Practice
- Writing and speaking: Write 500 words on why Miriam Joseph and John of Salisbury join grammar, logic and rhetoric, and where you think the join is weakest.
- Acts
- Understand exactly, Examine the reasons, Express it truly
Pass when: Write 500 words on why Miriam Joseph and John of Salisbury join grammar, logic and rhetoric, and where you think the join is weakest. You pass when the essay states each author's reason in that author's own terms, gives one objection to the join with your answer to it, and reads aloud without a sentence you have to restart.
On the site: The Order of the Seven Liberal Arts: Substance, Quantity and the Mind, The Seven Liberal Arts: a spiral curriculum
Level 96
What can you now do?
Grammar Logic Rhetoric
- Practice
- Method: List the tools Sayers says education should give. For each, point to a piece of your own work from Levels 1 to 95 that uses it, or say plainly that none does.
- Acts
- Understand exactly, Examine the reasons, Act and review
Pass when: List the tools Sayers says education should give. For each, point to a piece of your own work from Levels 1 to 95 that uses it, or say plainly that none does. You pass when each tool on your list is found in Sayers when you reopen the essay and each claim of use points to a dated notebook entry or a named piece of work.
On the site: The Weekly Loop: Read, Reconstruct, Make, Defend, Log
Level 97
The Foundations essay: the question
Logic Rhetoric
- Practice
- Writing and speaking: Choose a question raised by two or more Foundations readings, state it as a problem worth answering, and gather the passages that bear on it.
- Acts
- Understand exactly, Examine the reasons
Pass when: Choose a question raised by two or more Foundations readings and state it as a problem worth answering, in a paragraph. Gather the passages that bear on it, listing the work and part of each. You pass when the question can be answered from evidence in those texts, not by opinion alone, and the list holds at least one passage that pulls against the others.
On the site: Principles Ledger and Question Arcs
Level 98
The Foundations essay: the draft
Rhetoric Logic
- Practice
- Writing and speaking: Write a 1,500-word draft with a thesis, the evidence from the texts, the strongest objection and your reply.
- Acts
- Understand exactly, Examine the reasons, Express it truly
Pass when: Write a draft of about 1,500 words with a thesis, evidence from the texts, the strongest objection and your reply. You pass when the thesis can be stated in one sentence, the objection is one a thoughtful reader would hold, and each use of a text has been checked against the text for accuracy.
On the site: Technical Writing as Reasoning
Level 99
The Foundations essay: criticism and revision
Rhetoric Logic
- Practice
- Writing and speaking: Have someone read the draft and question you on it, or set it aside for three days and question it yourself with the five acts. Revise it, keeping a note of each change and its reason.
- Acts
- Examine the reasons, Express it truly, Act and review
Pass when: Have someone read the draft and question you on it, or set it aside for three days and question it yourself with the five acts. Revise it, keeping a note of each change and its reason. You pass when the revision log lists each change with a reason and the revised essay answers every question that was raised.
On the site: The Weekly Loop: Read, Reconstruct, Make, Defend, Log
Level 100
The Foundations examination
Logic Rhetoric Geometry Music Arithmetic
- Practice
- Writing and speaking: Give a fifteen-minute oral defence of your essay, then answer questions across the tier: restate a reading, rebuild an argument, demonstrate a proposition, sing an interval and solve a base-rate problem.
- Acts
- Understand exactly, Examine the reasons, Express it truly
Pass when: Give a fifteen-minute oral defence of your essay, then answer questions across the tier: restate a reading, rebuild an argument, demonstrate a proposition, sing an interval and solve a base-rate problem. Record the defence and write the questions beforehand. You pass when the recording runs about fifteen minutes and each answer survives checking against the text, the proof in the book and a recomputation.
On the site: The Seven Liberal Arts: a spiral curriculum
Every level is self-paced and self-assessed, and no credential is awarded. The design is inspired by St. John's College, Khan Academy and WGU; this site is not affiliated with any of them. Levels marked Draft are first versions, still being checked and refined; their numbers will not change.