The Canon: Sourced Quotations on Reason, Number and Music

All things that are known have number; without number nothing could be thought or known.

Philolaus of Croton, Fragment DK 44 B4, via Stobaeus

ReportedPresocratic

Examine

What it claims: Measure is a precondition of articulate knowledge: to know precisely is to know how much.
Where it breaks: Much that we know well resists number — a face, a grief, a joke. Number is a condition of transmissible knowledge, not of all knowing.
Exercise: Name one thing you know well but cannot number, then name one number that would capture part of it.

They supposed the elements of numbers to be the elements of all things, and the whole heaven to be harmonia and number.

Aristotle, on the Pythagoreans, Metaphysics 985b23–986a3

AttestedPresocratic

Examine

What it claims: Our best evidence for Pythagorean doctrine comes from a critic writing two centuries later. Pythagoras himself wrote nothing.
Where it breaks: Aristotle is summarising opponents, and compresses several generations of a secretive school into one thesis.
Exercise: Write down one belief you hold that you have only ever met in a summary by someone who disagreed with it.

Nature loves to hide.φύσις κρύπτεσθαι φιλεῖ

Heraclitus, Fragment DK 22 B123

ReportedPresocratic

Examine

What it claims: The structure of things is not on the surface; appearances are the beginning of inquiry, not its end.
Where it breaks: Sometimes the obvious explanation is the true one. This aphorism has licensed a great deal of profitable mystification.
Exercise: Take one thing you find obvious about your practice and look for the mechanism underneath it.

Much learning did not teach Hesiod and Pythagoras, nor yet Xenophanes and Hecataeus.

Heraclitus, Fragment DK 22 B40, via Diogenes Laertius IX.1

ReportedPresocratic

Examine

What it claims: Accumulation is not understanding. Polymathy without grasp of the logos is a heap.
Where it breaks: Learning is nonetheless the raw material of understanding; the fragment is a rebuke to hoarders, not a defence of ignorance.
Exercise: Count the courses, books or videos you finished last year. Then count what you can now demonstrate.

The hidden harmony is better than the obvious.

Heraclitus, Fragment DK 22 B54, via Hippolytus

ReportedPresocratic

Examine

What it claims: The deepest order is structural rather than sensory; you reach it by analysis, not by looking harder.
Where it breaks: "Hidden" is not a synonym for "true". Concealment is not evidence.
Exercise: Find the hidden ratio in something you already hear: play a triplet against a duplet and name the interval it makes in time.

No man has seen the certain truth, nor will there be anyone who knows about the gods and all the things I speak of; for even if he should chance to say the complete truth, yet he himself does not know it.

Xenophanes, Fragment DK 21 B34, via Sextus Empiricus

ReportedPresocratic

Examine

What it claims: The first clear statement of fallibilism: you can be right and still not know that you are right.
Where it breaks: It proves too much if taken absolutely — that very claim would be unknowable. Read it as a warning about scope, not a doctrine of despair.
Exercise: Identify a belief you are right about but cannot demonstrate. Say what would turn luck into knowledge.

Concerning invisible things, and concerning mortal things, the gods have certainty; but to us, as men, only inference is possible.

Alcmaeon of Croton, Fragment DK 24 B1

ReportedPresocratic

Examine

What it claims: Human knowledge is inferential by nature. We reason from signs, and signs can mislead.
Where it breaks: Inference is not thereby weak — modern medicine is inference — but it must be labelled as inference.
Exercise: Take a conclusion you hold and write the chain of inference beneath it, marking each weak link.

In reality we know nothing about anything; belief is a reshaping in each of us.

Democritus, Fragment DK 68 B7 / B9

ReportedPresocratic

Examine

What it claims: From the man who proposed atoms, an unexpected caution: the senses report the effects of atoms upon us, not the atoms.
Where it breaks: Democritus continued doing physics regardless — evidence that this scepticism was methodological, not paralysing.
Exercise: Distinguish, for one perception today, what you sensed from what you inferred.

The knowledge at which geometry aims is knowledge of the eternal, not of what comes into being and passes away.

Plato, Republic 527b

AttestedPlatonic

Examine

What it claims: Mathematics is the model discipline because its objects do not change, so error is entirely on our side.
Where it breaks: It tempts a metaphysics — a separate realm of Forms — that the mathematics itself does not require.
Exercise: Prove a small theorem, then say what in it could have been otherwise. If nothing, you have met necessity.

The soul of the geometer is compelled to use hypotheses, and, taking them as absolute beginnings, cannot give an account of them.

Plato, Republic 510c–511a (the Divided Line)

AttestedPlatonic

Examine

What it claims: Even mathematics starts from unexamined premises; dialectic is the attempt to climb behind them to the principle itself.
Where it breaks: Plato thought that ascent could be completed. Gödel gives us reason to doubt that it can.
Exercise: Take one hypothesis you work from daily and try to justify it from something more basic. Note where you stop.

Knowledge is true belief together with an account.

Plato, Theaetetus 201c–210b

ParaphrasePlatonic

Examine

What it claims: The classical definition of knowledge: truth, belief, and a reason that ties them together.
Where it breaks: Plato refutes it in the same dialogue, and Gettier (1963) broke the modern repair in three pages. Still the best starting point we have.
Exercise: Take a belief that is true and see whether your account is the reason it is true, or a story that happens to fit.

The fairest of bonds is that which makes itself and the things it binds most completely one, and proportion is by nature the fairest accomplisher of this.

Plato, Timaeus 31c

AttestedPlatonic

Examine

What it claims: Proportion — not substance — is what unifies. Structure is prior to material.
Where it breaks: Elegant, and empirically empty as physics; the Timaeus is cosmological poetry with mathematics inside it.
Exercise: Find a proportion that binds two parts of your practice. Then check whether the binding is real or merely pleasing.

God ever geometrises.ἀεὶ ὁ θεὸς γεωμετρεῖ

attributed to Plato by Plutarch, Quaestiones Convivales VIII.2, 718c

DoubtfulPlatonic

Examine

What it claims: That the order of the world is fundamentally geometrical.
Where it breaks: It appears nowhere in Plato. Plutarch reports it five centuries later as a saying. Beloved, unsourced — and printed here with its mark on.
Exercise: Search for this line online and count how many sites present it as a direct quotation from Plato.

Let no one ignorant of geometry enter.ἀγεωμέτρητος μηδεὶς εἰσίτω

attributed to the Academy, reported inscription Elias, in Cat. 118.18 (6th c. CE); Tzetzes, Chiliades VIII.972

DoubtfulPlatonic

Examine

What it claims: That mathematical training is the entry requirement for philosophy, because it teaches what a proof feels like.
Where it breaks: A thousand years separate the Academy from our earliest witness. Excellent advice; poor evidence. Both facts belong on the sign.
Exercise: Decide whether the advice survives the collapse of its provenance — and say why.

All men by nature desire to know.

Aristotle, Metaphysics 980a21

AttestedAristotelian

Examine

What it claims: Curiosity is not a virtue acquired but a fact of the species; the delight we take in the senses is its evidence.
Where it breaks: Observably false of many people much of the time. Read it as a claim about capacity, not about behaviour.
Exercise: Name what you wanted to know before anyone paid you to know anything. Begin there again this week.

We must not seek the same degree of accuracy in all things, but in each according to the subject matter.

Aristotle, Nicomachean Ethics 1094b12–27

AttestedAristotelian

Examine

What it claims: Precision is a virtue relative to a domain; demanding mathematical rigour in ethics is itself a failure of judgement.
Where it breaks: It is the standard excuse for vagueness. The test is whether you can say how much precision the subject admits, and why.
Exercise: State the achievable precision of one claim you made this week — and then meet it.

Demonstration must proceed from premises that are prior to and better known than the conclusion; and since the regress cannot be infinite, there must be principles known otherwise than by demonstration.

Aristotle, Posterior Analytics I.2–3, 71b–72b

ParaphraseAristotelian

Examine

What it claims: The regress argument for first principles: without an unproved starting point, nothing whatever is proved.
Where it breaks: It does not tell you which principles, and history shows we choose them badly and revise for centuries.
Exercise: Ask "why?" of one belief five times. Write down where you stopped and whether it was a principle or fatigue.

We become just by doing just acts, temperate by doing temperate acts, brave by doing brave acts.

Aristotle, Nicomachean Ethics II.1, 1103a–b

AttestedAristotelian

Examine

What it claims: Character is produced by repeated action, not by understanding. Knowing the good is not being good.
Where it breaks: Repetition alone entrenches error too. Aristotle assumes a teacher and a target; unguided practice makes you excellent at your mistakes.
Exercise: Choose the smallest correct action you can repeat daily and do it, badly, for a week.

We are what we repeatedly do. Excellence, then, is not an act, but a habit.

Will Durant, The Story of Philosophy 1926, p. 87 — summarising Aristotle

ParaphraseAristotelian

Examine

What it claims: A brilliant compression of Nicomachean Ethics II.1 — and the most misattributed sentence in self-improvement.
Where it breaks: Aristotle never wrote it. Durant did, as a gloss. The paraphrase is smoother than the original, which is exactly why it spread.
Exercise: Compare it with the actual passage above. Note what the compression quietly removed: the teacher, and the target.

A point is that which has no part.

Euclid, Elements I, Definition 1

AttestedPlatonic

Examine

What it claims: The opening sentence of the most successful textbook ever written begins by fixing a term, not by asserting a truth.
Where it breaks: The definition does no logical work in the proofs — modern axiomatics leaves "point" undefined. Its value is orientation.
Exercise: Write the first definition of your own field as Euclid would: seven words, no metaphor.

There is no royal road to geometry.

Euclid, to Ptolemy I, anecdote Proclus, Commentary on Euclid I, 68

ReportedPlatonic

Examine

What it claims: No shortcut exists for a king or for anyone; the work is the only route to the understanding.
Where it breaks: Pedagogy genuinely improves; some roads are better. What cannot be delegated is the walking.
Exercise: Identify a shortcut you are currently hoping exists. Then estimate the honest hours instead.

Give me a place to stand and I will move the earth.

Archimedes, on the lever Pappus, Collection VIII

ReportedHellenistic & Roman

Examine

What it claims: A principle, correctly applied, multiplies force without limit. Leverage is a mathematical fact before it is a metaphor.
Where it breaks: The metaphorical use is now so worn that the mechanics is forgotten. The claim is about torque, and it is exactly true.
Exercise: Find the actual lever in a problem you face: the smallest input with the largest proven ratio of effect.

It is impossible for a man to begin to learn what he thinks he already knows.

Epictetus, Discourses II.17.1

AttestedHellenistic & Roman

Examine

What it claims: Supposed knowledge is the specific obstacle to real knowledge — not ignorance, which is merely empty.
Where it breaks: Chronic self-doubt blocks learning as effectively as false confidence. The target is unexamined assurance.
Exercise: Name one thing you are sure you already know about your instrument. Test it today, and record the result honestly.

If anyone can refute me and show me that I am mistaken in any point, I shall gladly change; for it is truth that I seek, and truth never harmed anyone.

Marcus Aurelius, Meditations VI.21

AttestedHellenistic & Roman

Examine

What it claims: Correction is a gift received, not a wound suffered. Written privately by the most powerful man alive.
Where it breaks: Easier to write than to do, as he knew. The value is in having fixed the standard where it can be checked.
Exercise: Invite one specific correction from someone competent this week, and thank them in writing.

We learn not for life but for school.non vitae sed scholae discimus

Seneca, Epistulae Morales 106.12

AttestedHellenistic & Roman

Examine

What it claims: A complaint, not a motto: Seneca is attacking education that produces cleverness rather than conduct.
Where it breaks: It is now quoted reversed — "non scholae sed vitae" — as a school slogan, with the polarity of the original destroyed.
Exercise: Ask of your current study: does it change what you do, or only what you can say?

Not to know what happened before you were born is to be a child for ever.

Cicero, Orator 34.120

AttestedHellenistic & Roman

Examine

What it claims: History is a component of adult competence, not a decoration on it.
Where it breaks: Knowing the past does not confer judgement about the present; antiquarianism is its own kind of childishness.
Exercise: Trace one technique you use back to the person who first wrote it down.

What then is time? If no one asks me, I know; if I wish to explain it to one who asks, I know not.

Augustine, Confessions XI.14

AttestedLate antique & medieval

Examine

What it claims: The exact phenomenology of tacit knowledge, seventeen centuries before the term existed.
Where it breaks: Physics has since said a great deal about time; the puzzle he names is about our access to it, not its nature.
Exercise: Explain the difference between tempo and rhythm aloud, in plain words, to someone who does not play.

There are three kinds of music: the music of the cosmos, the music of the human being, and the music made by instruments.

Boethius, De institutione musica I.2

ParaphraseLate antique & medieval

Examine

What it claims: Musica mundana, humana, instrumentalis: the same proportion appears in the heavens, the person and the string. This scheme governed European education for a thousand years.
Where it breaks: The cosmic tier is false as astronomy. The insight that survives is structural: one mathematics, several materials.
Exercise: Take one ratio — 3:2 — and find it in pitch, in rhythm and in a proportion of your daily schedule.

Truth is the conformity of thing and intellect.adaequatio rei et intellectus

Isaac Israeli, quoted by Aquinas, De Veritate q.1 a.1

ReportedLate antique & medieval

Examine

What it claims: The correspondence theory in five words: a thought is true when it fits what is.
Where it breaks: It does not tell you how to check the fit, which is where all the difficulty lives.
Exercise: For one belief, describe the fit you are claiming, and the observation that would show a gap.

The seeker after truth is not one who studies the writings of the ancients and puts his trust in them, but rather one who suspects his faith in them and questions what he gathers from them.

Ibn al-Haytham, Aporias against Ptolemy c. 1027

ReportedLate antique & medieval

Examine

What it claims: The experimental attitude, stated plainly in Cairo six centuries before Bacon, by the man who tested optics with apparatus.
Where it breaks: Suspicion without competence is merely noise; al-Haytham earned his doubts with instruments and mathematics.
Exercise: Take one claim from a respected teacher and design the smallest test that could embarrass it.

Reserve your right to think, for even to think wrongly is better than not to think at all.

attributed to Hypatia of Alexandria, — no ancient source; appears in modern collections

DoubtfulLate antique & medieval

Examine

What it claims: Intellectual courage as a duty rather than a temperament.
Where it breaks: Hypatia's own writings are lost and this sentence has no ancient attestation. It is almost certainly a 20th-century composition. A good line wrongly dressed.
Exercise: Hold the sentiment and drop the attribution. Notice how much less shareable it becomes, and ask why.

I do not teach; I relate.

Montaigne, Essays III.2, "On Repentance"

AttestedEarly modern

Examine

What it claims: A refusal of authority in favour of testimony: here is what happened to me, examined.
Where it breaks: Testimony is weak evidence about the world, though strong evidence about the witness.
Exercise: Write one paragraph of what actually happened in your practice today, with no lesson attached.

If a man will begin with certainties, he shall end in doubts; but if he will be content to begin with doubts, he shall end in certainties.

Francis Bacon, The Advancement of Learning I.v.8 (1605)

AttestedEarly modern

Examine

What it claims: Method reverses the felt order of confidence: doubt first, deliberately, to earn assurance later.
Where it breaks: Bacon's own inductive programme was too simple, and he underrated hypothesis. The maxim outlived the method.
Exercise: Start today's work from the thing you are least sure of rather than the thing you enjoy.

The human understanding, when it has once adopted an opinion, draws all things else to support and agree with it.

Francis Bacon, Novum Organum I.46 (1620)

ParaphraseEarly modern

Examine

What it claims: Confirmation bias, named and diagnosed three hundred and forty years before the psychologists measured it.
Where it breaks: Naming a bias does not remove it; Bacon believed method could, and method only partly does.
Exercise: Write the evidence against your current favourite theory before writing any more for it.

Philosophy is written in this grand book, the universe, which stands continually open to our gaze — but it cannot be understood unless one first learns the language in which it is written. It is written in the language of mathematics, and its characters are triangles, circles and other geometrical figures.

Galileo, The Assayer 1623

AttestedEarly modern

Examine

What it claims: Nature is legible, but only to the mathematically literate. The manifesto of modern physical science.
Where it breaks: It quietly excludes whatever resists quantity, and generations of thinkers took that exclusion for non-existence.
Exercise: Write one thing you care about in mathematical form, and one thing that resists it. Do not pretend the second is the first.

Geometry is one and eternal, a reflection out of the mind of God. That men share in it is one reason to call man an image of God.

Kepler, Conversation with Galileo's Sidereal Messenger 1610

AttestedEarly modern

Examine

What it claims: Mathematical truth as necessary and shared — the same for us as for any mind whatever.
Where it breaks: The theology is optional. The necessity is not: 317 is prime in every possible universe.
Exercise: Prove something small enough to hold in your head, and notice that you did not invent it.

Divide each of the difficulties under examination into as many parts as possible, and as might be necessary for its adequate solution.

Descartes, Discourse on the Method Part II (1637)

AttestedEarly modern

Examine

What it claims: Analysis: complexity is handled by decomposition into inspectable parts.
Where it breaks: Some systems are destroyed by division — an ecology, a phrase of music, a person. Decomposition presumes separability.
Exercise: Take a passage you cannot play and divide it until each part is trivially easy. Then find where the joins fail.

I think, therefore I am.cogito, ergo sum

Descartes, Principles of Philosophy I.7 (1644); as "je pense, donc je suis" in the Discourse (1637)

AttestedEarly modern

Examine

What it claims: One proposition that survives maximal doubt, used as the fixed point from which to rebuild knowledge.
Where it breaks: It establishes far less than it seems — that thinking is occurring, not that a persistent self exists. Everything after it in Descartes is contested.
Exercise: Find your own smallest indubitable premise about your practice, and see how little it supports.

Not to laugh, not to lament, not to curse, but to understand.non ridere, non lugere, neque detestari, sed intelligere

Spinoza, Tractatus Politicus I.4

AttestedEarly modern

Examine

What it claims: A discipline of attention: emotional reaction, however justified, is not yet comprehension.
Where it breaks: Understanding does not exhaust the appropriate responses to cruelty. Spinoza's calm is a method, not a complete ethics.
Exercise: Take something in your work that irritates you and write its mechanism instead of your complaint.

Nature is pleased with simplicity, and affects not the pomp of superfluous causes.

Newton, Principia Mathematica Book III, Rules of Reasoning, Rule I (1687)

AttestedEarly modern

Examine

What it claims: Parsimony as a working rule: admit no more causes than suffice to explain the appearances.
Where it breaks: "Simple" is theory-relative, and nature has repeatedly turned out baroque — quantum field theory is not simple. The rule is heuristic, not metaphysical.
Exercise: Remove one term from your explanation of something and check whether the explanation still fits the data.

If I have seen further, it is by standing on the shoulders of giants.

Newton, letter to Robert Hooke 5 February 1675

AttestedEarly modern

Examine

What it claims: Knowledge is cumulative; individual genius is mostly good inheritance well used.
Where it breaks: The image is not Newton's — Bernard of Chartres used it c. 1120 (John of Salisbury, Metalogicon III.4) — and Newton, writing to a rival he despised, may have meant it sourly.
Exercise: Name the three shoulders you are standing on right now, by name and by work.

Music is a hidden arithmetical exercise of a soul unconscious that it is calculating.

Leibniz, letter to Christian Goldbach 17 April 1712

AttestedEnlightenment

Examine

What it claims: The pleasure of music is the mind's unconscious detection of ratio.
Where it breaks: It reduces a total human experience to counting, and cannot explain why particular ratios move particular cultures differently.
Exercise: Play a 3:2 and a 45:32 over a drone. Report what your ear counted before you knew what it was.

A wise man proportions his belief to the evidence.

David Hume, An Enquiry concerning Human Understanding X.1 (1748)

AttestedEnlightenment

Examine

What it claims: Confidence should be a quantity, tracking the strength of the grounds — not a temperament or a loyalty.
Where it breaks: It presumes that evidence can be weighed on a common scale, which for competing theories is often the whole problem.
Exercise: Give a percentage to three of your beliefs. Then write the evidence for each and see whether the numbers survive.

Thoughts without content are empty; intuitions without concepts are blind.

Kant, Critique of Pure Reason A51 / B75 (1781)

AttestedEnlightenment

Examine

What it claims: Neither raw experience nor pure reasoning is knowledge; the two must meet, and either alone is a failure mode.
Where it breaks: Kant's own list of necessary concepts included Euclidean space, which relativity retired. The structure of the insight survived his examples.
Exercise: Diagnose your last mistake: was it empty theory, or blind data?

Convictions are more dangerous enemies of truth than lies.

Nietzsche, Human, All Too Human §483 (1878)

AttestedModern

Examine

What it claims: A liar knows the truth and hides it; a conviction has replaced the truth with itself and feels virtuous doing it.
Where it breaks: Some convictions are correct, and paralysis is not a virtue. The target is conviction held as identity.
Exercise: Name a conviction you would be socially embarrassed to abandon. That embarrassment is the measurement.

There are no facts, only interpretations.

Nietzsche, posthumous notebooks KSA 12:7[60], published in The Will to Power (1901)

DoubtfulModern

Examine

What it claims: Usually quoted to license relativism about everything.
Where it breaks: It comes from unpublished notes assembled by his sister, and Nietzsche elsewhere insists on intellectual honesty above all. Quoting a notebook as a doctrine is exactly the error the site exists to prevent.
Exercise: Try to state this claim in a form that does not refute itself. Notice what it costs.

Do not block the way of inquiry.

C. S. Peirce, "The First Rule of Logic" 1899

AttestedModern

Examine

What it claims: The single positive duty of the inquirer: never adopt a position that makes further questioning pointless.
Where it breaks: Some inquiries should be closed for now on grounds of cost or ethics; the rule forbids declaring them closed in principle.
Exercise: Write one belief you treat as settled, and the observation that would reopen it.

The essence of belief is the establishment of a habit.

C. S. Peirce, "How to Make Our Ideas Clear" 1878

AttestedModern

Examine

What it claims: A belief is not a stored sentence but a disposition to act. What you believe is visible in what you do under pressure.
Where it breaks: It can slide into behaviourism and lose the phenomenon of belief altogether.
Exercise: Infer one of your real beliefs from your behaviour this week rather than from your opinions.

It is by logic that we prove, but by intuition that we discover.

Henri Poincaré, Science and Method 1908

AttestedModern

Examine

What it claims: Discovery and demonstration are different faculties with different disciplines; a curriculum that trains only the second produces no mathematicians.
Where it breaks: It flatters intuition, which is mostly compressed experience — and is worthless without the labour that compressed it.
Exercise: Guess the answer first, then prove it. Note honestly which part you have practised less.

Civilisation advances by extending the number of important operations which we can perform without thinking about them.

A. N. Whitehead, An Introduction to Mathematics 1911

AttestedModern

Examine

What it claims: Notation, habit and automaticity free attention for the next problem. Fluency is not the enemy of thought but its precondition.
Where it breaks: Operations performed without thought are also errors propagated without thought. Automate only what you have verified.
Exercise: Choose one operation you still think about, drill it to silence, and then check it is still correct.

Seek simplicity and distrust it.

A. N. Whitehead, The Concept of Nature 1920

AttestedModern

Examine

What it claims: Both halves are obligatory: reach for the simple account, then treat your success as suspicious.
Where it breaks: Taken alone the second half becomes a licence to complicate for status.
Exercise: Write the simplest version of your current theory, then list what it fails to explain.

Mathematics, rightly viewed, possesses not only truth but supreme beauty — a beauty cold and austere, like that of sculpture.

Bertrand Russell, "The Study of Mathematics" 1907

AttestedModern

Examine

What it claims: Aesthetic response is real evidence of structure and a legitimate motive for rigour.
Where it breaks: Beauty is a fallible guide: elegant wrong theories are the most persuasive kind, and Russell's own logicism was one.
Exercise: Find a proof you consider beautiful and state what specifically produced the feeling.

317 is a prime, not because we think so, or because our minds are shaped in one way rather than another, but because it is so, because mathematical reality is built that way.

G. H. Hardy, A Mathematician's Apology §24 (1940)

AttestedModern

Examine

What it claims: Mathematical truth is discovered, not constructed — the clearest statement of working Platonism in English.
Where it breaks: Formalists and intuitionists deny it, and the debate is unsettled. It is a philosophical position, not a theorem.
Exercise: Verify that 317 is prime by trial division up to 17. Then ask what your verifying added to the fact.

Beauty is the first test: there is no permanent place in the world for ugly mathematics.

G. H. Hardy, A Mathematician's Apology §10 (1940)

AttestedModern

Examine

What it claims: Elegance predicts durability, because economical arguments generalise.
Where it breaks: "First test", not the only one. Plenty of ugly mathematics is true and useful — and stays.
Exercise: Rewrite one explanation of yours until it is shorter and truer. Keep both versions.

Whereof one cannot speak, thereof one must be silent.

Wittgenstein, Tractatus Logico-Philosophicus §7 (1921)

AttestedModern

Examine

What it claims: The limits of sense are the limits of assertion; where language fails, assertion should stop rather than mystify.
Where it breaks: Wittgenstein himself later regarded the framework as mistaken. And silence has been used to dismiss whole subjects prematurely.
Exercise: Find something in your practice you cannot yet state precisely. Say only what you can, and mark the rest as not yet.

He must, so to speak, throw away the ladder after he has climbed up it.

Wittgenstein, Tractatus Logico-Philosophicus §6.54 (1921)

AttestedModern

Examine

What it claims: Some structures are scaffolding: correct as instruments, false as furniture. Discard the method once it has done its work.
Where it breaks: Discarding too early leaves you on nothing. Know whether you are standing on the ladder or on the floor.
Exercise: Name one crutch — a shape, a mnemonic, a chart — that you should now be able to throw away. Test whether you can.

A theory that is not refutable by any conceivable event is non-scientific. Irrefutability is not a virtue but a vice.

Karl Popper, Conjectures and Refutations 1963

AttestedContemporary

Examine

What it claims: The demarcation criterion: a claim earns scientific standing by specifying in advance what would sink it.
Where it breaks: Real science tolerates anomalies for decades rather than abandoning theories on one refutation; Kuhn and Lakatos made this stick.
Exercise: For one belief, write the observation that would refute it. If none exists, relabel it as taste or as commitment.

The first principle is that you must not fool yourself — and you are the easiest person to fool.

Richard Feynman, "Cargo Cult Science", Caltech commencement address 1974

AttestedContemporary

Examine

What it claims: Scientific integrity is primarily a discipline against self-deception, not against other people's dishonesty.
Where it breaks: Willpower is not enough — which is why science invented blinding, pre-registration and adversarial review.
Exercise: Record your practice and listen back before judging it. The recording is the referee.

What I cannot create, I do not understand.

Richard Feynman, blackboard at the time of his death 1988

ReportedContemporary

Examine

What it claims: Understanding is generative: the test is whether you can build the thing, not recognise it.
Where it breaks: Many well-understood things cannot be created — supernovae, the past. Read it as a test for craft and mechanism.
Exercise: Recreate today's idea from nothing: blank page, no notes, from the first line.

Attention is the rarest and purest form of generosity.

Simone Weil, letter to Joë Bousquet 13 April 1942

AttestedContemporary

Examine

What it claims: Attention is an ethical act, not merely a cognitive one — to attend to something is to grant it reality.
Where it breaks: Attention can also be predatory. Weil's sense requires the surrender of the self's agenda, which is far harder than concentration.
Exercise: Give twelve minutes of undivided attention to one bar of music, and notice what you had been supplying from memory.

Love is the extremely difficult realisation that something other than oneself is real.

Iris Murdoch, "The Sublime and the Good" 1959

AttestedContemporary

Examine

What it claims: The same discipline underlies love and objectivity: letting something be what it is rather than what suits you.
Where it breaks: It sets a standard almost nobody meets, and can be used to disparage ordinary affection.
Exercise: Practise on an inanimate case: let one note be out of tune and hear it as it is, without excusing it.

We know more than we can tell.

Michael Polanyi, The Tacit Dimension 1966

AttestedContemporary

Examine

What it claims: Skill outruns articulation: a rider balances, a player phrases, and neither can state the rule.
Where it breaks: It is regularly used to excuse mystification and unteachable teaching. Tacit knowledge is real; unexamined tacit knowledge is also where bad habits hide.
Exercise: Take one thing your hands do well and try to state the rule. Then check whether the statement matches the recording.

Either mathematics is too big for the human mind, or the human mind is more than a machine.

Kurt Gödel, remark recorded by Hao Wang A Logical Journey, 1996

ReportedContemporary

Examine

What it claims: His own reading of the incompleteness results — presented as a dilemma, not a conclusion.
Where it breaks: It is a conversational remark, not a theorem, and the theorems do not establish either horn. Beware Gödel quotations that prove things about minds.
Exercise: State what the incompleteness theorems actually prove, in one sentence, without mentioning consciousness.

My methods are really methods of working and thinking; this is why they have crept in everywhere anonymously.

Emmy Noether, letter to Helmut Hasse 1931

AttestedContemporary

Examine

What it claims: The deepest contributions are often methodological, and therefore invisible: everyone uses them and nobody cites them.
Where it breaks: It also describes how credit is denied to people whose work becomes infrastructure — as much of hers was.
Exercise: Identify a method you use daily and find out who invented it. Say the name out loud.

To know when you know, and to know when you do not know — that is wisdom.

Confucius, Analects 2.17 (translation varies)

AttestedEastern

Examine

What it claims: The core competence is calibration: mapping your confidence onto your actual reliability.
Where it breaks: Heavily translation-dependent; the Chinese is terser and less tidy than most English versions.
Exercise: Before your next attempt, predict whether you will succeed. Then record whether you did. Keep score for a week.

To know that you do not know is best; to think you know when you do not is a disease.

Laozi, Tao Te Ching ch. 71 (translation varies widely)

AttestedEastern

Examine

What it claims: Epistemic humility as health, and false certainty as pathology — the same diagnosis as Socrates, independently reached.
Where it breaks: The text is layered, of contested authorship and date, and the English versions diverge sharply. Read at least two.
Exercise: Compare three translations of this chapter. Note how much of the "wisdom" was the translator's.

One thing I know: that I know nothing.

attributed to Socrates, — not in Plato; cf. Apology 21d

DoubtfulPlatonic

Examine

What it claims: Usually offered as the summit of philosophical humility.
Where it breaks: Plato's Socrates says something subtler and better: that he is wiser than another only in not thinking he knows what he does not know. The famous version is self-refuting; the real one is a description of calibration.
Exercise: Write out both versions and say which one you could actually act on tomorrow.

Quotations you can check.