Philosophy
Arguments you can test, beliefs you can measure, choices you can rank: philosophy taught through the structures it is made of — validity, consistency, credence, expected value, equilibrium, collective choice and possible worlds — from the first argument to the hardest paradox. Ten courses and 108 lessons are available.
- Courses
- 10
- Lessons
- 108
- Level
- Beginner → Advanced
- Assumes
- school arithmetic only; the logic is taught inside
Overview
Arguments come first because everything that follows is an argument. Validity, consistency and the counterexample are the three tools every later lesson reaches for, and a reader who cannot yet tell a valid argument from a persuasive one will misread the strongest positions in the Subject as the weakest.
Knowledge and evidence come second because credence is the currency of the next six courses. Updating on evidence is introduced there once, with exact fractions, and used without re-derivation in Science, Induction and Causation, in Decision and Rationality and in every paradox of probability at the end.
Decision precedes games, and both precede ethics and justice, because expected utility, equilibrium and the n-player dilemma are the instruments with which the ethical theories are compared rather than merely described. Utilitarianism is an aggregation rule; Kant’s test is an outcome at universal adoption; the social contract is a game.
Metaphysics, mind and language come late because they need modal logic and first-order models, which are introduced where they are first used and nowhere earlier. Paradoxes come last because a paradox is where all of these tools are needed at once, and because by then the reader has met most of them in passing and can be asked to classify the exit.
Courses
Each course assumes the ones before it and nothing else. Knowledge and Evidence uses the validity and consistency tests of Arguments and Validity; Decision and Rationality uses the credences of Knowledge and Evidence; Games and the Social Contract uses expected utility; Ethics and the Arithmetic of Welfare uses decision matrices, the n-player dilemma and the causal models of Science, Induction and Causation; Identity, Modality and Freedom introduces modal logic and Mind, Language and Meaning builds on it; Paradoxes and Their Exits uses all of it.
Tell a valid argument from a persuasive one. Set out a passage as premises and a conclusion, test it by looking for a counterexample row, decide whether a set of beliefs can all be true, and refute a bad form with a better case.
What it takes to know something, and what it takes to believe it to a degree. A definition of knowledge is tried against cases until one row disagrees; skepticism and the regress are written as arguments and sets of claims; and credence is computed with exact fractions, from a Dutch book to a posterior.
Hume said the future cannot be deduced from the past; here is exactly what must be added, and what it costs. Weigh evidence by a Bayes factor, see what a theory forbids, find what a failed test refutes, search a table of cases for a cause, watch a pooled rate reverse, and test a cause by flipping it in a model.
Lay a choice out as acts against states and see what each rule says. Money pumps, dominance, maximin and regret, expected utility and the value of information, then five puzzles in which the rule seems to give the wrong answer, each computed to the figure at which it turns.
Take a social-contract argument and write it as a game. Read a payoff table, find every cell where no one gains by moving alone, see why the cell can be worse for everyone than another, and compute exactly what changes it: a repeated game, a sovereign's penalty, a fee, a change in who meets whom.
Put a number on a moral view and see what it commits you to. Add up welfare and find who the sum ignores, count the people needed to beat a flourishing life, weigh the worse off, forbid an act and watch a recommendation flip, and test a duty by asking what happens when everyone does it.
Choose a society from behind a veil and watch two rules disagree, rank distributions by their worst-off member, measure what a free exchange does to equality, and tell a gap in treatment from a gap in outcome. Then count the ballots: find the profile where the majority goes in a circle, the one where three rules elect three candidates, the voters who gain by lying, the court whose majorities contradict themselves, and the electorate that gets wiser as it grows only when its voters are better than chance.
Treat the oldest questions in metaphysics as questions about structure. Evaluate a claim of necessity at a world, find out which axioms a frame forces, decide where a modal argument goes wrong, and see what each position on identity, freedom and evil has to give up.
Test the arguments that mind and language are made of. Evaluate a necessity claim with and without the world it needs, compute what a mimic does to a judge, count a lookup table, and then read a sentence in a model, find the scope it hides, and run the heap under four treatments of vagueness.
A paradox is a valid-looking argument from plausible premises to a conclusion no one can accept. Here each one is computed: a sentence with no satisfying row, a series with an exact limit, a posterior that depends on a likelihood model, a modal sentence true at one world and believed at none. The labs find where the argument turns, and the choice of exit is left to you.
Recommended background
School arithmetic: fractions, percentages, and the willingness to add up a column. Every number on this path is a fraction or a whole number, and the labs do the arithmetic; what is asked of you is to read it.
No logic. Arguments and Validity teaches every piece of logic the Subject uses, starting from what an argument is. If you have met truth tables before you will move quickly through its first half; if you have not, it is where to start.
No probability. Knowledge and Evidence introduces credence and Bayes’ rule from a table of a million people, and nothing later assumes more than that lesson gives. Discrete Probability, in Discrete Mathematics, covers the same ground more formally and is a fine companion, not a prerequisite.
Patience with premises. The hard part of philosophy is not following an argument but deciding which premise to doubt, and the labs cannot do that for you. They will tell you an argument is valid; whether to accept its conclusion or reject a premise is the question every lesson leaves open on purpose.