Map
Arrows point from what you learn first to what it opens. Point at a concept to light up its chain and where it comes back deeper. Right-click a concept (or press and hold it) for its lessons and stories.
- Proven to depth123
- Open
- Locked
- Comes back deeper
Depth 2Depth 2Depth 2Depth 2Depth 2Depth 2All, some and noneAnd and orAppeal to authorityArgumentArgument from analogyAttacking the personBandwagonCause or coincidenceCircular reasoningClaimConditional statementsCounterexampleDeduction and inductionEquivocationFalse dilemmaHasty generalisationHidden premiseIndicator wordsLoaded questionLogical fallacyNeeded and enoughNegationObjection and replyOnly if and unlessPrinciple of charityProof by contradictionSlippery slopeSoundnessStraw manSyllogismValidityExpertiseIn Epistemology
Learning path
In the order the concepts build on each other.
- ClaimReadyA sentence that is either true or false, even if nobody knows which yet. Questions, orders, greetings and wishes are not claims, and a sentence about taste tells us about the speaker.
- All, some and noneLockedQuantity words say how much of a group a claim is about. In logic "some" means at least one, the opposite of "all are" is "some are not", and an "all" claim can't be turned around.Opens after: Claim
- ArgumentLockedIn logic, a set of claims where some (the reasons, or premises) are given to support another (the conclusion) - not a quarrel. Shouting or repeating a claim adds no reasons.Opens after: Claim
- Conditional statementsLocked"If... then" claims about a link: whenever the if part happens, the then part does too. One is broken only when the if part is true and the then part false - so a wet street doesn't prove it rained.Opens after: Argument
- Hidden premiseLockedA reason an argument needs but doesn't say out loud. Most everyday arguments leave one out, and it is often the part worth checking.Opens after: Argument
- Indicator wordsLockedSignpost words that show the parts of an argument: "so" and "therefore" come before a conclusion, "because" and "since" before a reason.Opens after: Argument
- NegationLockedThe negation of a claim is its real opposite: true exactly when the claim is false. The negation of "all passed" is "not all passed" - not "none passed".Opens after: Claim, All, some and none
- ValidityLockedAn argument is valid when its conclusion must be true if its reasons are true. It is about the shape of the argument, not whether the reasons are true.Opens after: Argument
- And and orLockedAn and-claim is true only when both parts are; an or-claim when at least one is. "Or" usually allows both, and the opposite of "cold and windy" is "not cold or not windy".Opens after: Negation
- CounterexampleLockedOne case that shows an "all" claim is false, or a case where an argument's reasons are true and its conclusion false. One is enough.Opens after: Validity
- Deduction and inductionLockedDeduction aims for a conclusion that must be true if the reasons are. Induction goes from examples to a conclusion that is likely, stronger or weaker - and never completely sure.Opens after: Validity
- Loaded questionLockedA question with a claim built into it, so that any short answer agrees with the claim - "Have you stopped cheating at cards?" The way out is to answer the hidden claim.Opens after: Claim, Hidden premise
- Logical fallacyLockedA common pattern of reasoning that seems to support a conclusion but doesn't. Spotting one shows the reasons fail - not that the conclusion is false.Opens after: Validity
- Needed and enoughLockedSomething is needed (a necessary condition) when the result can't happen without it, and enough (a sufficient condition) when it makes the result sure. Air is needed for a fire, but not enough.Opens after: Conditional statements
- Proof by contradictionLockedShowing a claim is false by pretending it is true and following it to something impossible (reductio ad absurdum). If it leads to the impossible, its opposite must be true.Opens after: Validity, Negation
- SoundnessLockedA sound argument passes two checks: its conclusion follows (it is valid) and all its reasons are true - so its conclusion must be true.Opens after: Validity
- SyllogismLockedAn argument with two reasons and a conclusion, each an "all", "some" or "no" claim about groups, linked by a middle group. Circle diagrams show whether it is valid.Opens after: All, some and none, Validity
- Appeal to authorityLockedUsing what an expert says as a reason. It is a good reason from a real expert on their own field, especially when experts agree; it is a fallacy when someone speaks outside their field.Opens after: Logical fallacy, Expertise
- Argument from analogyLockedReasoning that because two things are alike in some ways, they are alike in another. It is strong when they are alike in the ways that matter for the conclusion.Opens after: Deduction and induction
- Attacking the personLockedAnswering an argument by attacking the person who made it - insults, "you do it too", "who are you to say" - instead of their reasons.Opens after: Logical fallacy
- BandwagonLockedTreating "many people believe it" or "everyone does it" as a reason that it is true or right. A claim is true or false depending on the world, not a vote.Opens after: Logical fallacy
- Cause or coincidenceLockedOne thing coming after another, or two things happening together, doesn't show that one causes the other: it could be chance, or a third thing causing both.Opens after: Deduction and induction
- Circular reasoningLockedUsing the conclusion, or the same idea in other words, as a reason for itself (begging the question). It can be valid and still give no reason to believe anything.Opens after: Argument, Logical fallacy
- EquivocationLockedUsing one word in two meanings in the same argument, so that it only seems to follow - like reading a "Fine for parking" sign as praise.Opens after: Logical fallacy, Validity
- False dilemmaLockedOffering only two choices when there are really more, so that rejecting one seems to force the other.Opens after: Logical fallacy
- Hasty generalisationLockedJumping to a claim about all of a group, or about what always happens, from too few examples or from examples all of one kind.Opens after: Deduction and induction
- Only if and unlessLocked"Only if" names something needed: "you may swim only if you wear a cap" means no cap, no swimming - not that a cap lets you in. "Unless" means "if not".Opens after: Needed and enough
- Slippery slopeLockedA chain of ifs from a small step to something terrible. The chain's shape is valid, but if each link is only likely, the whole chain is much less likely than any link.Opens after: Deduction and induction, Logical fallacy
- Straw manLockedChanging someone's argument into a weaker or sillier one - bigger, with "all" or "never" added - and arguing against that instead.Opens after: Logical fallacy
- Principle of charityLockedUnderstanding someone's argument in its best, most sensible form before answering it - and changing your mind when their reasons are better.Opens after: Straw man
- Objection and replyLockedAn objection is a reason to doubt an argument: a reason is false, or the reasons don't support the conclusion. A reply answers it - it's false, it doesn't matter much, or the plan changes.Opens after: Counterexample, Principle of charity
Connections to other domains
- Conditional statements leads to ConditionalsControl Flow
- Argument leads to Moral reasoningEthics
- Cause or coincidence, depth 2 needs Clinical trialHealth Evidence
- Hasty generalisation leads to Survivorship biasEpistemology
- Conditional statements leads to PredictionPhilosophy of Science
- Cause or coincidence leads to Random assignmentPhilosophy of Science
- Hasty generalisation leads to Sample sizePhilosophy of Science
- Cause or coincidence leads to CausationMetaphysics
- Appeal to authority needs ExpertiseEpistemology
- Proof by contradiction leads to Prime numbersNumber Theory
- Counterexample leads to Mathematical proofSets and Proof