Critical thinking · 32 pages
Logic & critical thinking
Answer-first explainers for logical fallacies, argument structure, and reasoning — the neutral, standards-grade reference for what each term means, with examples and common misconceptions.
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All 32 logic & critical thinking pages
Ad hominem
Ad hominem (Latin for "to the person") is an informal fallacy of relevance in which someone rejects or attacks an argument by criticising the person advancing it rather than the reasoning. Because a claim’s truth does not depend on who states it, the personal attack is logically irrelevant. Not every criticism of a person is fallacious — questioning a witness’s honesty can be legitimate.
DefinitionRed herring
A red herring is an informal fallacy of relevance in which a speaker introduces an irrelevant or distracting topic to draw attention away from the original issue. The diversion may seem related, but it does not address the point in dispute. The term comes from the idea of dragging a strong-smelling fish across a trail to mislead tracking hounds.
DefinitionCritical thinking
Critical thinking is the disciplined, self-directed process of analysing and evaluating reasoning, evidence and claims so as to reach a well-justified conclusion rather than accepting them uncritically. It involves clarifying questions, weighing evidence, identifying assumptions and logical fallacies, considering alternatives and judging fairly. It is a skill set and a disposition — being open-minded yet sceptical, and willing to follow the evidence.
DefinitionPremise
A premise is a statement offered in support of a conclusion. In an argument, premises are the reasons or evidence given, and the conclusion is the claim they are meant to establish. An argument typically has one or more premises and exactly one main conclusion. For example, "All humans are mortal" and "Socrates is human" are premises supporting "Socrates is mortal".
DefinitionSyllogism
A syllogism is a deductive argument consisting of two premises and a conclusion, in which the conclusion follows necessarily from the premises. The classic categorical syllogism links three terms across the statements, as in: All humans are mortal; Socrates is human; therefore Socrates is mortal. A syllogism is valid when its form guarantees the conclusion, regardless of the content.
DefinitionStraw man
A straw man is an informal fallacy in which someone misrepresents, exaggerates or oversimplifies an opponent’s argument and then refutes the distorted version, falsely claiming to have defeated the original. Because the "argument" attacked is a fabrication, the opponent’s actual position remains untouched. The fallacy is named for the idea of fighting a stuffed dummy rather than a real adversary.
DefinitionSlippery slope
A slippery slope is an informal fallacy that asserts a comparatively minor first action will inevitably set off a chain of events culminating in a significant, usually undesirable, outcome — without providing evidence that each step actually follows from the one before. The reasoning fails when the inevitability of the chain is assumed rather than demonstrated. A well-supported causal chain, by contrast, is not fallacious.
DefinitionCircular reasoning
Circular reasoning is an informal fallacy in which the conclusion of an argument is assumed, in some form, within its premises. The argument loops back on itself — the premise depends on the conclusion that it is meant to support — so it offers no independent reason to accept the claim. It is closely related to begging the question, where the conclusion is smuggled into the premises.
DefinitionFalse dichotomy
A false dichotomy, also called a false dilemma, is an informal fallacy that presents only two options or outcomes as if they were the only possibilities, when in reality further alternatives exist. By artificially narrowing the choices, it pressures the audience to accept one of the offered options. The flaw is the false claim of exhaustiveness — that the two stated options cover every case.
DefinitionNon sequitur
A non sequitur (Latin for "it does not follow") is an argument whose conclusion does not follow logically from its premises. There is a gap or disconnect between the evidence offered and the claim drawn from it, so even true premises fail to support the conclusion. In its broadest sense, every formal logical fallacy is a kind of non sequitur.
DefinitionBegging the question
Begging the question (Latin petitio principii) is an informal fallacy in which the conclusion of an argument is assumed within its premises, so the argument presupposes what it claims to prove. Because the premise already takes the conclusion for granted, it provides no independent support. In logic it is essentially a form of circular reasoning, and it does not mean "to raise a question".
DefinitionAppeal to authority
An appeal to authority (argumentum ad verecundiam) is the move of supporting a claim by citing an authority. It is fallacious only when the authority is irrelevant to the topic, unqualified, biased, or speaking against a genuine expert consensus. Citing a relevant, qualified expert who reflects the consensus is legitimate evidence, not a fallacy — the error is in misusing authority, not in referencing it.
DefinitionAppeal to emotion
An appeal to emotion (argumentum ad passiones) is an informal fallacy that tries to win acceptance for a conclusion by arousing feelings — fear, pity, anger, pride or flattery — instead of providing relevant evidence or reasons. The emotion may be real, but it does not bear on whether the claim is true. Evoking emotion is only fallacious when it replaces, rather than accompanies, genuine support.
DefinitionHasty generalisation
A hasty generalisation is an informal fallacy in which a general conclusion is drawn from insufficient, biased or unrepresentative evidence — often too few cases. Because the sample does not adequately reflect the whole population, the conclusion is unwarranted even if it happens to be true. It is a fallacy of weak induction, sometimes called jumping to conclusions or the fallacy of insufficient sample.
DefinitionFalse cause
The false cause fallacy (non causa pro causa) infers a causal relationship from insufficient grounds — typically from one event preceding another, or from two things correlating. Its best-known forms are post hoc ergo propter hoc ("after this, therefore because of this") and cum hoc ergo propter hoc ("with this, therefore because of this"). Sequence and correlation alone do not establish causation.
DefinitionBandwagon fallacy
The bandwagon fallacy (argumentum ad populum) is an informal fallacy that treats the popularity of a belief or practice as evidence of its truth or correctness. "Everyone believes it, so it must be true" is fallacious because widespread acceptance does not make a claim true — popular beliefs have often been wrong. It is also called the appeal to popularity or appeal to the majority.
ComparisonValid vs sound argument
The difference is that validity is about form and soundness adds truth. An argument is valid if its conclusion follows necessarily from its premises — that is, if the premises were true, the conclusion would have to be true. An argument is sound if it is both valid and all its premises are actually true. A valid argument can have a false conclusion when a premise is false; only a sound argument guarantees a true conclusion.
GuideLogical fallacies
A logical fallacy is a flaw in reasoning that undermines the logic of an argument. Fallacies divide into two broad classes: formal fallacies, where the argument’s structure is invalid, and informal fallacies, where the error lies in the content, relevance or assumptions rather than the form. This guide defines the most common fallacies in each category and links to detailed explanations.
DefinitionSunk cost fallacy
The sunk cost fallacy is a cognitive bias and logical error in which someone continues an action because of past investments of time, money or effort — even when continuing is irrational. Because sunk costs are irrecoverable, they should have no bearing on future decisions. The error was studied in behavioural economics by Arkes & Blumer (1985) and Thaler (1980).
DefinitionFalse equivalence
False equivalence is an informal logical fallacy that treats two things as equivalent when they are not relevantly similar. It creates a misleading impression of symmetry between positions that differ substantially in evidence, scale or significance. It is common in media "balance" coverage that presents fringe and mainstream positions as equally credible.
DefinitionCognitive dissonance
Cognitive dissonance is the psychological discomfort experienced when holding two or more contradictory beliefs, values or behaviours simultaneously. Coined by Leon Festinger (1957), the theory proposes that people are motivated to reduce this inconsistency by changing beliefs, adding new cognitions or trivialising the conflict. It is one of the most studied phenomena in social psychology.
DefinitionConfirmation bias
Confirmation bias is the tendency to search for, interpret, favour and recall information in ways that confirm existing beliefs. Identified by Francis Bacon and formalised by Peter Wason (1960) via the 2-4-6 task. It affects reasoning in science, medicine, law, journalism and everyday decision-making, and is a key target of evidence-based epistemology.
DefinitionOccam’s razor
Occam’s razor is the principle that among competing explanations, the one with the fewest unnecessary assumptions should be preferred. Named after 14th-century philosopher William of Ockham, it is widely used in science, medicine and machine learning as a guide to parsimony. It is a heuristic, not a proof that simpler explanations are always correct.
DefinitionWhataboutism
Whataboutism is a rhetorical tactic and logical fallacy that deflects criticism by pointing to a different, unrelated wrongdoing — essentially arguing "but what about what you did?" It is a variant of the tu quoque fallacy and is widely used in political discourse to avoid addressing legitimate criticism. The term gained currency during Cold War Soviet propaganda.
DefinitionGambler’s fallacy
The gambler’s fallacy is the mistaken belief that prior independent random events affect the probability of future events — for example, believing a coin is "due" to land heads after several tails. Because each fair coin flip is statistically independent, the probability remains 50% regardless of history. It reflects a misunderstanding of the law of large numbers.
DefinitionNo true Scotsman fallacy
The no true Scotsman fallacy is an informal logical fallacy in which someone redefines a claim to exclude counterexamples, rather than accepting the counterexample as a refutation. Named by philosopher Antony Flew (1975), the typical form is: "No true X would do Y" — where the definition of X is revised after the fact to protect the generalisation.
DefinitionAppeal to nature fallacy
The appeal to nature is a logical fallacy that assumes something is good or safe because it is natural, and bad or harmful because it is artificial. Natural things can be harmful (arsenic, botulinum toxin, cyanide) and artificial things beneficial (vaccines, antibiotics, clean water). Naturalness is not a reliable indicator of safety, efficacy or moral worth.
DefinitionBurden of proof
The burden of proof is the obligation to provide evidence for a claim. Whoever makes a positive claim bears the burden of proving it; the default position is scepticism. Shifting the burden to critics — expecting them to disprove a claim without evidence — is itself a fallacy. Hitchens’s razor states: "What can be asserted without evidence can be dismissed without evidence."
DefinitionModus ponens and modus tollens
Modus ponens ("affirming the antecedent") is: if P then Q; P is true; therefore Q. Modus tollens ("denying the consequent") is: if P then Q; Q is false; therefore P is false. Both are valid deductive argument forms in propositional logic — the conclusion necessarily follows from true premises. Affirming the consequent and denying the antecedent are invalid forms.
DefinitionFalse analogy
A false analogy is an informal logical fallacy in which two things are compared as analogous when they are not relevantly similar in the way the argument requires. Analogical reasoning is legitimate and valuable — in science, law and ethics — but an analogy fails when the compared cases differ in ways that matter to the conclusion.
DefinitionAnecdotal evidence fallacy
The anecdotal evidence fallacy occurs when someone treats a personal story or isolated case as sufficient evidence for a general claim, ignoring systematic data. Anecdotes are not worthless — they generate hypotheses and identify rare events — but they cannot establish causal relationships or population-level patterns because they are subject to selection bias and cannot be verified or replicated.
DefinitionSpecial pleading
Special pleading is an informal logical fallacy in which someone applies a general principle to others but claims an exemption for themselves or their preferred case, without a principled reason for the exception. It violates the principle of universalisability: similar cases should be treated similarly unless there is a relevant, stated difference that justifies the distinct treatment.
