Conditional reasoning
Inference from 'if...then' statements, where two moves are valid and two are tempting fallacies.
What it means
Conditional reasoning is inference based on 'if P then Q' statements, the workhorse of everyday and scientific logic. Two inferences are logically valid — modus ponens (given P, conclude Q) and modus tollens (given not-Q, conclude not-P) — while two are fallacies that people nonetheless frequently endorse: affirming the consequent (given Q, concluding P) and denying the antecedent (given not-P, concluding not-Q). People also make pragmatic invited inferences, often treating 'if' as 'if and only if,' and their conclusions are powerfully shaped by content, believability, and the availability of counterexamples rather than by pure form. Mental model theory explains the pattern by which possibilities reasoners represent and which they omit. Conditional reasoning sits at the heart of hypothesis testing, the Wason task, and the broader study of human rationality.
The endorsement gradient
People do not treat the four inference forms alike. Across dozens of studies, endorsement falls in a stable order: modus ponens first, then modus tollens, then the two fallacies, affirming the consequent and denying the antecedent. Modus ponens is close to universal, accepted by roughly nine in ten adults or more; modus tollens, though equally valid, drops to around two-thirds because it demands an indirect, suppositional step. The fallacies are still endorsed by large minorities, and more so when the conditional invites a biconditional reading. The ordering is robust across the broader literature, and surface features shift acceptance in predictable ways; a meta-analysis by Schroyens, Schaeken and d'Ydewalle (2001) documented in particular how negations in the clauses reshape processing.
Why one valid move is harder than the other
Modus ponens is direct: given 'if P then Q' and P, the conclusion Q is simply read off. Modus tollens is not. To conclude not-P from not-Q, a reasoner must suppose P, notice that Q would then have to hold, see that it contradicts the known not-Q, and reject the supposition. Mental model theory ties the difficulty to representation. People initially picture only the case where P and Q both hold and keep the rest in reserve, fleshing out the further possibilities only with effort and working memory. Modus tollens needs that fuller set, so it is skipped more often, drawn more slowly, and made more accurately by those who can juggle several possibilities at once.
Content can suppress a valid inference
Formal validity does not settle what people will infer; background knowledge does. Byrne (1989) showed that adding a second requirement — 'if she has enough money, she will go to the play' alongside 'if she meets her friend, she will go' — leads reasoners to withdraw the modus ponens conclusion they had just accepted, though the logic is untouched. Cummins (1995) traced the pattern to memory: the more alternative causes and disabling conditions a conditional brings to mind, the less people endorse the inference. A rule with many exceptions is treated as defeasible. This is a feature, not a flaw — everyday conditionals usually are defeasible — but it means laboratory 'errors' often reflect sensible inference under uncertainty.
The probabilistic turn
Much recent work abandons binary logic as the yardstick. On the 'new paradigm' view (Oaksford & Chater, 2020), people read 'if P then Q' as the conditional probability of Q given P being high, judged by imagining P and assessing Q — the Ramsey test. This explains why cases where P is false strike them as irrelevant rather than confirming, producing the 'defective' truth table, and why endorsement tracks believability and exception frequency. Reasoning becomes a matter of degree, not proof. The account fits the suppression and content data, though it stays in live debate with mental model theory over whether probability or represented possibilities is the more basic currency. Both agree that formal logic poorly describes how people actually reason.
Examples
Told 'if it rains, the match is canceled' and that the match was canceled, many wrongly infer it rained — committing the fallacy of affirming the consequent, since other causes could cancel the match.
Told 'if the server is down, the site is slow,' an engineer finds the server up and concludes the site is fine — denying the antecedent, when plenty else could slow it.
'If you studied, you'll pass.' She passed, so she studied? Not necessarily — an easy paper passes too. The valid move runs the other way: she failed, so she cannot have studied.
'If the patient has strep, the throat culture is positive.' The culture came back negative, so the clinician correctly rules out strep — a clean modus tollens, the fallacy-free move most people find hardest.
'If the login is fraudulent, it comes from a new device.' A login arrives from a new device, so the analyst flags it as fraud — affirming the consequent, since honest travelers use new devices.
First described in Wason & Johnson-Laird (1972); mental model theory.
Key references
- Oaksford, M., & Chater, N. (2020). New paradigms in the psychology of reasoning. Annual Review of Psychology, 71, 305-330. doi.org/10.1146/annurev-psych-010419-051132
- Johnson-Laird, P. N., & Byrne, R. M. J. (2002). Conditionals: A theory of meaning, pragmatics, and inference. Psychological Review, 109(4), 646-678. doi.org/10.1037/0033-295X.109.4.646
- Schroyens, W., Schaeken, W., & d'Ydewalle, G. (2001). The processing of negations in conditional reasoning: A meta-analytic case study in mental model and/or mental logic theory. Thinking & Reasoning, 7(2), 121-172. doi.org/10.1080/13546780042000091
- Cummins, D. D. (1995). Naive theories and causal deduction. Memory & Cognition, 23(5), 646-658. doi.org/10.3758/BF03197265
- Byrne, R. M. J. (1989). Suppressing valid inferences with conditionals. Cognition, 31(1), 61-83. doi.org/10.1016/0010-0277(89)90018-8