Anindicative conditional is a natural-languageconditional sentence (an "if" sentence) used to talk about what may actually be the case, as in: "If Leona is at home, she isn't in Paris." Indicatives are commonly contrasted withcounterfactual conditionals, which typically bear special grammatical marking (e.g., "would have") and are used to discuss ways things might have been but are not.
Indicative conditionals are central inphilosophy of language,philosophical logic (especiallyconditional logic), andlinguistics. Debates concern (i) what semantic value, if any, such conditionals have; (ii) how their contribution composes with surrounding material; and (iii) how competing accounts explain observed patterns of assertion, reasoning, and embedding. Prominent proposals include truth-functional analyses, pragmatics-augmented accounts, probabilistic ("suppositional") approaches, possible-worlds semantics, and restrictor treatments ofif.
Many authors reserve "indicative" for conditionals whose matrix clause is in the indicative mood (e.g., withis,will), in contrast to counterfactuals (withwould). Others argue that some "future-open" indicatives pattern more like counterfactuals. Despite disagreements in classification, there is broad consensus that everyday "if A, B" claims used to guide belief and action are a distinctive target for theory.[1]
Early formal work identified natural-language indicatives with the truth-functionalmaterial conditional: "If A then B" is false only in the caseA ∧ ¬B and otherwise true (equivalently¬A ∨ B). This analysis validates familiar inferences (e.g.,modus ponens), but faces well-known "paradoxes of material implication": with a true consequent (B) or false antecedent (A), any "if A, B" comes out true—even whenA andB are intuitively unrelated.[2]
A classic response (inspired byH. P. Grice) keeps the material truth conditions but explains everyday resistance viapragmatics: speakers are expected to make the strongest, most informative appropriate assertion; when one knows ¬A, asserting "If A, B" can be true yet misleading.[3] Others (notably Jackson) supplement material truth with special rules ofassertability keyed to how robustly one would continue to acceptB upon learningA (often cashed out as highconditional probabilityP(B|A)).[4] Critics argue that many tensions arise at the level ofbelief and probability, not merely assertion norms.[1]
TheRamsey test holds that to assess "if A, B" one shouldsuppose A and then evaluateB under that supposition. Developed by Ernest W. Adams, the suppositional view takes the degree of belief in "if A, B" to beP(B|A) and offers a probabilistic account of valid inference (arguments are "good" when they preserve or suitably constrain probability).[5] This explains why many everyday inferences (e.g.,modus tollens with high but sub-certain premises) can be risky, and why rules likestrengthening the antecedent andtransitivity often fail in practice.[1]
A challenge for propositional semantics isLewis's "triviality" results: in general there is no proposition ⟦A⇒B⟧ whose probability always equalsP(B|A). This pressures the idea that indicative conditionals are standard truth-evaluable propositions with classical truth conditions.[6]
Robert Stalnaker proposed that "if A, B" is true at a worldw just in caseB holds at the contextuallynearest (most similar)A-world tow; for indicatives, conversational context constrains which worlds count as live possibilities.[7] Such accounts vindicate many Adams-style patterns but face issues about similarity metrics, uniqueness of nearest worlds, and probabilistic judgments (e.g., lottery-like "short straw" cases). Context-dependentstrict conditional views and the influential "if as arestrictor of modals" approach (Kratzer) treatif not as a binary connective but as narrowing the domain of a modal/quantifier; "bare" conditionals are often analyzed as containing an unpronounced epistemic necessity operator.[8]
To reconcile probabilistic behavior with compositional embedding, several frameworks treat conditionals as non-classical contents. One line (de Finetti; later, Jeffrey, van Fraassen) models "if A, B" as a three-valued or random-variable-like object whose expectation equalsP(B|A); another (Bradley) represents conditionals via ordered pairs/tuples of worlds encoding both the actual state and the "potential A-state," enabling truth conditions for many embeddings while preserving theP(B|A) link.[9][10]
Indicatives embedded under negation, disjunction, or in antecedents raise hard questions for all theories (e.g., theimport–export principle relating "if A and B, C" to "if A, if B, C").Vann McGee's "election" example challengesmodus ponens for certain nested indicatives if their readings shift across embeddings; different frameworks diagnose the phenomenon differently (scope/reading shifts vs. probabilistic risk vs. ambiguity).[11][12]
Some authors separate our fast, reliable-enoughheuristics for evaluating conditionals (Ramsey-Adams suppositional reasoning) from their underlying "semantic" treatment (e.g., material truth conditions that rationalize long-run practice). Tensions remain because material truth values often overstate the probability of conditionals with unlikely antecedents (byP(¬A) + P(A)·P(B|A)).[13][1]
Experimental work on indicatives, causal conditionals and counterfactuals finds robust endorsement ofmodus ponens; rates formodus tollens are variable and context-sensitive, improving under causal or counterfactual formulations and with enriched background knowledge.[14][15][16] Probabilistic ("suppositional") accounts have been argued to align closely with observed reasoning patterns, especially where participants condition on the antecedent and assess the likelihood of the consequent.[1]
