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Concept
Conditionnels contrefactuels
Résumé
Counterfactual conditionals (also subjunctive or X-marked) are conditional sentences which discuss what would have been true under different circumstances, e.g. "If Peter believed in ghosts, he would be afraid to be here." Counterfactuals are contrasted with indicatives, which are generally restricted to discussing open possibilities. Counterfactuals are characterized grammatically by their use of fake tense morphology, which some languages use in combination with other kinds of morphology including aspect and mood.
Counterfactuals are one of the most studied phenomena in philosophical logic, formal semantics, and philosophy of language. They were first discussed as a problem for the material conditional analysis of conditionals, which treats them all as trivially true. Starting in the 1960s, philosophers and linguists developed the now-classic possible world approach, in which a counterfactual's truth hinges on its consequent holding at certain possible worlds where its antecedent holds. More recent formal analyses have treated them using tools such as causal models and dynamic semantics. Other research has addressed their metaphysical, psychological, and grammatical underpinnings, while applying some of the resultant insights to fields including history, marketing, and epidemiology.
The difference between indicative and counterfactual conditionals can be illustrated by the following English minimal pair:
Indicative conditional: If Sally owns a donkey, then she beats it.
Simple past counterfactual: If Sally owned a donkey, she would beat it.
These conditionals differ in both form and meaning. The indicative conditional uses the present tense forms "owns" and "beats" and therefore conveys that the speaker is agnostic about whether Sally in fact owns a donkey. The counterfactual example uses the fake tense form "owned" in the "if" clause and the past-inflected modal "would" in the "then" clause. As a result, it conveys that Sally does not in fact own a donkey.
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Indicative conditional
In natural languages, an indicative conditional is a conditional sentence such as "If Leona is at home, she isn't in Paris", whose grammatical form restricts it to discussing what could be true. Indicatives are typically defined in opposition to counterfactual conditionals, which have extra grammatical marking which allows them to discuss eventualities which are no longer possible. Indicatives are a major topic of research in philosophy of language, philosophical logic, and linguistics.
Implication (logique)
En logique mathématique, l'implication est l'un des connecteurs binaires du langage du calcul des propositions, généralement représenté par le symbole « ⇒ » et se lisant « ... implique ... », « ... seulement si ... » ou, de façon équivalente, « si ..., alors ... » comme dans la phrase « s'il pleut, alors il y a des nuages ». L'implication admet des interprétations différentes selon les différents systèmes logiques (logique classique, modale, intuitionniste, etc.).
Implication stricte
In logic, a strict conditional (symbol: , or ⥽) is a conditional governed by a modal operator, that is, a logical connective of modal logic. It is logically equivalent to the material conditional of classical logic, combined with the necessity operator from modal logic. For any two propositions p and q, the formula p → q says that p materially implies q while says that p strictly implies q. Strict conditionals are the result of Clarence Irving Lewis's attempt to find a conditional for logic that can adequately express indicative conditionals in natural language.