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. Open questions include which logical operation indicatives denote, how such denotations could be composed from their grammatical form, and the implications of those denotations for areas including metaphysics, psychology of reasoning, and philosophy of mathematics.
Early analyses identified indicative conditionals with the logical operation known as the material conditional. According to the material conditional analysis, an indicative "If A then B" is true unless A is true and B is not. Although this analysis covers many observed cases, it misses some crucial properties of actual conditional speech and reasoning.
One problem for the material conditional analysis is that it allows indicatives to be true even when their antecedent and consequent are unrelated. For instance, the indicative "If Paris is in France then trout are fish" is intuitively strange since the location of Paris has nothing to do with the classification of trout. However, since its antecedent and the consequent are both true, the material conditional analysis treats it as a true statement. Similarly, the material conditional analysis treats conditionals with false antecedents as vacuously true. For instance, since Paris is not in Australia, the conditional "If Paris is in Australia, then trout are fish" would be treated as true on a material conditional analysis. These arguments have been taken to show that no truth-functional operator will suffice as a semantics for indicative conditionals. In the mid-20th century, work by H.P.
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Discrete mathematics is a discipline with applications to almost all areas of study. It provides a set of indispensable tools to computer science in particular. This course reviews (familiar) topics a
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.
Conditional sentences are natural language sentences that express that one thing is contingent on something else, e.g. "If it rains, the picnic will be cancelled." They are so called because the impact of the main clause of the sentence is conditional on the dependent clause. A full conditional thus contains two clauses: a dependent clause called the antecedent (or protasis or if-clause), which expresses the condition, and a main clause called the consequent (or apodosis or then-clause) expressing the result.
Modal logic is a kind of logic used to represent statements about necessity and possibility. It plays a major role in philosophy and related fields as a tool for understanding concepts such as knowledge, obligation, and causation. For instance, in epistemic modal logic, the formula can be used to represent the statement that is known. In deontic modal logic, that same formula can represent that is a moral obligation. Modal logic considers the inferences that modal statements give rise to.
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