Where does conditional collide?

In probability theory, a conditional probability P(A|B) is the probability of one event given that another has occurred, defined for P(B) > 0 as the ratio P(A ∩ B) / P(B), and it generalises to conditional expectation and conditional distributions. Kolmogorov's Foundations of the Theory of Probability placed this on a measure-theoretic footing. The referent is a renormalised probability relative to given information, a numerical object quite unlike a logician's connective or a grammarian's clause.[1]

Unit

The probability of an event given that a conditioning event has occurred

Recovery means

Not applicable

Measured by

Computed as P(A ∩ B) / P(B), or as a conditional expectation characterised by its defining measure-theoretic property

In grammar and linguistics, a conditional is a sentence or clause type, canonically "if P, (then) Q", that presents one situation as a condition on another, marked across languages by dedicated moods, tenses, particles, and clause order. Haiman's 1978 Conditionals are topics argued that the if-clause functions as the topic of the sentence it governs. The referent is a construction and its marking in natural language, not a probability ratio or a truth-functional operator.[2]

Unit

The clause or construction that marks one situation as a condition on another

Recovery means

Not applicable

Measured by

Identified by conditional morphosyntax (conjunctions, mood and tense marking, and clause order) across languages

In logic, the conditional is the connective joining an antecedent to a consequent (most simply the truth-functional material conditional, which is false only when the antecedent is true and the consequent false), while indicative and counterfactual conditionals in ordinary reasoning depart from this and remain contested. Edgington's 1995 On conditionals surveys why no purely truth-functional account captures ordinary "if." The referent is a sentential operator and its logic, distinct from a probabilistic ratio or a grammatical construction.[3]

Unit

The truth or assertibility of "if P then Q" as a function of its parts

Recovery means

Not applicable

Measured by

Analysed via truth tables for the material conditional and via probabilistic or possible-worlds accounts for indicative and counterfactual conditionals