One way to hedge a claim is to make it conditional on another one, limiting one’s responsibility for the truth of the first claim to cases where the second is true. The English word if is used for this purpose. We will refer to the resulting compound (and the connective used to form it) as a conditional. Its two components are distinguished as the antecedent (which expresses the condition placed on the claim and appears as a subordinate clause in English) and the consequent (which is the claim that is made conditional and appears as a main clause). Although, the two components have a different significance in the compound, they can be stated in either order in English, with the antecedent preceded by if. The rightwards and leftwards arrows, → and ←, provide our signs for the if-conditional; the two components may be written in either order but the arrow should be chosen to point from the subordinate to the main clause. As English notation, we write if φ then ψ for φ → ψ and yes ψ if φ for ψ ← φ. When parentheses are to be used for grouping, we can use if for ← but we must resort to implies for → (understanding this to indicate material implication rather than the logical implication that is a special case of entailment).
The truth table incorporating this description presents a conditional as false only when its antecedent is true and its consequent is false. This account was first offered in antiquity and has been controversial ever since. Current thinking distinguishes between indicative and subjunctive conditionals. The latter are held not to have truth tables (but to instead be true when their consequents are true in all the nearest worlds in which the antecedent is true). Indicative conditionals are held to have truth tables even though implicatures obscure this fact.
The rule of the thumb that if precedes the antecedent is the key to analyzing English conditionals, but some thought can be required to determine how much of the sentence constitutes the corresponding main clause. English conditionals about the future usually have antecedents in the present tense, so a change of tense is required to obtain an independent component with the correct meaning. When a branching conditional is stated in English, the term otherwise (which amounts to if that is not the case) is often used to state one of the antecedents.