Conditional statements: grammar, meaning and logic

Conditional statements connect a condition with a consequence. Their grammar distinguishes habits, possibilities, hypothetical situations and unrealised alternatives; their logical meaning depends on the relationship between the clauses rather than on either clause alone.

Clauses and punctuation

A conditional has an if-clause, called the antecedent or protasis, and a main clause, called the consequent or apodosis. ¹ The consequent can stand as a sentence, while the antecedent is dependent, introduced by a subordinating conjunction such as “if”, “when” or “unless”. ² The antecedent acts adverbially, setting limiting conditions on a statement or command. ²

The antecedent need not come first: an opening antecedent is separated by a comma, as in “If I were you, I would not do that”, whereas a following antecedent is not, as in “I would not do that if I were you”. ² “Then” can mark the consequent but is optional: “If the light is green, [then] you can go.” ² Either part can contain coordinated clauses, as in “When it is warm outside and the sun is shining, I ride my bicycle and she goes swimming.” ²

Purposes and interpretation

Conditionals can express what is always, generally or occasionally true, or true only under specified conditions. ¹ They can describe statistical or causal relationships, establish rules, make promises or threats, issue warnings and express feelings. ¹ Similar grammatical forms can therefore carry different meanings. ¹

A medical writer should consider three issues when interpreting a conditional. ¹

1. Intelligibility: is the statement grammatical and meaningful?
2. Modality: is the antecedent definitely true, possibly true or impossible, and does the consequent express a fact, possibility, command, threat or something else?
3. Relationship: how tightly are the clauses' truth values related, does the relationship reflect causation, and are relevant conditions left unstated?

¹

Types of conditional

Five basic types differ in purpose and grammatical form. ³

Zero-order conditionals

Zero-order conditionals describe facts, habits and rules, often using the simple present in both clauses: “If the solution is alkaline, the litmus paper turns blue” and “Whenever she leaves the house, she takes her cellphone.” ⁴ Timing can remain unspecified, and the consequent can even describe an event preceding the antecedent. ⁴ The conditional as a whole can state a fact without asserting that the condition has actually occurred. ⁴

A zero-order conditional need not describe an exceptionless relationship: “always”, “usually”, “generally”, “sometimes” and “occasionally” clarify its frequency, as in “If you call her during business hours, she usually answers.” ⁴ “When” or “whenever” can replace “if”, and the clauses can be negative: “If the sun is not shining, the solar oven does not work.” ⁴

First-order conditionals

First-order conditionals describe consequences of realistic, likely or possible events. ⁵ The antecedent uses the present tense even when it refers to a future event, while the consequent uses the future tense. ⁵ Negotiations use this form: “If you finish the work early, I will give you a bonus.” ⁵ Threats, warnings and superstitions can use it too, although the consequence may not follow even if the condition is met. ⁵

Examples of these uses are: ⁵

• “If you hit me, I will hit you back.”
• “If you don’t control your blood sugar, you will have serious complications.”
• “If you break a mirror, you will have 7 years of bad luck.”

⁵

Second-order conditionals

Second-order conditionals express hypothetical situations, including uncertain or impossible conditions. ⁶ Their antecedent uses a verb form resembling the indicative past even when the imagined event lies in the future. ⁶

• “If I won the lottery, I would buy a fancy new car.”
• “If I were to start training today, I would be ready to run a marathon by next summer.”

⁶

Inverting subject and verb can replace “if”: “Were we to give up this fight, it would mean the end of democracy.” ⁶ The form can also express a counterfactual present: “If wishes were horses, then beggars would ride.” ⁶

Third-order conditionals

Third-order conditionals describe what would have happened in the past if an unmet condition had been fulfilled. ⁷ The if-clause uses the past perfect, and the main clause uses “would have” plus a past participle: “If I had known that you were coming, I would have baked you a cake.” ⁷

Mixed conditionals

Mixed conditionals can connect counterfactual conditions and consequences across different times. ⁸ Three basic patterns are: ⁸

1. A different past with present consequences: past perfect in the if-clause and “would” in the main clause. “If Julie had scored higher on her MCAT, she would be in medical school today.”
2. A different past with future consequences: past perfect in the if-clause, with “would” and an expression of future time in the main clause, sometimes “would be” plus a present participle or “would” plus a bare infinitive and a future-time expression. “If she had booked the flight earlier, she would be going with us on Wednesday”; “If she hadn’t forgotten to book the flight, she would go with us on Wednesday.”
3. A counterfactual present condition with a past consequence: “If I were rich, I would have given you the money.”

⁸

Questions, commands and idioms

An antecedent can qualify a question, as in “What do we do if the patient is allergic to penicillin?”, or a command, as in “If you think that someone is having a stroke, call an ambulance immediately.” ⁹

Relevance or “biscuit” conditionals have a consequent whose truth does not depend on the antecedent: “There are biscuits in the pantry, if you want some” leaves the biscuits there regardless of the listener's wishes. ⁹ “If you ask me, she’s out of her mind” is another example. ⁹ “If only” can express a wish: “If only it would stop raining!” ⁹

Necessary and sufficient conditions

When the consequent is always true whenever the antecedent is true, the antecedent is sufficient for it. ⁴ When the antecedent must be true for the consequent to be true, it is necessary, but its presence need not guarantee the consequent. ⁴ Necessity can be expressed as “If patients with scurvy don’t get vitamin C, they don’t recover”, “Unless they get vitamin C, patients with scurvy don’t recover”, or “Patients with scurvy recover only if they get vitamin C”. ⁴ Vitamin C given too late illustrates how a necessary condition may be present without recovery following. ⁴ In medical examples, outcomes can depend on additional factors that are unstated or unnoticed. ⁴

A conditional whose antecedent is both necessary and sufficient is biconditional: the antecedent and consequent have the same truth value, both true or both false. ⁴

Truth values and related statements

In formal logic, P and Q stand for propositions, statements that can be true or false, including suppositions accepted for an argument. ¹⁰ P→Q means “if P is true, then Q is true”, and is itself a proposition. ¹⁰ For an exceptionless rule, P→Q is false only when P is true and Q is false. ¹⁰

A biconditional is written P↔Q, expressed as “if and only if”, abbreviated “iff”, or by adding “and conversely”. ¹¹

A conditional can be true even when both clauses are false. ¹ With an impossible antecedent, the formal implication is true regardless of its consequent: “If you pick up a guinea pig by the tail, its eyes fall out” depends on guinea pigs having no tail to pick up, not on their eyes. ¹²

The inverse, contrapositive and converse change the original “If I am king of the forest, I get respect” in different ways. ^{13, 14, 15}

• The inverse negates both clauses: ~P→~Q, “If I am not king of the forest, I don’t get respect.” It need not share the original's truth value: someone who is not king can still be respected.
• The contrapositive negates and swaps the clauses: ~Q→~P, “If I do not get respect, then I am not king of the forest.” It is logically equivalent to the original, so proving either proves the other.
• The converse swaps the clauses: Q→P, “If I get respect, I am king of the forest.” It need not share the original's truth value, since respected people need not be kings; it is logically equivalent to the inverse.

^{13, 14, 16, 15}

Negating a negative statement makes it positive: the negation of “There are no cookies in the jar” is “There are cookies in the jar”. ¹³

Arguments using conditionals

Conditional propositions can serve as premises in arguments. ^{17, 18} The symbol ∴ marks the conclusion and means “therefore”. ¹⁸ An argument is valid if true premises cannot produce a false conclusion, and sound if it is valid and its premises are true. ¹⁹

Two valid forms are: ¹⁹

• Modus ponens: P→Q and P imply Q.
• Modus tollens: P→Q and a false Q imply a false P.

¹⁹

Formal fallacies arise from an argument's form; informal fallacies can instead arise from problems such as misunderstanding words. ²⁰ Two formal errors involving conditionals are: ²⁰

• Affirming the consequent: from P→Q and Q, inferring P. This is the converse error or confusion of necessity and sufficiency; P can be false while both premises are true.
• Denying the antecedent: from P→Q and a false P, inferring a false Q. This is the inverse error; Q can remain true while both premises are true.

²⁰