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A conditional sentence expressing an implication (also called a factual conditional sentence) essentially states that if one fact holds, then so does another. (If the sentence is not a declarative sentence , then the consequence may be expressed as an order or a question rather than a statement.)
Prototypical conditional sentences in English are those of the form "If X, then Y". The clause X is referred to as the antecedent (or protasis), while the clause Y is called the consequent (or apodosis). A conditional is understood as expressing its consequent under the temporary hypothetical assumption of its antecedent.
In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements.For example, in the conditional statement: "If P then Q", Q is necessary for P, because the truth of Q is guaranteed by the truth of P.
Wherever logic is applied, especially in mathematical discussions, it has the same meaning as above: it is an abbreviation for if and only if, indicating that one statement is both necessary and sufficient for the other. This is an example of mathematical jargon (although, as noted above, if is more often used than iff in statements of definition).
These conditionals differ in both form and meaning. The indicative conditional uses the present tense form "owns" 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 ...
These examples, one from mathematics and one from natural language, illustrate the concept of vacuous truths: "For any integer x, if x > 5 then x > 3." [11] – This statement is true non-vacuously (since some integers are indeed greater than 5), but some of its implications are only vacuously true: for example, when x is the integer 2, the statement implies the vacuous truth that "if 2 > 5 ...
In propositional logic, affirming the consequent (also known as converse error, fallacy of the converse, or confusion of necessity and sufficiency) is a formal fallacy (or an invalid form of argument) that is committed when, in the context of an indicative conditional statement, it is stated that because the consequent is true, therefore the ...
A conditional statement may refer to: A conditional formula in logic and mathematics, which can be interpreted as: Material conditional; Strict conditional;
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