Hypothetical syllogism
Introduction
Hypothetical syllogism, also known as the chain argument, is a valid rule of inference in logic. It is a type of argument in which a conclusion is drawn from two given or assumed propositions (premises), each of which shares a term with the conclusion, and shares a common or middle term not present in the conclusion.
Definition
A hypothetical syllogism is a syllogism in which at least one of the premises is a conditional, the antecedent or consequent of which may appear in the other premises or the conclusion. It is a syllogism having a conditional statement for one or both of its premises. If both premises are conditionals, the syllogism is a pure hypothetical syllogism; if not, it is a mixed hypothetical syllogism.
Structure
The structure of a hypothetical syllogism is as follows: - If P then Q (Premise 1) - If Q then R (Premise 2) - Therefore, if P then R (Conclusion)
This is also known as a chain argument due to the chain-like structure of conditionals. The term 'hypothetical' refers to the 'if-then' structure of the statements, which are also known as hypothetical propositions or conditionals.
Types of Hypothetical Syllogisms
Hypothetical syllogisms can be divided into three types: pure hypothetical syllogisms, mixed hypothetical syllogisms, and disjunctive syllogisms.
Pure Hypothetical Syllogism
A pure hypothetical syllogism is a syllogism in which both premises and the conclusion are all conditional statements.
Mixed Hypothetical Syllogism
A mixed hypothetical syllogism is a syllogism in which one premise is a conditional statement, the other premise is a categorical statement, and the conclusion is a categorical statement.
Disjunctive Syllogism
A disjunctive syllogism is a syllogism in which the major premise is a disjunctive proposition, the minor premise denies one of the disjuncts, and the conclusion affirms the remaining disjunct.
Validity of Hypothetical Syllogisms
The validity of a hypothetical syllogism depends on the logical structure of the argument, not the truth of the premises or the conclusion. A hypothetical syllogism is valid if the conclusion follows logically from the premises.
Use in Logic
Hypothetical syllogisms are used in various fields of logic, including formal logic, informal logic, and symbolic logic. They are a fundamental tool in deductive reasoning, allowing one to derive a conclusion from two or more premises that are assumed to be true.