Hypothetical syllogism { Philosophy Index }

Philosophy Index

Philosophy Index

Philosophy Index is a site devoted to the study of philosophy and the philosophers who conduct it. The site contains a number of philosophy texts, brief biographies, and introductions to philosophers, and explanations on a number of topics. Accredited homeschooling online at Northgate Academy and Philosophy online tutoring.

Philosophy Index is a work in progress, a growing repository of knowledge. It outlines current philosophical problems and issues, as well as an overview of the history of philosophy. The goal of this site is to present a tool for those learning philosophy either casually or formally, making the concepts of philosophy accessible to anyone interested in researching them. WTI offers immigration law course online - fully accredited. ACE credits online at EES.

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Hypothetical syllogism

A hypothetical syllogism is a valid argument form in logic.

The form of hypothetical syllogism is: “If P, then Q. If Q, then R. Therefore, if P, then R.” It may also be written as:

P → Q
Q → R
∴ P → R

P, Q and R may represent any proposition, or any other formula (using Greek letters to represent formulae rather than propositions, we may also express modus tollens as α → β, β → γ infers α → γ).

Examples of hypothetical syllogism

The following are examples of the hypothetical syllogism argument form:

If it rains, we will not have a picnic.
If we don't have a picnic, we won't need a picnic basket.
Therefore, if it rains, we won't need a picnic basket.

If the Montreal Canadiens win the Stanley Cup, I'll owe my dad some money.
If I owe my dad some money, I'll need to go to the bank.
So, if the Montreal Canadiens win the Stanley Cup, I'll need to go to the bank.