# Chapter 3 Hypothetical Syllogisms

Hypothetical Syllogisms

As stated in Chapter 2, a hypothetical syllogism is a syllogism with at least one conditional premise, that is, at least one ―if…then…‖ premise. The ―If…then…‖ relationship may be expressed in ordinary language by using a number of different terms.

In checking hypothetical syllogisms expressed in ordinary language for their validity, it is therefore useful to be able to translate such conditional vocabulary into standard conditional form.

The Vocabulary of Conditional Statements

A conditional statement can be said to be in standard conditional form when it is stated with the antecedent stated first and the consequent stated second, and when the antecedent is preceded by the term ―If‖ and the consequent by the term ―then.‖ For example, the following statement is in standard conditional form:

If it rains then the roof will leak

In contrast, the following statement is not in standard conditional form:

The roof will leaks if it rains

The following table provides some common conditional vocabulary and illustrates how to translate it into standard conditional form:

Conditional

Vocabulary

Only if

Example

Standard Conditional Form

It rains only if there are clouds.

Only if there are clouds does it rain.

If it rains then there are clouds

1

If and only if

You are eligible to vote if and only if you have a valid voter registration card If you have a valid voter registration card then you are eligible to vote

&

If you are eligible to vote then you have a valid voter registration card

On condition that I will go on condition that you pay me. If I you pay me then I will go.

Entails,

Bachelorhood entails being unmarried. If one is a bachelor then one is unmarried Implies

Bachelorhood implies being unmarried In the event that

In the event that there’s a fire, take the stairs.

If there is a fire then take the stairs

When

When he lies, his left eye twitches.

If he lies then his left eye twitches

Where

Where there’s smoke,