Lecture Notes by Christopher Lay

Los Angeles Pierce College

Department of History, Philosophy, and Sociology

 

 

 

 

Mathew Van Cleave's 2016 Introduction to Logic and Critical Thinking

 

https://open.umn.edu/opentextbooks/BookDetail.aspx?bookId=457

 

 

 

 

Chapter 4 "Informal fallacies", § 1 "Formal vs. Informal Fallacies"

 

"A fallacy is simply a mistake in reasoning." 

 

"Some fallacies are formal and some are informal." 

 

In this excerpt, we'll deal with the formal fallacies found in hypothetical syllogisms. 

 

 

 

 

 

 

 

 

Formal, Hypothetical Syllogistic Validity / and Formal, Hypothetical Syllogistic Fallacies

 

We will learn that there are two valid hypothetical syllogisms, affirming the antecedent and denying the consequent. 

 

We will learn that there are two invalid hypothetical syllogisms, denying the antecedent and affirming the consequent. 

 

 

 

 

 

 

 

 

 

 

Syllogisms

 

Don't forget, syllogisms are arguments with two premises and one conclusion. 

 

 

 

 

 

 

 

 

 

Hypothetical Statements

 

A hypothetical statement is an if/then statement. 

 

 

 

 

 

 

 

 

 

 

Hypothetical's Parts

 

The part of the hypothetical that comes after the "if" and before the "then" is called the antecedent

 

The part of the hypothetical that comes after "then" is called the consequent

 

 

 

 

 

 

 

 

 

Hypothetical Syllogism's Parts

 

Hypothetical syllogisms start with a hypothetical statement in the first premise. 

 

In the second premise you will find one part of that hypothetical. 

 

In the conclusion you will find the other part of that hypothetical. 

 

 

 

 

 

 

 

 

 

Handling Negations in the First Premise, and Handling Affirmations and Denials in the Second Premises and the Conclusions of Hypothetical Syllogisms

 

Unlike categorical syllogisms, when it comes to the first premise, the hypothetical statement itself, negations are parts of the contents of the antecedent or the consequent and so are not considered parts of the form of the argument. 

 

For the second premise and the conclusion, affirmations and denials are treated as parts of the form of the argument, not the content. 

 

 

 

 

 

 

 

 

 

 

 

Formal, Hypothetical Syllogistic Validity

 

There are two valid hypothetical syllogisms, affirming the antecedent and denying the consequent. 

 

This may be helpful: when determining validity here, you are to see that the premises are to be taken as true, even if they are not actually true. 

 

Moreover, consider the first premise, the hypothetical statement, to be a kind of rule. 

 

 

 

 

 

 

 

 

Affirming the Antecedent

 

1) Hypothetical statement.

2) Affirmation of antecedent from hypothetical statement in 1), above. 

C) Affirmation of consequent from hypothetical statement in 1), above. 

 

 

 

 

 

 

 

Denying the Consequent

 

1) Hypothetical statement.

2) Denial of consequent from hypothetical statement in 1), above. 

C) Denial of antecedent from hypothetical statement in 1), above. 

 

 

 

 

 

 

 

 

 

Formal, Hypothetical Syllogistic Fallacies

 

There are two invalid hypothetical syllogisms, denying the antecedent and affirming the consequent.