Chapter 10: Deduction and Induction: A Closer Look

Deductive Argument

Advanced with the aim of proving its conclusion with complete certainty, in such a way that its conclusion must be true if its premises all are true

Inductive Argument

Intended to show that its conclusion is probably or likely true, though not certainly true, if its premises all are true; establishes the intended conclusion with a high degree of probability - not with complete certainty

Valid Deductive Argument

If its premises all are true, then its conclusion must be true

Invalid Deductive Argument

It is not the case that its conclusion must be true if its premises all are true; the conclusion may be false even if its premises are true

The Intuitive Test for Validity

Step 1: Ask the following: If the premises were to be true, would it be possible for the conclusion to be false? Are there any possible circumstances in which the premises would all be true while the conclusion is false?

Step 2: If the answer is no, then the argument is valid; if the answer is yes, then the argument is invalid

Counterexample to a Deductive Argument (Method of Counterexample)

A description of a possible situation or circumstance in which the premises of the argument would all be true while the argument’s conclusion would be false

Argument Form

An abstract pattern of reasoning that many different arguments, about many different subjects, can follow, and will always be valid
1. All A are B → 2. All B are C → 3. Therefore, certainly all A are C

Substitution Instance

A specific argument of an argument form if it can be produced by replacing the variables in the form with the content of the argument

Valid Argument Form

If every substitution instance of it is a valid argument

Categorical Sentences

Sentences that relate one category of things to a second category of things

Categorical Arguments

Arguments composed of categorical sentences

Categorical Logic

The branch of logic where an argument’s form can be specified using variables and equations, making it extremely exact