Philosophy - Proofs

Chapter 1 Section 3 Reference Document

Terms:

· “Categorical Statement” A statement that relates two classes or categories, where a class is a set or collection of things.

· There are four kinds of categorical statements. They have these forms:

#1) [Universal Affirmative]: “All S are P”

#2) [Universal Negative]: “No S are P”

#3) [Particular Affirmative]: “Some S are P”

#4) [Particular Negative]: “Some S are not P”

· EXAMPLE: “All pigs are mammals.” is a universal affirmative.

· EXAMPLE: “No circles are shapes that possess angles.” is a universal negative.

· EXAMPLE: “Some vampires are creatures with souls.” is a particular affirmative.

· EXAMPLE: “Some vampires are not creatures with souls.” is a particular negative.

· “Argument Form”: A pattern of reasoning

· Valid Argument Form: A pattern of reasoning that is always valid for any substitution instance.

· Invalid Argument Form: A pattern of reasoning that is always invalid for any substitution instance.

· “Substitution Instance”: A substitution instance of an argument form is an argument that results from uniformly replacing the variables in that form with statements or terms.

· “Symbolic Argument”: A symbolic argument is an argument form in which statements or terms have been uniformly replaced with variables, while retaining the most logically sensitive version of the argument.

· “Counterexample”: A counterexample to an argument form is an argument that has obviously true premises and an obviously false conclusion.

Counterexample Method: to construct a counterexample:

1. Symbolize the argument, so that statements and terms have been replaced with variables while the most logically sensitive form of the argument has been preserved.

2. Construct a substitution instance to that symbolic argument such that the premises are all obviously true and the conclusion is obviously false.