Logic: Forms and Validity

Constructive Dilemma

1. Either A or B 2. If A, then C 3. If B, then D So, 4. Either C or D

Disjunctive Syllogism

1. Either A or B 2. Not A So, 3. B OR 1. Either A or B 2. Not B So, 3. A

Modus Ponens

1. If A, then B 2. A So, 3. B

Hypothetical Syllogism

1. If A, then B 2. If B, then C Therefore, 3. If A, then C

Modus Tollens

1. If A, then B 2. Not B So, 3. Not A

Argument Forms

A pattern of reasoning

Disjunctive Statements

Either-or statements; Have atomic parts called disjuncts;

Valid argument forms

Forms such that every substitution instance is a valid argument; If an argument is a substitution instance of a valid form, then the argument is valid

Modus Ponens

IDENTIFY WHICH FORM THIS IS: "Affirmative action is preferential treatment of disadvantaged groups and preferential treatment of disadvantaged groups is reverse discrimination. If affirmative action is preferential treatment of disadvantaged groups and preferential treatment of disadvantaged groups is reverse discrimination, then affirmative action is wrong. So, affirmative action is wrong."

Disjunctive Syllogism

IDENTIFY WHICH FORM THIS IS: "Either Jones is an innocent bystander or Jones fired a shot at the mayor. Jones is not an innocent bystander. Therefore, Jones fired a shot at the mayor"

Constructive dilemma

IDENTIFY WHICH FORM THIS IS: "Either the "eye for an eye" principle is interpreted literally or it is interpreted figuratively. If it is interpreted literally, then the state should torture torturers, maim maimers, and rape rapists. If the "eye for an eye" principle is interpreted figuratively, then it does not necessarily demand death for murderers. So, either the state should torture torturers, maim maimers, and rape rapists, or the "eye for an eye" principle does not necessarily demand death for murderers."

Constructive dilemma

IDENTIFY WHICH FORM THIS IS: "Either you marry young or you wait. If you marry young, you incur a high risk of divorce. If you wait, the field of available partners grows ever smaller. So, you either incur a high risk of divorce or the field of available partners grows ever smaller.

Constructive Dilemma

IDENTIFY WHICH FORM THIS IS: "If God can arbitrarily decide what is morally right, then God can make cruelty right. And if God cannot arbitrarily decide what is morally right, then morality is not entirely in God's control. But either God can arbitrarily decide what is morally right, or God cannot arbitrarily decide what is morally right. Therefore, either God can make cruelty right, or morality is not entirely in God's control."

Modus Tollens

IDENTIFY WHICH FORM THIS IS: "If the solution turns blue litmus paper red, then the solution contains acid. The solution does not contain acid. So the solution does not turn blue litmus paper red"

Modus Ponens

IDENTIFY WHICH FORM THIS IS: "If the solution turns blue litmus paper red, then the solution contains acid. The solution turns blue litmus paper red. So, the solution contains acid."

Hypothetical syllogism

IDENTIFY WHICH FORM THIS IS: "If you study hard, you refine your communication skills. If you refine your communication skills, then your job opportunities increase. Hence, if you study hard, your job opportunities increase."

Modus Tollens

IDENTIFY WHICH FORM THIS IS: "Overeating is foolish only if it causes disease. Overeating does not cause disease. So, overeating is not foolish"

Modus Ponens

IDENTIFY WHICH FORM THIS IS: "The death penalty is inequitably applied to the poor and to minorities. And given that the death penalty is inequitably applied to the poor and to minorities, it is unjust. Therefore, the death penalty is unjust."

Modus Ponens

IDENTIFY WHICH FORM THIS IS: "The state cannot uphold the value of life by taking it. And if the state cannot uphold the value of life by taking it, then the death penalty should be abolished. So, the death penalty should be abolished."

Constructive Dilemma

IDENTIFY WHICH FORM THIS IS: "You must either love or hate. If you love, then you suffer when your loved ones suffer. If you hate, then you suffer when your enemies flourish. So, either you suffer when your loved ones suffer or you suffer when your enemies flourish."

Hypothetical Syllogism

IDENTIFY WHICH FORM THIS IS: "A severe depression will occur given that the economy collapses. The economy collapses if inflation soars. So, inflation soars only if a severe depression will occur."

Conditional Statements

If-then statements such as "if A then B"

Variables

Stand in for statements (often atomic) and are typically represented as letters

Negation

The denial of a statement

Syllogism

This refers to putting statements together to form a pattern of reasoning

Substitution instance

Uniformly replacing the variables in an argument form with statements or terms