Deductive Arguments

A deductive argument is one whose premises are claimed to provide conclusive grounds for the truth of its conclusion.

If a deductive argument is valid, it is impossible for its premises to be true without its conclusion also being true.

Example 1Everything made of copper conducts electricity. [P]This wire is made of copper. [P]Therefore, this wire will conduct electricity. [C]

Example 2If Joe signed the contract, then the contract is binding. [P]If the contract is binding, then Joe owes Jed $100. [P]Therefore, if Joe signed the contract, Joe owes Jed $100. [C]

Take Note…

Remember that the validity of an argument has nothing to do with whether its premises are factual or true.

Take Note…

Validity has to do with the nature of the connection between premises and conclusion.

Example 3All green cheese smells like daisies. [P]The moon is made of green cheese. [P]Therefore, the moon smells like daisies. [C]

Deductive Argument Forms

1. Disjunctive Syllogisms

2. Hypothetical Syllogisms

3. Categorical Syllogisms

1. Disjunctive Syllogism

Contains a compound, disjunctive (alternative) premise asserting the truth of at least one of its alternatives, and a premise that asserts the falsity of one of those alternatives.

Disjunctive Proposition

Either A or B is true.

A and B are called the disjuncts or alternatives.

Disjunctive Syllogism

Either A or B is true.A is not true. (or B is not true.)Therefore B is true. (or A is true.)

ExampleEither the next Olympics will be held in Atlanta or in Athens.It won't be held in Athens.It will be held in Atlanta.

2. Hypothetical Syllogism

Contains one or more compound, hypothetical (or conditional) propositions, affirming that if one of its components (the antecedent) is true then the other (the consequent) is also true.

Hypothetical Proposition

If A, then B.

A is called the antecedent.

B is called the consequent.

2.A. Pure Hypothetical Syllogism

Contains conditional propositions only.If A is true, then B is true.If B is true, then C is true.Therefore, if A is true, then C is true.

ExampleIf I win the lotto, then I will have money.If I have money, then I can pay my debts.Therefore, if I win the lotto, then I can pay my debts.

2.B. Mixed Hypothetical Syllogism

Contains both a conditional premise and a categorical premise.Subdivided into two types: modus ponens and modus tollens.

2.B.i. Modus PonensIf A is true, then B is true.A is true.Therefore B is true.From Latin ponere, “to affirm.”

ExampleIf today is Tuesday, then the garbage truck will arrive.Today is Tuesday.Therefore the garbage truck will arrive.

2.B.ii. Modus TollensIf A is true, then B is true.B is not true.Therefore A is not true.From Latin tollere, “to deny.”

ExampleIf the dog detects an intruder, then the dog will bark.The dog did not bark.Therefore the dog did not detect an intruder.

3. Categorical Syllogism

Contains two premises (a major and a minor premise) and a conclusion, all of which are in the form of categorical propositions.

Categorical SyllogismAll A are B. All C are A. Therefore all C are B.

There are 15 valid forms of the categorical syllogism.

ExampleAll men are patriots. All boxers are men. Therefore all boxers are patriots.

Three Formal Fallacies

Caveat

Fallacies are errors in reasoning. Formal fallacies are errors in the structure of an argument.

1. Affirming a Disjunct

The truth of one disjunct does not mean that the other is false. Both of the disjuncts may be true.

Either A or B is true.A is true.Therefore B is not true.

ExampleEither he will buy the drinks or she will make the popcorn. He will buy the drinks.Therefore she will not make the popcorn.

2. Affirming the Consequent

The conditional statement “If A, then B” claims that if A happens, B follows. It does not claim that if B happened, A preceded it.

If A, then B.B.Therefore A.

ExampleIf Francis Bacon wrote Hamlet, then he was a great writer.Francis Bacon was a great writer.Therefore he wrote Hamlet.

3. Denying the AntecedentIf A, then B.

Not A.Therefore not B.

The conditional statement “If A, then B” claims that if A happens, B follows. It does not claim that if A does not happen, B will not happen.

ExampleIf it rains, then the school grounds will be wet.The school grounds are wet.Therefore it rained.