a deductive argument is one whose premises are claimed to provide conclusive grounds for the truth...
TRANSCRIPT
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Deductive Arguments
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A deductive argument is one whose premises are claimed to provide conclusive grounds for the truth of its conclusion.
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If a deductive argument is valid, it is impossible for its premises to be true without its conclusion also being true.
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Example 1Everything made of copper conducts electricity. [P]This wire is made of copper. [P]Therefore, this wire will conduct electricity. [C]
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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]
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Take Note…
Remember that the validity of an argument has nothing to do with whether its premises are factual or true.
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Take Note…
Validity has to do with the nature of the connection between premises and conclusion.
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Example 3All green cheese smells like daisies. [P]The moon is made of green cheese. [P]Therefore, the moon smells like daisies. [C]
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Deductive Argument Forms
1. Disjunctive Syllogisms
2. Hypothetical Syllogisms
3. Categorical Syllogisms
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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.
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Disjunctive Proposition
Either A or B is true.
A and B are called the disjuncts or alternatives.
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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.)
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Example
Either the next Olympics will be held in Atlanta or in Athens.It won't be held in Athens.It will be held in Atlanta.
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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.
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Hypothetical Proposition
If A, then B.
A is called the antecedent.
B is called the consequent.
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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.
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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.
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2.B. Mixed Hypothetical Syllogism
Contains both a conditional premise and a categorical premise.Subdivided into two types: modus ponens and modus tollens.
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2.B.i. Modus Ponens
If A is true, then B is true.A is true.Therefore B is true.From Latin ponere, “to affirm.”
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ExampleIf today is Tuesday, then the garbage truck will arrive.Today is Tuesday.Therefore the garbage truck will arrive.
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2.B.ii. Modus Tollens
If A is true, then B is true.B is not true.Therefore A is not true.From Latin tollere, “to deny.”
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ExampleIf the dog detects an intruder, then the dog will bark.The dog did not bark.Therefore the dog did not detect an intruder.
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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.
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Categorical Syllogism
All A are B. All C are A. Therefore all C are B.
There are 15 valid forms of the categorical syllogism.
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ExampleAll men are patriots. All boxers are men. Therefore all boxers are patriots.
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Three Formal Fallacies
Caveat
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Fallacies are errors in reasoning. Formal fallacies are errors in the structure of an argument.
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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.
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Example
Either he will buy the drinks or she will make the popcorn. He will buy the drinks.Therefore she will not make the popcorn.
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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.
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Example
If Francis Bacon wrote Hamlet, then he was a great writer.Francis Bacon was a great writer.Therefore he wrote Hamlet.
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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.
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ExampleIf it rains, then the school grounds will be wet.The school grounds are wet.Therefore it rained.