Reasoning and Critical Thinking

Validity and Soundness

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What is logic?

Logic is the study of methods for evaluating whether the premises of an argument adequately support (or provide evidence for) its conclusion.

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All arguments are either valid or invalid. • An argument is valid if and only if it is not

possible that all of its premises are true and its conclusion is false.

• An argument is invalid if and only if it is possible that all of its premises are true and its conclusion is false.

 

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Examples

All beagles are dogs.Snoopy is a beagle.So, Snoopy is a dog.

All beagles are dogs.Lassie is a dog.So, Lassie is beagle.  

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Examples

All beagles are dogs.Snoopy is a beagle. VALIDSo, Snoopy is a dog.

All beagles are dogs.Lassie is a dog. INVALIDSo, Lassie is beagle.  

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So we have the first division of our subject:

Arguments

Invalid

Valid

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Consider these two arguments: 1. Jack and Jill almost always agree about whether a movie

is good or bad. They saw Hannibal last night. Jill said she loved it. So, Jack loved it too.

2. Marge and Homer sometimes agree about whether a

movie is good or bad. They saw Rambo 13 last night. Homer loved it. So, Marge loved it too.

 

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For all invalid arguments, it is possible that the conclusion is false while its premises are true. But how likely is it to be false while its premises are true?

Invalid Arguments

Possible that conclusion is false while premises are true

Given the premises are true, the conclusion is probably true

Given the premises are true, the conclusion is not probably true.

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Inductive LogicInductive logic is the part of logic that concerns tests for strength and weakness.

Invalid Arguments

Possible that conclusion is false while premises are true

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Strong Argument: Given the premises are true, the conclusion is probably true

Weak Argument: Given the premises are true, the conclusion is not probably true.

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Two Notions of Support: Validity and StrengthLogic is the study of methods for evaluating whether the premises of an argument adequately support (or provide good evidence for) its conclusion. • Evaluate support in terms of whether an argument is valid or invalid. (Deductive logic)

• For invalid arguments, evaluate support in terms of strength or weakness. (Inductive logic)

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Arguments

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Valid

Weak

Strong

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Deductive Logic

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Validity • An argument is valid if and only if it is not

possible that all of its premises are true and its conclusion is false.

• An argument is invalid if and only if it is possible that all of its premises are true and its conclusion is false.

 

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Validity: First Point 1. An argument can have one or more false premises and

still be valid.

Example:

All beagles are dogs.All dogs are birds.So, all beagles are birds.

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Validity: Second Point 2. You can’t assume that an argument is valid just because

all its premises are true.

Example:

All beagles are dogs.All collies are dogs.So, all beagles are collies.

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Validity: Third Point 3. Validity preserves truth. Valid arguments never go from true

premises to a false conclusion. Whenever a valid argument has a false conclusion, it must have a false premise.

Examples:

All beagles are dogs. All beagles are dogs.All dogs are birds. All dogs are mammals.So, all beagles are birds. So, all beagles are mammals.

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Validity: Fourth Point 4. Validity does not preserve falsehood. A valid argument

can go from false premises to a true conclusion.

Example:

All beagles are birds.All birds are mammals.So, all beagles are mammals.

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Validity and Actual Truth Note: The definition of validity makes no mention of whether the premises are actually true or false.

That is part of the point: we can evaluate arguments in terms of validity/invalidity without having to say whether the premises of the argument are in fact true or false.

If an argument is invalid, we can reject it without further ado.

If an argument is valid, we need to ask one more question before accepting it: are the premises true?

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Two Phases of Argument Evaluation

PHASE 1: ANALYZE SUPPORTIf invalid, reject.If valid, move to phase 2.

PHASE 2: ANALYZE TRUTH OF THE PREMISESIf valid with a false premise, reject.If valid with all true premises, accept.

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Soundness A sound argument is a valid argument with all true premises. 

Sound = valid + all true premises  

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Limits of Logic Ultimately, we are interested in whether or not an argument is deductively sound. In general, however, logic per se has little to say about whether the premises of an argument are in fact true or false.  Thus, logic can establish that an argument is unsound by showing that it is either invalid or weak, but it cannot in general establish that an argument is sound.  

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Arguments

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Valid

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All premises true = deductively sound

At least 1 premise false = deductively unsound

At least 1 premise false = inductively unsound

All premises true = inductively sound

Inductively unsoundNote that all invalid arguments are deductively unsound