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.
So, Snoopy is a dog.
VALID
All beagles are dogs.
Lassie is a dog.
So, Lassie is beagle.
INVALID
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So we have the first division of our subject:
Valid
Arguments
Invalid
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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
Given the premises
are true, the
conclusion is probably
true
Possible that
conclusion is false
while premises are
true
Given the premises are
true, the conclusion is
not probably true.
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Inductive Logic
Invalid Arguments
Possible that
conclusion is false
while premises are
true
Inductive Logic
Inductive logic is the part of logic that concerns tests for
strength and weakness.
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 Strength
Logic 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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Strong
Invalid
Inductive Logic
Arguments
Deductive Logic
Valid
Weak
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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 dogs are birds.
So, all beagles are birds.
All beagles are dogs.
All dogs are mammals.
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 SUPPORT
If invalid, reject.
If valid, move to phase 2.
PHASE 2: ANALYZE TRUTH OF THE PREMISES
If 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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At least 1 premise false =
deductively unsound
Strong
Invalid
Note that all invalid arguments
are deductively unsound
Inductive Logic
Arguments
Deductive Logic
Valid
All premises true =
deductively sound
All premises true =
inductively sound
At least 1 premise false
= inductively unsound
Weak
Inductively unsound
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