Validity
Validity
All UH students are communists.
All communists like broccoli.
All UH students like broccoli.
Validity
All UH students are communists.
All communists like broccoli. GOOD
All UH students like broccoli.
Validity
All UH students are communists.
All communists like broccoli. GOOD
All UH students like broccoli.
Logic does not try to decide which statements are true.
The issue for logic is:
Is the REASONING good?
Validity
All UH students are communists.
All communists like broccoli.
All UH students like broccoli.
Premises
Conclusion
Validity Defined:
1. Assuming the premises are (all) T,
the conclusion has to be T.
2. It is impossible for the premises to be T,
and the conclusion to be F.
Validity and Truth
All UH students are communists. False
All communists like broccoli.
False
All UH students like broccoli.
False
The statements in the argument are FALSE but…
The argument is VALID.
Valid Defined:
1. Assuming the premises are (all) T,
the conclusion has to be T.
2. It is impossible for the premises to be T,
and the conclusion to be F.
Validity and Truth
All canaries have feathers.
True
Some pets have feathers.
True
Some pets are canaries.
True
Validity and Truth
All canaries have feathers.
True
Some pets have feathers.
True
Some pets are canaries.
True
The statements in the argument are TRUE but…
The argument is INVALID.
Validity and Truth
All canaries have feathers.
True
Some pets have feathers.
True
Some pets are canaries.
True
The statements in the argument are TRUE but…
The argument is INVALID.
Validity Defined:
1. Assuming the premises are (all) T,
the conclusion has to be T.
2. It is impossible for the premises to be T,
and the conclusion to be F.
Validity and Truth
IMAGINE this:
Canaries just never ended up being pets;
but parrots and mynas are still pets.
So it is possible for
the premises to be T,
and the conclusion F.
All canaries have feathers.
True
Some pets have feathers.
True
Some canaries are pets.
False
Validity and Truth
All UH students are communists.F
All canaries have feathers. T
All communists like broccoli.
F
Some pets have feathers. T
All UH students like broccoli.
F
Some canaries are pets.
Do Not Ask: Are the statements T?
Ask Instead: Assuming the premises are T,
must the conclusion be T?
Validity Defined:
1. Assuming the premises are (all) T,
the conclusion has to be T.
2. It is impossible for the premises to be T,
and the conclusion to be F.
T
Validity and Argument Form
Logic is the study of Argument Form not Truth.
All UH students are Communists. F
All Us are Cs.
All Communists like Broccoli.
F
All Cs are Bs.
All UH students like Broccoli.
F
All Us are Bs.
Any argument with this form will be valid,
regardless of how false (or silly) its premises
may be.
Validity and Argument Form
Logic is the study of Argument Form not truth.
All Canaries have Feathers. T
All Cs are Fs.
Some Pets have Feathers.
T
Some Ps are Fs.
Some Canaries are Pets.
T
Some Cs are Ps.
Any argument with this form will be invalid,
regardless of how true its premises may be.
Just because all Cs are Fs and some Ps are Fs,
It does not follow that some Cs are Ps.
Validity and Argument Form
Logic is the study of Argument Form.
All Cats have Feet.
T
All Cs are Fs.
Some Pigs have Feet. T
Some Ps are Fs.
Some Cats are Pigs.
Some Cs are Ps.
F
Just because all Cs are Fs and some Ps are Fs,
It does not follow that some Cs are Ps.
Validity is Different From Truth
It is crucial that you distinguish validity from truth.
All canaries have feathers. T
All Cs are Fs.
Some pets have feathers.
T
Some Ps are Fs.
Some canaries are pets.
T
Some Cs are Ps.
Validity is Different From Truth
It is crucial that you distinguish validity from truth.
All canaries have feathers. T
All Cs are Fs.
Some pets have feathers.
T
Some Ps are Fs.
Some canaries are pets.
T
Some Cs are Ps.
INVALID
Invalid arguments may have true conclusions.
Validity is Different From Truth
It is crucial that you distinguish validity from truth.
All UH students are communists. F
All Us are Ws.
All communists like broccoli.
F
All Ws are B.
All UH students like broccoli.
F
All Us are B.
Validity is Different From Truth
It is crucial that you distinguish validity from truth.
All UH students are communists. F
All Us are Ws.
All communists like broccoli.
F
All Ws are B.
All UH students like broccoli.
F
All Us are B.
VALID
Valid arguments may have false conclusions.
Validity is Different From Truth
It is crucial that you distinguish validity from truth.
The truth values of the statements in an
argument do not allow you to predict
whether it is valid.
With one exception …
If the premises are T and the conclusion is F,
Then the argument has to be invalid.
Valid Defined:
1. Assuming the premises are (all) T,
the conclusion has to be T.
2. It is impossible for the premises to be T,
and the conclusion to be F.
A Common Mistake
It is crucial that you distinguish validity from truth.
When I ask for the definition of validity,
students say:
The premises are T and the conclusion is T.
Valid Defined:
1. Assuming the premises are (all) T,
the conclusion has to be T.
2. It is impossible for the premises to be T,
and the conclusion to be F.
A Common Mistake
It is crucial that you distinguish validity from truth.
When I ask for the definition of validity,
students say:
The premises are T and the conclusion is T.
WRONG!
If the premises are T then the conclusion
must be T.
RIGHT!
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