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 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

All UH students are communists.

All communists like broccoli.

All UH students like broccoli. Conclusion

Premises

False

False

False

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 UH students are communists.

All communists like broccoli.

All UH students like broccoli.

The statements in the argument are FALSE but…

The argument is VALID.

True

True

True

Validity and Truth

All canaries have feathers.

Some pets have feathers.

Some pets are canaries.

True

True

True

Validity and Truth

All canaries have feathers.

Some pets have feathers.

Some pets are canaries.

The statements in the argument are TRUE but…

The argument is INVALID.

True

True

True

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 canaries have feathers.

Some pets have feathers.

Some pets are canaries.

The statements in the argument are TRUE but…

The argument is INVALID.

Validity and Truth

All canaries have feathers.

Some pets have feathers.

Some canaries are pets.

True

False

True

So it isis possible for the premises to be T,and the conclusion F.

IMAGINE this:Canaries just never ended up being pets;but parrots and mynas are still pets.

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.F

All communists like broccoli. F

All UH students like broccoli. F

All canaries have feathers. T

Some pets have feathers. T

Some canaries are pets. T

Do Not Ask: Are the statements T?Ask Instead: Assuming the premises are T, must the conclusion be T?

Validity and Argument Form

All UH students are Communists. F

All Communists like Broccoli. F

All UH students like Broccoli. F

All Us are Cs.

All Cs are Bs.

All Us are Bs.

Logic is the study of Argument Form not Truth.

Any argument with this form will be valid,regardless of how false (or silly) its premisesmay be.

Validity and Argument Form

All Canaries have Feathers. T

Some Pets have Feathers. T

Some Canaries are Pets. T

All Cs are Fs.

Some Ps are Fs.

Some Cs are Ps.

Logic is the study of Argument Form not truth.

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

All Cats have Feet. T

Some Pigs have Feet. T

Some Cats are Pigs. F

All Cs are Fs.

Some Ps are Fs.

Some Cs are Ps.

Logic is the study of Argument Form.

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

All canaries have feathers. T

Some pets have feathers. T

Some canaries are pets. T

All Cs are Fs.

Some Ps are Fs.

Some Cs are Ps.

It is crucial that you distinguish validity from truth.

INVALID

Invalid arguments may have true conclusions.

Validity is Different From Truth

All canaries have feathers. T

Some pets have feathers. T

Some canaries are pets. T

All Cs are Fs.

Some Ps are Fs.

Some Cs are Ps.

It is crucial that you distinguish validity from truth.

Validity is Different From Truth

All UH students are communists. F

All communists like broccoli. F

All UH students like broccoli. F

All Us are Ws.

All Ws are B.

All Us are B.

It is crucial that you distinguish validity from truth.

VALID

Validity is Different From Truth

All UH students are communists. F

All communists like broccoli. F

All UH students like broccoli. F

All Us are Ws.

All Ws are B.

All Us are B.

It is crucial that you distinguish validity from truth.

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.

If the premises are T then the conclusion must be T.

WRONG!

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RIGHT!