Categorical Syllogisms

Assessment of Categorical Syllogisms
When we evaluate an argument, we should distinguish between two questions: Are the premises true? Do the premises support the conclusion? The second question pertains to the logical strength of the argument. We measure strength by estimating the logical gap between premises and conclusion.

Validity
For deductive arguments, we use the term validity to designate logical strength, and validity is all or nothing. A valid syllogism has no internal gap whatever: if the premises are true, the conclusion must be true; you cannot accept the premises and deny the conclusion without contradicting yourself. An invalid syllogism, on the other hand, is a non sequitur -- the premises confer no support on the conclusion.
The validity of a syllogism is determined by its form. If two syllogisms have the same form, they are either both valid or both invalid, even if one has true premises and the other has false ones.
Example:

All fish are animals. All bananas are animals.

All trout are fish. All trout are bananas.

All trout are animals.
All trout are animals.

These are both AAA-1 syllogisms. The only difference is that the middle term has been changed, making the premises of the second argument false. However, both syllogisms are valid.

Comprehension Questions

1. In a valid syllogism, if the premises are true, then the conclusion

a) could be true

b) could be false

c) must be true

d) must be false

2. In an invalid syllogism, if the premises are true, then the conclusion

a) could be true

b) could be false

c) must be true

d) must be false

3. The validity of a categorical syllogism is determined by

a) the truth of its premises

b) the mood and figure of the syllogism

Rules of Validity
Assessment of Categorial Syllogisms by Venn Diagrams

All fish are animals.	All bananas are animals.
All trout are fish.	All trout are bananas.
All trout are animals.	All trout are animals.

1.	*In a valid syllogism, if the premises are true, then the conclusion*

	a)	could be true
	b)	could be false
	c)	must be true
	d)	must be false


2.	*In an invalid syllogism, if the premises are true, then the conclusion*

	a)	could be true
	b)	could be false
	c)	must be true
	d)	must be false


3.	*The validity of a categorical syllogism is determined by*

	a)	the truth of its premises
	b)	the mood and figure of the syllogism