Mr. Nance,

Tomorrow morning I will be explaining why EIO-2 is valid but IEO-2 is invalid. The only problem is that I think both ought to be valid. I do not understand why reversing the order of the premises invalidates the syllogism, especially when the placement of the middle term remains the same. Thank you in advance.

Good question!

Reversing the order of the premises makes the syllogism an entirely different form, and the IEO-2 form is invalid. Remember that the major term is always in the major premise, which is stated first, and the minor term is always in the minor premise, stated second. Thus the difference of these two forms involves more than just a position switch.

Consider the two schemas:

EIO-2
No P is M
Some S is M
.: Some S is not P

IEO-2
Some P is M
No S is M
.: Some S is not P

The IEO-2 has an illicit major (the major term is distributed in the conclusion but not in the premise). The EIO-2 does not.

Or consider this counterexample for the IEO-2:

Some animals are mammals.
No lizards are mammals.
Therefore, some lizards are not animals.

This has true premises and a false conclusion, and is thus an invalid form. But no corresponding counterexample can be written for EIO-2. If you tried, you might get something like this:

No lizards are mammals.
Some animals are mammals.
Therefore, some animals are not lizards.

Note that I had to switch the subject and predicate to put the major and minor terms in their proper position. Note that in this syllogism the conclusion is true, thus this is no counterexample.

Here is the key point: It is impossible to make a syllogism of the form EIO-2 with true premises and a false conclusion. It is easy to make a syllogism of the form IEO-2 with true premises and a false conclusion. Thus, the former is valid, the latter is invalid, and the difference between them is far more than the arrangement of the premises. Feel free to write back with any further questions.

Blessings on your lesson!