Answer

Categorical Syllogism

1. It must be the case that all animals are able to think. Since all animals feel pain, and all things that feel pain are able to think.

 

All things that feel pain are able to think

All animals feel pain

All animals are able to think

 

Major term: to think

Minor term: All animals

Middle term: feel pain

 

Figure:

All M are P

All S are M

All S are P

(Figure 1)

M   P

S   M

Mood:

Listing the above statement forms in standard order (Major premise, minor premise, conclusion), the mood is noted as AAA

 

Venn Diagram:

Testing for validity:

From a Boolean Standpoint, test for validity involves shading the Venn diagram while avoiding entering the conclusion. If the conclusion is already represented (after the shading), then the syllogism is valid.

Doing this for the above syllogism reveals it is indeed valid, implying no rule has been violated.

 

AAA-1

 

 

2. All messengers who bring bad news are unwelcome. All messengers who bring bad news are punished. Therefore, some unwelcome persons are punished.

 

All messengers who bring bad news are unwelcome.

All messengers who bring bad news are punished.

Therefore, some unwelcome persons are punished.

Major term: Punished

Minor term: unwelcome

Middle term: All messengers who bring bad news

 Figure:

All M are P

All M are S

Some S are P

M   P

M   S

S   P 

(Figure 3)

 

Mood:

Listing the above statement forms in standard order (Major premise, minor premise, conclusion), the mood is AAI

 

 

Testing for validity:

Following the procedure of shading without entering the conclusion area, it emerges that this area is already included (after completion). It is, therefore, valid because the information in the conclusion is already included in the premises. Thus, no rule has been violated.

 

3. No syllogisms are arguments with four terms. Some arguments with four terms are invalid. So, no syllogisms are invalid.

No syllogisms are arguments with four terms.

Some arguments with four terms are invalid.

No syllogisms are invalid.

Major term:  invalid

Minor term:  Syllogisms

Middle term: arguments with four terms

 

Figure:

As it were, figure is determined by position of the middle term

No P are M

Some M are S

No P are S

 

P    M

M   S

S   P

(Fourth Figure)

Mood:

Listing the above statement forms in standard order (Major premise, minor premise, conclusion), the mood is EIO

Testing for validity:

Adopting a Boolean Standpoint, start shading the Venn diagram while avoiding entering the conclusion area. If the conclusion is already included after shading, syllogism is valid. Clearly, this one is valid. No rule is violated.

EIO-2

4. Whales have lungs, but no fish do; so whales aren’t fish.

Whales have lungs

But no fish have lungs

So whales aren’t fish

 

Major term: fish

Minor term:  Whales

Middle term: Have lungs

Figure:

 Look out for position of middle term

(Second Figure)

P are M

No S are M

P are not S

P  M

S  M

S  P

(Second figure)

Mood:

Listing the above statement forms in standard order (Major premise, minor premise, conclusion), the mood is EAE.

 

 

Testing for validity:

Shading without entering the conclusion area yields an already shaded conclusion upon completion. This implies the syllogism is valid. No rule has been violated.

 

 

5. No students are boring, and some professors are boring.

No students are boring

Some professors are boring

??

 

No P are M

Some S are M

 Figure

P  M

S  M

 (Second Figure)

 

Apparently, there is no conclusion here, just two premises.

It goes without saying that this is not even a syllogism because a categorical syllogism must contain two premises and one conclusion. The absence of a conclusion in this case merits omission of any further analysis.

 

 

1. QUESTION