Part II: Examples

1. All birds are animals.
   All animals are alive.
   Therefore, all birds are alive.

• This syllogism is both valid and sound. 
• The premises are “All birds are animals” and “All animals are alive.”
• The conclusion is “All birds are alive.” 
• The minor term is “birds.” 
• The major term is “alive.”
• The middle term is “animal.” 
• The minor premise is “All birds are animals.” Note that this is the second premise of the syllogism, whereas in the original example the minor premise was the first premise. 
• The major premise is “All animals are alive.” Note that this is the first premise of the syllogism, whereas in the original example the major premise was the second premise. 

2. Everything that’s salty is good for cooking.
   Sand is salty.
   Therefore, Sand is good for cooking.

• This syllogism is valid. However, it is not sound, because its first premise is untrue (since it is clearly not the case that all salty things are good for cooking!)
• The premises are “Everything that’s salty is good for cooking” and “Sand is salty.” 
• The conclusion is “Sand is good for cooking.” 
• The minor term is “sand.”  
• The major term is “good for cooking.” 
• The middle term is “salty” or “things that are salty.” 
• The minor premise is “Sand is salty.”
• The major premise is “Everything that’s salty is good for cooking.”  

3. Amy hates all critters.
   A thing that hates critters is a thing that hates cockroaches.
   So, Amy hates cockroaches

The syllogism above doesn’t have the same format as the ones above; however, it can easily be reformulated to match the other syllogisms. To review, look at the earlier lesson, Propositions and their Parts. This yields the following equivalent syllogism: 

Amy is a thing that hates all critters.

A thing that hates critters is a thing that hates cockroaches.

So, Amy is a thing that hates cockroaches. 

• This syllogism is both valid and sound.
• The premises are “Amy is a thing that hates all critters” and “A thing that hates all critters is a thing that hates cockroaches”
• The conclusion is “So Amy must be a thing that hates all critters.”  
• The minor term is “Amy.” 
• The major term is “a thing that hates cockroaches.”
• The middle term is “a thing that hates all critters.” 
• The minor premise is “Amy is a thing that hates all critters.”
• The major premise is “A thing that hates all critters is a thing that hates cockroaches”

Activity: Consider the syllogism below. Is the syllogism valid? Is it sound? Place a #1 next to the first premise, a #2 next to the second premise, and a C next to the conclusion. Draw a circle around the minor term. Draw a square around the major term. Underline the middle term. Put one star next to the minor premise. Put two stars next to the major premise. When you’re done, compare your answers with a partner. 

All Swans are beautiful.
I love all beautiful things.
I love swans.