Distribution for (PA) and (PN) propositions can be quite confusing. Let’s look at another kind of example for both in order to clear up any difficulties.
[Activity] Take an example (PA) proposition – “Some cats are albino.” Say your friend says that because we know this, we know that “all cats have pale skin.” But is your friend correctly inferring here? Discuss with a partner!
Let’s take a different kind of example for (PN) propositions, using “Some snakes are not poisonous.” Suppose we have 10 snakes and 10 poisonous things in our world. Of the 10 snakes, 7 are not poisonous, and 3 are poisonous. Then, we have 7 non-poisonous snakes, 3 poisonous snakes, and 7 non-snake poisonous things. When we say “Some snakes are not poisonous”, we are taking the 7 snakes that are not poisonous and subtracting them from the entire category of poisonous things (snakes or otherwise). That is why the predicate is not distributed, while the subject is.
[Activity] How would you represent the above example visually? Think of using dots to represent the objects in the extensions of each term’s category. Find a partner, share illustrations, and explain your choice of illustration.
[Activity] Can you find some other examples of your own? Asking yourself how different expressions we use commonly when we speak can be paraphrased as or correlated to logical forms can be a very helpful mechanism for a logician and a useful way to practice what you learn.