The author uses the word "immediacy" (line 39) most likely in order to express

Rosanna on April 16, 2020

No Xs are Ys

Hello, Can you negate the first variable in this topic? "No mammals are cold-blooded" ~M-->CB ~CB-->M or One cannot be in both Los Angeles and New York at the same time. ~LA-->NY ~NY-->LA Would that be consistent with other examples? Thanks!

Reply

Shunhe on April 16, 2020

Hi @Rosanna,

Thanks for the question! No, you can’t negate the first variable in the topic like that. That’ll result in incorrect diagrams which might lead you to the wrong answer choice. Let’s take a look at the statement “no mammals are cold-blooded.” What this is really telling us if if something is a mammal, then it is not cold-blooded. In other words, we’re being told that:

M —> ~CB

And the contrapositive of this is

CB —> ~M

In other words, if something is cold-blooded, then it is not a mammal. This is in accord with how we would normally interpret those statements. Let’s take a look at what you diagrammed:

~M —> CB

The statement above is telling us that if something is not a mammal, then it is cold-blooded. But clearly, this is false, and since we know that the original statement “No mammals are cold-blooded” is actually true, we can think of some examples to show why. Birds, for example, are not mammals, but are also not cold-blooded. Rocks are also not mammals, and they are also not cold-blooded. Similarly, the contrapositive of this statement is:

~CB —> M

Or if something is not cold-blooded, then it is a mammal. But once again, there are things that aren’t cold-blooded (like rocks and birds) that also aren’t mammals.

Similarly, take the sentence “One cannot be in both LA and NY at the same time.” The proper way to diagram this is:

LA —> ~NY
NY —> ~LA (the contrapositive)

And these statements tell us that if someone is in LA, they’re not in NY. Similarly, if someone is in NY, they’re not in LA. Thus, they can’t be in both at the same time. What you diagrammed is:

~LA —> NY
~NY —> LA

Which tells us that if someone is not in LA, then they must be in NY, and vice versa, basically suggesting that NY and LA are the only two places on the planet. There are, obviously, tons of other places people could be, and so this diagram is wrong.

Hope this helps. Feel free to ask any further questions that you might have.