# First Order Logic “More Than One”?

I'm trying to figure out how to express "More than one" in first order logic.

What I have so far is:

$$\exists S_1 \exists S_2 IsGreen(S_1) \wedge IsGreen(S_2)$$

But that definitely doesn't sound right.

It would be great if someone could point me in the right direction.

Thanks for reading!

• You should also require that $S_1 \neq S_2$ – dani_s Mar 29 '14 at 5:07

## 1 Answer

That looks right but you are missing one part. You have nothing saying that $S_1 \neq S_2$ Without that you aren't saying anythings more than that one exists.

If it looks like this you do say that though $$\exists S_1 \exists S_2\, [IsGreen(S_1) \wedge IsGreen(S_2) \wedge (S_1 \neq S_2)]$$

This asserts that there are at least $2$ different objects that are green.

• "$2$ unique objects" is oxymoronic. I think you mean "$2$ different objects." – bof Mar 29 '14 at 6:31
• Changed it thanks – ruler501 Mar 29 '14 at 14:52