What does it mean to use the words “not” and “without” in the same sentence?

Question

For example:

1. I won't study without you.

2. I can't finish this project without you.

3. Don't eat without me.

4. There is no way to do this without taking risks.

5. I didn't play this game without him.

When I see sentences like these, I usually just cancel out the "not"/"no" and "without" and form a positive meaning. But I'm not sure if that's the right way to think because in some cases the meaning can change completely. What does using the 2 words mean exactly and why is it used like this? Some more examples would be nice too.

Answer 1

Canceling them out is close but not quite enough. Here are your examples with one small tweak:

1. I will only study with you.
2. I can only finish this project with you.
3. Eat only with me.
4. The only way to do this is with taking risks.
5. I only play this game with him.

The “only” is necessary to invert the sentences from double-negative to positive without accidentally including other options.

Why? Consider the first example:

• I won’t study without you.

This does not allow me to study alone, nor does it allow me to study with someone other than you. I cannot study unless you are there.

• I will study with you.

Simply saying this does not restrict me from studying alone or with others. It only says what I will do when you’re there, not what I will do when you aren’t.

• I will only study with you.
• I will study only with you.

The addition of “only”, in either location, again prevents me from studying alone or with others like in the original.

It is the same with all of your examples.