Why, if two wrongs don't make a right, do two negatives make a positive in mathematics?
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Answer:
I think you may be trying to mix the worlds of morals and mathematics, which doesn’t really work. You also need to take magnitude into account.
If you break my window and then I go and break yours, it might temporarily make me feel better, in a childish way, but the world is hardly better for two broken windows rather than one, though some people might see that as reasonable. If I escalate this and, say, set fire you your car in retaliation, we may well wonder where this will all end. Wars have started from such small incidents.
Mathematics is much more precise. If I owe you fifty dollars then I’m in debt; effectively I have a negative amount of money.
But if someone else also owes me sixty dollars then I notionally have ten dollars and I’m not in debt. If I’m only owed forty dollars I still have a ten dollar debt, or if I’m owed fifty it’s zero.
Numbers are not morality. Numbers are meant to model certain types of structures, and morality is not one of them.
Besides that, “two negatives make a positive” is not exactly right. A negative plus a negative is an even more negative number. If you multiply negatives, yes, that makes a positive. So which one should you use to model any particular structure? Plus or multiplication? It first depends on whether the thing you're trying to model behaves like numbers do. It then depends on whether the particular action in the structure is more like plus or more like times.
Take the idea of force in physics. If you exert one force in one direction and another force in the opposite direction, should you model this with plus or times? Turns out forces combine like a plus, so that forces in opposite directions cancel each other out, and the stronger of the two forces “wins”.
But if you multiply a force … well what does that even mean? You can do something twice as hard, that’s obvious. But how can you do something negatively-many-times? The only sense you can give this is to say that a negative force just is a regular force but in the other direction. That’s all a negative means.
Anyway, there’s aren’t very good reasons for thinking that this sort of structure is good for the ideas of right and wrong. It’s not clear that right and wrong are additive. It’s not clear that they’re just the same thing but in opposite directions.