Here's a simple proof that moral nihilism is false.
1. Suppose moral nihilism is true.
2. Then it would be incorrect to think that boiling a human child alive for pleasure is morally wrong.
3. But clearly (2) is false.
4. Therefore (1) is false.
You might wonder how we can know (3). The answer is that (3) appears to us to be true, and we have no good reason to think it is not true. This has been called the "Principle of Phenomenal Conservatism" in philosophy books, and it's the same principle that justifies our belief in physical/scientific facts (e.g., that tables exist, or that evolution is true). But it also implies that moral facts exist as well!
Of course, sometimes things appear to us to be true, but we eventually discover reasons strong enough override those appearances. For example, if you stick a pencil in a cup of water, it appears to us that the pencil is broken in half. But through scientific rigor, we have learned that this appearance is just an illusion. But this is not the case with (3). It both appears us that it is wrong to cause needless harm to children for fun, and any reason we might consider to doubt this fails to be strong enough to persuade us otherwise.
1. Suppose moral nihilism is true.
2. Then it would be incorrect to think that boiling a human child alive for pleasure is morally wrong.
3. But clearly (2) is false.
4. Therefore (1) is false.
You might wonder how we can know (3). The answer is that (3) appears to us to be true, and we have no good reason to think it is not true. This has been called the "Principle of Phenomenal Conservatism" in philosophy books, and it's the same principle that justifies our belief in physical/scientific facts (e.g., that tables exist, or that evolution is true). But it also implies that moral facts exist as well!
Of course, sometimes things appear to us to be true, but we eventually discover reasons strong enough override those appearances. For example, if you stick a pencil in a cup of water, it appears to us that the pencil is broken in half. But through scientific rigor, we have learned that this appearance is just an illusion. But this is not the case with (3). It both appears us that it is wrong to cause needless harm to children for fun, and any reason we might consider to doubt this fails to be strong enough to persuade us otherwise.