### Goodness and Existence

So, I was trying to think of a way to show that the following claim is true.

(*) Necessarily, if something, x, is maximally good, then x exists necessarily.

Here's one (not unproblematic) way that I was considering.

First, consider the property of being morally good. That, I take it, is a better making property. That is, something that is morally good is better than something that is not morally good. And, something that is morally good to degree, n, is better than something that is morally good to degree n-1. So, the best thing (the thing that satisfies the antecedent of (*)(if there is such)) will be maximally morally good. That is, it will be good to degree, n, where there is no degree of goodness, m, which is such that m>n.

Say that something is durably morally good if and only if it is morally good to some degree, n, and, at the nearest possible worlds, it is morally good to at least degree n.

Durable moral goodness comes in degrees as well. My moral goodness might, for instance, be more durable than yours. This would be so if the space of possible worlds free of a world, w, such that my goodness is diminished at it is larger than the space of worlds free of a world, w', such that your goodness is diminished at it.

So, suppose that possible worlds are ordered in possibility space by a similarity relation. The closer a world, w, is to a world, w', the more similar w is to w'. Consider a series of concentric circles centered on the actual world in possibility space. If there is some world, w, such that your degree of goodness in w is less than your degree of goodness in the actual world, and the circular region of possibility space with the smallest diameter in which w is located has a smaller diameter than the circular region of possibility space in which a world where my degree of goodness is less than it is in the actual world can be found, then I am more durably morally good than you.

Say that something is maximally durably morally good (MDMG) if and only if it is durably morally good to degree, n, and there is no degree of durable moral goodness, m, such that m>n.

So, here's a quick argument for the claim that maximal goodness entails necessary existence.

1. Necessarily, if something, x, is maximally good, then x is MDMG.

2. Necessarily, if something, x, is MDMG, then x exists necessarily.

3. So, necessarily, if something, x, is maximally good, then x exists necessarily.

Why think one is true?

Here's an argument for one.

1'. Suppose, for reductio, that at some world, w, something, x, is maximally good at w, and not MDMG at w.

2'. If x is not MDMG at w, then x would be better by being more durably good.

3'. If x would be better by being more durably good, then x is not maximally good at w.

4'. So, for all worlds, w, it is not the case that something, x, is both maximally good at w and not MDMG at w.

Why think two is true?

Here's an argument for two.

1''. Suppose, for reductio, that at some world, w, something, x, exists contingently and is MDMG.

2''. If x exists contingently, then there is some world, w', such that x does not exist in w'.

3''. If there is some world, w', such that x does not exist in w', then x is less good in w' than x is in w.

4''. If x is less good in w' than x is in w, then x is not MDMG in w.

5''. So, for all worlds, w, it is not the case that something, x, exists contingently and is MDMG in w.

So, initially I thought this argument is good. I think it's probably not now.

What do you guys think?

(*) Necessarily, if something, x, is maximally good, then x exists necessarily.

Here's one (not unproblematic) way that I was considering.

First, consider the property of being morally good. That, I take it, is a better making property. That is, something that is morally good is better than something that is not morally good. And, something that is morally good to degree, n, is better than something that is morally good to degree n-1. So, the best thing (the thing that satisfies the antecedent of (*)(if there is such)) will be maximally morally good. That is, it will be good to degree, n, where there is no degree of goodness, m, which is such that m>n.

Say that something is durably morally good if and only if it is morally good to some degree, n, and, at the nearest possible worlds, it is morally good to at least degree n.

Durable moral goodness comes in degrees as well. My moral goodness might, for instance, be more durable than yours. This would be so if the space of possible worlds free of a world, w, such that my goodness is diminished at it is larger than the space of worlds free of a world, w', such that your goodness is diminished at it.

So, suppose that possible worlds are ordered in possibility space by a similarity relation. The closer a world, w, is to a world, w', the more similar w is to w'. Consider a series of concentric circles centered on the actual world in possibility space. If there is some world, w, such that your degree of goodness in w is less than your degree of goodness in the actual world, and the circular region of possibility space with the smallest diameter in which w is located has a smaller diameter than the circular region of possibility space in which a world where my degree of goodness is less than it is in the actual world can be found, then I am more durably morally good than you.

Say that something is maximally durably morally good (MDMG) if and only if it is durably morally good to degree, n, and there is no degree of durable moral goodness, m, such that m>n.

So, here's a quick argument for the claim that maximal goodness entails necessary existence.

1. Necessarily, if something, x, is maximally good, then x is MDMG.

2. Necessarily, if something, x, is MDMG, then x exists necessarily.

3. So, necessarily, if something, x, is maximally good, then x exists necessarily.

Why think one is true?

Here's an argument for one.

1'. Suppose, for reductio, that at some world, w, something, x, is maximally good at w, and not MDMG at w.

2'. If x is not MDMG at w, then x would be better by being more durably good.

3'. If x would be better by being more durably good, then x is not maximally good at w.

4'. So, for all worlds, w, it is not the case that something, x, is both maximally good at w and not MDMG at w.

Why think two is true?

Here's an argument for two.

1''. Suppose, for reductio, that at some world, w, something, x, exists contingently and is MDMG.

2''. If x exists contingently, then there is some world, w', such that x does not exist in w'.

3''. If there is some world, w', such that x does not exist in w', then x is less good in w' than x is in w.

4''. If x is less good in w' than x is in w, then x is not MDMG in w.

5''. So, for all worlds, w, it is not the case that something, x, exists contingently and is MDMG in w.

So, initially I thought this argument is good. I think it's probably not now.

What do you guys think?