Great-making properties: Properties that are better to have than not. Knowledge is plausibly a great-making property, as opposed to ignorance. Being free is plausibly a great-making property, rather than being in an isolation cell.
Maximal Greatness (M): Having all great-making properties, and having them all maxed out. M is itself a great-making property. If you didn't have M before, and then you acquired it, you would be greater than you were.
Non-Maximal Greatness (~M): A lesser-making property. If you didn't have ~M before, and then you acquired it, you would become less great than you were.
A great-making property cannot entail a lesser-making property: If it did, then it would no longer be, by definition, a great-making property. So if something is by definition a great-making property (such as M), then logically it cannot entail a lesser-making property (such as ~M). So M cannot logically entail ~M.
- If M is not possible, then all properties entail ~M
- M cannot logically entail ~M
- Therefore, M is possible