The wording of the argument would need to changed to avoid circular reasoning. You couldn't have, "Moral behaviour cannot be based on egoism", as a premise, and, "Therefore, moral behaviour cannot be based on egoism", contained in the conclusion. — Sapientia
proof by exhaustion as it isn't given in your argument that egoism, malice, and empathy are the only possible things that moral behaviour could be based on. — Michael
I think that Schopenhauer is wrong to rule out egoism in advance, due to his conception of behaviour that has moral worth, and I think that him doing so conveniently paths the way for his desired conclusion. But, if you accept his terms, then the rest does seem to follow, and it does seem to qualify as, or could be formulated as, a proof by exhaustion. — Sapientia
1. There are only three kinds of moral behaviour: egoistic, malicious, and compassionate.
2. The only kind of moral behaviour which has moral worth seeks to prevent harm to another and seeks another’s well-being, i.e. it is just and philanthropic.
3. Egoistic behaviour only has regard only for one's own well-being, and therefore cannot be philanthropic.
4. Malicious behaviour seeks to cause harm to another, and therefore cannot be just.
5. Therefore, neither egoistic behaviour nor malicious behaviour can have moral worth.
6. Compassionate behaviour seeks to prevent harm to another and seeks another’s well-being, i.e. it is just and philanthropic.
7. Therefore, the only kind of moral behaviour which has moral worth is compassionate behaviour. — Sapientia
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