Any conception of happiness that cannot also incorporate some measure of pain, suffering and misery strikes me as what? Feeble? Anemic? Weak? Deficient? Laughable, even? Or maybe cowardly? Escapist? Or instead how about limited? Impoverished? Unimaginative? Uninteresting? Boring?
No one enjoys pain and suffering for their own sakes. Ascetics and neurotics bring pain on themselves in order to achieve something else. Setting self-inflicted pain and suffering, pain and suffering are an inescapable part of being human life. Even Christians admit this, but they use this fact as grounds for finding human life deficient and therefore in need of redemption, if not in this world, then in the world to come. Chasing after happiness and running away from unpleasant sensations is doomed to failure.
Clearly happiness, if such a thing is possible for mere mortals, must be something besides a simple abundance of pleasant sensations. Buddhism, Nietzsche and studies on gratitude strongly imply that happiness lies in one's attitude towards the objects of consciousness: thoughts, feelings, concepts, memories and the like. Happiness as metacognitive: thinking about thinking. Less abstractly and less meta, one's habits and style of thinking. This also means that happiness is not a matter of truth and falsehood anymore than any other practice such as martial arts, being a Christian, or literary interpretation. A person learns to be happy.
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It is impossible for me not to think of some of Nietzsche's last writings, especially Ecce Homo and his amor fati. I'd like to suggest a perverse reading of Nietzsche: Nietzsche as a utilitarian.
Jeremy Bentham in thinking through utilitarianism came up with an elaborate scheme of assigning a numerical value to various kinds of pleasures. This quantification of the different pleasures made it relatively easy and straightforward to calculate the greatest pleasure of the greatest number. Maximization of the quantities of pleasure or happiness for society at large was to be the yardstick by which to evaluated laws, customs, social policies etc.
But now, think about Nietzsche and his insistence on his own happiness. Could one person experience such intense and prolonged pleasure that it would be so much greater than aggregations of lesser (but no less real) pleasures and happinesses? Could one person experience such an intense and lasting happiness (or pleasure) so that it would in Bentham's reckonings and tables of pleasures outweigh the misery of millions? This sounds very Nietzschean and very aristocratic.
Of course such an extreme offends our sense of equality. If we bring our feeling for equality to bear on this extreme situation, what do we get? A mediocre happiness for the greatest number, or rather a relatively easy to achieve goal: avoidance and reduction of unhappinesses. Will and desire are dampened for the sake of everyone else's happiness. No one in this scheme is particularly happy or particularly unhappy, and worrying about the happiness of others is of paramount importance.
Just to be clear, a notion of personal happiness that doesn't have room for the happiness of others lacks imagination and subtlety.