Happiness can be attained a great many ways, but the question changes completely depending on how you're using the word 'pure'. The simplest way to read that phrase would have it "absolutea happiness", and I don't think that absolute happiness is possible. One could argue that someone can "feel nothing but happiness" in a single given instant (the moments of orgasm and death being the two most likely candidates), but I think the more common interpretation of the word happiness itself would require it to be at least moderately persistent. And in considering what persistent absolute happiness would be like, one also has to consider it in terms of the selfish gene theory. And from what I understand, the genes would by no means be best served by anyone attaining absolute happiness, ever. Someone absolutely happy has no incentive to do much of anything, especially something that would threaten that happiness, such as reproduce.
Now, a more useful discussion might be one about where *any* happiness can be found. And as to that, I would point out that the wants and desires (or more generally, the motivations) of an individual living in a society commonly include those introduced by the society itself. The values and motivational priorities of a society usually end up being shared by many of its individual members (creating what they call the superego). As such, it can be said that because some of an individual's motivations are usually also those of the society, the two routes to happiness are in fact inextricable, and that maximizing happiness (in the game theory sense, among others) is best achieved by balancing the two sets of motivations when and if they come into conflict.
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