Question: Simon Blackburn is describing the Poetic Interpretation of ascending from Plato's Cave:

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> Part of the charm of Plato is the sense of being in a world in which these fractures did not exist. Ours may be a world in which there is a division between fact on the one hand, and value on the other. But his world is, in the phrase of the godfather of modern sociology, Max Weber, an enchanted world, in which ideas like proportion and harmony efface any such division. Beauty makes both goodness and truth manifest, so its perception and the love it engenders together give us the first step out of the Cave. Beauty is the first erasure of the distinction between fact and value. It is borne in upon us, in erotic experience, like facts. But it is intrinsically or essentially connected with the values of pleasure and love. And just as it erases the fact-value distinction, so beauty erases the tyranny of the self. In loving something or someone for beauty’s sake we are, as Iris Murdoch says, ‘unselfed’. **Selfish desire has no place in the pure aesthetic experience.**
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Does it mean that purity comes with the consequence of selflessness? That if one is clean and pure they must be selfless?

Answer: 
"Does [Selfish desire has no place in the pure aesthetic experience] mean that purity comes with the consequence of selflessness? That if one is clean and pure they must be selfless?"

No, no, no. the causal relationship is the other way around. It is not the selflessness that allows you to experience purity, but it is the purity of (aesthetic) experience that allows you to become self-less. Purity of (aesthetic) experience happens, when you read a great poem or watch an awesome movie, and you lose you spatio-temporal self and become the person in the poem or the movie. When I finally understood Robert Francis' Pitcher, I lost myself and became the Pitcher for a moment (the poem provided at the end of this post). 

Selflessness, for Blackburn, is not meant to be the opposite to selfishness. Rather it is the sublime self who is able to see things for their intrinsic values, no longer interpreting everything as an instrument to further one's needs and desires. By this way, the sublime self can also experience other values like the goodness. The hitherto self-interested self comes to understand that experiencing (doing) the good is intrinsically valuable, just as experiencing the beauty. In other words, the selflessness activated by the aesthetic experience is transmitted into the moral self (other-regarding self). This is why some argue that aesthetics is the mother of ethics (e.g., Marcia Eaton)

The possibility of self-lessness through the aesthetic experience is important to Blackburn since such a possibility allows him to elaborate his projection theory. According to him, the reason that this world is a moral world, despite the absence of moral facts in this world (so-called the analytic world, world inhabited by brute facts), is that our moral values, just like aesthetic values, acquired through language games, are projected (or spread) onto the analytic world.

Pitcher
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His art is eccentricity, his aim

How not to hit the mark he seems to aim at,

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His passion how to avoid the obvious,

His technique how to vary the avoidance.

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The others throw to be comprehended. He

Throws to be a moment misunderstood.

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Yet not too much. Not errant, arrant, wild,

But every seeming aberration willed.

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Not to, yet still, still to communicate

Making the batter understand too late.
I believe that the phrase explains that beauty in aesthetics is an a priori knowledge that is simultaneously the highest positive value and personification of truth. Aesthetics is an experiential phenomena that is external to ourselves and, ostensibly, is an appreciation for the truth of beauty (which is perceived as a universal concept in the author's theory). It is not related to one's person satisfaction, but an a priori truth and value accessed through this appreciation. Therefore, it is intrinsically "unselfed".

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> Does it mean that purity comes with the consequence of selflessness? That if one is clean and pure they must be selfless?
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I believe that the author's intent is that the practice of aesthetics -*appreciation of true beauty* - is itself unselfish - neither the beautiful thing, nor the actor, is unselfish. It is more descriptive of the person's experiencing the beauty (in that moment), rather than the beautiful thing in-itself.