Can art only be valued in monetary terms?

Answer 1

No.

While the value of art in a capitalist society is measured primarily by it's market or exchange value, there are many other models under which you could evaluate the value of a piece of art. Intrinsic value, or the value that a piece has as an end itself, could be used to describe intangible (and subjective) qualities such as the piece's ability to inspire or elicit emotion. This relates to the inherent value, which is a quality that the piece itself has that allows it to elicit that response. These concepts are typically closely tied to ethics, and shared value-sets within a culture.

Under postmodernism, as works themselves provide a starting point or material for other artists, some art could be said to have affordance or afforded value, as was the case for Duchamp and his relationship to The Mona Lisa -- or the urinal, for that matter.

It should be noted that capitalism has the freakish ability to convert any of these values into exchange value -- for instance, the intrinsic value would tend to increase the monintary value of a piece, which is part of the reason an original Renoir is worth a lot of money. A lack of exchange value however, does not mean that a piece is without value.

A great deal has been written about this issue in the field of Critical Theory, and the 'value' of art itself has arguably been one of the greatest points of debate through the modern and postmodern periods. You might check out the writing of Theodor Adorno, Walter Benjamin or Herbert Marcuse as a starting point. Alternately Roger Scruton has done a great deal of writing on the subject which is more accessable, more pretentious and less ranty.