The artist Dena Shottenkirk has a varied biography. A svelte blonde from Kansas with sons named Dodge and Arliss and a daughter, Molly, she has a Ph.D. in philosophy as well as an MFA degree. She writes art criticism and teaches as well as making art. She spent the last couple of years as dean of the Glasgow School of Art, and has two books on the way: Nominalism and Its Aftermath from Cambridge Scholars Publishing and a book on art and censorship from Springer. She pals around with art-world big-shots and the tough guys on her block in Brooklyn.

But with her new show at Michael Steinberg Fine Art, she wants to teach us about philosophy.

She hopes to do this with paintings, a video animation, an installation and an online game (at www.denashottenkirk.com). The issue at hand, the artist says, is "exactly how art works transmit their meanings to viewers." As is usually the case in philosophy, this question involves a certain amount of navel-gazing: participants in the game are asked to describe what makes the color red "red," for instance, and what makes a square "square."

The paintings are simple if cryptic pictorial diagrams done in earth colors like Venetian red, ochre and Payne’s gray. The red square makes its appearance, as do outlined figures from a Giotto fresco, which represent the "image as such," as the art theorists used to say in the 1970s. One painting features a Cartesian graph, with beauty on one axis measured against "generality" on the other, showing that the most perfect features are the most ordinary ones. Several paintings include small doors, which open as if to reveal the answer.

The paintings are handsome, which is not to say that they are helpful as philosophical demonstrations, or cast any light on "sense data and symbol systems," to use the artist’s words once again. Rather, the paintings present signs of meaning whose allure comes from their mystery rather than their revelation.

In the back room is a video animation illustrating Plato’s Allegory of the Cave. Plato imagined prisoners confined forever in a dark room, strapped to chairs with their heads immobilized -- rather like a condemned man in an electric chair -- able to hear sounds from outside but see only shadows. Plato’s shadows aren’t even real, but are cast on the wall by puppets. Today as then, as this scenario makes all too clear, idealism ends up being another face of barbarism. Ah, philosophers.