Ludwig Wittgenstein is the Austrian architect, elementary school teacher and soldier who many believe revolutionized the practice of philosophy. Three of his brothers committed suicide. He died of a brain tumor on April 29, 1951. When told he had only a few days to live, Wittgenstein reportedly replied, "Good."

But these facts about Wittgenstein, however significant they may be, provide only vague clues to deciphering "Wittgenstein's Mistress," a new novel by David Markson.In fact, the novel has very little to do with Wittgenstein, despite the alluring title and the somber black-and-white cover photo of a deserted beach, which make the book look an awful lot like one of those scholarly, artsy biographies only Wittgenstein groupies would read (especially at $20 a pop).

"Wittgenstein's Mistress" is about a woman who is convinced she is the last person on earth. She ruminates relentlessly in stream-of-consciousness fashion about Giovanni Keats, Van Gogh, menstruation, cats - whatever comes into her head. She talks of her travels to Mexico, to Greece, to Russia and of her efforts to find other people by scrawling her address on street corners.

Well, actually the book does echo of Wittgenstein. The narrator, Kate, does quote short fragments from Wittgenstein's famous "Tractatus Logico-Philosophicus," even though she claims not to know where the lines came from. She also occasionally reflects on the limits and quirks of language, both obsessions of Wittgenstein. She wonders, for example, whether the second-floor toilet in the home she burned down can really still be on the second floor when the second floor has been reduced to ashes.

And because she's an artist, she uses famous paintings as metaphors for various parts of her fractured life, a technique that may perhaps be a subtle sendup of Wittgenstein's famous "picture theory" of meaning.

It's also fair to say the book sometimes captures, at a subliminal level at least, the feeling of Wittgenstein and reflects a somewhat Wittgensteinian world view. There is that somber sense of puzzlement at the strange ways pieces of our lives and our world fit - and don't fit - together. And perhaps Kate's bizarre solipsism is meant to represent the insanity and futility of attempting to live in the philosopher's empyrean realm of bleak perplexities and brutal logic.

The book does have its high points, particularly toward the conclusion as Kate picks apart Greek tragedy for the far-fetched and sometimes absurd things that motivate its characters. For instance, she asks, why was Orestes so intent on avenging the murder of his father, Agamemnon, when he was the jerk who sacrificed his daughter just to appease the gods? And can one really believe Penelope turned away all of those suitors hanging about during the 20 years Odysseus was out adventuring? And would it have been different if The Odyssey had been written by a woman?

Overall, however, the book doesn't really work well. Markson aspires to the kind of aphoristic, highly condensed insights of a Nietzsche or a Kundera. Or a Wittgenstein. All too often, however, Kate's observations seem aimed at working out some private joke between herself and Markson - a joke the reader glimpses only on rare occasions.