The Platonic picture may be pleasing, but it is hard to square with what we have learned from neuroscience. Everything that gives each of us our personal identities — consciousness, character, memories and so on — seems rooted in the electrochemical processes of our brains. As Bertrand Russell observed, “A virtuous person may be rendered vicious by encephalitis lethargica, and . . . a clever child can be turned into an idiot by a lack of iodine.” The dependence is most cruelly apparent in cases of Alzheimer’s disease, where the dissolution of the self proceeds in direct proportion to the physical deterioration of the brain.

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Where does this leave those who, while secular in outlook, still pine after immortality? A little more than a century ago, the American philosopher William James proposed an interesting way of keeping open the door to an afterlife. We know that the mind depends on the physical brain, James said. But that doesn’t mean that our brain processes actually produce our mental life, as opposed to merely transmitting it. Perhaps, he conjectured, our brains allow our minds to filter through to this world from some transcendent “mother sea” of consciousness. Had James given his lecture a few decades later, he might have used the radio as a metaphor. When a radio is damaged, the music becomes distorted. When it is smashed, the music stops altogether. All the while, however, the signal is still out there, uncorrupted.

James’s idea of immortality may sound far-fetched, but for him and other scientifically minded thinkers of his time it had one great virtue. It explained the existence of what were thought to be psychic phenomena: ghostly apparitions, communications from the dead at séances and seeming cases of reincarnation. Alas, little of this supposed evidence for an afterlife has held up under the scrutiny of rigorous investigation.

In the 1970s, a new hope for survivalists emerged: the near-death experience. In the best-selling book “Life After Life,” a doctor and parapsychologist named Raymond A. Moody Jr. presented a number of cases in which patients who had flat-lined and then been revived told of entering a long tunnel and emerging into a dazzling pool of light, where they communed with departed loved ones. In 1988, the atheist philosopher A. J. Ayer had such an adventure when he choked on a piece of smoked salmon and his heart stopped for a few minutes. Soon afterward, Ayer reported that his near-death experience, in which he saw a red light that seemed to govern the universe, “slightly weakened my conviction that my genuine death . . . will be the end of me.” But he later dismissed it as a hallucination caused by a temporary lack of oxygen in his brain.

The most interesting possibilities for an afterlife proposed in recent years are based on hard science with a dash of speculation. In his 1994 book, “The Physics of Immortality,” Frank J. Tipler, a specialist in relativity theory at Tulane University, showed how future beings might, in their drive for total knowledge, “resurrect” us in the form of computer simulations. (If this seems implausible to you, think how close we are right now to “resurrecting” extinct species through knowledge of their genomes.) John Leslie, a Canadian who ranks as one of the world’s leading philosophers of cosmology, draws on quantum physics in his painstakingly argued new book, “Immortality Defended.” Each of us, Leslie submits, is immortal because our life patterns are but an aspect of an “existentially unified” cosmos that will persist after our death. Both Tipler and Leslie are, in different ways, heirs to the view of William James. The mind or “soul,” as they see it, consists of information, not matter. And one of the deepest principles of quantum theory, called “unitarity,” forbids the disappearance of information. (Stephen Hawking used to think you could destroy your information by heaving yourself into a black hole, but a few years ago he changed his mind.)