For a long time I was more or less agnostic about life after death. "No data," I thought, "so no conclusions can be drawn." (Actually, there's a fair amount of data, if you include ghost sightings, visions of spirits and gods, mediums, and such like. But I think all these are more easily explained psychologically than supernaturally. When photography was young there were often claims of ghosts captured on film. Now that cameras are nearly ubiquitous, one doesn't hear of such claims very often. Strange that the ghosts have gotten so shy....)
After an (embarrassingly long) time, it occurred to me that there may not be any reliable reports from those who have died, but there is actually quite a bit of positive data about how the mind works. And what all this data points to is that the mind is entirely dependent on the brain, which is a machine that functions according to electro-chemical principles. As strongly as we may feel that there is an "I" that exists separate from the body, that feeling is an illusion.
If you have ever had a glass of wine you have done the experiment (on) yourself. Introduce the chemical alcohol into the bloodstream, and your mental function is affected. Of course there are many more such mind-altering chemicals, with greater or lesser effects. Psychological experiments have revealed much more dramatic changes occur when the brain is physically altered. In split brain patients (whose corpus callosum - the bundle of connections between right and left brain hemispheres - has been surgically cut to prevent seizures), the left hand literally does not seem to know what the right hand is doing. Or consider the case of Phineas Gage, a railroad worker who had a three-foot-long iron rod blasted through his skull. Afterward, he was able to function more or less normally, but his doctor noted a distinct personality change. Even our most cherished aspects of ourselves - our personalities that, we feel, make us who we are - are tied to the material structure of the brain.
EEGs record the electrical activity of the brain, and are so well correlated with brain functionality that brain activity is now what determines who is legally alive and who is legally dead. A newer technique, known as functional MRI, is helping scientists map out what brain functions are carried out in what regions of the brain. At a much cruder level, electroconvulsive therapy demonstrates the influence of electricity on brain function, as, of course, does electrocution.
In short, everything we know about mental processes and the brain indicates that physical processes are responsible for everything that makes us us. It follows that when those physical processes stop, we stop existing.
This may seem terribly obvious and trivial to you, as it does to me now. But, as I said, it took me a long time to make this connection, so I'm laying it out for anyone else who is trying to think these things through.