How do we know the soul exists, if modern science doesn't acknowledge it?
All living beings—plants, animals, or humans—possess consciousness and exhibit it in varying degrees. Consciousness does not arise from matter but is a symptom of the soul, which is an irreducible element of reality. Try as they may, scientists cannot create life in a laboratory by mixing lifeless chemicals.
We are the conscious spiritual soul within the body, and our departure from the body is called death. The phrase “passed on” is, therefore, an accurate description of what takes place when someone dies.
Consciousness means self-awareness, or the sense of “I am.” It also means awareness of our own thoughts and sensations. No computer—no matter how sophisticated—is conscious.
Ordinary, material science can't detect spirit or its symptom—consciousness. They're beyond the scope of matter. Spirit can be studied, though, by spiritual science, such as that given in the Vedas.
In our original pure state, we are conscious of our eternal identity in relationship to God. Now our consciousness is absorbed in matter, and we think we are whatever body we inhabit at the moment.
Besides consciousness, other evidence suggests that our identity is separate from our bodies—for example, past-life memories and out-of-body experiences.
More on this topic in Bodies and souls