Strobel at one point in the book interviewed J.P. Mooreland, who is an Evangelical philosopher that claims that science and philosophy can prove the existence of the soul. He offers a number of arguments.
First, most cultures around the world are aware of the existence of a soul and talk in terms of soul/body dualism. In other words, it appears to be a general intuition of human beings that they have a soul. I suspect that this possibly is tied up with our moral awareness that Paul described in Romans 2. If there is a soul, then humans are moral agents with volition rather than material objects that have no control where and what pushes them around. If they are moral agents, then they are accountable to a moral legislator and judge, which again, most cultures are all too aware that we will face in the afterlife.
A second argument has to do with the fact that our thoughts and consciousness are simply not material. One cannot cut open a person's head and see their consciousness or thoughts. One can also see in the brain the effects of consciousness, but not consciousness itself. One of the better points that Mooreland makes is that the decisions of consciousness and activities of consciousness actually change the brain by burning new neural pathways. For example, people who worry a lot (like myself!) actually have the visible effects on their brains. This goes for people who are addicted to certain activities as well (food, gaming, pornography). This is of course different than drug addiction because it is a chosen activity and state of mind, rather than a substance introduced into the brain that gives off certain obvious chemical effects.
Materialist scientists admit that they cannot account for consciousness, but they are confident that conscious could emerge from material causes. Why? Because they are materialists. In fact, if you think about it doesn't make a lot of sense. How could a bunch on things without consciousness give rise to consciousness? Unconscious matter is unconscious matter is unconscious matter. Mooreland states that only consciousness and mind could create consciousness and mind. Hence to account for our conscious minds, there must be a creator God who is a conscious mind himself.
Materialists don't buy this though. One odd explanation made by these folks is the idea that there is a "pre-conscious potentiality" in inanimate matter. Sounds like a weird sort of pantheism! This is an interesting argument, because as the Roman Catholic theologian Henri De Lubac said in his book The Drama of Atheistic Humanism, materialism actually represents a kind of mysticism. There is, notes De Lubac, in the atheistic worldview, a single substance that mystically self-evolves into the meaning, consciousness, and purpose we find in the universe. This makes matter possess certain God-like qualities. Since everything is the same thing (i.e. God-like matter), then we are all aspects of God-rather like Hindu "Atman is Brahman."
One last note: If consciousness necessitate the soul, then I think this validates the idea that animals have souls- contra Decartes! In the Bible, animals certainly do have the breath of life. I have observed my cat having emotions. She is certainly aware of her environment. I've seen her and other cats dream as well (they seem to be chasing some sort of animal, possibly prey). This also means that I do not think it is illegitimate to think that animals have an afterlife as well. The Bible seems to suggest that there are animals in the new creation- why not animals that we know now? This is of course speculative, but I don't think its illegitimate speculation. One might also make a similar argument for plants having a primitive soul, as Aristotle claimed, but that's way off the map.