If indeed the difference between “soul” (that is, as a metaphysical entity) and “mind” (a conscious construct in “meatspace”, if you will) is as simple as the difference between a painting of food and food itself, then the question would not be nearly as interesting.
Your analogy is seriously flawed, for you have taken a comparison between two completely empirical things (the difference between “apple” and “painting of apple”) and used it to bolster your conception of logical immunity of the decidedly non-empirical. It’s as if one is positing the mere fact that something is non-empirical makes that thing impervious to the sharper edges of critical thought. I would argue instead that, even if there is no certain knowledge of any particular subject, we should at least attempt as much empiricism as we can bring to bear on the subject.
If the idea of logic being applied to souls seems absurb to you, it begs the question, why? Why shouldn’t the “soul” be subject to examination? And if it is found to be an unnecessary idea, or an idea in need of revision, why should it not be either revised or thrown out in favor of the alternatives?
After all, many intelligent people used to believe that the sun, stars, and planets revolved around the earth on crystal spheres. A fair segment of the population continued to believe this long after its usefulness as a theory had been exhausted.
To answer the OP, I doubt there is a soul, as I think it is far more likely that all those things we like to think about as “spiritual” can be (or will eventually be) described by psychology and a greater understanding of how the brain incorporates itself into consciousness.
Are there dangers in reductionism? Perhaps for those who see mostly negative connotations in connecting ourselves with the physical more than with the spiritual (or possibly imagined). Yet from my point of view, even if possible, the ideal of non-corporeal existence is at least potentially distracting and worst a panacea, for whatever lies beyond death, if anything, is a mystery. What we can see, what we can experience here and now–there is little reason to believe that it does not exist. As such, we have the ability, however small it might be, to change things here, to make an effect here, to improve the world here, regardless of what happens after. But if this world is only transient, these bodies mere hotels for immortal beings, of what importance are they?
Maybe there are such things as “souls” or “gods”, but even if there are, they do not seem to have any measurable impact on our lives unless we decide that they do. Perhaps for some people, such a belief enriches their lives. shrugs So be it. But for as much potential doubt as there is about any given afterlife, there is as much certainty that we are responsible for our little domains on the planet upon which we live and the other creatures we interact with there.
To me, the question is not so much whether souls exist, but rather what will people do with them even if they do?