When giving this paper at various places, one sort of reactions encountered came from people with good background in logic, but no previous experience with philosophy whatsoever. The reaction boils down to a rather blind stare and comments like "who cares about arguments for the existence of the soul?" or "Why is anyone doing this stuff?". The answers are simple. "Philosophers." to the first question. "Because it's more interesting than using complex mathematical tools to solve problems that only two to three people in the world care about." to the second one.
I prefer to use slightly less elaborate mathematical machinery to deal with philosophically motivated issues than to get into very complex and hermetic issues in, say, inaccessible set theory or computer science. This doesn't mean they aren't interesting. I just find philosophical problems more entertaining and important. And I think it is, in a sense, the responsibility of a philosopher and a logician to spend some time looking at what philosophical arguments are around about claims people care about and what can be said about their correctness, instead of locking themselves in the ivory tower of elaborate and detached purely mathematical problems. But again, it's a matter of choice.
Richard Swinburne (Swinburne and Shoemaker 1984; Swinburne 1986) argues that human beings currently alive have non-bodily immaterial parts called souls. In his main argument in support of this conclusion (modal argument), roughly speaking, from the assumption that it is logically possible that a human being survives the destruction of their body and a few additional premises, he infers the actual existence of souls. After a brief presentation of the argument we describe the main known objection to it, called the substitution objection (SO for short), which is raised by Alston and Smythe (1994), Zimmerman (1991) and Stump and Kretzmann (1996). We then explain Swinburne's response to it (1996). This constitutes a background for the discussion that follows. First, we formalize Swinburne's argument in a quantified propositional modal language so that it is logically valid and contains no tacit assumptions, clearing up some notational issues as we go. Having done that, we explain why we find Swinburne's response unsatisfactory. Next, we indicate that even though SO is quite compelling (albeit for a slightly different reason than the one given previously in the literature), a weakening of one of the premises yields a valid argument for the same conclusion and yet immune to SO. Even this version of the argument, we argue, is epistemically circular.
We would like to express our gratitude to all the people who discussed these issues with us and commented on earlier versions of this paper. We are grateful to participants of the events where the paper has been presented: Workshop & Young Researcher's Day in Logic, Philosophy and History of Science in Brussels, 2008, Jeffrey Ketland's Omega-seminar in Edinburgh, 2008, and Formal Methods in the Epistemology of Religion in Leuven, 2009. The main ideas of this paper originated after a number of discussions about philosophy of religion and mind with Professor Jack MacIntosh (Calgary). Comments provided by Professor Richard Swinburne (Oxford), who was in the audience when this paper was presented in Leuven in June 2009, were also very helpful, and it was interesting to learn that Professor Swinburne agrees with all our main points, apart from our final assessment of the modified argument. It was Lara Buchak (Berkeley) who observed that our version of the argument developed in response to SO results from a weakening of one of the premises. We also owe gratitude to Paul Draper for his invaluable editorial comments.