You and I believe, hope, fear, and have all sorts of other intentional thoughts. We think about things. If physicalism is true, then none of us have intentional thoughts. Since we plainly do, physicalism is false.
Physicalism is the view that all existent entities are describable by theories of physics. On physicalism, one cannot provide a description of a soul. Thus, souls do not exist. Same goes for abstract objects, divine beings, and inbuilt purposes. But what about those mental states of intentional thoughts? Can they be described in purely physical terms? The answer is: no. Here’s one reason why.
I believe that the best days are sunny. Me believing that the best days are sunny is an instance of me thinking something about something. If it is a genuine intentional thought, then it is connected to all sorts of other beliefs. For example, to believe that the best days are sunny requires that I believe that they are better than some other days, rainy ones for example. Further, to believe that what makes something better than something else is to prefer some things to other things.
With a little reflection, one can quickly produces a vast array of other connected beliefs from just one belief. Moreover, intentional thoughts seem to be connected to thoughts of other kinds. For example, my belief that the best days are sunny seems to entail that I would hope that tomorrow is sunny and not rainy.
It is also the case that intentional thinking is subject to change. I might experience thirty straight days of 100 degree heat, all sun and no A/C. After such an experience, I might begin to believe that the best days are rainy days. Or perhaps, we move to Seattle. If I am to live happily in Seattle, it would be prudent to like rain. Somehow, I should try to enjoy the rain. Perhaps I persuade myself that rainy days are the best days. Or perhaps someone shows me the quality of a rainy day, the way the trees drip or the pleasant noise of rain on the roof tops. Perhaps I begin to look forward to rainy days and form a hope that it rains tomorrow.
Consider the kind of thinking that is supposed to be intentional but is not connected to other thoughts. Say, again, I believe that the best days are sunny. It is not connected to any other intentional thoughts and does not entail any either. Let’s say it is an isolated thought. Would this thought be intentional? It appears not. If I could provide a description of the thought in non-intentional terms and that description is simpler than one in which intentionality is required, then I could assume that having the single ‘thought’ is not intentional. Here is one way: The supposed belief is describable as a disposition to avoid the sun. Dispositions don’t have intentionality (a glass being disposed to break when hit does not require any intentionality) and thus, I don’t have a belief (or an intentional thought). Is there any more to say about it? Did I leave something out? It doesn’t appear so. Thus, if I have an intentional thought, it must be connected to other intentional thoughts.
Consider physicalism. On physicalism if I have intentional thought, then the thought is identical to a physical part (of my brain). Indeed, on physicalism, everything is composed of physical parts. Now it is also possible to disconnect one physical part from another. Consider what would happen if one could isolate my belief that the best days are sunny from all my other beliefs and other intentions. If I did so, then my thought would be describable without reference to other intentional states. But then it would not be intentional.
No problem, you might say. Surely we could say that the thought has intentionality in the brain but not when it is detached. However, this would entail that the thought does not have its own intentionality. It would entail that it only has intentionality when it is given it by a more basic intentionality, say from the rest of the parts of the brain. But then, if physicalism is true, all the parts of the brain–and all the intentional states–are separable from each other. Thus, no part of the brain has intentionality if it is possibly disconnected. Thus, physical things cannot have their own intentionality. On physicalism, we either get intentionality from some non-physical thing or intentionality is not real.
Mental things like souls are not so decomposable into parts. In fact, that is a feature of a mental substance: it is not composed of parts detachable from one another. Thus, if we have intentional thoughts those thoughts are had by non-physical entities, most plausibly, by our souls.
Apparently, the argument about the essential connection of intentional thoughts is found in “Semantic Theory and Tacit Knowledge” by G. Evans and “Theories of Meaning and Speakers Knowledge” by C. Wright (summary from Philosophy of Language by Alexander Miller). I found the argument about detachment of physical parts in Richard Swinburne’s Mind, Brain, and Free Will.