Dreams often tell us that we are in dangerous situations, and if they can do that, then how do you know your mundane situation right now isn’t also a dream? Any evidence or test you can appeal to you might just be part of the dream.
Nature of Sensations
Since sensations are just neuronal firings, then it is easy to see how in principle they can be faked.
Demon or Brain-in-a-vat
Or, per Descartes, perhaps a demon is tricking you and feeding you sensations, and nothing is real at all except you and the demon. Or you are plugged into the Matrix.
Since we can’t trust our senses completely, then we can’t rely solely on empiricism. We do have knowledge, so it must be at least partially from rationalism, or a priori reasoning.
Indirect Realism (Causal Realism, Representative Realism)
Descartes was not a solipsist and agreed that the external world exists, but that we can have no direct knowledge of it. Like when watching TV, just from watching a live broadcast we can’t know whether there really is a real broadcast happening or not, unless we have other information than from just our direct watching of the TV.
But indirect realism means only that we could be right that the external world is there; it doesn’t mean we are right. So perhaps indirect realism is not enough; we need a better way. Unfortunately, no matter what we do, we could still be dreaming and so indirect realism might be the best it gets. Still, is there a way to avoid skepticism?
Descartes appeal to the existence of God, an all-good being. An all-good being would not allow Descartes to be tricked by a demon about everything. Obviously, this is contentious, and so something better is needed.
Perhaps the simplest explanation is the most likely. If it’s just you, and a demon, then wouldn’t that be the simplest explanation? Simpler than postulating an entire complex world? But the demon would have to be even more complex, for it would have to have knowledge of a (phony) external world, and be capable of tricking us and know what it is doing.
Appearance and Reality, Mind and Matter
If the Occam’s Razor argument is correct, then we can at least have a somewhat good argument for the external world. So that takes care of the epistemological concerns. What about the metaphysical concerns? Due to the thought experiments above, we can see that the mind has experience (qualia), ability reason, and intentionality (thinking about things other than itself). Clearly, this is different from the material physical things that the external world is made up of, so what is the nature of the mind and how can it arise from physical matter?