Epistemology
Can we know that a mind-independent external world exists?
We cannot know that an external world exists, because no experience rules out that we are dreaming or being deceived.
Even granting that some truths survive doubt, beliefs about a mind-independent world do not, because the dreaming and deceiver scenarios are subjectively indistinguishable from waking veridical experience.
We know ordinary truths about physical objects more securely than we know the premises of any argument against them, so it is the sceptical argument that should be given up.
Abductive reasoning develops or selects an explanatory hypothesis because it would explain the available evidence better than the live alternatives.
Methodic doubt provisionally withholds assent from beliefs vulnerable to doubt in order to find a secure basis from which knowledge can be reconstructed.
Phenomenological reduction brackets ordinary existential commitments so that the inquirer can examine how objects and world are given in experience.
Even a thinker who finds some truths beyond doubt can still ask whether our perceptual beliefs reach a world outside the mind at all. The skeptic argues that no experience distinguishes a veridical perception from a matching dream or deception, so the existence of mind-independent things is never secured by experience.
The doubt is local rather than global: it can grant that some things are known while denying that knowledge reaches a world beyond the mind.