<P> Hume concluded that such things as belief in an external world and belief in the existence of the self were not rationally justifiable . According to Hume these beliefs were to be accepted nonetheless because of their profound basis in instinct and custom . Hume's lasting legacy, however, was the doubt that his skeptical arguments cast on the legitimacy of inductive reasoning, allowing many skeptics who followed to cast similar doubt . </P> <P> Most of Hume's followers have disagreed with his conclusion that belief in an external world is rationally unjustifiable, contending that Hume's own principles implicitly contained the rational justification for such a belief, that is, beyond being content to let the issue rest on human instinct, custom and habit . According to an extreme empiricist theory known as phenomenalism, anticipated by the arguments of both Hume and George Berkeley, a physical object is a kind of construction out of our experiences . Phenomenalism is the view that physical objects, properties, events (whatever is physical) are reducible to mental objects, properties, events . Ultimately, only mental objects, properties, events, exist--hence the closely related term subjective idealism . By the phenomenalistic line of thinking, to have a visual experience of a real physical thing is to have an experience of a certain kind of group of experiences . This type of set of experiences possesses a constancy and coherence that is lacking in the set of experiences of which hallucinations, for example, are a part . As John Stuart Mill put it in the mid-19th century, matter is the "permanent possibility of sensation". Mill's empiricism went a significant step beyond Hume in still another respect: in maintaining that induction is necessary for all meaningful knowledge including mathematics . As summarized by D.W. Hamlin: </P> <P> (Mill) claimed that mathematical truths were merely very highly confirmed generalizations from experience; mathematical inference, generally conceived as deductive (and a priori) in nature, Mill set down as founded on induction . Thus, in Mill's philosophy there was no real place for knowledge based on relations of ideas . In his view logical and mathematical necessity is psychological; we are merely unable to conceive any other possibilities than those that logical and mathematical propositions assert . This is perhaps the most extreme version of empiricism known, but it has not found many defenders . </P> <P> Mill's empiricism thus held that knowledge of any kind is not from direct experience but an inductive inference from direct experience . The problems other philosophers have had with Mill's position center around the following issues: Firstly, Mill's formulation encounters difficulty when it describes what direct experience is by differentiating only between actual and possible sensations . This misses some key discussion concerning conditions under which such "groups of permanent possibilities of sensation" might exist in the first place . Berkeley put God in that gap; the phenomenalists, including Mill, essentially left the question unanswered . In the end, lacking an acknowledgement of an aspect of "reality" that goes beyond mere "possibilities of sensation", such a position leads to a version of subjective idealism . Questions of how floor beams continue to support a floor while unobserved, how trees continue to grow while unobserved and untouched by human hands, etc., remain unanswered, and perhaps unanswerable in these terms . Secondly, Mill's formulation leaves open the unsettling possibility that the "gap - filling entities are purely possibilities and not actualities at all". Thirdly, Mill's position, by calling mathematics merely another species of inductive inference, misapprehends mathematics . It fails to fully consider the structure and method of mathematical science, the products of which are arrived at through an internally consistent deductive set of procedures which do not, either today or at the time Mill wrote, fall under the agreed meaning of induction . </P>

Who abandoned the study of metaphysics to study the science of man