This paper discusses the problem of induction and how it impacts current knowledge and approach to science. This discussion revolves primarily around works of David Hume and Karl Popper due to the former theorising on induction more than any other philosopher and the latter revealing inapplicability of induction for science and scientific method.
Alan Musgrave (2004) in his critique of induction problem introduces Hume's argument as the basis for understanding the dilemma. Musgrave distinguishes Hume's three points, namely: (1) we reason, and must reason, inductively; (2) inductive reasoning is logically invalid and (3) to reason in a logically invalid way is irrational. Thus, the problem of induction is a problem confronted by scientists and philosophers concerned with science, but more specifically it is a problem for scientific method. Furthermore, it is a problem for the practice of science, for scientific endeavor, and it is a problem for the procedures of science. From the critical perspective, as science is or ought to be, it faces and must solve the problem of induction.
David Hume created a philosophical system to explain his understanding of human nature. He provided a solid non-metaphysical explanation of the nature of human thought to use as a foundation to his philosophy. As an empiricist, Hume believed our knowledge is of the phenomenal world and is gained through experience. The following passage addresses not only his opinion regarding metaphysics, but his basic belief regarding the significance of ideas and impressions:
All ideas, especially abstract ones, are naturally faint and obscure: the mind has but a slender hold of them: they are apt to be confounded with other resembling ideas; and when we have often employed any term, though without a distinct meaning, we are apt to imagine it as a determinate idea annexed to it. On the contrary, all impressions, that is, all sensations, either outward or inward, are strong and vivid; the limits between them are more exactly determined: nor is it easy to fall into any error or mistake with regard to them (Hume, 1985, p.49).
Hume built a unique system of knowledge. Creating complex ideas by comparing or combining simple ideas is the province of understanding, which includes imagination as well as the intellect. Everything we believe comes from experience, either as a simple idea derived from direct experience or as a complex of related ideas abstracted from experience. Human understanding comes from applying the intellect and imagination to ideas in order to form beliefs about the phenomenal world. Hume claimed there are only three types of connection between ideas: resemblance, contiguity in time and space, and cause and effect (Hume, 1999, p.101). Therefore, beliefs are gained by applying the intellect and imagination to ideas to abstract what they have in common, including location