Hume,
David (1711-1776):
Scottish philosopher and historian.
What is now called the problem of induction was set by Hume, who himself did not use the word in this context. Hume represented the nerve of all argument from experience as an attempted syllogism, the problem being to show how we can be entitled to move from a first premise that all observed so-and-sos have been such and such to the conclusion that all so-and-sos without restriction have been, are, and will be such and such.
A second premise that would complete a valid syllogism is that all so-and-sos have in fact been observed. But this suggestion is disqualified, since where it applies we have an analysis of not an argument from experience. This latter essentially involves a going beyond what is given, a use of cases examined to guide expectations about those that have not been examined. The only alternative second premise considered by Hume would make reference to the uniformity of nature. This he ruled out on the grounds that it could only be known to be true by a question-begging appeal to arguments of the very kind here in question...
A Dictionary Of Philosophy. Second edition. (Pan Books 1984).