Abstract: This book is an extended discussion of Hume's famous sceptical argument that we have no reason to believe that the future will resemble the past. In the context of scientific methodology, this implies that however stringent the process of experimentation, the data supplied does not in itself support any one general hypothesis over another. There have been many attempts since Hume published this argument to show that it is mistaken, or that it itself begs the question. These attempts, which fall under the various headings of probabilism, reliabilism, deductivism, the No-Miracles argument, and naturalism, are examined and are all found to be wanting. It is then argued that Hume's argument is sound, but that conceding this does not show that there are no valid inductive inferences. The final sections of the book are devoted to showing that there are such arguments, namely probabilistically valid arguments, whose premises are assignments of prior probability. Such arguments are clearly conditional, like those of deductive logic, their conclusions depending on the premises. Indeed, this book argues that the laws of probability are as authentically logical principles as those of deductive logic, mediating like them non-ampliative inferences from premises to conclusion. Hume's position, that all inductive arguments depend on assumptions about the likely course of nature, is endorsed, since these assumptions can be identified with the prior probability assignments. Thus, though Hume was correct, there is nevertheless room for a genuine logic of inductive inference, supplied by the laws of probability.

Keywords: belief, deductivism, Colin Howson, David Hume, induction, inductive inference, justification, logic, No-Miracles argument, probabilism, reliabilism, scepticism