Above all other titles, Charles Sanders Peirce (1839-1914) prized that of logician. He thought of logic broadly, such that it includes not merely formal logic but an examination of the entire process of inquiry. His works are replete with detailed investigations into logical questions. Peirce is especially concerned to show that valid inferential processes, diligently followed, will eventually root out error and alight on the truth. Peirce on Inference draws together diverse strands from Peirce's lifelong reflections on logic in order to develop a comprehensive perspective on Peirce's theory of inference.
Peirce argues that each genus of inference--deduction, induction, and abduction--has a different truth-producing virtue. An inference is valid just in case the procedure used in fact has the truth-producing virtue claimed for it and the person making the inference adheres to the procedure. In successive chapters, this book shows how Peirce supports the thesis that these genera of inference have the truth-producing virtues claimed for them and how Peirce responds to objections. Among the objections given consideration are the liar paradox, Hume's problem of induction, Goodman's new riddle of induction, that this may be a chance world, and that we are incapable of conceiving the true hypothesis. The book defends several controversial theses, including that Peirce does not so strongly object to Bayesianism as is sometimes claimed and that prior to 1900 Peirce had no explicit theory of abduction. It also proposes a novel account of abduction.
If we type "Peirce" and "Abduction" into Google Scholar, we will get approximately 30,000 results. Such a scenario may suggest that Peirce's perspectives on inference are sufficiently known and understood, leading us to believe that perhaps we do not need another book on the subject. However, if we drew that conclusion, we would be completely wrong.
Atkins, besides being a profound connoisseur of Peirce's work, is clear and systematic in his presentations. Several confusions existing in the literature - some of which, interestingly enough, can be found being repeated even in cutting-edge works, such as the recently released The Oxford Handbook of Charles S. Peirce - are finally disentangled.
The book explores how the different species of inference recognized by Peirce relate to one another, their validity, strengh, potential objections and, along the way, helps us to think deeply about various contemporary and philosophically significant topics, such as bayesian epistemology, confirmation theory, ravens paradox, Goodman's new riddle of induction, underdetermination and more. A delightful read.