How can a learner, be it a human or otherwise, be guaranteed of arriving at a correct result before it encounters novel situations or acquires new knowledge? How reliable is the learning process at the time it is adopted? The author, in this lengthy and detailed treatise, tries to answer these questions in the framework of what he calls `formal learning theory.' This branch of learning theory is more mathematical than others, and studies to what extent a learning system can be judged as reliable. This book certainly outlines the main results, but it is difficult to see their relevance, as the author does not relate them to practical learning systems. This is not a surprise of course, given the nature of formal learning theory. In addition, there are many places in the book that seem to be a mere relabeling of certain results in set-theoretic topology, thus making them appear vacuous from a mathematical standpoint.

The author also agrees to the standard definition of induction (ala Sextus Empiricus), with its goal of establishing a "universal" in terms of a particular (finite) set of observations. Thus induction will not be a reliable learning strategy, since some of the particulars may be omitted and conflict with the universal. One cannot include all of the particulars, since they form an infinite collection. But there are other views of induction that are being used in contemporary learning theory and artificial intelligence. The author is apparently unaware (or does not consider it relevant) of the research in inductive logic programming that have given a deductive foundation to inductive, scientific reasoning based on `inverse resolution'. In a first order theory, hypotheses can be generated deductively using background knowledge and examples, and by using a particular notion of language bias to constrain the search for the hypotheses. These systems of hypothesis generation even have practical use, and serve as a counterexample to the author's contention that inductive inference is not deductive. Of course, the way he understands it, i.e. taken from the literature on the philosophy of science, it is certainly not deductive. Hence, induction, as viewed by the author, will never yield a certain result, i.e. one obtained by deduction, and so he endeavors to find measures of convergence for inductive systems that will "logically guarantee" convergence to the "truth."

The notion of truth as a scientist may hold to it is not really discussed in any detail in the book. Instead, some rather vague notions of truth, such as "correctness" or "predictiveness" are used, which are (in a major portion of the book) only supposed to depend on the hypothesis and the data stream. Data streams are taken to sequences of natural numbers that encode discrete "observations", and the author rather cavalierly allows the existence of infinite data streams, despite his assumption that truth or correctness is to be an "empirical' relation. The scientist is also viewed as a passive observer, with the data stream not depending on the actions that the scientist takes. This of course means that data streams coming from quantum systems will not be modeled by this approach. In addition, the difference between closed and open sets cannot be detected in real-world computations, thus casting further doubt on the relevance of the author's results to real scientific practice.

Since the author wants to stay in the framework of mathematical logic, and since this is a book on philosophy, no attempt is made to compare the results derived in the book with historical practices in scientific research. Such a comparison would lend more credence to the formal models of hypothesis creation or theory construction that are put forward by the author. The construction of formal models for scientific research or other types of learning is fairly straightforward as this book shows. These models are abstracted from the processes that one observes in science and one can believe that they do represent what scientists actually do. However, if one is to have great confidence that these models are accurate, one must compare them to actual case histories in scientific research. This is not done in this book, and neither in any other one on the same topic that this reviewer is aware of. This aggravates the view held by many professional scientists that philosophers of science are engaging in sheer speculation and fantasies of thought. It is fair to say that such a view is very close to the truth, and unfortunately this book is evidence for that view.

**出版社:**OUP USA (1996年2月15日)**丛书名:**Logic and Computation in Philosophy Series**精装:**448页**语种：**英语**ISBN:**0195091957**条形码:**9780195091953**商品尺寸:**16.5 x 2.9 x 24.3 cm**商品重量:**816 g**ASIN:**0195091957**用户评分:**分享我的评价