Does the law contain implicit exceptions to its own rules? If so, what consequence does that have for understanding the relationship between law and morality? This collection gathers leading legal philosophers to analyse the logical structure of legal norms, advancing the understanding of the general philosophy of law.

The study presented in this book was entered upon by me from a legal point of view. 'Legal logic' has been known for a long time, concerning itself with the methodology of legal and in particular judicial reasoning. In modern days, however, this 'legal logic' is sometimes also connected with modern formal logic, as it has been developed in the works of G. Boole, A. de Morgan, G. Frege, C.S. Peirce, E. Schroder, G. Peano, A.N. Whitehead, B. Russell and others. For me this gave rise to the as yet not very specific question about the meaning of modern symbolic logic for law. Already in an early stage it appeared that, although traditional legal logic and modern symbolic logic both concern logic, this may not create the misapprehension that a similar matter is at issue. Both concern themselves (among other things) with reasonings and reasoning. Traditional legal logic is, however, as it was said by the German legal theoretician K. Engisch: "a material logic that wants us to reflect on what we have to do if we -within the limits of actual possibility- wish to reach true, or at least correct judgements" (Engisch, 1964, p.5). Modern symbolic logic on the other hand is not concerned with the truth or correctness of the result of an argument, but with its validity, i.e. the question when or under which conditions the truth (correctness) of the conclusion is guaranteed by the truth (correctness) of the premisses.

This book has two related aims: to investigate the frequently voiced claim that legal argument is nonformal in nature and, within the limits of such an investigation, to ascertain the most general proper ties of law as a rational system. Examination of a number of views of legal argument, selected from recent discussions in Germany, Belgium, and the English-speaking countries, will lead to the follow ing main conclusions. The nonformalistic conceptions of the logic of legal argument are ambiguous and unclear. Moreover, insofar as these conceptions are capable of clarification in the light of recent analytical methodology, they can be seen to be either mistaken or else compatible with the formalistic position. Because law is socially directive and coordinative, it is dependent upon theoretical psycho sociology and calls, in principle, for a deontic and inductive logic. The primary function of legal argument is to provide continuing reinterpretation and confirmation of legal rules, conceived as theo retical prescriptions. On the basis of this conception, the old juris prudential conflict between formalism and rule-scepticism appears substantially resolved. Aristotle, the founder of the theory of argument, conceived it as "the science of establishing conclusions" (bnO'l;~fl'YJ &no~e!"u,,~), designed to guide people in rational argumentation. In time, how ever, logic forsook its practical function and developed as a highly abstract and disinterested study, today called "formal logic"; and the theory of practical argument was either neglected or relegated to an appendix to rhetoric.

The best introduction for the general reader to Georg Wilhelm Friedrich Hegel's Phenomenology of Spirit.

"Maddy's short monograph looks at Wittgenstein's philosophy of logic, from the perspective of the form of naturalism that she calls "second philosophy." That view takes an empirical approach to logical truth -- essentially arguing that if philosophers want to understand the world, they should start from a position informed by scientific understandings of the world, because science is often a reliable guide to how the world works. Similarly, just like science, logic is also grounded in the structure of our world, and our basic cognitive machinery is tuned by evolutionary pressures to detect that structure where it occurs. Ludwig Wittgenstein (particularly in the "Tractatus") also linked the logical structure of representation with the structure of the world, but still insisted that the sense of our representations must be given prior to -- independently of -- any facts about how the world happens to be. When that requirement is removed, Wittgenstein's position in the Tractatus approaches Maddy's Second Philosophy -- that logic is grounded in the structure of the world and our representational systems reflect that structuring. The later Wittgenstein also hews closely to Second Philosophy, holding that our logical practices are grounded in our interests and motivations, and our natural inclinations, and the features of the world. In this sense, logic is no different from other descriptions of the world -- just more general and responding to features so basic and ubiquitous that they tend to go unnoticed. Maddy's Second Philosophy finds Wittgenstein as an important precursor and kindred spirit, and promotes a new view of him as a naturalistic phliosopher"--

Introduction to Logic is clear and concise, uses interesting examples (many philosophical in nature), and has easy-to-use proof methods. Its key features, retained in this Third Edition, include: simpler ways to test arguments, including an innovative proof method and the star test for syllogisms; a wide scope of materials, suiting it for introductory or intermediate courses; engaging examples, from philosophy and everyday life; useful for self-study and preparation for standardized tests, like the LSAT; a reasonable price (a third the cost of some competitors); and exercises that correspond to the free LogiCola instructional program. This Third Edition: improves explanations, especially on areas that students find difficult; has a fuller explanation of traditional Copi proofs and of truth trees; and updates the companion LogiCola software, which now is touch friendly (for use on Windows tablets and touch monitors), installs more easily on Windows and Macintosh, and adds exercises on Copi proofs and on truth trees. You can still install LogiCola for free (from http://www.harryhiker.com/lc or http://www.routledge.com/cw/gensler).

Modern mathematical logic would not exist without the analytical tools first developed by George Boole in The Mathematical Analysis of Logic and The Laws of Thought. The influence of the Boolean school on the development of logic, always recognised but long underestimated, has recently become a major research topic. This collection is the first anthology of works on Boole. It contains two works published in 1865, the year of Boole's death, but never reprinted, as well as several classic studies of recent decades and ten original contributions appearing here for the first time. From the programme of the English Algebraic School to Boole's use of operator methods, from the problem of interpretability to that of psychologism, a full range of issues is covered. The Boole Anthology is indispensable to Boole studies and will remain so for years to come.