We are taught in high school that science is a perfect example of rational thought. Scientific creativity is a consequence of applying the hypothetico-deductive method. So what is the place of inconsistency in science? The articles in this book attempt to answer this question. The most important and influential minds at the First World Congress on Paraconsistency (Ghent University, Belgium, 1997) attended a workshop on “The Role of Inconsistency in the History and Philosophy of Science” and their papers are included in this collection. Some other papers have been written specifically for this book to provide a comprehensive picture of the role of inconsistency in science and mathematics. Kuhn proposed that the role of an inconsistency (antinomy) in a scientific theory is to drive the scientists to revise that theory into a new and consistent theory. This is a creative spur and may require revolutionary changes to the theory. The authors of these articles provide numerous examples from the history of science that inconsistencies do not always drive one to try to replace the theory. Often inconsistencies are tolerated and each conflicting part of the inconsistency is used to explain something about the world. Retaining the conflicting elements allows a pragmatic application of the theory and further creative development of the theory. Classical logic cannot tolerate inconsistency so we need to describe reasoning strategies which are inconsistency-tolerant. A number of the articles in this book provide us with detailed alternatives to classical logical reasoning.

The first article by Thomas Nickles challenges the view that the role of science is to produce theories and explanations about the world. He suggests that we can have an alternative view of science as consisting of a toolbox of problem solving devices. These recipes only apply in the particular context of use and so inconsistencies do not arise. If we do accept that the goal of science is to produce comprehensive explanations about the world then we have to address the problem of inconsistency. Scientific theories are fallible guesses about what the world is like. They evolve as newer, more accurate observations become available. Inconsistencies can be avoided by restricting our theories to very specific contexts (or models). However, inductive creativity requires the opposite, that we can extend our theories to broad contexts. This leads Nickles (19) to address the question “When is it fruitful to insist on consistency, and when not?” He argues that it may be more fruitful to accept an inconsistent theory rather than discard it altogether “as long as they continue to promise interesting results.… heuristic fertility trumps consistency” (20). In practice scientists are seen as pragmatists, however this means they must adopt a reasoning style which allows them to handle inconsistencies. The other writers in this book address this question.

Arthur I. Miller provides examples of three different ways in which erroneous methods have led to the correct results. I don't think we should classify all of these cases as inconsistencies and I believe that his three examples show we need to be extremely careful in how we define inconsistency in science. This highlights the complexity of reasoning methods, especially creative ones, in science.

The next two chapters by Van Bendegem and Bueno turn to inconsistency in mathematics. Van Bendegem considers the case of infinitesimals, where we have a paradigm case of an inconsistency and he argues that we manage the inconsistency by generating local models which provide semantic heuristics to select between the inconsistent possibilities. Bueno provides a general logical formalism in terms of Partial Structures and Quasi-truth for this model-theoretic isolation of inconsistencies.

Bryson Brown proposes we adopt a realist view of science and this requires a notion of approximate truth. He further argues that approximate truth commits us to a paraconsistent logic.

Da Costa and French next provide a useful overview of the problems posed by inconsistencies for a simple truth-based theory of science. Like Bueno they isolate the inconsistencies to local “partial structures” and develop a notion of truth based on these structures. Since truth has been weakened, a new concept to replace deductive closure is considered and this is a key element in creativity in the face of inconsistency.

In contrast to approaches which attempt to isolate inconsistencies, Priest argues that we must accept inconsistent information in our scientific theories and instead adopt a paraconsistent logic.

In the next three chapters Batens, Meheus, and Weber and De Clercq present inconsistency-adaptive logics as a way of handling the inevitable inconsistencies which arise not just in science but also in our every day interactions with the world. An inconsistency-adaptive logic uses both classical logic and a paraconsistent logic depending on context. This gives it the best of both worlds. A mechanism tracks the antecedents of a conclusion and when an inconsistency arises only these antecedents are subject to a paraconsistent logic, otherwise the full deductive power of classical logic is applied.

The final two chapters in this book by Norton and Nersessian provide interesting historical accounts of inconsistencies in Newtonian Gravitation theory and Maxwell's derivation of electrodynamics. Nersessian argues that a method of generic modelling allows creative development and advancement of a theory to such an extent that considerations of consistency do not initially come into play.

Overall this is a diverse collection of articles giving a good overview of the problem of inconsistency in science and its impact on creative development.