The progress of science depends partly, upon the acceptance of indeterminate tacit premisses about the nature of science and the object of science. These premisses are tacit because (i) they extend to what is beyond the limitations of present data, -not the empirical or the imaginative- and therefore involve heuristic anticipations. (ii) they also involve personal and interpersonal mechanisms such as the personal presuppositions and commitments of the scientist operating within a given community. This community confers values on scientific work in the form of publications, research grants, professional positions, etc.. This transcends the objective subjective dichotomy since the scientist submits to requirements acknowledged by himself with universal intent, that is the scientist's responsibility to pursue his research and confer his judgements as his vision of reality would have him hold as universally necessary. (iii)their acceptance is largely a-critical - they are functional interpretative systems rather than static objects. Although when they are the object of study, they are facts, they are not the fact since they play a vectorial role in establishing facts. They make factuaiity possible. There is a strong case for tacit knowledge. Therefore, Polanyi submits, we should question a concept of scientific objectivity which rests solely upon logical and empirical foundations. Even though numerous mathematics and technical procedures can be employed, the objective value of a scientific theory cannot be wholly formally assessed. Polanyi's theory, in differentiating rationality from formal inference, shows the way towards a non-normative but non-subjectivist epistemology of science beyond the accounts of the practice of science of Kuhn, Lakatos and Laudan.

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This thesis presents a structural model of one aspect of science, the theory-driven discovery of empirical laws, in terms of the knowledge structures and reasoning processes that it involves; and describes a machine learning system designed to embody the major features of the model, called OZ, which is designed to investigate the transport properties of an unknown membrane separating two solutions. Inductive data-driven discovery is an important process in science, but takes place within very tightly constrained limits defined by theoretical reasoning. An explicit specification of the possible search space for a law is a <i>law framework</i>; this takes the form of a law with some undetermined parameters. Inductive law discovery is the search for the values of these free parameters. According to the model <i>informal qualitative models</i> (IQMs) describing the essential structural features of a physical system are used to guide the selection of appropriate variables for scientific law discovery, and the selection of an appropriate mathematical function for a law. Our analysis differs from previous work in machine discovery in stressing the importance of models of internal structure in scientific discovery. OZ comprises a domain independent control structure and a set of domain independent procedures, plus a set of domain dependent heuristics for the membrane properties domain. It constructs a set of candidate IQMs for the unknown membrane, and designs goal-directed experiments to determine which IQM is the right one, generating and testing qualitative predictions about the patterns to be expected in numerical data. When it has identified a single model as correct, it constructs law frameworks for possible laws describing the transport properties of the membrane, then designs different experiments to gather data to supply to an inductive law discovery function, which looks for a law of the type specified by each law framework.

Functional programming languages such as Haskell allow numerical algorithms to be expressed in a concise, machine-independent manner that closely reflects the underlying mathematical notation in which the algorithm is described. Unfortunately the price paid for this level of abstraction is usually a considerable increase in execution time and space usage. This thesis presents a three-part study of the use of modern purely-functional languages to develop numerical software. In Part I the appropriateness and usefulness of language features such as polymorphism. pattern matching, type-class overloading and non-strict semantics are discussed together with the limitations they impose. Quantitative statistics concerning the manner in which these features are used in practice are also presented. In Part II the information gathered from Part I is used to design and implement FSC. all experimental functional language tailored to numerical computing, motivated as much by pragmatic as theoretical issues. This language is then used to develop numerical software and its suitability assessed via benchmarking it against C/C++ and Haskell under various metrics. In Part III the work is summarised and assessed.

Thesis (M.S. - Renewable Natural Resources)--University of Arizona. / Includes bibliographical references (leaves 244-251).

Thesis--University of Illinois. / Vita. Bibliography: leaves 112-118. Also issued in print.

Thesis (MPhil)--University of Stellenbosch, 2008. / Bibliography. Also available via the Internet.

Thesis (Ph. D.)--Columbia University, 1921. / Vita.

Thesis (Ed.D.)--Teachers College, Columbia University, 1969. / Typescript; issued also on microfilm. Sponsor: Robert W. Lynn. Dissertation Committee: Patricia A. Graham. Includes bibliographical references.

Thesis (PH. D.)--Columbia University, 1921. / Vita. Also issued in print.