Abstract

The first hypothesis proposed is that Peirce conceived of his work in terms of a comprehensive and unified System of Science and that a familiarity with this System is essential to understanding the interdependent relationships between his contributions to mathematics, certain special sciences, and philosophy. Peirce did not have the opportunity to finish the book in which this System would have been fully presented, but there is ample evidence from existent manuscripts that most of the work had been completed. Indeed, the System can be reconstructed by following his classification of the sciences which represents the analogous relationships one would find in a thorough examination of his System of Science. As Peirce frequently noted, the classification of the sciences was the key to approaching the overall pattern of his thought. ;This classification model indicates that the System of Science was a theory developed to explain the derivations and nature of methods of scientific thought. Within his System philosophy is only one of the sciences. Therefore, scientific methodology and not philosophy is the general category of his thought. Mathematics is the most basic science in terms of its methods. Philosophy must be interpreted in terms of science and presupposes an understanding of mathematical methods. The scientific method of semiotic is adapted from mathematics and is then used for analyzing scientific methods as they appear in the other sciences. Peirce's analysis of mathematical reasoning and four mathematical theories which he incorporated into his System of Science are discussed at length. ;The second hypothesis is that an adaptation of the diagrammatic reasoning used to acquire mathematical knowledge can contribute to interpreting works of visual art. According to Peirce, scientific or objective investigations rely on experimentation and observation, and must provide for intersubjectivity. From the observer's perspective there are certain analogies which can be drawn between diagrams and works of art which suggest that diagrammatic reasoning about works of art would satisfy the requirements of scientific inquiry and could promote an enhanced and objective interpretation of the conceptual relations represented visually in works of art