We define a "representation" as an external object with which we denote another object and present information about it to ourselves or others. All the following objects count as representations in our sense: a set of Japanese declarative sentences describing Mount Fuji, a time table of the Boston subway system, a geometry diagram used to demonstrate the Pythagorean theorem, a state map of the United States, a relief map of a Rocky terrain, a ball-and-stick model of a molecular, and a (...) scale model of the Rockefeller center. ;The dissertation studies how different modes of presenting information exhibit different degrees and kinds of efficacy as an aid for human reasoning. The main hypothesis, which we dub the "Constraint Hypothesis," is that the variance in inferential potentials of different modes of representation is largely attributable to particular ways in which structural constraints on representations match and mismatch with constraints on their targets. The hypothesis is intended to provide a definite perspective for the general study of information representation, which is gradually taking the shape of an independent branch of science. ;As the basis for our analysis, we adopt the mathematical framework of the "qualitative information theory" being developed by Dretske, Barwise, Perry, and Seligman. We analyze several key properties that account for the efficacy of particular modes of representation, including the capacity of providing "free rides" in inference, the property of being over-specific in representing information, and the property of being self-consistent in information content. We also propose an analysis of the conceptual boundary between the "linguistic" modes and the "graphical" modes of representation, and explain some of the important differences in their cognitive potentials. All of these analyses crucially refer to structural constraints on representations and their match and mismatch with constraints on the targets, and hence lend piecemeal yet sturdy supports to our main hypothesis. (shrink)

One effect of information technology is the increasing need to present information visually. The trend raises intriguing questions. What is the logical status of reasoning that employs visualization? What are the cognitive advantages and pitfalls of this reasoning? What kinds of tools can be developed to aid in the use of visual representation? This newest volume on the Studies in Logic and Computation series addresses the logical aspects of the visualization of information. The authors of these specially commissioned papers explore (...) the properties of diagrams, charts, and maps, and their use in problem solving and teaching basic reasoning skills. As computers make visual representations more commonplace, it is important for professionals, researchers and students in computer science, philosophy, and logic to develop an understanding of these tools; this book can clarify the relationship between visuals and information. (shrink)

L'emploi du raisonnement par l'absurde a été source de contestations au cours de l'histoire des sciences. L'auteur en propose une définition, puis montre comment un tel raisonnement indirect peut se retourner en un raisonnement direct qui lui soit logiquement équivalent, ce dont Aristote avait pressenti la possibilité...

This chapter provides a survey of issues about diagrams in traditional geometrical reasoning. After briefly refuting several common philosophical objections, and giving a sketch of diagram-based reasoning practice in Euclidean plane geometry, discussion focuses first on problems of diagram sensitivity, and then on the relationship between uniform treatment and geometrical generality. Here, one finds a balance between representationally enforced unresponsiveness (to differences among diagrams) and the intellectual agent's contribution to such unresponsiveness that is somewhat different from what one has come (...) to expect in modern logic. Finally, challenges and opportunities for further work are indicated. (shrink)

This chapter gives a detailed study of diagram-based reasoning in Euclidean plane geometry (Books I, III), as well as an exploration how to characterise a geometric practice. First, an account is given of diagram attribution: basic geometrical claims are classified as exact (equalities, proportionalities) or co-exact (containments, contiguities); exact claims may only be inferred from prior entries in the demonstration text, but co-exact claims may be asserted based on what is seen in the diagram. Diagram control by constructions is necessary (...) for this to work. Case-branching occurs when a construction renders a diagram un-representative. The roles of diagrams in reductio arguments, and of objection in probing a demonstration, are discussed. (shrink)

Model theory is the branch of mathematical logic looking at the relationship between mathematical structures and logic languages. These formal languages are free from the ambiguities of natural languages, and are becoming increasingly important in areas such as computing, philosophy and linguistics. This book provides a clear introduction to the subject for both mathematicians and the non-specialists now needing to learn some model theory.

The standard view of logical form is that logical forms are synthetic structures which are the forms of sentences and of other linguistic entities. This is often associated with a more general linguistic view of logic which is articulated in different ways by various authors. This paper contains a critical discussion of such linguistic approaches to logical form, with special emphasis on Quine’s formulation of a logical grammar in Philosophy of Logic. An account of logical forms as higher-order properties, which (...) essentially builds on Frege’s analysis of quantification as higher-order predication, is suggested at the end. (shrink)