The science of meaning

Is There a Science of Meaning

We answer "yes" to the question, "Is there a science of meaning?" Defense of this answer requires brief explications of (1) the nature of science: (2) the nature of meaning; (3) the ambiguity of meaning: (4) the multiplicity of scientific interpretations of meaning; and (5) the roIe of the psychiatrist in the production of meaning: (l) Science employs a "critical attitude. "This attitude requires that the validity of all scientific beliefs be ultimately decided by direct evidence. (2) "Meanings" are comprised of mental processes and their intended objects. These meanings, however,.are expressed in various ways. Expressions provide the evidence for a science of meaning. (3) Meanings are inherently ambiguous. Each meaning derives its meaningfulness from the broader context of meaning within which it exists. (4) Because of this inherent ambiguity, the same set of meanings can be interpreted in different ways. This multiplicity of interpretations remains scientific insofar as each interpretation can be justified by comparison with the direct evidence of the patient's expressions. (5) The psychiatrist is inescapably implicated in the production of the meaning which he or she then interprets.

Looks at the power of abstract forms in developing undwerstanding.

The British Journal for the Philosophy of Science, 1990

ABSTRACT Mathematicians and physical scientists depend heavily on the formal symbolism of mathematics in order to express and develop their theories. For this and other reasons the last hundred years has seen a growing interest in the nature of formal language and the way it expresses meaning; particularly the objective, shared aspect of meaning as opposed to subjective, personal aspects. This dichotomy suggests the question: do the objective philosophical theories of meaning offer concepts which can be applied in psychological theories of meaning? In recent years cognitive scientists such as Chomsky [1980], Fodor [1981] and MacNamara [1982] have used philosophical approaches to the meaning of formal language expressions as the basis for their psychological theories. Following this lead it seems appropriate to review some of the main treatments of meaning with a view to their transferability.

Mathematics Education Library, 2007

2000

The world is too complex to manage without radical functional simplification. Meaning appears to exist as the basis for such simplification. The meaning that guides functional simplification may be usefully considered as consisting of three classes. The first class consists of meanings of the determinate world. These are meanings based in motivation, emotion, and personal and social identity. First class

Measurement: Interdisciplinary Research & Perspective, 2007

The AERA 2007 Call for Proposals points out the need for researchers in education to look beyond their usual sources to other fields that have extensive experience in relevant theories and methods. In transitioning from a response to AERA’s Call for Proposals to the text of these articles on Assessing Measures of Mathematical Knowledge for Teaching, one cannot but be struck by (1) the heavy and repeated emphasis on interpretive arguments, their structure, and the relation of interpretation to validity; and (2) the complete lack of any use of, or even reference to, the decades and volumes of research and theorizing that have been invested in these issues in philosophy, history, anthropology, literary studies, sociology, psychology, and, most pointedly, the philosophy, history, and social studies of science. Thus, these papers provoke precisely the reaction that the authors of AERA’s Call for Proposals must also have often experienced when reading research in education. The authors are trying to reinvent concepts, methods, and tools that already have long-standing histories of success and failure in other fields. It would be bad enough if the existing applications were just in other fields, but obvious and relevant applications of these resources in mathematics education itself go unmentioned (to take just one example, see the work of Tony Brown). And the relevance of this work does not stop with “mere” philosophy, the “hermeneutic attitude,” or the rhetorical fads of deconstruction or postmodernism. What is more important, relevant, and exciting is the work that has been done extending the interpretive understanding of mathematics (Abraham, 1988; Heidegger, 1977; Kisiel, 1973) into a theory of science, technology, and, ultimately, measurement (Heelan, 1983, 1998; Ihde, 1991, 1998; Latour, 1987,

forthcoming in A Handbook of the History of Analytic Philosophy, ed. Michael Beaney

Online Submission, 2006

Algebra and calculus students have difficulties to express themselves in a statement of mathematical symbols and to comment on written mathematical statements to end with equivalent mathematical symbols statement. In this study, the reasons behind the meaning students load to the ...