ABSTRACT
Many take scientific representation to be, in the main, linguistic, perhaps thinking of science as producing descriptions and natural laws, and thinking of the principal vehicles for results in science as the research article, textbook, monograph, and treatise. There is a general reason for suspicion about any such conclusion. To be applicable, language must be based on extra-linguistic skills: abilities to discriminate objects, properties, characteristics, generally that to which basic meaningful units of language apply such as colors, shapes, and re-identifiable objects; as well as much more complex skills such as those involved in using a microscope. Such skills involve perceptual and probably many other non-linguistic forms of representation. Now, apply T. H. Huxley’s precept that science is scrupulously applied common sense. We should expect that science would make use of these extra-verbal representational tools and in fact build on, augment, develop, expand, and extend them. When we look, this is just what we find: from the role of construction by compass and straight edge in Greek geometry, through the use and development of maps, illustrations, diagrams, and graphical methods, to the current explosion in the extralinguistic tools enabled by information technology. Note that all of these provide a kind of epistemic access both to data and to theoretical (or modeling) conclusions that would otherwise be utterly out of reach. To emphasize with the extreme: imagine trying to understand the visual modeling output of sophisticated simulations in terms of a list of numbers or a print-out of the data and code used to produce the image! How should we think about the use of mathematics in scientific representation? Did Galileo not say that the book of nature is written in the language of mathematics, and is mathematics not presented linguistically? But it is debatable whether mathematical representation should count as linguistic. For example, when we represent the motion of a pendulum with the function, x 5 A Sin (ωt), the formula does not represent the motion directly. The formula represents a function, perhaps understood as a collection of ordered pairs of values, that, when interpreted as representing times and angles of deflection, in turn represent the motion of the pendulum. The representation succeeds
to the extent that the function and the course of values are similar in respects that are of current concern. The point generalizes. An abstract model – a piece of mathematics – can be used by representing agents to represent a target phenomenon by singling out form or structure shared by the model and its target. Often language facilitates picking out both the model and the relevant similarity used in the representation. Nonetheless it is the model, the abstract object, and the relevant similarity, not the language used to pick them out, which in the first instance function in the representational role. For that reason among others, an enormous amount of modern science is deeply extralinguistic. One must resist any temptation to wonder whether linguistic or extra-linguistic representation is the more important. Language cannot be applied without use of representation-driven tools of application – perceptual, abstract modeling, and probably much else. On the other hand, the recursive, combinatorial power of language to further structure, organize, and generally deploy representations – linguistic and others – immeasurably augments the power of our extra-linguistic representational tools. Linguistic and extra-linguistic representations are constitutively intertwined.
