"A map is a graphical representation of geographical or astronomical features, but this may range from a sketch of a subway system, to an interactive, zoomable, or animated map on a computer which constantly changes in front of the eyes." (Bas C van Fraassen, "Scientific Representation: Paradoxes of Perspective", 2008)
"A map is designed to help one get around in the landscape it depicts. [...]" (Bas C van Fraassen, "Scientific Representation: Paradoxes of Perspective", 2008)
"A model often contains much that does not correspond to any observable feature in the domain. Then, from an empiricist point of view, the model’s structure must be taken to reveal structure in the observable phenomena, while the rest of the model must be serving that purpose indirectly. It may be practically as well as theoretically useful to think of the phenomena as embedded in a larger - and largely unobservable - structure." (Bas C van Fraassen, "Scientific Representation: Paradoxes of Perspective", 2008)
"A scale model represents, and yields information about what it is a model of, by selective resemblance. [...] Scale models can be produced for the sheer aesthetic pleasure of it, but more typically they serve in studies meant to design the very things of which they are meant to be the scaled down versions." (Bas C van Fraassen, "Scientific Representation: Paradoxes of Perspective", 2008)
"A science presents us with representations of the phenomena through artifacts, both abstract, such as theories and mathematical models, and concrete such as graphs, tables, charts, and ‘table-top’ models. These representations do not form a haphazard compilation though any unity, in the range of representations made available, is visible mainly at the more abstract levels." (Bas C van Fraassen, "Scientific Representation: Paradoxes of Perspective", 2008)
"An algebra is a mathematical structure consisting of a set of elements and a collection of operators on those elements - though the term is variously defined in different contexts in mathematics, so as to narrow the meaning (e.g. an algebra is a vector space with a bilinear multiplication operation)." (Bas C van Fraassen, "Scientific Representation: Paradoxes of Perspective", 2008)
"[...] construction of a data model is precisely the selective relevant depiction of the phenomena by the user of the theory required for the possibility of representation of the phenomenon." (Bas C van Fraassen, "Scientific Representation: Paradoxes of Perspective", 2008)
"For unqualified adequacy of the theory, what is required is that the surface models of phenomena fit properly with or into the theoretical models. The surface models will provide probability functions for events that are classified as outcomes in situations classified as measurements of given observables." (Bas C van Fraassen, "Scientific Representation: Paradoxes of Perspective", 2008)
"In maps we have scale models of terrain, but projected onto a plane, thus producing occlusion of a sort not inherent to three-dimensional imaging. Maps do not usually have an obvious perspective; but we see perspectivity when, for example, the curvature of the earth makes marginal distortion inevitable as a result of this projection that lowers the dimensionality. A map too is the product of a measuring procedure, but they bring to light a much more important point about ‘point of view’, essentially independent of these limitations in cartography. The point extends to all varieties of modeling, but is made salient by the sense in which use enters the concept of ‘map’ from the beginning. A map is not only an object used to represent features of a terrain, it is an object for the use of the industrial designer, the navigator, and most of all the traveler, to plan and direct action. This brings us to an aspect of scientific representation not touched on so far, though implicit in the discussion of perspective, crucial to its overall understanding: its indexicality." (Bas C van Fraassen, "Scientific Representation: Paradoxes of Perspective", 2008)
"The general concept of a map is not so different from that of a model, though the one is extrapolated from a graph with spatial similarity to certain features of a landscape, and the other from a table-top contraption." (Bas C van Fraassen, "Scientific Representation: Paradoxes of Perspective", 2008)
'Model' is a metaphor, whose base is the simply constructed table-top model." (Bas C van Fraassen, "Scientific Representation: Paradoxes of Perspective", 2008)
"Scale modeling displays the characteristics of picturing, by relying on selective resemblance to achieve its aim, but in a way that is subject to inevitable occlusion or distortion." (Bas C van Fraassen, "Scientific Representation: Paradoxes of Perspective", 2008)
"Scientific theories represent how things are, doing so mainly by presenting a range of models as candidate representations of the phenomena. [...] A theory provides, in essence, a set of models. The 'in essence' signals much that must be delicately expanded and qualified; [...] These models - the theoretical models - are provided in the first instance to fit observed and observable phenomena. Since the description of these phenomena is in practice already by means of models - the ‘data models’ or ‘surface models’, we can put the requirement as follows: the data or surface models must ideally be isomorphically embeddable in theoretical models." (Bas C van Fraassen, "Scientific Representation: Paradoxes of Perspective", 2008)
"The activity of representation is successful in that case only if the recipients are able to receive that information through their ‘viewing’ of the representation. [...] In science the original creation of a model may have been a purely theoretical activity, but eventually it provides input for an application, where conditional predictions made on the basis of that model feed into planning and action." (Bas C van Fraassen, "Scientific Representation: Paradoxes of Perspective", 2008)
"The observable phenomenon makes its appearance to us first of all in the outcome of a specific measurement, or large set of such measurements - or at slight remove, in a data model constructed from these individual outcomes, or at a slightly further remove yet, in the surface model constructed by extrapolating the patterns in the data model to something finer than our instruments can register." (Bas C van Fraassen, "Scientific Representation: Paradoxes of Perspective", 2008)
"The physical sciences give us representations of nature, and scientific representation is in general three-faceted. From a purely foundational point of view, the theoretical models that depict the ‘underlying reality’ are the main thing. But some elements or substructures of those models are meant to represent the observable phenomena - the empirical substructures." (Bas C van Fraassen, "Scientific Representation: Paradoxes of Perspective", 2008)
"Theories represent the phenomena just in case their models, in some sense, 'share the same structure' with those phenomena - that, in slogan form, is what is called the semantic view of theories. [...] Embedding, that means displaying an isomorphism to selected parts of those models. Here is the argument to present the first challenge. For a phenomenon to be embeddable in a model, that means that it is isomorphic to a part of that model. So the two, the phenomenon and the relevant model part must have the same structure. Therefore, the phenomenon must have a structure, and this shared structure is obviously not itself a physical, concrete individual - so what is implied here is something of the order of realism about universals." (Bas C van Fraassen, "Scientific Representation: Paradoxes of Perspective", 2008)
"[...] when a theoretical model is said to represent certain phenomena, there is indeed reference to a matching, namely between parts of the theoretical models and the relevant data models - both of them abstract entities. Note now, the crucial word in this sentence: the punch comes in the word 'relevant'. There is nothing in an abstract structure itself that can determine that it is the relevant data model, to be matched by the theory. A particular data model is relevant because it was constructed on the basis of results gathered in a certain way, selected by specific criteria of relevance, on certain occasions, in a practical experimental or observational setting, designed for that purpose." (Bas C van Fraassen, "Scientific Representation: Paradoxes of Perspective", 2008)
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