By Karl Fink
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Additional resources for A Brief History Of Mathematics
The tension between the Semantic View of theories and case study–based approaches provides fertile ground for proposing a distinction between models and theories at the end of the chapter. Answering the question of what models are about by saying that models are models of phenomena requires some attention to empirical aspects of what it is that is modeled—that is, what phenomena are. This is the topic of chapter 7. One lesson to learn from the so-called new experimentalism is that observation itself is rather a vague term.
Obviously, Thomson is right in requesting interpretations of abstract mathematical theories, but it is not obvious that they need necessarily be supplied by conventional mechanical models, nor was there any way of stopping the mathematization of physics itself (cf. Smith and Wise 1989, chapter 13, especially p. 445). 2 Scientific Models in the Mechanical Age Throughout the nineteenth century, physicists brought the skill of developing mechanical models to unprecedented heights, and they did so not just as a route to mathematization.
So why was it that Thomson attributed so much importance to mechanical models? ’” (Thomson  1987, p. 111). This desire to understand by means of a mechanical approach is further stressed in another famous quotation from Kelvin’s Baltimore Lectures—one that also contains the implicit criticism of Maxwell: “I never satisfy myself until I can make a mechanical model of a thing. If I can make a mechanical model I can understand it. , p. 206). Thomson does not tell us why he thinks that mechanical models promote understanding.
A Brief History Of Mathematics by Karl Fink