Notice added Book Recommendation by Qmechanic♦ occurred Nov 27 '18 at 12:16 4 edited tags; Post Made Community Wiki | link edited Nov 27 '18 at 12:16 Qmechanic♦ 111k1212 gold badges214214 silver badges13081308 bronze badges 3 maybe for classical mechanics | link edited Sep 11 '13 at 8:01 Abhimanyu Pallavi Sudhir 4,61444 gold badges2727 silver badges4545 bronze badges 2 added 173 characters in body edited Sep 11 '13 at 4:44 Hypercube 11344 bronze badges Often when I am learning physics I start to think about whether the laws I'm learning are mere definitions or experimentally determined, and usually the textbook does not make this clear. As Thomas Kuhn writes in The Structure of Scientific Revolutions, These generalizations look like laws of nature, but their function for group members is not often that alone. Sometimes it is: for ex­ample the Joule-Lenz Law, $$H = RI^2$$. When that law was discovered, community members already knew what $$H$$, $$R$$, and $$I$$ stood for, and these generalizations simply told them something about the behavior of heat, current, and resistance that they had not known before. But more often, as discussion earlier in the book indicates, symbolic gen­eralizations simultaneously serve a second function, one that is ordi­narily sharply separated in analyses by philosophers of science. Like $$f = ma$$ or $$I = V/R$$, they function in part as laws but also in part as definitions of some of the symbols they deploy. Furthermore, the bal­ance between their inseparable legislative and definitional force shifts over time. In another context these points would repay detailed anal­ysis, for the nature of the commitment to a law is very different from that of commitment to a definition. Laws are often corrigible piecemeal, but definitions, being tautologies, are not. For example, part of what the acceptance of Ohm's Law demanded was a redefinition of both 'current' and 'resistance'; if those terms had continued to mean what they had meant before, Ohm's Law could not have been right; that is why it was so strenuously opposed as, say, the Joule-Lenz Law was not. Another example is conservation of momentum; is momentum conserved because it is defined as a quantity that is conserved or because it has been observed to be conserved? Are there any physics textbooks (maybe for classical mechanics) that take a more axiomatic approach, clearly distinguishing definitions from laws determined by experiment? Often when I am learning physics I start to think about whether the laws I'm learning are mere definitions or experimentally determined, and usually the textbook does not make this clear. As Thomas Kuhn writes in The Structure of Scientific Revolutions, These generalizations look like laws of nature, but their function for group members is not often that alone. Sometimes it is: for ex­ample the Joule-Lenz Law, $$H = RI^2$$. When that law was discovered, community members already knew what $$H$$, $$R$$, and $$I$$ stood for, and these generalizations simply told them something about the behavior of heat, current, and resistance that they had not known before. But more often, as discussion earlier in the book indicates, symbolic gen­eralizations simultaneously serve a second function, one that is ordi­narily sharply separated in analyses by philosophers of science. Like $$f = ma$$ or $$I = V/R$$, they function in part as laws but also in part as definitions of some of the symbols they deploy. Furthermore, the bal­ance between their inseparable legislative and definitional force shifts over time. In another context these points would repay detailed anal­ysis, for the nature of the commitment to a law is very different from that of commitment to a definition. Laws are often corrigible piecemeal, but definitions, being tautologies, are not. For example, part of what the acceptance of Ohm's Law demanded was a redefinition of both 'current' and 'resistance'; if those terms had continued to mean what they had meant before, Ohm's Law could not have been right; that is why it was so strenuously opposed as, say, the Joule-Lenz Law was not. Are there any physics textbooks (maybe for classical mechanics) that take a more axiomatic approach, clearly distinguishing definitions from laws determined by experiment? Often when I am learning physics I start to think about whether the laws I'm learning are mere definitions or experimentally determined, and usually the textbook does not make this clear. As Thomas Kuhn writes in The Structure of Scientific Revolutions, These generalizations look like laws of nature, but their function for group members is not often that alone. Sometimes it is: for ex­ample the Joule-Lenz Law, $$H = RI^2$$. When that law was discovered, community members already knew what $$H$$, $$R$$, and $$I$$ stood for, and these generalizations simply told them something about the behavior of heat, current, and resistance that they had not known before. But more often, as discussion earlier in the book indicates, symbolic gen­eralizations simultaneously serve a second function, one that is ordi­narily sharply separated in analyses by philosophers of science. Like $$f = ma$$ or $$I = V/R$$, they function in part as laws but also in part as definitions of some of the symbols they deploy. Furthermore, the bal­ance between their inseparable legislative and definitional force shifts over time. In another context these points would repay detailed anal­ysis, for the nature of the commitment to a law is very different from that of commitment to a definition. Laws are often corrigible piecemeal, but definitions, being tautologies, are not. For example, part of what the acceptance of Ohm's Law demanded was a redefinition of both 'current' and 'resistance'; if those terms had continued to mean what they had meant before, Ohm's Law could not have been right; that is why it was so strenuously opposed as, say, the Joule-Lenz Law was not. Another example is conservation of momentum; is momentum conserved because it is defined as a quantity that is conserved or because it has been observed to be conserved? Are there any physics textbooks (maybe for classical mechanics) that take a more axiomatic approach, clearly distinguishing definitions from laws determined by experiment? 1 asked Sep 11 '13 at 4:36 Hypercube 11344 bronze badges