It is only when mixing two or more pure substances along a reversible path that the entropy of the mixing can be made physically manifest. It is not, in this case, a mere mathematical artifact. This mixing requires a process of successive stages. In any finite number of stages, the external manifestation of the entropy change, as a definite and measurable quantity of heat, isa fully continuous function of the relevant variables. It is only at an infinite and unattainable limit (...) thata non-uniform convergence occurs. And this occurs when considered in terms of the number of stages together with a distinguishability parameter appropriate to the particular device which is used to achieve reversibility. These considerations, which are of technological interest to chemical engineers, resolve a paradox derived in chemical theory called Gibbs'' Paradox. (shrink)

The rationality of scientific concept formation in theory transitions, challenged by the thesis of semantic incommensurability, can be restored by theChains of Meaning approach to concept formation. According to this approach, concepts of different, succeeding theories may be identified with respect to referential meaning, in spite of grave diversity of the mathematical structures characterizing them in their respective theories. The criterion of referential identity for concepts is that they meet a relation ofsemantic embedding, i.e. that the embedding concept can be (...) substituted by the embedded one in classical limit situations. Three case studies from contemporary physics theories will be used to show that the Chains of Meaning approach not only yields meaning comparisons for already established concepts (as for Newtonian and Schwarzschild mass) but is also well suited to characterize actual scientific strategies of concept formation in yet open cases such as black hole entropy or relativistic thermodynamics. (shrink)