The Logic of Thermodynamics

Scientific theory relies on the logic of deductive reasoning. Each scientific deduction builds on one or more premises of the theory and leads to conclusions that can be tested experimentally. 

Scientific theories themselves can be distinguished as deductive or inductive in nature, according to the underlying character of their premises. In a deductive theory, the fundamental premises are axioms or postulates that are neither questionable nor explainable within the theory itself. Outstanding examples of deductive theories include Euclidean geometry (based on Euclid s five axioms) and quantum mechanics (based on Schrodinger s prescription for converting classical trajectory equations into wave equations). An inductive theory, on the other hand, is based on universal laws of experience that express what has always been found to be true in the past, and may therefore be reasonably expected to hold in the future. Thermodynamics is the pre-eminent example of an inductive theory. 

Although we cannot prove that an inductive law of experience will continue to hold tomorrow (any more than we can prove Euclid s fifth axiom), every day s continued success adds confidence to the predictions of the theory with respect to new phenomena. Every rigorous prediction of the theory is demanded to exhibit the same universality and infallibility as the underlying inductive laws themselves, further supporting our confidence in the generality and power of the theory. Few if any theories can now rival the confidence that scientists place in thermodynamics (frontispiece). 

What are the empirical inductive laws on which thermodynamics rests For future reference, Table 2.1 lists the six general statements IL-l-IL-6 of observational experience on which the present exposition will be based. Several of these require additional definitions or explanations before they can be properly understood. Each will be introduced explicitly in the text as its definitional basis is properly laid and its logical role in the formal construction of the theory becomes apparent. 

Examples or illustrations of each law will be provided as they are introduced. However, if one merely understands in equilibrium to mean at the same temperature, one can 

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HB Callen, Thermodynamics and an Introduction to Thermostatistics, 2nd edition, Wiley, New York, 1985. The classic text on the axiomatic approach to thermodynamics. The logic of thermodynamics is explained with great clarity. ... 

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