 Consider first the relatively simple case of gas temperature, which has often been supposed reducible to the average kinetic energy of the gas’s molecules (cf. Nagel 1961, p. 343). A particular average kinetic energy of the molecules is only a necessary condition for having a given temperature, however. Only gases at equilibrium have a definite temperature, when all the spatial parts have the same temperature as the whole (reflecting the fact that temperature is an intensive property). A sufficient condition would need to complement the average kinetic energy with a microscopic correlate of the macroscopic condition of being at thermodynamic equilibrium. Statistical mechanics specifies the relevant correlative condition as that of the energy being distributed over the gas molecules in accordance with the Boltzmann distribution. But the Boltzmann distribution is expressed as a function of the temperature, and its derivation from Boltzmann’s microscopic construal of entropy appeals to the thermodynamic law connecting entropy with temperature. Accordingly, the necessary and sufficient microscopic condition for gas temperature becomes circular when construed as a reduction of the concept of temperature (Needham 2009b; Bishop 2010)