In science, the Spencerian dilemma refers to the conflict between the view of “social equilibrium” as a state of piece, and “thermodynamic equilibrium” as a state of total disintegration, according to the heat death view of the second law. [1]

Overview
The phrase “Spencerian dilemma”, common to sociology, dates back to at least the 1930s, and refers to the dilemma English philosopher-scientist Herbert Spencer faced in the use of the concept of equilibrium in his evolution theories when he was told by Irish physicist John Tyndall in circa 1858 that that equilibrium in thermodynamics, which contains the two all-pervasive laws of the universe, refers to system death, according to the second law, in the logic of heat death. [2] In short, whereas Spencer originally viewed ultimate equilibrium or “equilibration” to be a state or utopia of social bliss, he was told by Tyndall that ultimate equilibration is ultimate disorder, at which point he was "staggered", becoming ill in spirits over the next several days. Spencer supposedly he never found his way out of this dilemma; at least over the next forth years in his mind. [3]

Resolutions
In 1939, English political scientist George Catlin gave the following definition of the dilemma:


He goes on to state that French sociologist Émile Durkheim (1858-1917) provided a solution of the dilemma. [4] According to one 1970s view, what is refers to as the "Prigogine equation", i.e. Belgian thermodynamicist Ilya Prigogine's 1954 division of entropy into two parts:

that exchanged at the boundary deS and that inside the body diS, is said to have “sidestepped the Spencerian dilemma.” [3] Likewise, according to American sociologist Kenneth Bailey, "the Prigogine equation allows complete escape from the Spencerian dilemma". [6]

In general, the dilemma was supposedly resolved in circa 1950, in the minds of many sociologists, when Austrian biologist Ludwig Bertalanffy introduced the idea of “open systems” into sociology and biology via his general systems theory. [5]

See also
● Boltzmann brain problem

References
1. Bailey, Kenneth D. (1994). Sociology and the New Systems Theory (pg. 148). SUNY Press.
2. (a) Anon. (1984). Systems Research (pgs. 34, 39, 41). V. 1-2. Pergamon Press.
(b) Bailey, Kenneth D. (1990). Social Entropy Theory (section: “The Spencerian Dilemma”, pg. 55-59). State University of New York Press.
3. Anon. (c. 1970). Quality and Quantity (pgs. 122-23).
4. Catlin, George E.D. (1939). The Story of the Political Philosophers (pg. 749).
5. Ritzer, George. (2005). Encyclopedia of Social Theory: A-M (pgs. 312-13). Vol 1. Sage Publications.
6. ibid, Bailey (1990) (pgs. 71-72).