
First page of James Maxwell's poem "A Paradoxical Ode", his last and final poem on his views concerning thermodynamics, evolution, immortality, morality, soul, and consciousness reasoned down to the atomic level, sent to Peter Tait in jest of his 1875 conservation of energy theory of immortality, co-written with Balfour Stewart. [5]

First page of James Maxwell's poem "A Paradoxical Ode", his last and final poem on his views concerning thermodynamics, evolution, immortality, morality, soul, and consciousness reasoned down to the atomic level, sent to Peter Tait in jest of his 1875 conservation of energy theory of immortality, co-written with Balfour Stewart. [5]

In human thermodynamics, philosopher’s paradox is a mental syndrome, common to thermodynamic philosophers, particularly when discussing ingrained cherished concepts, such as life vs. death, consciousness, feelings, immortaility, soul, morality, etc., in the context of the physical sciences, where objective prophetic visions, theoretical implications, or hypotheses often tend to become skewed, scientifically empty, and generally biased on the premise that each supposition leads back to the subjective view and vested interests of the writer. [1]

Scottish physicist James Maxwell, in his 1878 Nature review of Balfour Stewart and Peter Tait’s religion-sided science-crouched books The Unseen Universe (1875) and followup sequel Paradoxical Philosophy (1878), gave the following depiction of the paradoxical philosopher: [2]

“Paradoxical philosophers [are those] eminent men of science, ‘driven,’ as they tell us, ‘by the exigencies of the subject,’ [who] having laid down all the instruments of their art, shaken the very chalk from their hands, and, locked up their laboratories, have betaken themselves to those blissful country seats where Philonous long ago convinced Hylas that there can be no heat in the fire and no matter in the world; and where in more recent times, Peacock and Mallock have brought together in larger groups the more picturesque of contemporary opinions.”

Paradoxes that arise in the paradoxical philosophy mindset, as discussed by Maxwell, include the "double mind", the "binding problem", the unbridgeable gap issue or “leveling up policy”, as Maxwell called it, the "continuity issue" (morality or immortality), among others.

Double mind
Maxwell goes on to comment how the scientists with philosopher’s paradox often tend to conclude with the conception of the “double mind” and cites the following passage of German physician-physiologist Emil de Bois-Reymond as an example:

“On the one side the acting, inventing, unconscious material mind, which puts the muscles into motion, and determines the world's history; this is nothing else but the mechanics of atoms, and is subject to the causal law, and on the other side the inactive, contemplative, remembering, fancying, conscious, immaterial mind, which feels pleasure and pain, love, and hate; this one lies outside of the mechanics of matter, and cares nothing for cause and effect.”

Maxwell then goes on to comment “we might ask professor Du Bois-Reymond which of these [two minds] it is that does right or wrong.” Maxwell also give the example of how the paradoxical philosopher may lead to the contradictory conclusion that “all matter is, in some occult sense, alive”, i.e. the panpsychism or panexperientialism, in modern parlance, such as posited by a doctor Hermann Stoffkraft, in one chapter of Paradoxical Philosophy.

Binding problem
In his discussion of the “leveling up” policy [extrapolate up vs. extrapolate down], a name which he gives to the view of Dr. Stoftrakft that all kinds of matter have their motions accompanied with certain simple sensations or that all matter is to some sense alive, Maxwell also brings up the recent 1877 lecture “The Limits of Natural Knowledge” by Swiss-born German botanist Carl von Nageli, wherein Maxwell summarizes as follows: [7]

“He can draw no line across the chain of being [unbridgeable gap], and say that sensation and consciousness do not extend below that line. He cannot doubt that every molecule possesses something related, though distantly, to sensation, ‘since each one feels the presence, the particular condition, the peculiar forces of the other, and, accordingly, has the inclination to move, and under circumstances really begins to move—becomes alive as it were; ... If therefore, the molecules feel something which is related to sensation, then this must be pleasure if they can respond to attraction and repulsion, i.e., follow their inclination or disinclination; it must be displeasure if they are forced to execute some opposite movement, and it must be neither pleasure nor displeasure if they remain at rest’.”

Maxwell goes on to speculate as to whether or not atoms can have pleasure, in terms of pure dynamics, and concludes with the remark “even if a man were built up of thinking atoms would the thoughts of the man have any relation to the thoughts of the atoms?” This is what is known as the “binding problem” in modern philosophical parlance, a 1890 expression of American psychologist William James who commented “how can many consciousnesses be at the same time one consciousness?” This is what is called, according to American philosopher Christian de Quincey, the main issue in any standard critique of any form of panpsychism. [8]

A Paradoxical Ode
In followup to his review, in 1878 Maxwell penned a satirical three-part poem entitled “A Paradoxical Ode”, addressed to Hermann Stoffkraft (the so-called materialistic hero of Paradoxical Philosophy), which he sent to Tait poking fun at their work, themed on the alluded to premise that his soul was an amphicheiral knot, a knot that can be deformed into its mirror image, in a scientific sense, which curiously was Maxwell’s last poem, as he died in midlife, at the age of 48 (in 1879) and knew he was dying as he wrote it.

Paradoxical philosophers | modern
In modern times, a recent example of a paradoxical philosopher is English physicist Philip Moriarty who argues and teaches that entropy can apply to arrangements of atoms and molecules in statistical systems, supposedly viewed in terms of the Max Planck 1900 black body-multiplicity of atomic states model of entropy, but that that "thermodynamic entropy", in his own words, cannot be applied to the arrangements of students in a field. His view was discussed and argued at length in the 2009 Moriarty-Thims debate.

Another example of the paradoxical philosopher, i.e. one who used contradictory phrases and statements in argument, is Czech black hole thermodynamicist, string theorist, and former MIT physics professor Lubos Motl, who when confronted with the view that thermodynamics governs human relationships, commented in hasty objection to the work of American chemical engineer Libb Thims, on 20 Nov 2010, that:

“It is blatant absurdity to model laws governing human relationships using rules of thermodynamics, a set of rules that only apply at the molecular level and human beings are NOT molecules.” (his capital use).

This statement, however, contradicts Motl's previously stated views on how thermodynamics applies to black holes. In 2003, for example, he stated: [6]

"Entropy defined statistically as the logarithm of the number of microstates always behaves in the same approximate thermodynamic way if the systems become large, and black holes are no exception."

This paradoxical contradiction of views is sort of akin to the "double blind placebo effect", being that: (a) theorizing objectively on something external to oneself, e.g. the thermodynamic behavior of bacteria or black holes, tends to have no observer bias, for the most part (unless say the theorizer is being funded by an entity with ulterior interests in mind, which tends to skew results and conclusions), but (b) theorizing objectively on oneself may very well often tend to lead to skewed thinking, e.g. Motl switching his choice of words to "rules of thermodynamics" (in arguing against thermodynamic human modeling), from his standard "laws of thermodynamics" in his journal articles on black hole thermodynamics. In other words, for black holes Motl becomes objective and not subject to observer bias, but when he thinks about how thermodynamics applies to himself, he becomes mentally confused and contradicts himself, to conclude that no thermodynamics cannot be scaled up as systems become large (such as in human societies).

References
1. Myers, Greg. (1985). “Nineteenth-Century Popularizations of Thermodynamics and the Rhetoric of Social Prophecy.” Victorian Studies, 29: 35-66.
2. Maxwell, James. (1878). “Review: Paradoxical Philosophy”, in: Scientific Papers, II, pg. 451; in Nature, 19 (19 Dec 1878): 141-43; in: Scientific Papers, 2, 756-62.
3. Stewart, Belfour and Tait, Peter G. (1878). Paradoxical Philosophy: a Sequel to the Unseen Universe. Macmillan.
4. (a) Maxwell, James. (1878). “A Paradoxical Ode / After Shelley”, in: Life of Maxwell, pgs. 649-51; in: Knott, Life of Tait, pgs. 242-43.
(b) Knott, Cargill G. (1911). Life and Scientific Work of Peter Guthrie Tait (pg. 241-42). Cambridge University Press.
5. (a) Silver, Daniel S. (2007). “My Soul’s an Amphicheircal Knot: the Last Poem of James Clerk Maxwell”, SouthAlabama.edu.
(b) Brown, Adam. (2006). “Maxwell’s Paradoxical Ode”, research paper, University of South Alabama, Fall Term.
(c) Original copy of "Paradoxical Ode" contained in Tait's scrapbook donated to the James Maxwell Foundation in Edinburgh.
6. Motl, Lubos. (2003). “Black hole thermodynamics question”, NatScience.com Forum.
7. Von Nageli, Carl. (1877). “The Limits of Natural Knowledge”, Nature, 16: 531-35, Oct 18.
8. (a) De Quincey, Christian. (2002). Radical Nature: Rediscovering the Soul of Matter (section: Binding Problem, pgs. 230-37). Invisible Cities Press.
(b) James, William. (1890). Principles of Psychology (ch. 6: Mind Stuff Theory). Publisher.
(c) Binding problem – Wikipedia.

Further reading
● Harman, P.M. (2001). The Natural Philosophy of James Clerk Maxwell (pg. 192). Cambridge University Press.
● Porter, Theodore M. (2005). Karl Pearson: the Scientific Life in a Statistical Age (pgs. 38-39). Princeton University Press.