On the Structure of Pleasure - A Tale of Measurement Theory and Classical Mythology


Tiresias, mythical mathematical psychologist

Tiresias is a legendary blind prophet in Greek myth. His story has many versions. In this tract, I'll draw primarily from the account of ancient mythographer Pseudo-Apollodorus.

As the narrative goes, while traveling in Mount Cyllene, Tiresias beheld a pair copulating snakes and struck the female with his walking stick. For this display of animal cruelty, he was cursed to live as a woman. With the body and mind of a woman, Tiresias experienced sex; according to versions of the legend, he did so quite intensely, becoming a prostitute of great renown.

Seven years had passed after this incident and female Tiresias had the opportunity to re-encounter an event similar to the one that caused his transformation. This time, he left the reptiles undisturbed and in that, he was allowed to regain his former manhood.

Having lived as both a man and a woman, Tiresias was privileged with a unique perspective on the varieties of sexual experience across the sexes. For that, he was consulted by the Olympians themselves. Zeus and Hera willed to settle once and for all the question of who enjoys greater pleasure in carnal love - man or woman. Tiresias provided an outstanding answer for the Gods:

Of ten parts [of sexual pleasure] a man enjoys one only; but a woman enjoys the full ten parts in her heart.

This passage is remarkable in theoretical depth. The divine couple requested from the mortal soothsayer an ordinal evaluation and received more than what they had bargained. In his statement, Tiresias is claiming that events of (sexual) pleasure not only can be ranked, but that they have magnitudes whose proportions can be meaningfully compared and expressed.

In measurement-theoretic terms, this is the claim that pleasure is a ratio-scalable property or attribute. This is what one usually has in mind when someone says that something is 'quantitative'.

It's a bold ontological claim. The story of Tiresias however is also daring epistemologically; it stipulates that information about the value of the magnitude of pleasure instantiated in a given psychological state is obtainable through introspection with a certain precision. It is also supposedly reliably registrable in long-term memory; the mind is used as a truthful scale of itself.

From ancient myth to modern science

It took over two millenia for the ideal of Tiresias to come into fruition. The earliest robust attempts happened in the German tradition of psychophysics, by physicists Gustav Fechner and Hermann von Helmholtz. Somewhat unexpectedly, this tradition arguably culminated with mathematician Otto Hölder [1].

The quest of psychophysics has been to establish an interface between subjective mind and objective world by uncovering functional relations between 3rd-person fact and 1st-person unknown. For example, the investigation of how psychological brightness co-varies with physical luminance. For these tasks, psychophysicists have developed several methods for subjective magnitude estimation of sensations from given controlled stimuli as input to verbal and motor reports as output.

Measurement theorist Louis Narens has defended that formally, these forms of measurement can have a foundation as strong as other prototypical practices of experimental science [2].

A lot of progress has been made on the investigation of the structure of sensations. Affective states such as pleasure and pain, however, still remain very murky.

Is pleasure quantifiable?

On closer inspection, Tiresias' proposition that pleasure is quantitative does not seem to be particularly bold after all. It has received widespread uncritical support for quite some time - from the dawn of utilitarianism in modern moral philosophy to the use of visual analog scales for pain assessments in contemporary clinical medicine and cardinal utility in economics. They have become ingrained in our common sense. Queries like "from a scale to 0 to 10, how do you feel?" have become staples of modern managerial society.

But is it true? Unfortunately for Tiresias, the hypothesis that pleasure and other similar affective states such as pain have a quantitative structure has not been empirically established with satisfaction. Not even the other rather intuitive hypothesis that pleasure and pain have a structure that allows representation as opposite intervals of a same axis.

To stipulate that a given feature has a quantitative structure is not a matter of pragmatic choice but of experimental fact. This claim has been vigorously defended by measurement theorist Joel Michell [3]. Michell condemns gratuitous cursory admissions that a given psychological feature is quantitative without previous evidential justification. Conceptual residue from operationalist philosophy in experimental psychology is at fault.

The fact of the matter is that the stakes for an empirical feature to be ratio-scalable are very high. This will be exposed in greater detail in another entry.

[1] J. Michell and C. Ernst, "The axioms of quantity and the theory of measurement," Journal of mathematical psychology, vol. 41, iss. 4, pp. 345-356, 1997.
author = {Michell, Joel and Ernst, Catherine},
citeulike-article-id = {13559112},
journal = {Journal of mathematical psychology},
number = {4},
pages = {345--356},
posted-at = {2015-03-23 22:50:07},
priority = {2},
publisher = {Elsevier},
title = {The axioms of quantity and the theory of measurement},
volume = {41},
year = {1997}
[2] L. Narens, "The irony of measurement by subjective estimations," Journal of mathematical psychology, vol. 46, iss. 6, pp. 769-788, 2002.
author = {Narens, Louis},
citeulike-article-id = {13559113},
journal = {Journal of Mathematical Psychology},
number = {6},
pages = {769--788},
posted-at = {2015-03-23 22:50:07},
priority = {2},
publisher = {Elsevier},
title = {The irony of measurement by subjective estimations},
volume = {46},
year = {2002}
[3] J. Michell, "Quantitative science and the definition of measurement in psychology," British journal of psychology, vol. 88, pp. 355-383, 1997.
author = {Michell, Joel},
citeulike-article-id = {13531650},
journal = {British Journal of Psychology},
pages = {355--383},
posted-at = {2015-03-02 22:50:46},
priority = {2},
title = {Quantitative science and the definition of measurement in psychology},
volume = {88},
year = {1997}

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