Hu's On First - The Algebra of Pleasure

Epicurus famously includes a statement n his letter to Menoeceus that is translated as “by pleasure we mean the absence of pain.” The purpose of this article is to evaluate that statement in light of three passages relating to pleasure in the form of an exchange between Cicero and Torquatus in “On Ends” - the challenge of Chrysippus' Hand,1) the sarcastic comparison of the pleasure of the Pouring Host to that of the Drinking Guest,2) and the sweeping assertion by Torquatus that all men who are not in pain are at the height of pleasure.3)

Before I suggest a way these questions might be resolved, I suggest a review of a discussion between two other contentious friends - Abbott and Costello:


My suggestion is that the dispute between Abbott and Costello provides a path to understanding the dispute between Cicero and Torquatus, and that we should think of Torquatus's application of Epicurean terminology as a paradigm4) which cannot be understood without recognizing that Epicurus (and all true Epicureans) are speaking according to a formula which anchors their view of every experience in life.

In short, the Epicurean paradigm is anchored by Epicurus' decision to regard every non-painful experience in life as pleasurable. The reasons for this choice of terminology are important but will be reserved for the closing part of this essay.

An Algebraic Paradigm

Expressing the issue in formulaic - or algebraic - terms, rather than in terms of isolated particular pleasures and pains, allows us to more easily see how the best life under any circumstances can be defined as that of greatest pleasure and least pain. “Algebraic” seems like an appropriate label because Wikipedia5) states that Algebra derives from Arabic ‏الجبر‎ al-jabr “reunion of broken parts, as in “bonesetting,” which involves balancing by moving terms from one side of an equation to another. The result of considering all experiences which are not painful to be pleasurable is to rejoin all aspects and experiences of pleasure and pain into a coherent whole by rebalancing the way we understand their relation to each other.

Viewed as a paradigm,6) and without regard to the particular pleasures or pains being experienced by the particular person at the particular moment, we start with the proposition that at every instant the total of individual mental and physical pleasures we are experiencing at any moment amounts to a sum in which the quantity of pleasure is the inverse of the amount of pain. Under this paradigm, once the full sum of the human experience is filled with pleasure, the total of those individual pleasures by definition cannot be increased. This state of fullness constitutes the meaning of the “limit of pleasure,” and rather than constituting a new type of pleasure in itself, serves as a paradigm to insulate the Epicurean view from the attack that the experience of pleaure can forever be improved, and thus suffers from incompleteness.

This is not to say that the algebraic perspective is sufficient in itself. Practical observation of life experiences through the senses and other canonical faculties is the ultimate test of truth in Epicurean philosophy. In fact it is only because we experience these observations as true in practice that the algebraic perspective can be considered to be valid. But what the algebraic perspective provides, which no individual comparison of particular pleasures and particular pains can provide, is the confident expectation that no new experience of pleasure or pain wil be outside this perspective. For those who are willing to embrace and think in these terms, no anxiety arises from an otherwise infinite chain of questions such as “what about the pleasure of X or the pain of Y?”

So long as the paradigm is understood and affirmed, no hypothetical experience of pleasure or pain can undermine one's confidence that so long as one chooses to continue to live, one can find pleasure. The confidence that this algebraic approach is true without exception overrides any concern that some new experience may invalidate it. While this insight cannot change the fact that human life is finite and must at some point come to an end, this perspective embraces the finite aspect of human life and allows a reasonable comparison of a human life full of pleasure to the life of an Epicurean god full of pleasure, with the difference of duration and success in eliminating every pain as a matter of difference only of degree rather than of kind.

In algebra we use symbolic formulas such as: “A+B=C,” and we combine them into propositions such as:

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If “A + B = C” then “C - B = A”

We accept the result that subtracting B from C equals A with confident certainty because of our definitions as to what A, B, and C represent. We are explicitly defining all things of a certain type to be represented by “A,” all things of another type to be represented by “B,” and the all things of the two types combined as represented by “C.”

Epicurean Sources

In Epicurean philosophy we equate all good with pleasure and all bad with pain:

  • Letter to Menoeceus [129] - “And for this cause we call pleasure the beginning and end of the blessed life. For we recognize pleasure as the first good innate in us, and from pleasure we begin every act of choice and avoidance, and to pleasure we return again, using the feeling as the standard by which we judge every good.”
  • Torquatus: “ The problem before us then is, what is the climax and standard of things good, and this in the opinion of all philosophers must needs be such that we are bound to test all things by it, but the standard itself by nothing. Epicurus places this standard in pleasure, which he lays down to be the supreme good, while pain is the supreme evil; and he founds his proof of this on the following considerations.”
  • Diogenes Laertius: “The internal sensations they say are two, pleasure and pain, which occur to every living creature, and the one is akin to nature and the other alien: by means of these two choice and avoidance are determined. Of investigations some concern actual things, others mere words.”

Given these positions we can determine the best life, in which all good is judged by pleasure, and all bad is judged by pain, we need only substitute pleasure, pain, and the full life as the symbolic definition to be used in the symbolic algebraic notation:

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  • A = All Pleasures of Life, Mental and Bodily
  • B = All Pains of Life, Mental and Bodily
  • C = All the experiences (perceptions) of Life


If for these three sets of A, B, and C we presume that A+B=C, then what we are saying, which Epicurus does say (as seen in Diogenes Laertius and PD03), that all experiences of life (“C”) are either pleasurable (“A”) or painful “B”). Symbol “B” includes all experiences which painful or “bad” or “evil” in any way. More controversially, symbol “A” includes not only food, wine, and music, but also any healthy and pain free action of the body or mind no matter how calmly or euphorically experienced. And even more controversially and unacceptably to the Platonists, Stoics, and Religionists, “A” includes experience of wisdom, worth, meaningfulness, virtue, nobility, or whatever other glorious word they might assert to be outside and above the scope of pleasure. Epicurus is saying that every experience of life (symbol “C”) is either pleasurable or painful, and as a result there are no experiences in life which fall outside of A and B.

Again, in order to see this formula as valid we must hold that there are no non-A or non-B experiences in life. This is why all assertions of “neutral” or “mixed” states must be excluded from consideration. This is also why any non-painful experience must be categorized as pleasurable, and as we see Epicurus state in PD03, “Wherever pleasure is present, as long as it is there, there is neither pain of body, nor of mind, nor of both at once.”

The "On Ends" Hypotheticals

Once we so identify that pleasure and pain are mutually exclusive, and that there are no experiences other than pleasure and pain, the application of the formula provides a clear explanation for the hypotheticals given in On Ends:

Chryssippus' Hand

First, Chrysippus is wrong in saying his hand feels a lack of pleasure, because it is understood in the hypothetical that his hand is not experiencing any pain. Once it is understood that his hand is “feeling no pain,” Torquatus is seen to be right in his refutation of Chrysippus, because it is then understood algrebraicly that the the hand is in the greatest state of pleasure possible to it, where C (all the experiences felt by the hand) are pure A (pleasure), because B (pain) is understood to be non-existent.

The Pouring Host and the Drinking Guest

Second, Cicero is wrong in sarcastically implying that the guest who is drinking is in a more pleasurable state that the host who is pouring because it has not been asserted in the hypothetical that the host is himself feeling any pain. Torquatus is right in rejecting Cicero's sarcasm as quibbling because Torquatus has previously made very clear in his explanation of Epicurus' philosophy (and Torquatus knows that Cicero knows this himself) that Epicurus has established A(pleasure) + B (pain) = C (all the experiences of life) by affirming that there is no non-A or non-B experience. Cicero is quibbling by refusing to accept that the assertion that all mental and physical non-painful functioning is pleasurable. Rather than simply saying “I don't agree that all non-painful functioning should be considered pleasurable” Cicero chooses to ignore the Algebraic approach of considering all pleasures to be referenced as “A” and all pains to be referenced as “B” and the entire human life to be referenced as “C.” Cicero approahes the issue by asking stubbornly and obnoxiously, time after time, “But what about this experience?” or “What about that experience?” because he refuses to accept the definitional viewpoint that all individual pleasures can be considered to be included in the word “Pleasure.”

Torquatus' Flat Assertion That All Who Are Not In Pain Are In The Greatest Pleasure

And third, in the example that is most clear because it is most starkly simple, Torquatus is correct in Book 2 (V)16 in the way he responds when Cicero asks: “Who can fail to see that there are in the nature of things these three states: one when we are in pleasure, another when we are in pain, the the third, the state in which I am now, and I suppose you too, when we are neither in pain nor in pleasure? … Do you not see that between these extremes lies a great crowd of men who feel neither delight nor sorrow?”

Torquatus need know nothing about the particulars of the experiences of the “great crowd of men,” in which Cicero includes himself and Torquatus at the moment othet than that they are not in pain. Torquatus knows that it is impossible to experience anything other than pleasure or pain, and so it is of no relevance that Cicero seeks to prejudice the jury by listing “delight” or “sorrow” as the only two possible experiences. All Torquatus need do is reference the general formula of C-B=A, which applies at all times to allow us to conclude that life without pain equals pleasure. It is on the basis of the general formula - the established relationships between A, B, and C - that Torquatus can say: “Not at all, and I affirm that all who are without pain are in pleasure, and in that the fullest possible.”

The abstract nature of an algebraic paradigm lets us see this point with all distractions removed. Embracing what we see through the formula allows us to be certain of the result. An Epicurean can state these issues with the confidence that Cicero alleges to be characteristic of the school. The disparagement that such statements sound as though delivered straight from the halls of the Intermundia is of no effect. This is because Epicurus is not relying on the authority of gods, but rather he holds firmly to the view that all experiences in life are either pleasurable or painful, and that there are no neutral or non-pleasurable / non-painful experiences. And it is important to note here that neither the length of time the exprience is felt, nor the particular activity of mind or body that generated the experience, is of any relevance to the result. All pleasurable experiences of life, no matter their duration or source or part of body or mind that is effected, are included within A=Pleasure. All painful experiences of life, no matter what their duration or source or part of the body or mind that is effected, are included within B=Pain. Together these two make up “C”- the total sum of the individual human's experience in life.

Living As Gods Among Men

In this context I suggest combining two observations by DeWitt:

First: “The fact that the name of pleasure was not customarily applied to the normal or static state did not alter the fact that the name ought to be applied to it; nor that reason justified the application; nor that human beings would be the happier for so reasoning and believing.”

Second: “The gods win eternal life by maintaining their own pleasures perpetually. This conceit appealed to Menander, who exploited it in his Eunuchus. It survives through transfer to the Andria of Terence, where the happy lover is made to exclaim: “I think the life of the gods to be everlasting for the reason that their pleasures are perpetual, because immortality is assured to me if no grief shall intervene to mar this joy.” This is labeled as “Epicurean dogma” by the Donatus commentary.”

It seems to me that a grasp of Epicurus' view that the normal state of life is pleasure serves as a critically important tool for emulating “the gods” which allows us to “live as gods among men.” The most desirable state for both gods and men is that of continuous /sustained pleasure.7) This attitude would explain why Torquatus so tenaciously holds to the formulaic / algebraic approach in the face of challenge after challenge from Cicero. This perspective is far too important to become muddied by implication that “absence of pain” constitutes a higher type of pleasure that is different in kind from any other type of pleasure that we ordinarily recognize through perception of the senses to be pleasurable. Understanding the nature and use of this formula allows us to have confidence that it is Pleasure, rather than supernatural gods or the idealistic Platonists or Humanists, that determines what is the best life.

On Ends Book One, XI, And even at Athens, as I have heard my father say, when he was jesting in a good-humoured and facetious way upon the Stoics, there is a statue in the Ceramicus of Chrysippus, sitting down with his hand stretched out; and this attitude [pg 112] of the hand intimates that he is amusing himself with this brief question, “Does your hand, while in that condition in which it is at present, want anything?”—Nothing at all. But if pleasure were a good, would it want it? I suppose so. Pleasure, then, is not a good. And my father used to say that even a statue would not say this if it could speak. For the conclusion was drawn as against the Stoics with sufficient acuteness, but it did not concern Epicurus. For if that were the only pleasure which tickled the senses, as it were, if I may say so, and which overflowed and penetrated them with a certain agreeable feeling, then even a hand could not be content with freedom from pain without some pleasing motion of pleasure. But if the highest pleasure is, as Epicurus asserts, to be free from pain, then, O Chrysippus, the first admission was correctly made to you, that the hand, when it was in that condition, was in want of nothing; but the second admission was not equally correct, that if pleasure were a good it would wish for it. For it would not wish for it for this reason, inasmuch as whatever is free from pain is in pleasure.
On Ends Book Two, V - “Do you, then, say that the man who, not being thirsty himself, mingles some wine for another, and the thirsty man who drinks it when mixed, are both enjoying the same pleasure?”
On Ends Book Two, V - “What! do you not see a vast multitude of men who are neither rejoicing nor suffering, but in an intermediate state between these two conditions? No, indeed, said he; I say that all men who are free from pain are in pleasure, and in the greatest pleasure too. ”
4) In this case the third definition is intended: “a philosophical and theoretical framework of a scientific school or discipline within which theories, laws, and generalizations and the experiments performed in support of them are formulated.”
5) - _FCKG_BLANK_TD_ The word algebra comes from the Arabic romanized al-jabr lit.   'reunion of broken parts, [1] _FCKG_BLANK_TD_ bonesetting [2] ' from the title of the early 9th century book ʿIlm al-jabr wa l-muqābala “The Science of Restoring and Balancing” by the Persian mathematician and astronomer al-Khwarizmi . In his work, the term al-jabr referred to the operation of moving a term from one side of an equation to the other, المقابلة al-muqābala “balancing” referred to adding equal terms to both sides.
Other paradigmatic approaches in Epicurean philosophy would probably involve (1) the nature of the gods as having no characteristics incompatible with blessedness and incorruptibility, (2) the size of the sun as being what it appears to be, (3) the nature of virtue as being actions which promote happiness rather than rather than absolute and unchanging.
U116 Plutarch, Against Colotes, 17, p. 1117A: Such is … the man who, in in the letter to Anaxarchus can pen such words as these: “But I, for my part, summon you to sustained pleasures and not to empty virtues, which fill us with vain expectations that destroy peace of mind.”