Opposites Do Not Mingle

venn diagram of p, not p, and q

Epistle 17. Posted on 2019-04-22. Edited on 2019-04-25.

How good are you at identifying a contrariety? Did you know that the vast majority of your mistakes are due to this failure? In logic, contrariety — or contrariness — refers to contrary propositions. Contradiction and contrariety are often confused and used interchangeably, but this distinction is useful in everyday life.

Contradiction and contrariety are defined here as follows:

Contradiction: Given two contradictory propositions (two contradictories), it is conceptually impossible that both are true, conceptually impossible that both are false, and it is conceptually necessary that one is true when the other is false, or that one is false when the other is true.

Contrariety: Given two contrary propositions (two contraries), it is conceptually impossible that both are true, conceptually possible that both are false, and it is conceptually necessary that one is false when the other is true.

The difference is that both of two contradictories cannot be false, but two contraries may be false.

The distinction between contradiction and contrariety is usually introduced in Aristotelian logic via the square of opposition. The usual example is that “All p are q” and “Some p are not q” are contradictories, because both propositions cannot be false. In contrast, “All p are q” and “No p are q” are contraries, because although it is conceptually impossible for both to be true, both can be false, such as in the case that “Some p are q.”

Aristotelian logic is certainly impressive, but I prefer its ancient replacement: Stoic logic. Here’s an example from Seneca (c. 4 BC – AD 65):

“Respect means love, and love and fear cannot be mingled.”

In this example, the predicates — love and fear — cannot be mingled (combined, mixed), implying that the following proposition is false:

Both x loves y and x fears y.

Contrariety, rather than contradiction, is the relation between love and fear, because it is conceptually possible that

Both Not x loves y and Not x fears y.

Or, colloquially, “x neither loves nor fears y.” One may love and not fear something, fear and not love it, or neither love nor fear it, but one cannot both love and fear it. Machiavelli (1469 – 1527) thought it more advantageous for a prince to be feared than loved. If love and fear were contradictory predicates in this sense, it would be conceptually impossible to neither love nor fear something. As a counterexample, this article neither loves nor fears its reader.

Near the end of his life, Seneca wrote an essay that has become known as “On Providence” (De Providentia in Latin). In the beginning of its second chapter, he wrote non miscentur contraria. In 1900, Aubrey Stewart translated it as “contraries cannot combine.” In 1928, John W. Basore translated this as “opposites do not mingle” for the Loeb Classical Library. More recently, James Ker translated it in “Seneca: Hardship and Happiness” (2014, p. 313) as “Opposites do not mix.”

From what I gather about Latin, miscentur is derived from misceo, meaning to mix or confuse, and contraria is derived from contrarius, meaning opposites or contraries. At this point, each translation seems as good as the other.

But I interpret Stoicism as a logical philosophy. And Seneca was a Roman Stoic, of sorts. I propose that Seneca meant logical contraries, quite literally, and that Aubrey Stewart happened to have the better translation with respect to contraria.

If Seneca is interpreted literally and logically, he declared in “On Providence” that it is conceptually impossible that misfortune happens to a fortunate person, because his friend cannot be predicated as both fortunate and unfortunate. Since neither contradictory nor contrary predicates mix or mingle within a subject, such predicates also cannot occur together in degrees. Experiencing a misfortune cannot make his friend less fortunate, when the question is whether or not he is fortunate; either he is or he is not. In this way, evil cannot befall a good man, and a good man knows that there is no experience of evil. Seneca further explores this perspective, which is based on the companions of contradiction and contrariety.

Contrariety is used most frequently in Stoicism to distinguish between being in accord with nature and being contrary to nature. When your ethical proposition is a desire for the contradictory of your natural proposition of the same subject, you have a disposition that is contrary to nature. For example, greedy Gretchen desires to have a spouse, but does not have one. In this case, her desire contradicts the state of nature, because while nature is “p,” she desires it to be “Not p.” However, her desire is contrary to nature while nature is “p” and she desires it to be “q,” where “q” is merely one of many imaginable versions of “Not p.” Rather than desiring for the contradictory of nature, which would be to have any husband, greedy Gretchen desires to have a certain category of a husband. In this case, greedy Gretchen has a desire that is contrary to nature.

Let us consider greedy Gretchen in the context of wealth, such that greedy Gretchen regards herself to be povertous and desires instead to be wealthy. There become at least three categories of wealth: being in poverty, being wealthy, and neither being in poverty nor being wealthy. Not being in poverty is the contradictory of being in poverty, and being wealthy is one of at least two such contraries of being in poverty.

In summary, a desire that is not in accord with nature is usually a desire that is contrary to nature, rather than contradictory to nature — the desire for nature to be any way other than it is. Each desire that is contrary to nature is a desire for a particular alternative to nature — put otherwise, a particular figment of imagination, a particular fantasy. Every desire that is either contradictory or contrary to nature is a desire in error, and every desire that is contrary to nature also involves a contradiction.

In the beginning, I promised that learning the distinction between contradiction and contrariety is useful in everyday life, and now it is appropriate to explain. As you endeavor to live according to nature, you seek to avoid contradiction, to live consistently. To avoid a contradiction, it will be most expedient for you to be able to identify it. However, be forewarned, many if not most contradictions occur in thought as contrarieties, and the associated contradictions are semantic and require investigation before becoming evident. If someone proposes that

“John is a married bachelor,”

the contradiction is inevident because it is a conflict between part of the definition of a bachelor — a bachelor is an unmarried male — and one of the evident parts of the proposition, that John is married. By substitution, the proposition is

“John is married & John is unmarried & John is male.”

Nobody would agree with the expanded proposition because the contradiction is evident between being both married and unmarried. However, that contradiction is inevident in the original proposition, which proposes two contraries: a married person and a bachelor. One cannot be both married and a bachelor, although one can be married and not a bachelor, or unmarried and a bachelor, or unmarried and not a bachelor.

If each contradiction in one’s thoughts were evident, one would err less. But it is precisely because most contradictions are due to contraries that these contradictions are semantic only, that they are inevident. In this case, your skill in identifying a contradiction depends on your skill in identifying a contrariety. Otherwise, you may err by regarding both of two contraries as true, thereby assenting to its inevident contradiction. The lesson is to ponder contrariety with piety. I hope that you do not ignore this skill while seeking the good life, else you will think you are pursuing your advantage but will in reality often be pursuing your disadvantage by accident, by mistake.

To return to non miscentur contraria, miscentur is probably translated better as “mixing” rather than “mingling,” due to the doctrine of mixing in Stoic physics, leaving us instead with “Contraries do not mix.” Nonetheless, I still enjoy Basore’s translation. Hopefully, now, it is better understood what Seneca meant when he asserted that “opposites do not mingle,” due to a better understanding of contrariety.

Vale (pronounced WAH-lay is Latin for “Farewell”),

Ron Hall

Ron Hall

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