RECIPROCITY
1. Reciprocal (Symmetric) Verbs
Consider a statement linking two noun phrases: N 1 — Verb — N2.
By permuting the actants, we get the statement: N 2 — Verb —N1.
— In general, these statements have different meanings:
Big fish eat small fish: A eats B.
Small fish eat big fish: B eats A.
— In some cases, the two statements have the same meaning. The verbs that allow the permutation of the complements are called symmetrical (or reciprocal)
The weight of the apples is equal to that of the cherries
is equivalent to:
The weight of the cherries is equal to that of the apples.
<being equal to>, <being the friend of>, <being the brother or sister of>, <meeting> are reciprocal.
Peter is Paul’s friend = Paul is Peter’s friend = Peter and Paul are friends. Peter and Paul are equal for the friendship relationship.
If a has met b, then b has a, in other words, a and b have met. The following argument would make sense in a detective novel; it can only be rejected by accusing Peter of lying:
If Peter confessed to meeting Paul at the bar,then, we must assume that Paul met Peter. Paul cannot deny the obvious.
The distance from one point to another point is a symmetrical relationship, but the time it takes to travel that distance is not necessarily so.
Logical and Linguistic Aspects of Reciprocity
In mathematics, the relation of reciprocity is strict: if a function F is reciprocal, then F(ab) is strictly equivalent to F(ba). This is not the case in ordinary language:
Peter has met Paul:
The situation develops from Peter’s point of view.
In other words, we follow Peter and meet Paul.
Paul met Peter:
The situation develops from Paul’s point of view.
We follow Paul and meet Peter.
The difference between a mathematical function < F(a, b)> and an ordinary verb <to be friend with> is that ordinary language presents events from a particular perspective. This is a trace of subjectivity in language.
The relation of reciprocity (symmetry) is considered as “quasi-logical” by Perelman & Olbrechts-Tyteca. Quine would probably say that there is a a stylistic difference (see connectives) between the logical construction and the grammatical construction. Both lead to their elimination.
1. Principle of Reciprocity
In some human groups, reciprocity is a moral and social imperative. Reciprocity is a kind of egalitarian principle, defined on the basis of the set of actions that bind two persons.
The strict principle of reciprocity says that that if A does something positive to/for B, then B must reciprocate to A, by doing the same thing to/for A.
This is the principle of returning favors. The individuals A and B are equal in this relationship.
If A has given B a gift, such as an invitation to dinner, then B concludes that he must do the same, i.e. give A some gift or invitation.
The principle of reciprocity acts as a constraint: « If you invite me to dinner, I must invite you to dinner.
If A has given B a decisive advantage, then B must do something equivalent for A when the situation arises: “a favor is never lost.
As a form of natural morality, the imperative of reciprocity is a correlative of the principle:
Do to others as you would have them do to you. (Gospel of Luke, 6:31)
Do not do to others what you do not want done to you.
In the latter form, “do not do to others what you do not want them to do to you,” this second principle opposes to the talion principle, « an eye for an eye ». This is a special case of the “you too!” argument.
The principle of reciprocity is a resource that can be used to regulate social interactions, for example in arguments such as « I am polite to you, so be polite to me.
The speaker defines himself and his partner as members of the same category, who must be treated in the same way, see rule of Justice.
The principle of reciprocity can only be strictly applied only to acts for which A and B can be treated as equals. It makes no sense if there is a fundamental inequality between A and B: if A gives B alms, or if A fines B, there is no question of B mechanically applying the strict reciprocity. But in a romance novel, B may save A‘s life, and in a detective novel B may take revenge on the person who condemned him.
In modern times, we might consider nuclear deterrence, based on the certainty of mutual destruction, as a concrete application of this principle.
Reciprocity as a legal principle allows different states to assert their equal international dignity, and possibly to justify a retaliation:
if country A requires a visa for the nationals of country B, it is right for country B to require a visa for nationals of country A as well.
Reciprocity can be used for retaliation and revenge: « An eye for an eye, a tooth for a tooth. If A has wronged B in some way, then B can legitimately do the same wrong to A.
If your jilted lover has disfigured you with vitriol, the court grants you the right to treat him in the same way.