a. [ad. med.L. commūtātīv-us (F. (14th c.) commutatif, -ive), f. L. commūtāt- ppl. stem of commūtāre to COMMUTE: see -IVE.]
† 1. Pertaining to exchange or mutual dealings.
1612. T. Taylor, Comm. Titus i. 8. Obseruing equality both in contracts and exchanges, which we call commutative.
1631. Bp. Webbe, Quietn. (1657), 177. Actions commutative consist in mutual traffick and dealings betwixt man and man.
b. Commutative justice; = L. commutativa justitia, a term used by Aquinas and others as equivalent to Aristotle’s τὸ ἐν τοῖς συναλλάγμασι διορθωτικὸν δίκαιον, i.e., ‘the justice which is corrective in transactions between man and man.’ [From commutatio, which in the old Latin version of Aristotle’s Ethics (c. 1250) is put to represent the Gr. συνάλλαγμα.]
1531. Elyot, Gov., III. i. Justice … is described in two kyndes or spices. The one is named iustyce distributiue … the other is called commutatiue or by exchaunge, and of Aristotell it is named in Greeke Diorthotice, whiche is in englysshe correctiue.
1557. Recorde, Whetst., B j b. In Lawe twoe kyndes of Iustice are the somme of the studie: Iustice Distributive, and Iustice Commutative.
1605. Bacon, Adv. Learn., II. v. § 3. Is there not a true coincidence betweene Commutatiue and distributiue Iustice, and arithmeticall and geometricall proportion?
1629. Symmer, Spir. Posie, II. v. 38. Commutative Iustice is that Common Equity, which should be practised in our civill Commerce.
1651. Hobbes, Leviath., I. xv. 75. Commutative Justice, is the Justice of a Contractor; that is, a Performance of Covenant.
a. 1652. J. Smith, Sel. Disc., VII. vi. (1821), 369. We must not think to deal with God in the method of commutative justice, and to challenge eternal life as the just reward of our great merits.
1758. Ld. Mansfield, in Burrows’ Rep., I. 492. Upon the foot of commutative justice merely, there is no colour why the insurers should not pay the insured the whole, for they have received a premium for the whole risk.
1890. J. Martineau, Seat Authority Relig., II. i. 159. A rule which made all banking business a breach of ‘commutative justice.’
2. Relating to or involving substitution or interchange; as the commutative principle in arithmetic and algebra, i.e., the principle by which the order of terms or factors may be altered.
1858. B. Price, Infin. Calc. (ed. 2), I. xix. 601. If the two operations indicated by φ and ψ are performed successively on u one on the back of the other, let us assume the result to be the same whatever is the order in which they are performed: two such symbols of operation are said to be commutative, and to satisfy the law of commutation.
1875. T. Hill, True Order Studies, 42. The commutative principle of arithmetic may be shown by dividing six into three twos, or two threes, still using beans.
3. spec. Relating to or involving the commutation of a payment or penalty.
1836. J. Gilbert, Chr. Atonem., ii. (1852), 32. Exceptions … founded on a commutative arrangement.
1855. Milman, Lat. Chr. (1864), II. III. v. 46. Where every injury or crime had its commutative fine.
1871. T. J. Crawford, Atonem., ii. (1883), 21. Ἀντίλυτρον … conveys more strongly the commutative sense than the simple word λύτρον.
