subcontraryadj.n.

Brit.

/ˌsʌbˈkɒntrəri/, U.S.

/ˌsəbˈkɑnˌtrɛri/

Origin: A borrowing from Latin. Etymon: Latin subcontrarius.

Etymology: < post-classical Latin subcontrarius (in logic) incapable of being false at the same time as its pair (6th cent.), somewhat adverse (15th cent. in a British source), (in geometry), designating a section of an oblique cone (1566 or earlier) < classical Latin sub- sub- prefix + contrārius contrary adj., after ancient Greek ὑπεναντίος opposite, contrary, (in mathematics), designating a mean, in Hellenistic Greek also (in mathematics) designating a section (Apollonius of Perga) and in Byzantine Greek, designating logical propositions. Compare Middle French subcontraire (14th cent., rare), French sous-contraire (17th cent. or earlier).

A. adj.

†1. Somewhat contrary or opposing; (also) partially opposed to something. Obsolete.

ΘΚΠ

the world > relative properties > relationship > contrariety or contrast > [adjective] > somewhat or partially

subcontrarya1548

a1548 N. Bacon in J. Strype Life M. Parker (1711) App. ii. 5 (modernized text) Conscience and the Law stand Subcontrary in Figura.

1697 J. Sergeant Solid Philos. 314 Finding his Discourse in other Places Sub-contrary to what I took to be his Thoughts.

1844 Brit. Mag. & Monthly Reg. 25 324 The compact on which parties holding subcontrary opinions can honestly act together.

1897 R. D. Blackmore Dariel xxix. 256 A conclusion not directly counter, but sub-contrary..to the view which her husband had ventured to form.

2. Logic.

a. Designating a proposition which is incapable of being false at the same time as its pair; (of a pair of propositions) related in such a way that both can be true, but both cannot be false. Cf. contrary propositions at contrary adj. 6.

ΘΚΠ

the mind > mental capacity > philosophy > logic > logical proposition > [adjective] > of universal or particular propositions

universalc1450

particular1551

subaltern1566

subcontrary1566

singular1654

lemmatical1665

indefinite1773

indesignate1844

semi-definitea1856

1566 R. Horne Answeare M. J. Fekenham f. 100 Being propositions, they are not one against the other contrary, subcontrary, subalterne nor contradictory.

1656 tr. T. Hobbes Elements Philos. i. iii. 31 Subcontrary, are Particular Propositions of different Quality; as Some Man is learned, Some Man is not learned.

1773 E. Bentham Introd. Logick ii. ii. 40 A particular affirmative and particular negative are termed subcontrary.

1873 W. H. Hill Elem. Philos. iii. 34 Subcontrary propositions are both particular, and they differ in quality; that is, one is affirmative and the other negative; as, ‘some men are honored’; ‘some men are not honored’.

1883 T. K. Abbott Elem. Logic iii. i. 33 Subcontrary propositions are those of which one affirms particularly what the other denies particularly. They must be I and O: Some men are black; Some men are not black, are subcontraries.

1962 J. T. Oesterle tr. St. Thomas Aquinas & T. Cajetan Aristotle: On Interpr. ii. iv. 153 The finite particular affirmative and the infinite particular negative are equal in meaning, and consequently each of these is subcontrary to the simple particular negative.

1994 Internat. Jrnl. for Philos. Relig. 35 10 Standing in subcontrary opposition, [propositions] (12) and (13) can both be true.

†b. Of or relating to subcontraries (sense B. 1b). Cf. contrary terms at contrary adj. 6. Obsolete. rare.

ΚΠ

1856 W. D. Wilson Elem. Treat. Logic i. i. §9. 41 There are properties also which may coëxist in the same substance, yet in such a way that the more of the one the less of the other... ‘Bitter’ and ‘sweet’ are words which denote two sub-contrary spheres.

3. Geometry. Designating a section of an oblique cone formed by a plane cutting the cone at an angle which makes a triangle geometrically similar to the triangle formed by the cone and the base, but oppositely oriented; (of a line) lying in such a section; (of triangles) such as arise in the construction of such a section, sharing a vertex and having their bases not parallel, the angles of their bases being equal but on opposite sides of the vertex. Also: relating to such a section or triangle.Such sections cut the cone in a circle, just as do sections parallel to the base.

ΘΚΠ

the world > relative properties > number > geometry > shape or figure > [adjective] > relationship between

subcontrary1669

the world > relative properties > number > geometry > shape or figure > [adjective] > two-dimensional > triangular > other

nonelike1551

quadrantal1616

subcontrary1669

orthic1920

1669 Philos. Trans. (Royal Soc.) 4 933 They are still circles (by reason of the sub-contrary Sections of the Visual Cones).

1706 W. Jones Synopsis Palmariorum Matheseos 254 If cut Parallel, or Subcontrary to the Base, the Section will be a Circle.

1773 tr. H. Hamilton Geom. Treat. Conic Sections 8 Another triangle ADI be cut similar to ABL, but in a subcontrary position, that is, so that the angle ATD be equal to the angle ABL.

1854 A. E. Church Elements Analyt. Geom. (ed. 2) ii. 276 If the cone is a right cone with a circular base, it is a surface of revolution, and the sub-contrary sections unite in one, perpendicular to the axis or parallel to the base.

1921 T. L. Heath Hist. Greek Math. II. xiv. 135 All sections parallel to the base are also circles, and..there is another set of circular sections subcontrary to these.

1975 Phronesis 20 177 Apollonius uses the term ‘subcontrary’ to designate the relation, in an inessential way generalized, between the pair of triangles in our construction.

2007 K. Andersen Geom. Art iv. 141 (caption) A proof that the stereographic image of a circle is a subcontrary section to the circle.

4. Mathematics. Designating the harmonic mean (cf. harmonic adj. 5a). historical.

ΘΚΠ

the world > relative properties > number > arithmetic or algebraic operations > [adjective] > mean

meana1450

medial1570

subcontrary1914

1914 J. Burnet Greek Philos.: Thales to Plato ii. 48 8 and 9 are related to the extremes 6 and 12 as means... The term 8..exceeds and is exceeded by the same fraction of the extremes; for 8 = 12 − ¹²/ ₃ = 6 + ⁶/ ₃. This was called the subcontrary (ὑπεναντíα), or later..the harmonic mean.

1945 Ann. Math. 46 246 Iamblicus says that Hippasus concerned himself with the theory of proportions and ‘means’ and was the first to change to ‘harmonic mean’ the name of what had previously been called the contrary, or, as some translate, the subcontrary, mean... But Nicomachus attributes this change in terminology to Philolaus.

1963 Jrnl. Amer. Musicol. Soc. 16 8 The early Pythagoreans knew that the musical consonances involved the subcontrary as well as the arithmetic and geometric relationships.

2005 C. A. Huffman Archytas of Tarentum ii. 166 On Law and Justice, whose authenticity is doubtful, does refer to the subcontrary mean.

B. n.

1. Logic.

a. A proposition having the same terms as another, and related to it in such a way that while both can be true, both cannot be false.

ΘΚΠ

the mind > mental capacity > philosophy > logic > logical proposition > [noun] > opposite or contradictory proposition(s)

contradictionc1400

contradictoryc1400

repugnantc1475

contradictory propositions1605

contrary1656

opposite1656

subcontrary1657

contrary propositions1739

principle (or law) of contradiction1850

contrapositive1870

contradictory terms1887

contrary terms1887

antilogism1902

1657 J. Tombes Anti-pædobaptism: 3rd Pt. c. 906 He would infer, that because subcontraries may be both true, therefore that proposition, Some infants may be baptized, must be true.

1697 tr. F. Burgersdijck Monitio Logica i. xxxiii 113 Subcontraries are, some man is just, some man is not just... Contraries, the negation added or taken away, contradict subcontraries.

1725 I. Watts Logick ii. ii. §3 If two particular propositions differ in quality, they are subcontraries.

1858 E. V. Gerhart Introd. to Stud. Philos. 259 In reference to subcontraries it is necessary to observe: 1. That both may be true, because the same particular subject-conception may be connected with opposite predicate-conceptions; e.g., Some bodies are transparent: and, Some bodies are not transparent.

1864 F. C. Bowen Treat. Logic vi. 164 Sub-Contraries can be called ‘opposites’ only in a qualified and technical sense.

1918 E. G. Spalding New Rationalism ii. xvi. 139 Thus A and O, and E and I are pairs of contradictory opposites; and A and E, I and O, of contrary opposites, with the latter two called subcontraries, as distinct from A and E as contraries.

2005 Erkenntnis 63 337 In a nutshell, Shogenji's measure does not adequately treat subcontraries.

†b. Each of two properties which are not opposites, but are related in such a way that the more there is of the one, the less there is (likely to be) of the other. Obsolete. rare.

ΚΠ

1856 W. D. Wilson Elem. Treat. Logic i. i. §9. 41 There are properties also which may coëxist in the same substance, yet in such a way that the more of the one the less of the other—these are called Sub-contraries.

†2. Geometry. A subcontrary section of a cone. Obsolete. rare.

ΘΚΠ

the world > relative properties > number > geometry > curve > [noun] > conic section

conical section (also conical line)1570

conic section1570

subcontrary1842

conic1863

1842 Penny Cycl. XXIII. 185/1 In a right cone every section has its subcontrary, except only the circle which generates the cone, and its parallels.

Derivatives

subconˈtrarily adv.

ΘΚΠ

the world > relative properties > number > geometry > shape or figure > [adverb] > with specific properties

subcontrarily1599

ordinately1653

perspectively1865

1599 T. Blundeville Art of Logike iii. viii. 67 They [sc. modal propositions] are said to be opposite fowr manner of waies, euen as absolute propositions are, that is to say, contrarily, subcontrarily, contradictorily, [etc.].

a1652 S. Foster Elliptical Horologiography (1654) 130 A compressed Cylinder, which Cylinder being cut two wayes, (that is subcontrarily) will again reveile the originall Circle.

1728 E. Chambers Cycl. at Subcontrary If the scalenous Cone BVD be so cut by the Plane CA, as that the Angle at C = D; the Cone is then said to be cut Subcontrarily to its Base BA.

1886 P. K. Ray Text-bk. Deductive Logic (ed. 2) ii. i. 78 Two particular propositions having the same subject and predicate, but differing in quality, are said to be subcontrarily opposed to each other.

This entry has been updated (OED Third Edition, June 2012; most recently modified version published online June 2022).

单词	subcontrary
释义	subcontraryadj.n. Brit. /ˌsʌbˈkɒntrəri/, U.S. /ˌsəbˈkɑnˌtrɛri/ Origin: A borrowing from Latin. Etymon: Latin subcontrarius. Etymology: < post-classical Latin subcontrarius (in logic) incapable of being false at the same time as its pair (6th cent.), somewhat adverse (15th cent. in a British source), (in geometry), designating a section of an oblique cone (1566 or earlier) < classical Latin sub- sub- prefix + contrārius contrary adj., after ancient Greek ὑπεναντίος opposite, contrary, (in mathematics), designating a mean, in Hellenistic Greek also (in mathematics) designating a section (Apollonius of Perga) and in Byzantine Greek, designating logical propositions. Compare Middle French subcontraire (14th cent., rare), French sous-contraire (17th cent. or earlier). A. adj. †1. Somewhat contrary or opposing; (also) partially opposed to something. Obsolete. ΘΚΠ the world > relative properties > relationship > contrariety or contrast > [adjective] > somewhat or partially subcontrarya1548 a1548 N. Bacon in J. Strype Life M. Parker (1711) App. ii. 5 (modernized text) Conscience and the Law stand Subcontrary in Figura. 1697 J. Sergeant Solid Philos. 314 Finding his Discourse in other Places Sub-contrary to what I took to be his Thoughts. 1844 Brit. Mag. & Monthly Reg. 25 324 The compact on which parties holding subcontrary opinions can honestly act together. 1897 R. D. Blackmore Dariel xxix. 256 A conclusion not directly counter, but sub-contrary..to the view which her husband had ventured to form. 2. Logic. a. Designating a proposition which is incapable of being false at the same time as its pair; (of a pair of propositions) related in such a way that both can be true, but both cannot be false. Cf. contrary propositions at contrary adj. 6. ΘΚΠ the mind > mental capacity > philosophy > logic > logical proposition > [adjective] > of universal or particular propositions universalc1450 particular1551 subaltern1566 subcontrary1566 singular1654 lemmatical1665 indefinite1773 indesignate1844 semi-definitea1856 1566 R. Horne Answeare M. J. Fekenham f. 100 Being propositions, they are not one against the other contrary, subcontrary, subalterne nor contradictory. 1656 tr. T. Hobbes Elements Philos. i. iii. 31 Subcontrary, are Particular Propositions of different Quality; as Some Man is learned, Some Man is not learned. 1773 E. Bentham Introd. Logick ii. ii. 40 A particular affirmative and particular negative are termed subcontrary. 1873 W. H. Hill Elem. Philos. iii. 34 Subcontrary propositions are both particular, and they differ in quality; that is, one is affirmative and the other negative; as, ‘some men are honored’; ‘some men are not honored’. 1883 T. K. Abbott Elem. Logic iii. i. 33 Subcontrary propositions are those of which one affirms particularly what the other denies particularly. They must be I and O: Some men are black; Some men are not black, are subcontraries. 1962 J. T. Oesterle tr. St. Thomas Aquinas & T. Cajetan Aristotle: On Interpr. ii. iv. 153 The finite particular affirmative and the infinite particular negative are equal in meaning, and consequently each of these is subcontrary to the simple particular negative. 1994 Internat. Jrnl. for Philos. Relig. 35 10 Standing in subcontrary opposition, [propositions] (12) and (13) can both be true. †b. Of or relating to subcontraries (sense B. 1b). Cf. contrary terms at contrary adj. 6. Obsolete. rare. ΚΠ 1856 W. D. Wilson Elem. Treat. Logic i. i. §9. 41 There are properties also which may coëxist in the same substance, yet in such a way that the more of the one the less of the other... ‘Bitter’ and ‘sweet’ are words which denote two sub-contrary spheres. 3. Geometry. Designating a section of an oblique cone formed by a plane cutting the cone at an angle which makes a triangle geometrically similar to the triangle formed by the cone and the base, but oppositely oriented; (of a line) lying in such a section; (of triangles) such as arise in the construction of such a section, sharing a vertex and having their bases not parallel, the angles of their bases being equal but on opposite sides of the vertex. Also: relating to such a section or triangle.Such sections cut the cone in a circle, just as do sections parallel to the base. ΘΚΠ the world > relative properties > number > geometry > shape or figure > [adjective] > relationship between subcontrary1669 the world > relative properties > number > geometry > shape or figure > [adjective] > two-dimensional > triangular > other nonelike1551 quadrantal1616 subcontrary1669 orthic1920 1669 Philos. Trans. (Royal Soc.) 4 933 They are still circles (by reason of the sub-contrary Sections of the Visual Cones). 1706 W. Jones Synopsis Palmariorum Matheseos 254 If cut Parallel, or Subcontrary to the Base, the Section will be a Circle. 1773 tr. H. Hamilton Geom. Treat. Conic Sections 8 Another triangle ADI be cut similar to ABL, but in a subcontrary position, that is, so that the angle ATD be equal to the angle ABL. 1854 A. E. Church Elements Analyt. Geom. (ed. 2) ii. 276 If the cone is a right cone with a circular base, it is a surface of revolution, and the sub-contrary sections unite in one, perpendicular to the axis or parallel to the base. 1921 T. L. Heath Hist. Greek Math. II. xiv. 135 All sections parallel to the base are also circles, and..there is another set of circular sections subcontrary to these. 1975 Phronesis 20 177 Apollonius uses the term ‘subcontrary’ to designate the relation, in an inessential way generalized, between the pair of triangles in our construction. 2007 K. Andersen Geom. Art iv. 141 (caption) A proof that the stereographic image of a circle is a subcontrary section to the circle. 4. Mathematics. Designating the harmonic mean (cf. harmonic adj. 5a). historical. ΘΚΠ the world > relative properties > number > arithmetic or algebraic operations > [adjective] > mean meana1450 medial1570 subcontrary1914 1914 J. Burnet Greek Philos.: Thales to Plato ii. 48 8 and 9 are related to the extremes 6 and 12 as means... The term 8..exceeds and is exceeded by the same fraction of the extremes; for 8 = 12 − ¹²/ ₃ = 6 + ⁶/ ₃. This was called the subcontrary (ὑπεναντíα), or later..the harmonic mean. 1945 Ann. Math. 46 246 Iamblicus says that Hippasus concerned himself with the theory of proportions and ‘means’ and was the first to change to ‘harmonic mean’ the name of what had previously been called the contrary, or, as some translate, the subcontrary, mean... But Nicomachus attributes this change in terminology to Philolaus. 1963 Jrnl. Amer. Musicol. Soc. 16 8 The early Pythagoreans knew that the musical consonances involved the subcontrary as well as the arithmetic and geometric relationships. 2005 C. A. Huffman Archytas of Tarentum ii. 166 On Law and Justice, whose authenticity is doubtful, does refer to the subcontrary mean. B. n. 1. Logic. a. A proposition having the same terms as another, and related to it in such a way that while both can be true, both cannot be false. ΘΚΠ the mind > mental capacity > philosophy > logic > logical proposition > [noun] > opposite or contradictory proposition(s) contradictionc1400 contradictoryc1400 repugnantc1475 contradictory propositions1605 contrary1656 opposite1656 subcontrary1657 contrary propositions1739 principle (or law) of contradiction1850 contrapositive1870 contradictory terms1887 contrary terms1887 antilogism1902 1657 J. Tombes Anti-pædobaptism: 3rd Pt. c. 906 He would infer, that because subcontraries may be both true, therefore that proposition, Some infants may be baptized, must be true. 1697 tr. F. Burgersdijck Monitio Logica i. xxxiii 113 Subcontraries are, some man is just, some man is not just... Contraries, the negation added or taken away, contradict subcontraries. 1725 I. Watts Logick ii. ii. §3 If two particular propositions differ in quality, they are subcontraries. 1858 E. V. Gerhart Introd. to Stud. Philos. 259 In reference to subcontraries it is necessary to observe: 1. That both may be true, because the same particular subject-conception may be connected with opposite predicate-conceptions; e.g., Some bodies are transparent: and, Some bodies are not transparent. 1864 F. C. Bowen Treat. Logic vi. 164 Sub-Contraries can be called ‘opposites’ only in a qualified and technical sense. 1918 E. G. Spalding New Rationalism ii. xvi. 139 Thus A and O, and E and I are pairs of contradictory opposites; and A and E, I and O, of contrary opposites, with the latter two called subcontraries, as distinct from A and E as contraries. 2005 Erkenntnis 63 337 In a nutshell, Shogenji's measure does not adequately treat subcontraries. †b. Each of two properties which are not opposites, but are related in such a way that the more there is of the one, the less there is (likely to be) of the other. Obsolete. rare. ΚΠ 1856 W. D. Wilson Elem. Treat. Logic i. i. §9. 41 There are properties also which may coëxist in the same substance, yet in such a way that the more of the one the less of the other—these are called Sub-contraries. †2. Geometry. A subcontrary section of a cone. Obsolete. rare. ΘΚΠ the world > relative properties > number > geometry > curve > [noun] > conic section conical section (also conical line)1570 conic section1570 subcontrary1842 conic1863 1842 Penny Cycl. XXIII. 185/1 In a right cone every section has its subcontrary, except only the circle which generates the cone, and its parallels. Derivatives subconˈtrarily adv. ΘΚΠ the world > relative properties > number > geometry > shape or figure > [adverb] > with specific properties subcontrarily1599 ordinately1653 perspectively1865 1599 T. Blundeville Art of Logike iii. viii. 67 They [sc. modal propositions] are said to be opposite fowr manner of waies, euen as absolute propositions are, that is to say, contrarily, subcontrarily, contradictorily, [etc.]. a1652 S. Foster Elliptical Horologiography (1654) 130 A compressed Cylinder, which Cylinder being cut two wayes, (that is subcontrarily) will again reveile the originall Circle. 1728 E. Chambers Cycl. at Subcontrary If the scalenous Cone BVD be so cut by the Plane CA, as that the Angle at C = D; the Cone is then said to be cut Subcontrarily to its Base BA. 1886 P. K. Ray Text-bk. Deductive Logic (ed. 2) ii. i. 78 Two particular propositions having the same subject and predicate, but differing in quality, are said to be subcontrarily opposed to each other. This entry has been updated (OED Third Edition, June 2012; most recently modified version published online June 2022). < adj.n.a1548
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