contrary

When speaking of philosophy and logic, one proposition is contrary to another if they cannot both be true, but they could both be false, or one false and one true.

This is compared to contradictory statements, in which both cannot be true and both cannot be false. If statements are truly contradictory, one is true, and one is false.

Contrary:
1. My pants are blue (and only blue).
2. My pants are red (and only red).

Contradictory:
A. My pants are blue.
B. My pants are not blue.

It is possible that my pants are purple, making 1., 2., and A. false. Contrary propositions leave room for alternative possibilities, in which both might be false. Contradictory propositions leave no room; one is true and one is not.

There is also the most excellent word subcontrary, in which one preposition must be true, and both may be true.

Con"tra*ry (? ∨ ?; 48), a. [OE. contrarie, contraire, F. contraire, fr. L. contrarius, fr. contra. See Contra-.]

1.

Opposite; in an opposite direction; in opposition; adverse; as, contrary winds.

And if ye walk contrary unto me, and will not hearken unto me. Lev. xxvi. 21.

We have lost our labor; they are gone a contrary way. Shak.

2.

Opposed; contradictory; repugnant; inconsistent.

Fame, if not double-faced, is double mouthed, And with contrary blast proclaims most deeds. Milton.

The doctrine of the earth's motion appeared to be contrary to the sacred Scripture. Whewell.

3.

Given to opposition; perverse; forward; wayward; as, a contrary disposition; a contrary child.

4. Logic

Affirming the opposite; so opposed as to destroy each other; as, contrary propositions.

Contrary motion Mus., the progression of parts in opposite directions, one ascending, the other descending.

Syn. -- Adverse; repugnant; hostile; inimical; discordant; inconsistent.

© Webster 1913.

Con"tra*ry, n.; pl. Contraries ().

1.

A thing that is of contrary or opposite qualities.

No contraries hold more antipathy Than I and such a knave. Shak.

2.

An opponent; an enemy.

Chaucer.

3.

the opposite; a proposition, fact, or condition incompatible with another; as, slender proofs which rather show the contrary. See Converse, n., 1.

Locke.

4. Logic

See Contraries.

On the contrary, in opposition; on the other hand. Swift. -- To the contrary, to an opposite purpose or intent; on the other side. "They did it, not for want of instruction to the contrary." Bp. Stillingfleet.

© Webster 1913.

Con"tra*ry, v. t. [F. contrarier. See Contrary, a.]

To contradict or oppose; to thwart.

I was advised not to contrary the king. Bp. Latimer.

© Webster 1913.