Implies



[im-plahy]

verb (used with object), implied, implying.
1.
to indicate or suggest without being explicitly stated:
His words implied a lack of faith.
2.
(of words) to signify or mean.
3.
to involve as a necessary circumstance:
Speech implies a speaker.
4.
Obsolete. to enfold.
/ɪmˈplaɪ/
verb (transitive; may take a clause as object) -plies, -plying, -plied
1.
to express or indicate by a hint; suggest: what are you implying by that remark?
2.
to suggest or involve as a necessary consequence
3.
(logic) to enable (a conclusion) to be inferred
4.
(obsolete) to entangle or enfold
v.

late 14c., “to enfold, enwrap, entangle” (the classical Latin sense), from Old French emplier, from Latin implicare “involve” (see implication). Meaning “to involve something unstated as a logical consequence” first recorded c.1400; that of “to hint at” from 1580s. Related: Implied; implying. The distinction between imply and infer is in “What do you imply by that remark?” But, “What am I to infer from that remark?”

logic
(=> or a thin right arrow) A binary Boolean function and logical connective. A => B is a true implication unless A is true and B is false. The truth table is
A B | A => B —-+——- F F | T F T | T T F | F T T | T
It is surprising at first that A => B is always true if A is false, but if X => Y then we would expect that (X & Z) => Y for any Z.
If A is actually an expression X & Y then the implication is called a syllogism.
(2009-10-28)

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