Etymology
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implication (n.)

early 15c., "action of entangling," from Latin implicationem (nominative implicatio) "an interweaving, an entanglement," noun of state from past participle stem of implicare "involve, entangle; embrace; connect closely, associate," from assimilated form of in- "into, in, on, upon" (from PIE root *en "in") + plicare "to fold" (from PIE root *plek- "to plait"). Meaning "that which is implied (but not expressed), inference drawn from what is observed" is from 1550s.

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Definitions of implication

implication (n.)
something that is inferred (deduced or entailed or implied);
his resignation had political implications
Synonyms: deduction / entailment
implication (n.)
a meaning that is not expressly stated but can be inferred;
the expectation was spread both by word and by implication
Synonyms: significance / import
implication (n.)
an accusation that brings into intimate and usually incriminating connection;
implication (n.)
a logical relation between propositions p and q of the form `if p then q'; if p is true then q cannot be false;
Synonyms: logical implication / conditional relation
implication (n.)
a relation implicated by virtue of involvement or close connection (especially an incriminating involvement);
he was suspected of implication in several robberies
From wordnet.princeton.edu