Three related words of the New Testament are the verb ησυχαζω, the noun ησυχια, and the adjective ησυχιος. In what follows, the meaning of these words is examined under the assumption that each of these words is used with a unique meaning in the New Testament. The conclusion is that the meanings of ησυχαζω and ησυχια correspond to the meaning of the adjective ησυχιος (quiet, tranquil). Emphasized here is the fact that quietness does not imply silence.
The verb ησυχαζω
This verb appears in the following verses.
(Luk 14:4) οι δε ησυχασαν και επιλαβομενος ιασατο αυτον και απελυσεν
(Luk 23:56) υποστρεψασαι δε ητοιμασαν αρωματα και μυρα και το μεν σαββατον ησυχασαν κατα την εντολην
(Act 11:18) ακουσαντες δε ταυτα ησυχασαν και εδοξαζον τον θεον λεγοντες αραγε και τοις εθνεσιν ο θεος την μετανοιαν εδωκεν εις ζωην
(Act 21:14) μη πειθομενου δε αυτου ησυχασαμεν ειποντες το θελημα του κυριου γενεσθω
(1Th 4:11) και φιλοτιμεισθαι ησυχαζειν και πρασσειν τα ιδια και εργαζεσθαι ταις ιδιαις χερσιν υμων καθως υμιν παρηγγειλαμεν
Lexicons include the following meanings for ησυχαζω: "to rest", "to lead a quiet life", and "to be silent". Note that the meanings "to rest" and "to be silent" do not fit all passages in which the verb appears. The meaning "to rest" does not fit 1Th 4:11. The passage is not urging people to rest but to work quietly with their own hands. The meaning "to rest" does not fit either Ac 11:18, which is not in the context of resting. The meaning "to be silent" does not fit Lk 23:56, since it would lead to a translation "and they were silent on the Sabbath according to the commandment", which does not fit the Bible context (there is no commandment to stop speaking on the Sabbath). The meaning "to be silent" does not fit either 1Th 4:11, since there are various kinds of jobs in which one is supposed to speak.
Let us verify next that the meaning "to be quiet, tranquil" fits all references in which the verb appears.
In Lk 14:4, the meaning "to be silent" would seem to fit. However, this is not the only meaning that could fit. The meaning "to be quiet, tranquil" would fit as well. It would imply that the opponents of the Lord were quiet, though not silent. We could reason that what they said was not significant enough to be recorded.
By applying the meaning "to be quiet, tranquil" in Lk 23:56, we obtain " ... and they were quiet on the Sabbath according to the commandment". The kind of quietness that is meant is indicated by the phrase "according to the commandment". They were quiet in the sense that they ceased from work and observed the Sabbath rest.
By applying the meaning "to be quiet" in Ac 11:18, we obtain " ... they were quiet and glorified the Lord ... ". Quietness here would refer to the fact that they stopped criticizing Peter. Note that since quietness does not imply silence, there is no need to assume that the phrases "they were quiet" and "glorified the Lord" describe things that did not take place at the same time.
By applying the meaning "to be quiet" in Ac 21:14 we can understand that they became quiet after they said "the will of the Lord be done". This does not imply that they stopped speaking, but that they stopped trying to persuade the apostle Paul that he should not go to Jerusalem.
Finally, by applying the meaning "to be quiet" in 1Th 4:11, we obtain the phrase "to love to be quiet". In the context of 1Th 4:11, this phrase would describe the attitude of a person who works without disturbing others.
The noun ησυχια
This word appears in the following verses.
(Act 22:2) ακουσαντες δε οτι τη εβραιδι διαλεκτω προσεφωνει αυτοις μαλλον παρεσχον ησυχιαν και φησιν
(2Th 3:12) τοις δε τοιουτοις παραγγελλομεν και παρακαλουμεν δια του κυριου ημων ιησου χριστου ινα μετα ησυχιας εργαζομενοι τον εαυτων αρτον εσθιωσιν
(1Ti 2:11) γυνη εν ησυχια μανθανετω εν παση υποταγη
(1Ti 2:12) γυναικι δε διδασκειν ουκ επιτρεπω ουδε αυθεντειν ανδρος αλλ ειναι εν ησυχια
Lexicons use the glosses "quietness" and "silence" to define the meanings of ησυχια. Note that the meaning "silence" does not fit well 2Th 3:12, since one may be expected to speak as part of his work. Thus, assuming that the word is used with a single meaning, "silence" cannot be that meaning. The meaning "silence" would not fit either with the meaning inferred under the same assumption for the verb ησυχαζω (see above) and for the adjective ησυχιος (see below).
Let us note that the meaning "quietness" fits well all references in which the noun ησυχια appears.
By applying the meaning "quietness" in Ac 22:2, we can understand that the crowd became even more quiet when they heard the apostle speaking Hebrew. Quietness here refers to the fact that the crowd ceased from its vehement manifestation of hostility in order to hear the words of the apostle. Earlier, the crowd had been very agitated (Ac 21:30-36).
By applying the meaning "quietness" in 2Th 3:12, we can understand that the verse speaks about working quietly. This is not the same as working silently, which may be impossible in certain contexts.
By applying the meaning "quietness" in 1Ti 2:11-12, we obtain "Let the woman learn quietly ... " in 1Ti 2:11 and " ... but to be quiet" in 1Ti 2:12. The expectation that the woman should learn quietly does not imply that the woman should learn silently. An expectation that she should be silent would keep her from sharing her insight. An interpretation of 1Ti 2:12 requiring silence, not quietness, would seem very unlikely if we consider that in 1Ti 2:12 the expectation is not limited to the context of learning but is in the general context of the relationship between a woman and her husband. A more detailed discussion of 1Ti 2:11-12 appears in part 3 of the article "Speaking in Church".
The adjective ησυχιος
This word appears in the following verses.
(1Ti 2:2) υπερ βασιλεων και παντων των εν υπεροχη οντων ινα ηρεμον και ησυχιον βιον διαγωμεν εν παση ευσεβεια και σεμνοτητι
(1Pe 3:4) αλλ ο κρυπτος της καρδιας ανθρωπος εν τω αφθαρτω του πραεος και ησυχιου πνευματος ο εστιν ενωπιον του θεου πολυτελες
Lexicons associate with ησυχιος the meaning "quiet, tranquil".
1Ti 2:2 speaks about having a tranquil life. Note that a tranquil life is not the same thing as a silent life. Indeed, we are not to be silent but to share the Gospel.
1Pe 3:4 says that a woman should have a quiet spirit. Note that a quiet spirit is not the same thing as a silent spirit. A quiet and tranquil spirit implies a peaceful disposition of mind, not silence.