Here’s an excerpt from my recently published Lexical Commentary on the Pastoral Epistles: First Timothy. The commentary below is on 1 Timothy 1:5, which is pretty much the thesis of the letter.
but the goal of our instruction
The word translated “goal” is τέλος. The basic meaning is that of ‘end, finish, or termination;’ though τέλος developed many supplemental and context-sensitive meanings over time. In this context, the meaning of ‘aim’ or ‘goal’ is appropriate as the context indicates that it is the end of the effort, thus the purpose or reason for expending the effort. The word translated “instruction” is παραγγελία, which is less common in the New Testament. The basic sense of the word is that of a message that essentially commands or orders someone (or a group) to do something. This is commonly known as a charge. Consider First Clement:
Therefore, having received commands and being fully convinced by the resurrection of our Lord Jesus Christ, and full of faith in the word of God, they went forth with the full assurance of the Holy Spirit, proclaiming the gospel, that the kingdom of God was about to come. (1Cl 42.3, emphasis added)
Here the charge or παραγγελία is received by the apostles and dutifully acted upon.
Paul does not establish a new charge for Timothy, but rather confirms that the charge is a common one. Paul includes Timothy in the fulfillment of the charge that has been laid on him by none other than Christ Jesus. Paul sets Timothy’s goal in service to the Ephesian fellowship: to oppose the false teachers, myths, and endless genealogies of verses 3–4.
is love from a pure heart
The phrase “a pure heart” is relatively straightforward in its meaning. The word for “pure” (καθαρός) generally means ‘clean’ though it does have some ceremonial, ritual and religious undertones in its primary senses. This leads to the preference of the translation “pure” instead of simply “clean” in this instance. This is the same language used in Ps 51:10 (lxx 50:12) when David pleads to God for mercy:
Create in me a clean heart, O God, and renew a right spirit in my inward parts. (Ps 51:10 [lxx 50:12], emphasis added)
The word for “heart” (καρδία) eventually becomes shorthand for all that “heart” actually means when it occurs in this sort of context. That is, καρδία refers to the figurative usage and assumes that the heart is the center or seat of ‘physical, spiritual and mental life.’ Its literal meaning is minimized and the figurative meaning becomes primary. Paul indicates that one’s innermost motivation must not be for impure motives, but rather for pure motives. Love is a result of these pure motives.
and a good conscience
Paul next mentions “a good conscience.” The word translated “good” (ἀγαθός) is a common word expressing the concept of good or goodness. The word for “conscience” (συνείδησις) has to do with being aware of information concerning something. The primary sense, however, seems to be a bit more refined and carries the connotation of moral consciousness or conscience. These imply the idea of not only knowledge but the ability to discern right from wrong.
Paul used this phrase in his testimony before the Sanhedrin, as is recorded in the book of Acts:
And looking intently at the Sanhedrin, Paul said, “Men and brothers, I have lived my life in all good conscience before God to this day.” So the high priest Ananias ordered those standing near him to strike his mouth. (Ac 23:1–2, emphasis added)
Paul is not weighed down by guilt from things he has done in the past, he instead considers his conscience clear. A similar usage is found in First Clement:
Each of us, brothers, in his own group, must be pleasing to God, being in good conscience, not going beyond the appointed rule of his ministry, with dignity. (1Cl 41.1, emphasis added)
In First Clement, the “good conscience” helps keep one’s mind on the task at hand. It allows one to focus on pursuing what is proper, and to dismiss what is not.
Paul desires for the Ephesian believers to have an innate ability to discern proper teaching from improper. At the time of the writing of this epistle, the Ephesians did not have this ability. They were falling prey to heretical teachers and false prophets. A “good conscience” contributes to the ability to discern proper teaching from improper teaching, hence Paul’s desire to instill “a good conscience” in them.
and a faith without hypocrisy
Finally, Paul mentions “a sincere faith.” Faith, in this context, carries the sense of trust. The word translated as “sincere” (ἀνυπόκριτος) means ‘genuine’ or ‘sincere’ or even ‘without play-acting’ when taken literally.
The word ἀνυπόκριτος could also be translated as “unfeigned.” This implies the idea of genuine, but also conveys the idea in the Greek that rather than simply being genuine, this faith is something more. It is not faked and is not false. The faith unfeigned is real, sincere faith.
Consider also the use of ἀνυπόκριτος in the Wisdom of Solomon:
… bringing your sincere command as sharp sword; and it stood and filled all things with death, and it touched the sky but stood on the earth. (Wis 18:16, emphasis added)
These three components of Paul’s goal are connected with conjunctions that indicate these three things—a pure heart, a good conscience, and faith unfeigned—all work together to display the love Paul desires the Ephesians to exhibit.
 bdag, p. 998. Occurs 40x in nt, only here in pe.
 bdag, p. 760. Occurs 5x in nt, 2x in pe: 1Ti 1:5, 18. The verb form of this word occurs in 1Ti 1:3. Cf. comments on both 1Ti 1:3 and 1Ti 1:18.
 Note that the charge is actually being explained and clarified from 1Ti 1:5 all the way through 1Ti 1:18. The basics of the charge, however, are in 1Ti 1:3–7.
 bdag, p. 489. Occurs 27x in nt, 7x in pe.
 bdag, p. 508. Occurs 156x in nt, 2x in pe: 1Ti 1:5, 2Ti 2:22.
 bdag, p. 3. Occurs 102x in nt, 10x in pe.
 bdag, p. 967. Occurs 30x in nt, 6x in pe: 1Ti 1:5, 19; 3:9; 4:2; 2Ti 1:3; Tt 1:15.
 bdag, p. 91. Occurs 6x in nt, 2x in pe: 1Ti 1:5; 2Ti 1:5.
 nrsv translates “authentic.”