FOR ON THE ONE HAND THERE IS A SETTING ASIDE: athetesis men gar ginetai (3SPMI) proagouses (PAPFSB) entoles: (Heb 7:11,12; 8:7-13; 10:1-9; Romans 3:31; Galatians 3:15,17)

Setting aside (115) (athetesis from atheteo = to annul, declare invalid, not recognize, make ineffective, inoperative or nonexistent) describes the doing away of something established. To set aside. To disannul. It was used of annulling a treaty, a promise, a law, a regulation. It was also used of removing a man’s name from a document. To make as of no value = putting away & "annulling" the former commandment [Gal 3:15] It means to refuse to recognize the validity of something and so to reject it or regard it as invalid (an annulment). It can describe the process of causing something not to continue. It can mean to act towards anything as though it were annulled. Atheteo was used commonly in the Greek papyri in a legal sense of making void.

In Hebrews 9:26 (the only other NT use, once in Lxx = 1Sa 24:12) athetesis refers to the fact that at the Cross, the guilt and power of sin were disannulled. 

Otherwise, He would have needed to suffer often since the foundation of the world; but now once at the consummation of the ages He has been manifested to put away sin by the sacrifice of Himself. (note Hebrews 9:26)

At the Cross not only as sin "set aside" or disannulled, but the whole paraphernalia of the sacrificial system, the whole ceremonial system, was canceled, annulled, done away with entirely. God assured its end in 70AD, when He allowed the Temple to be destroyed.

OF A FORMER COMMANDMENT BECAUSE OF ITS WEAKNESS AND USELESSNESS: proagouses entoles dia to autes asthenes kai anopheles: (Heb 7:19; 8:7,8; 9:9,10; 10:1-4; 13:9; Acts 13:39; Romans 8:3; Galatians 4:9,21; 1 Timothy 4:8)

Its weakness - Law had no capacity to make men perfect. The Law could not impart strength to fulfill its demands and thus could not bestow spiritual/eternal life. It could not justify a man and therefore could not bring men into fellowship with God (see note Romans 5:1).

The former was unprofitable in the sense that no one could be made righteous by keeping the law (See note Romans 4:13; 4:14).

Weakness (772) (asthenes from a = without + sthénos = strength, bodily vigor) (See study of related verb astheneo - note the concentration of asthenes/astheneo in epistles to Corinthians ~50% of NT uses) is literally without strength or bodily vigor. Asthenes describes one's state of limited capacity to do or be something and is used literally of physical weakness (most of the uses in the Gospels).

Asthenes is used figuratively here in Hebrews 7 to describe the weakness and powerlessness of the Law to produce righteousness and a life pleasing to God. Paul uses this same adjective asthenes with a similar meaning in his letter to the Galatians writing...

But now that you have come to know God, or rather to be known by God, how is it that you turn back again to the weak (asthenes) and worthless elemental things (in the spiritual sense the rudiments of Jewish religion had no ability to justify anyone), to which you desire to be enslaved all over again? (Galatians 4:9)

The related verb astheneo is used in Romans 8:3 with a similar meaning, referring to the weakness of the Law to save a man.

For what the Law could not do, weak as it was (astheneo) through the flesh, God did: sending His own Son in the likeness of sinful flesh and as an offering for sin, He condemned sin in the flesh (See note  in Romans 8:3)

The following is a summary the nuances of meaning of asthenes (modified from BDAG)...

(1) Pertaining to suffering from a debilitating illness - sick, ill

(2) Pertaining to experiencing some incapacity or limitation - weak

a) Of physical weakness - the flesh is weak = gives up too easily (Mt 26:41, Mark 14:38); weaker vessel = sex (1Peter 3:7); personal appearance is weak = unimpressive (1Cor 10:10)

b) Of relative ineffectiveness, whether external or inward weak = feeble, ineffectual (1Cor 4:10); the weaker, less important members (1Cor 12:22); what is weak in (the eyes of) the world (1Cor 1:27)

c) Of the inner life -

Helpless in a moral sense (Romans 5:6)

Of a weakness in faith, which through lack of advanced knowledge, considers externals of the greatest importance (1Cor 8:7, 9, 9:10, cp similar use of related verb astheneo in Romans 14:1 [note]; 14:2)

To those who are weak in faith I became as they are (1Cor 9:22) (Arndt, W., Danker, F. W., & Bauer, W. A Greek-English Lexicon of the New Testament and Other Early Christian Literature)

Uselessness (512) (anopheles from a = without + opheleo = to do good, to benefit, to profit) means not beneficial or serviceable and it pertains to not offering any special benefit. Here it speaks of the Law as not accomplishing that which the only the “better hope” could bring.

FOR THE LAW MADE NOTHING PERFECT: ouden gar eteleiosen o nomos: (Hebrews 7:11; 9:9; Acts 13:39; Romans 3:20,21; 8:3; Galatians 2:16)

Paul on his first missionary journey was invited to speak in the Jewish Synagogue and one of his topics was the Law...

Therefore let it be known to you, brethren, that through Him (see study below on "through Him" - the Messiah = the Christ) forgiveness (aphesis = action causing separation. legal term ~repay or cancel debt. Thru shedding of His blood Christ took the sins of world upon Himself and carried them an eternal, infinite distance away with no return possible!) of sins is proclaimed to you, and through Him everyone who believes (not a passive assent to truth but an active staking of one's life on the claims of God. Saving faith includes [1] a firm conviction which produces full acknowledgment of God's revelation of Truth [2] a personal surrender to the Truth and [3] a conduct inspired by and consistent with that surrender - in short truth faith is evidenced by genuine repentance or a changed life!) is freed (dikaioo - acquitted, vindicated) from all things, from which you could not be freed through the Law of Moses. (Acts 13:38-39) (Through Christ by faith not through the Law by works!)

In a parallel passage in his great epistle to the Romans in the section in which Paul argues for every man's desperate need to receive the gospel, he says that...

by the works of the Law no flesh (here refers to the physical flesh, the body, flesh and blood, not the evil disposition opposed to God - flesh) will be justified (declared righteous before God, a forensic or legal term = acquitted of all sins past, present and future) in His sight (cp Heb 7:19 "the Law made nothing perfect"); for through the Law comes the knowledge of sin (What then is one function of the Law? see also note Romans 7:7) But now (one of the best "but now's" in all time and eternity!) apart from (choris =  marker of dissociation indicating a distinct separation from) the Law the righteousness of God has been manifested (Paul teaches that the righteousness of God has been made known once for all in the incarnate Christ and His death on Calvary and the perfect tense =  “has been manifested and continues to lie open to view”), being witnessed (Paul personifies the OT as it were a witness called to the stand to testify!) by the Law and the Prophets (synonymous with entire OT) (see Messianic Prophecy), (See notes Romans 3:20; 3:21)

Finally writing to the Galatians who had begun well but were being hindered and encouraged to walk by sight and works not faith, Paul reiterated what they already knew...

that a man is not justified by the works of the Law but through faith in Christ Jesus, even we have believed in Christ Jesus, that we may be justified (declared righteous in God's sight and vindicated of any charge of sin in connection with failure to keep God's law) by faith in Christ, and not by the works of the Law; since by the works of the Law shall no flesh be justified. (Galatians 2:16) (Comment: Some have fallaciously argued that James contradicts Paul, saying that Abraham was "justified by works" [James 2:21]. However, he was not justified by "works of the law." Abraham even lived before God gave the Law to Moses! How could he be justified by it! In James 2, he also states clearly that Abraham was justified by faith in the eyes of God [see James 2:23] and justified by works in the eyes of man. In other words, Abraham was shown by his external works to have experienced justification by faith, which was now manifest before men as a changed life. Justified is used with the same meaning [show to be righteous] in Paul's description of God Who clearly does not need to be declared righteous! [see note Romans 3:4]. In sum, there is no contradiction, for genuine saving faith is inevitably demonstrated before men by "works of righteousness" [see notes Titus 3:5; see notes Ephesians 2:8; 2:9; 2:10]. In any case, Paul makes it clear to the Galatians that no one can ever be justified by keeping the Law. In fact, James himself makes it plain that no one can keep the law fully [James 2:10]).

Note the first word in the Greek sentence for emphasis - nothing!  The Law completed nothing. It was the tutor, the introduction, but not the completion of righteousness which is only by grace through faith.

Nothing (3762)  (oudeis from ou = absolutely  not +dé = but + heis = one) means literally "but absolutely not one" which emphasizes not even one.

Notice the recurrence of the idea of perfecting. The Old Covenant could REVEAL sin (see notes Romans 3:20 , Ro 7:7;  7:8; 7:9; 7:10;; 7:11; 7:12 Gal 3:24,25) but it could never REMOVE sin (see notes Hebrews 10:4, 10:8), and so itself had to be removed. It brought nothing to conclusion. It gave no security (see notes Romans 8:1, Ro 8:38; 8:39). It gave no peace (see notes Romans 5:1; 8:6). A man never had a clean conscience (see note Hebrews 10:22) (See related studies on Covenant - [1] Covenant: Abrahamic versus Mosaic ; [2] New Covenant in the Old Testament; [3] Why the New is Better; [4] Abrahamic vs Old vs New )

Made...perfect (5048) (teleioo related to teleios from telos = an end, a purpose, an aim, a goal, consummate soundness, idea of being whole) means to accomplish or bring to an end or to the intended goal (telos). It means to be complete, mature, fully developed, full grown, brought to its end, finished, wanting nothing necessary to completeness or in good working order. It does not mean simply to terminate something but to carry it out to the full finish which is picked up in the translation "perfected". Teleioo signifies the attainment of consummate soundness and includes the idea of being made whole. Interestingly the Gnostics used teleios of one fully initiated into their mysteries and that may have been why Paul used teleios in this epistle.

Telioo means

(1) to complete an activity, bringing it to an end or a point of accomplishment (Lu 13:32 "...I reach My goal", the Cross) (Lu 2:43 after Jesus' parents celebrated the feast of Passover "they were returning, after spending the full number of days" [literally having finished the days]).

(2) To overcome an imperfect state of things by one that is free thus bringing to its goal or accomplishment and make perfect. (as here in Hebrews 2:10, 5:9, 7:28).

(3) Fulfilling or carrying out a promise or prophecy (John 19:28 After this, Jesus, knowing that all things had already been accomplished [teleo], in order that the Scripture might be fulfilled [telioo], said, "I am thirsty.")

(4) To initiate - it was used with this meaning in the mystery religions.

Telioo is used 9 times (out of 24 total NT uses) in Hebrews, often in the sense of to make perfect or fully cleanse from sin in contrast to ceremonial (Levitical) cleansing. The writer is emphasizing the importance of perfection... (which should cause any Jew who is contemplating the worth of Christ and the New Covenant to realize his utter hopelessness to every attain perfection under the Old Covenant).

Hebrews 2:10 (note) For it was fitting for Him, for Whom are all things, and through Whom are all things, in bringing many sons to glory, to perfect the author of their salvation through sufferings.

Hebrews 5:9 (note) And having been made perfect, He became to all those who obey Him the source of eternal salvation,

Hebrews 7:19 (note) (for the Law made nothing perfect), and on the other hand there is a bringing in of a better hope, through which we draw near to God. (Comment: The old covenant could reveal sin but it could never remove sin, and so it had to be removed. It brought nothing to conclusion. It gave no security. It gave no peace. A man never had a clean conscience.)

Hebrews 7:28 (note) For the Law appoints men as high priests who are weak, but the word of the oath, which came after the Law, appoints a Son, made perfect forever.

Hebrews 9:9 (note) which is a symbol for the present time. Accordingly both gifts and sacrifices are offered which cannot make the worshiper perfect in conscience,

Hebrews 10:1 (note) For the Law, since it has only a shadow of the good things to come and not the very form of things, can never by the same sacrifices year by year, which they offer continually, make perfect those who draw near. (Contrast with Jesus in Hebrews 5:9 above)

Hebrews 10:14 (note) For by one offering He has perfected for all time those who are sanctified.

Hebrews 11:40 (note) because God had provided something better for us, so that apart from us they should not be made perfect.

Hebrews 12:23 (note) (But you have come...) 23 to the general assembly and church of the first-born who are enrolled in heaven, and to God, the Judge of all, and to the spirits of righteous men made perfect,

In sum the fundamental idea of telioo is the bringing of a person or thing to the goal fixed by God.

It is interesting and doubtless no mere coincidence that in the Septuagint (LXX) teleioo is translated numerous times as consecrated or consecration, especially speaking of consecration of the priests (cf Jesus our "great High Priest") (Ex 29:9, 29, 33, 35 Lv 4:5; 8:33; 16:32; 21:10; Nu 3:3). The LXX translators gave the verb teleioo a special sense of consecration to priestly service and this official concept stands behind the writer's use in this passage in Hebrews 5:9 (note). It signifies that Jesus has been fully equipped to come before God in priestly action.

Study the other 15 NT uses of telioo (other than the 9 in Hebrews)

Luke 2:43 and as they were returning, after spending the full number of days, the boy Jesus stayed behind in Jerusalem. And His parents were unaware of it,

Luke 13:32 And He said to them, "Go and tell that fox, 'Behold, I cast out demons and perform cures today and tomorrow, and the third day I reach My goal.' (Comment: "Today and tomorrow and the third day" means that God's timetable is unfolding for Jesus, and no king like Herod could shorten the time. When His work is accomplished or has reached its intended goal, His death and resurrection will be its perfection.)

John 4:34 Jesus said to them, "My food is to do the will of Him who sent Me, and to accomplish His work. (Comment: Teleioo does mean just to bring to an end but to perfect it. The work He had been sent to do was finished on the Cross, and thus He cried "It is finished! [ = related verb teleo]" John 19:30. Note that Jesus is not saying that He refrained from eating food but that the great goal of His life was not to cater to His body but rather to the will of His Father! Which do you cater to? Are you accomplishing His work in and through you? see note Ephesians 2:10)

John 5:36 "But the witness which I have is greater than that of John; for the works which the Father has given Me to accomplish, the very works that I do, bear witness of Me, that the Father has sent Me. (Comment: The Old Testament testifies to the mission and ministry of Jesus precisely what God said He would do in Scripture and what God told Jesus to do as He ministered.)

John 17:4 "I glorified Thee on the earth, having accomplished the work which Thou hast given Me to do. (Comment: Jesus had finished His work of teaching and witness, but His work of redemption had yet to be accomplished on the cross. He would then shout the great victory cry: "It is finished!" John 19:30) (J C Ryle explains how the Cross accomplished God's perfect will "The crucifixion brought glory to the Father. It glorified His wisdom, faithfulness, holiness, and love. It showed Him wise, in providing a plan whereby He could be just, and yet the justifier of the ungodly.—It showed Him faithful in keeping His promise, that the seed of the woman should bruise the serpent’s head.—It showed Him holy, in requiring His law’s demands to be satisfied by our great Substitute.—It showed Him loving, in providing such a Mediator, such a Redeemer, and such a Friend for sinful man as His co-eternal Son.")

John 17:23 I in them, and Thou in Me, that they may be perfected in unity, that the world may know that Thou didst send Me, and didst love them, even as Thou didst love Me. (Comment: "In unity" is literally “unto oneness” and represents the goal of the perfecting action, that goal being believers might be in a state of having achieved the unity intended for them; one which reflects the unity between the Father and the Son)

John 19:28 After this, Jesus, knowing that all things had already been accomplished (related verb teleo), in order that the Scripture might be fulfilled (teleioo), said, "I am thirsty." (Comment: Here Scripture "reaches it's goal" or is fulfilled in Jesus.)

Acts 20:24 "But I do not consider my life of any account as dear to myself, in order that I may finish my course (dromos = race, the course of one's life), and the ministry which I received from the Lord Jesus, to testify solemnly of the gospel of the grace of God.

2 Corinthians 12:9 And He has said to me, "My grace is sufficient (IS = It already is - we don't need to ask Him for more. We need to abide in the sufficiency of what He has already provided) for you, for power is perfected in weakness." Most gladly, therefore, I will rather boast about my weaknesses, that the power of Christ may dwell in me.

Philippians 3:12 (note) Not that I have already obtained it, or have already become perfect (reached my goal, accomplished), but I press on in order that I may lay hold of that for which also I was laid hold of by Christ Jesus.

James 2:22 You see that faith was working with his works, and as a result of the works, faith was perfected;

1 John 2:5 but whoever keeps His word, in him the love of God has truly been perfected. By this we know that we are in Him:

1 John 4:12 No one has beheld God at any time; if we love one another, God abides in us, and His love is perfected in us.

1 John 4:17 By this, love is perfected with us, that we may have confidence in the day of judgment; because as He is, so also are we in this world.

1 John 4:18 There is no fear in love; but perfect love casts out fear, because fear involves punishment, and the one who fears is not perfected in love.

AND ON THE OTHER HAND THERE IS A BRINGING IN OF A BETTER HOPE THROUGH WHICH WE DRAW NEAR TO GOD: epeisagoge de kreittonos elpidos di e eggizomen (1PPAI) to theoeggizomen to theo: (Galatians 3:24) (Hebrews 6:18; 8:6; 11:40; John 1:17; Romans 8:3; Colossians 1:27; 1 Timothy 1:1) (Hebrews 4:16; 10:19-22; Psalms 73:28; John 14:6; Romans 5:2; Ephesians 2:13-18; 3:12)

Bringing in (1898) (epeisagoge from epí = upon + eisagoge = introduction) means literally leading in upon and thus the bringing in or introduction of something additional. Josephus (Ant XI.6,2) uses it to describe the introduction of a new wife in place of the repudiated one!

Better (2909) (kreitton) servers as the comparative degree of agathos = intrinsically good and thus means excellent, better, more useful, more profitable.

A better hope - A better certainty, one which give absolute assurance of future good, an assurance that God will do good to me in the future because I am safe in Christ by grace through faith. In his first epistle to Timothy Paul explained the ultimate Source of the believer's better hope...

Paul, an apostle of Christ Jesus according to the commandment of God our Savior, and of Christ Jesus our Hope (1 Timothy 1:1)

Hope (1680) (elpis)  in Scripture is not the world's definition of "I hope so", with a few rare exceptions (e.g., Acts 27:20) but is is an absolute certainty of future good. Hope is defined as a desire for some future good with the expectation of obtaining it. Hope is confident expectancy. Hope is the looking forward to something with some reason for confidence respecting fulfillment. See related study on the Believer's Blessed Hope.

“a pathological belief in the occurrence of the impossible.”