Colossians 1:10 so that you will walk (AAN) in a manner worthy of the Lord to please Him in all respects  bearing fruit (PAPMPN) in every good work and increasing (PPPMPN) in the knowledge of God;  (NASB: Lockman)

SO THAT YOU MAY WALK: peripatesai (AAN): (Col 2:6, 4:5, Mic 4:5 Ro 4:12, 6:4 Eph 4:1, 5:2,15, Php 1:27, 1Th 2:12 )

So that - Not in Greek, but in context clearly the implied purpose of the prayer for the saints to be filled with spiritual knowledge. Paul was not an interested in pedantry (a "show" of one's knowledge) but in pragmatism (practice, conduct concordant with the the Truth)

Spurgeon preaching on Paul's prayer calls us to observe...

The Practical Result Of Spiritual Knowledge. Paul prays for his friends “that ye might be filled with the knowledge of His will in all wisdom and spiritual understanding; that ye might walk worthy of the Lord unto all pleasing.”

See, see the drift of his prayer- “that ye may walk.” Not that ye might talk, not that ye might sit down and meditate, and enjoy yourselves, but “that ye might walk.” He aims at practical results.

He desires that the saints may be instructed so that they may walk according to the best model. By walking worthy of the Lord Jesus we do not understand in any sense that he expected them to possess such worthiness as to deserve to walk with the Lord; but he would have them live in a manner that should be in accordance with their communion with Christ. You would not have a man walk with Christ through the streets to-day clothed in motley garments, or loathsome with filth: would you? No, if a man be a leper, Christ will heal him before he will walk with him. Let not a disciple walk so as to bring disgrace upon his Lord!

When you walk with a king, you should be yourself royal in gait; when you commune with a prince you should not act the clown. Dear friends, may you know so much of Jesus that your lives shall become Christ-like, fit to be put side by side with the character of Jesus, worthy of your perfect Lord.

This is a high standard, is it not? It is always better to have a high standard than a low one, for you will never go beyond that which you set up as your model. If you get a low standard you will fall below even that. It is an old proverb,

“He that aims at the moon will shoot higher than he that aims at a bush.”

It is well to have no lower standard than the desire to live over again the life of the Lord Jesus-a life of tenderness, a life of self-sacrifice, a life of generosity, a life of love, a life of honesty, a life of holy service, a life of close communion with God. Mix all virtues in due proportion, and that is the life of Jesus towards which you must press forward with all your heart (See the full sermon - Spiritual Knowledge: It's Practical Results)

Walk (4043) (peripateo from peri = about, around + pateo = walk, tread) means literally to walk around, to go here and there in walking, to tread all around.  The  39 uses in the Gospels always refer to literal, physical walking. Seven of the 8 uses in Acts are also in the literal sense (except Acts 21:21). (See Spurgeon's comments on what it means to walk)

Paul uses peripateo only in the metaphorical sense (32 times in his Epistles - see all the NT uses below) meaning to conduct one's life, to order one's behavior, to behave,  to make one's way, to make due use of opportunities, to live or pass one’s life (with a connotation of spending some time in a place).

Some lexicons state that Paul used peripateo in the Hebraic sense of living, regulating one's life or conducting one's self.

NIDNTT writes that...

peripateo (Aristophanes onwards) is found in classic Greek only with the literal meaning of strolling, stopping, (e.g. while one walks here and there in the market, Dem., Orationes 54, 7); the figurative meaning of walking, with reference to conduct, is lacking. Only in Philodemus (1st cent. B.C.) does one find the meaning to live (De Libertate 23, 3)... In the LXX peripateo is found in only 33 passages, of which more than half come from Wisdom literature...  Only occasionally does peripateo denote in the figurative sense way of life (2Ki. 20:3; Eccl 11:9). (Brown, Colin, Editor. New International Dictionary of NT Theology. 1986. Zondervan) 

How the Colossians (and saints today) "walked" was obviously important to Paul as he used peripateo in each chapter of Colossians -- In chapter 2 Paul charged the Colossians -

Conduct (present imperative = command to make this their lifestyle) yourselves with wisdom (living prudently and with discretion) toward outsiders (non-Christians), making the most of the opportunity (continually seizing, redeeming or buying up the opportunity). (see note Colossians 4:5) (Comment: Weymouth catches the thought well paraphrasing it "Behave wisely in relation to the outside world.")

Peripateo is found 4 times in Colossians and 95 times in the NT

GOSPELS: Matt. 4:18; 9:5; 11:5; 14:25, 26, 29; 15:31; Mk. 2:9; 5:42; 6:48, 49; 7:5; 8:24; 11:27; 12:38; 16:12; Lk. 5:23; 7:22; 11:44; 20:46; 24:17; Jn 1:36; 5:8, 9, 11,12; 6:19, 66; 7:1; 8:12; 10:23; 11:9, 10, 54; 12:35; 21:18;

ACTS: Acts 3:6, 8, 9, 12; 14:8, 10; 21:21;

PAULINE USES: Rom. 6:4; 8:4; 13:13; 14:15; 1 Co. 3:3; 7:17; 2 Co. 4:2; 5:7; 10:2, 3; 12:18; Gal. 5:16; Eph. 2:2, 10; 4:1, 17; 5:2, 8, 15; Phil. 3:17, 18; Col. 1:10; 2:6; 3:7; 4:5; 1Thess. 2:12; 4:1, 12; 2Thess. 3:6, 11

GENERAL: Heb. 13:9; 1Pet. 5:8;

JOHN: 1 Jn. 1:6, 7; 2:6, 11; 2Jn. 1:4, 6; 3Jn. 1:3, 4; Rev. 2:1; 3:4; 9:20; 16:15; 21:24

There are 25 uses of peripateo in the non-apocryphal Septuagint (LXX)

Ge 3:8, 10; Ex 21:19; Judges 21:24; 1Sam 17:39; 2Sam 11:2; 2Ki 20:3; Esther 2:11; Job 9:8; 20:25; 38:16; Ps 12:8; 104:3; 115:7; 135:17; Pr 6:22, 28; 8:20; 23:31; Eccl 4:15; 11:9; Isaiah 8:7; 59:9; Da 3:25; 4:29, 33

Here are two of the uncommon figurative uses of peripateo in the LXX...

2 Kings 20:3 "Remember now, O LORD, I beseech Thee, how I have walked (Lxx = peripateo) before Thee in truth and with a whole heart, and have done what is good in Thy sight." And Hezekiah wept bitterly.

Ecclesiastes 11:9 Rejoice, young man, during your childhood, and let your heart be pleasant during the days of young manhood. And follow the impulses of your heart (Lxx = "walk [peripateo in present imperative] in the ways of thy heart blameless") and the desires of your eyes. Yet know that God will bring you to judgment for all these things.

In the KJV peripateo is translated walk in all but three places in the NT uses. In these it is rendered go about (Mark 12:38), walk about (1Pet 5:8-note), and be occupied (Heb 13:9-note).

In the NAS peripateo is translated by a number of words:  behave(2), conduct ourselves (1), conduct yourselves (1), leading a life(1), leads a life (1), prowls about(1), walk(50), walk about(1), walk around(2), walked(7), walking(21), walking about(1),walks(5), were thus occupied (1).

In Romans Paul explains how it is possible to no long walk as the Gentiles writing (speaking of our spiritual baptism into Christ)

we have been buried with Him through baptism into death, in order that as Christ was raised from the dead through the glory of the Father, so we too might walk (peripateo - Paul's first use in the NT canon) in newness (a brand new kind of life never possible before) of life.  (See note Romans 6:4)

(God condemned sin in the flesh of His Son) in order that the requirement of the Law might be fulfilled in us, who do not walk (peripateo) according to the flesh, but according to the Spirit. (See note Romans 8:4)

Let us behave (peripateo) properly (fitting or becoming in a manner of behavior) as in the day, not in carousing and drunkenness, not in sexual promiscuity and sensuality, not in strife and jealousy. (See note Romans 13:13)

For if because of food your brother is hurt, you are no longer walking according to love. Do not destroy with your food him for whom Christ died. (See note Romans 14:15)

Some uses of peripateo in Corinthians...

For (explaining why they still need milk and cannot take solid food) you (babes in Christ) are still fleshly. For since there is jealousy and strife among you, are you not fleshly, and are you not walking like mere men? (1Cor 3:3)

for we walk by faith, not by sight (2 Cor 5:7)

For though we walk in the flesh, we do not war according to the flesh (2 Cor 10:3)

I urged Titus to go, and sent the brother with him. Titus did not take any advantage of you, did he? Did we not conduct ourselves in the same spirit and walk in the same steps? (2 Cor 12:18)

Paul charges believers to...

walk (present imperative = command to make this one's lifestyle) by the Spirit, and you will not carry out the desire of the flesh. (Gal 5:16)

Paul's classic description of unbelievers in Ephesians...

And you were dead in your trespasses and sins, 2 in which you formerly walked according to the course of this world, according to the prince of the power of the air, of the spirit that is now working in the sons of disobedience. (See notes Ephesians 2:1; 2:2)

Paul's contrasting description of believers...

For we are His workmanship, created in Christ Jesus for good works, which God prepared beforehand, that we should walk in them. (See note Ephesians 2:10)

After describing the wealth (in Christ Jesus, in the heavenly places) of believers in the first three chapters of Ephesians, Paul proceeds to exhort us to walk accordingly (note the concentration of peripateo in the second half of Ephesians)...

I, therefore, the prisoner of the Lord, entreat you to walk in a manner worthy of the calling with which you have been called, (See note Ephesians 4:1)

and walk in love, just as Christ also loved you, and gave Himself up for us, an offering and a sacrifice to God as a fragrant aroma. (See note Ephesians 5:2)

for you were formerly darkness, but now you are light in the Lord; walk (present imperative = command to make this one's lifestyle) as children of light (See note Ephesians 5:8)

Therefore be careful how you walk, not as unwise men, but as wise, 16 making the most of (redeeming, buying up every second) your time, because the days are evil. (See note Ephesians 5:15; Ephesians 5:16)

Here are a few of Paul's uses of peripateo in other epistles...

Brethren, join (present imperative = command to make this one's lifestyle)  in following my example, and observe (present imperative = command to make this one's lifestyle pay attention to, implying mental concentration regarding) those who walk according to the pattern you have in us. (See note Philippians 3:17) 18 For many walk, of whom I often told you, and now tell you even weeping, that they are enemies of the cross of Christ, (See note Philippians 3:18)

Finally then, brethren, we request and exhort you in the Lord Jesus, that, as you received from us instruction as to how you ought to walk and please God (just as you actually do walk), that you may excel still more. (See note 1Thessalonians 4:1)

John uses peripateo in the figurative sense affirming that,

F B Meyer (Our Daily Walk) - WALKING WITH JESUS (Col. 2:6-note)

But such a walk is only possible when we have learned to "crucify the flesh with the affections and lusts" (Gal. 5:24-note). The flesh is the assertion of our self-life, whether in lesser or grosser forms, but whenever self intrudes it exercises a baleful influence on our behavior and Conversation. Just as the iron of the steamer will deflect the needle of the compass, so the intrusion of our self-life will act as a drag upon our character and walk.

IN A MANNER WORTHY OF THE LORD:  axios tou kuriou:

Worthy (axios) is the Lamb that was slain to receive power and riches and wisdom and might and honor and glory and blessing. (Rev 5:12 see note) 

worthy to open the book and to break its seals? (Rev 5:2 see note)

I, therefore, the prisoner of the Lord, entreat you to walk in a manner worthy of the calling with which you have been called (Ep 4:1-note)

in a manner worthy of the calling with which you have been called with all humility and gentleness, with patience, showing forbearance to one another in love, being diligent to preserve the unity of the Spirit in the bond of peace." (see notes Ephesians 4:1; 4:2; 4:3)

contentment (1Co 7:17)

faith (2Co 5:7)

unity (Ep 4:3-note; Php 1:2-note)

love (Ep 5:2-note)

truth (3Jn 3, 4)

But you have a few people in Sardis who have not soiled their garments; and they will walk with Me in white; for they are worthy. (Re 3:4-note)

You honor God's name
When you call Him your Father
And live like His Son

“Am I conducting myself in a manner worthy of the Gospel?”
is a good question for us to ask ourselves regularly.

Right thinking should always lead to right conduct. Knowledge and obedience go together. One cannot separate learning from living. The idea of "worthy" is that the conduct of the saints weigh as much as the character of Christ Why? because when we are surrendered to His will, He is living His life through us. Ultimately His conduct is the only conduct which is truly worthy for no other conduct would balance God's perfect scales that look at hearts, motives, agendas, etc. Christ alone pleases the Father completely and as we allow Christ to rule and reign in our lives, our lives become pleasing to the Father. Our responsibility is purpose in our heart to be pleasing to Him.  We cannot work for God unless we are walking with GOD and we cannot walk with GOD if we are ignorant of His will. Having the knowledge of God’s Word controlling and renewing our minds is a key to righteous living for what controls your thoughts will control your behavior.

TO PLEASE HIM IN ALL RESPECTS: eis pasan areskeian en panti: (Col 3:20, Pr 16:7, 1Th 4:1, 2Ti 2:4, Heb13:16, 1Jn 3:22)

Spurgeon calls us to observe that...

Next, the apostle would have us get knowledge in order that we may so live as to be pleasing to our best friend-

“worthy of the Lord unto all pleasing.”

Is not that beautiful? To live so as to please God in all respects! Some live to please themselves, and some to please their neighbors, and some to please their wives, and some to please their children, and some live as if they wished to please the devil; but our business is to please Him in all things Whose servants we are. Without faith it is impossible to please Him; so away with unbelief! Without holiness no man shall see Him, much less please Him; therefore let us follow after holiness, and may the Lord work it in us.

“Unto all pleasing”-so that we may please God from the moment we rise in the morning to the time when we lie down, ay, and please Him even when we are asleep: that we may eat and drink so as to please Him; that we may speak and think so as to please Him; that we may go or stay so as to please Him; that we may rejoice or suffer so as to please Him- “walking worthy of the Lord unto all pleasing.”

Oh, blessed man,
whose life is pleasing to God in all respects!

The apostle Paul desires that we may be filled with knowledge to this very end. If I do not know the will of God how can I do the will of God? At least, how can there be anything pleasing to God which is ignorantly done without an intent to do His will? I fear that many children of God grieve their heavenly Father much through sins of ignorance-an ignorance in which they ought not to remain a single day. Be it clearly understood that sins of ignorance are truly sins. They have not about them the venom and the aggravation which are found in sins against light and knowledge, but still they are sins; for the measure of our duty is not our light, but the law of God itself. If a man pleads that he follows his conscience, yet this will ’not excuse his wrongdoing if his conscience is an unenlightened conscience, and he is content to keep it in the dark. You are to obey the will of the Lord: that will is the standard of the sanctuary. Our conscience is often like a deficient weight, and deceives us; be it ours to gather a clear knowledge of the word, that we may prove what is that perfect and acceptable will of God. The law makes no allowance for errors committed through false weights; when a man says, “I thought my weights find measures were all right,” he is not thereby excused. The law-deals with facts, not with men’s imaginations; the weights must actually be correct, or the penalty is exacted; so is it with conscience, it ought to be instructed in the knowledge of the divine will, and if it is not so, its faultiness affords no justification for evil. Hence the absolute necessity of knowledge in order to true holiness. God grant us grace to know His will, and then to obey it “unto all pleasing.” (See the full sermon - Spiritual Knowledge: It's Practical Results)

Please (699) (areskeia) means a desire or willingness to please, an endeavor to please, complaisance (disposition to please or comply), obsequiousness (marked by or exhibiting a fawning attentiveness). Areskeia is the desire to do something that produces satisfaction. Areskeia was used especially in public documents, descriptive of exceptional public service or expression of devotion. Interestingly, the root word areskos is combined with the Greek word for man (anthropos) to describe a "man pleaser". How would you describe yourself: "Man pleaser" or "God pleaser"?

One of the chief aims of our life should be to seek to please God and to do so because we love Him Who first loved us (1Jn 4:19), for true love obeys.  Everybody lives to please somebody. So the question is - Who are you seeking to please? Pleasing God ought to be the major motive of the Christian life. Children should live to please their father, and even more so should spiritual children seek to please their Father Who is in heaven. The Holy Spirit “is at work in you, both to will and to work for His good pleasure.” (Php 2:13-note).

Enoch walked with God (the Greek Septuagint of Gen 5:22 says "Enoch was well pleasing God"), and before God called him to heaven, Enoch “obtained the witness that before his being taken up he was pleasing to God" (He 11:5-note) What a testimony! 

Our Lord Jesus, the One we are to imitate and Who now indwells us in Spirit, while on earth as Man said "I always do the things that are pleasing to Him." (John 8:29). 

Pleasing God means much more than simply doing God’s will. The half hearted prophet Jonah illustrates that it is possible to obey God and yet not please Him, for Jonah did what he was commanded, but his heart was not in it. (see Jonah 4:1ff) God blessed His Word but He could not bless His servant, Jonah. So Jonah sat outside the city of Nineveh angry with everybody, including the Lord! Our obedience should

not (be) by way of eyeservice, as men-pleasers, but as slaves of Christ, doing the will of God from the heart. (see note Ephesians 6:6)

It is well-pleasing to God when we present our bodies to Him as living sacrifices (Romans 12:1 see note) and when we live so as to help others and avoid causing them to stumble (Romans 14:18 - note). God is pleased when His children separate themselves from the evil around them (Ephesians 5:10 - note), as well as when they bring their offerings to Him (Philippians 4:18 -note). He is pleased with children who submit to their parents (Colossians 3:20 - note), as well as with saints who permit Jesus Christ to work out His perfect will in their lives (Hebrews 13:20-note; Heb 13:21 - note).

Paul summarized what the goal should be for every saint

Therefore also we have as our ambition, whether at home or absent, to be pleasing to Him. (2Co 5:9)

Micah sums it up beautifully in the OT writing

He has told you, O man, what is good and what does the Lord require of you but to do justice, to love kindness, and to walk humbly with your God?" (Micah 6:8)

One of the tragic paradoxes in many modern evangelical circles is the emphasis on “spiritual knowledge” and “Christian service” without connecting these matters to purity of personal character (eg, holiness, godliness). God builds character before He calls to service. He must work in us before He can work through us. Knowledge, conduct, service, and character must always go together. We know God’s will that we might obey it; and, in obeying it, we serve Him and grow in Christian character. While none of us is perfectly balanced in these four factors, we ought to strive for that balance.

BEARING FRUIT IN EVERY GOOD WORK: ergo agatho karpophorountes (PAPMPN): (John 15:4-5, 15:8,16 Ro 7:4; 7:5;15:26, 27, 28 Gal 5:22,23 Eph 2:10; Php 1:11; Titus 3:1,14; Heb 12:11; 13:21; James 3:17 2Pe 1:8)

Spurgeon calls us to observe that...

“That ye might walk worthy of the Lord unto all pleasing, being fruitful” Paul would have us producing the best fruit. Without knowledge we cannot be fruitful; at least in the points whereof we are ignorant we must fail to bring forth fruit. Therefore would he have us to be right well taught, that we may abundantly produce fruit unto God’s glory.

He says, “fruitful in every good work”; and this means much. He desires us to be as full of good works as we can hold. Some are hindered in this because they do not know how to set about holy service. How can a man be fruitful as a preacher if he does not know what to preach? True, he may preach the elementary doctrine of the cross, but even that he will be apt to set forth in a blundering manner. For certain, a man cannot teach what he does not know. The zealous, but untaught man, would be much more fruitful if he had a clearer understanding of divine things. In daily life, if in knowledge you are ignorant as to the things of God, you will be ready to become the prey of any false teacher who may chance to pick you up. In hundreds of ways ignorance will make you run risks, lose opportunities of usefulness, and fall into dangerous mistakes. Knowledge is food to the true heart, and strengthens it for the Lord’s work. Oh, to have knowledge placed like good soil around the roots of the soul, to fertilize the mind, that thus the clusters of usefulness may be as large as those of Eshcol: beautiful, plentiful, sweet, and fall. May our Lord, the King of Israel, to Whom the vineyard belongs, receive an abundant reward for all His labor for the vines which He has planted.

There is another note in this verse, which I beg you to notice. Paul would have them cultivate a comprehensive variety of the best things. He says-

“Fruitful in every good work.”

Here is room and range enough- “in every good work.” Have you the ability to preach the gospel? Preach it! Does a little child need comforting? Comfort it! Can you stand up and vindicate a glorious truth before thousands? Do it! Does a poor saint need a bit of dinner from your table? Send it to her. Let works of obedience, testimony, zeal, charity, piety, and philanthropy all be found in your life. Do not select big things as your specialty, but glorify the Lord also in the littles- “fruitful in every good work.”

You never saw in nature a tree which yielded all sorts of fruit, and you never will. I have seen a tree so grafted that it produced four kinds of fruit at one time, but I remarked that it was a poor business in reference to two of the varieties; for one of the grafts, more natural than the others to the parent stem, drew off the most of the sap, and flourished well, but robbed the other branches. The second sort of fruit managed to live pretty fairly, but not so well as it would have done on its own stem. As for the third and fourth, they were mere attempts at fruit of the smallest size. This tree was shown to me as a great curiosity; it is not likely that practical gardeners will be encouraged by the experiment. But what would you think of a tree upon which you saw grapes, and figs, and olives, and apples, and all other good fruits growing at one time? This is the emblem of what instructed believers will become: they will produce all sorts of goodness and graciousness to the honor of their heavenly Father.

I have no doubt that you will naturally abound most in certain good works for which you have the largest capacity, but still nothing ought to come amiss to you. In the great house of the church we want servants who will not be simply cooks or housemaids, but general servants, maids of all work, prepared to do anything and everything. I have known persons in household employment in England who would not do a turn beyond their special work to save their masters’ lives: these are a sort of servants of whom the fewer the better. In India this is carried to a ridiculous extreme. The Hindoo water-bearer will not sweep the house, nor light a fire, nor brush your clothes-he will fetch water, and nothing else: you must, therefore, have a servant for each separate thing, and then each man will do his own little bit, but he will not go an inch beyond. When we enter into Christ’s church we should come prepared to wash the saints’ feet, or bear their burdens, or bind up their wounds, or fight their foes, or act as steward, or shepherd, or nurse. It has been well said that if two angels in heaven were summoned to serve the Lord, and there were two works to be done, an empire to be ruled, or a crossing to be swept, neither angel would have a choice as to which should be appointed him, but would gladly abide the will of the Lord. Let us be equally prepared for anything, for everything by which fruit can be produced for the Well-beloved.

Why is it that some are not fruitful in this comprehensive way?

Because they are not filled with knowledge in all wisdom. When a man says,

“You ask me to do the lowest work! Don’t you know that I am a man of remarkable ability who should have higher work to do?”

I venture to assert that he is an ignorant man. Self-assertion is ignorance on horseback. You have probably read of a certain renowned corporal in the American service a century ago. A general, as he rode along, saw a body of men endeavoring to lift timber. They were shorthanded, and the work lagged, but their famous corporal stood by ordering them about at a magnificent rate. The general passed and said,

“Why don’t you lend them help and put your shoulder to it?

“Why, sir,” said the great little officer, “how can you think of such a thing? Do you know who I am? I am a corporal!”

The general got off his horse, pulled off his coat, and helped to move the timber, and by his judicious help the soldiers achieved their task. Then he turned to the high and mighty gentleman and said,

“Mr. Corporal, next time you want a man to do such work as this you can send for me: I am General Washington.”

Just so the Lord Jesus Christ if He were here would gladly do a thousand things which His poor little servants are too great to touch. I know you, dear brother, you are too experienced, too old, too learned to help the Sunday school! I know you are too respectable to give away a tract! Pray get out of such ignorant ways of thinking, and ask to be useful in all possible ways. If you have done a little, do much; if you have done much, do more; and when you have more, ask for grace to proceed to the highest possible degree of usefulness for your Lord. (See the full sermon - Spiritual Knowledge: It's Practical Results)

Bearing fruit (2592) (karpophoreo from karpos = fruit, produce + phero = bear, bring)  literally means to bring forth fruit, to be fertile, productive. It is used figuratively to refer to bringing forth deeds or works (fruit), which depending on the context can be good fruit or bad fruit (see verses below, especially notes on Ro 7:4, 5-note)

In John 15:5 those who abide in the Vine Christ Jesus, will bring forth "much fruit" ("good works"). In this verse Paul says that they will continually (present tense) bear fruit in (every good work) every kind of activity undertaken for the name of Christ and in the operating power of the indwelling Holy Spirit, upon Whom the believer is entirely dependent.

Jesus used karpophoreo several times...

"And the one on whom seed was sown on the good soil, this is the man who hears the word and understands it; who indeed bears fruit (present tense) and brings forth, some a hundredfold, some sixty, and some thirty." (Matthew 13:23)

"The soil produces crops (present tense) by itself; first the blade, then the head, then the mature grain in the head. (Mark 4:28)

Comment: This is the only literal use of this verb in the NT

And the seed in the good soil, these are the ones who have heard the word in an honest and good heart, and hold it fast (refers to ongoing obedience), and bear fruit (present tense) with perseverance. (Luke 8:15)

Comment: These hearer of the word (seed) not only received the word but allowed it to mold their lives. They were teachable and obedient, and developed true Christ-like character and produced fruit that glorified their Father in heaven. They bore genuine spiritual fruit which evidenced that they possessed genuine spiritual life. As J Vernon McGee says these fruit bearers "are the hearers who are genuinely converted by the Word of God."- Thru the Bible Commentary)

Paul used karpophoreo in Romans 7 writing...

Therefore, my brethren, you also were made to die to the Law through the body of Christ, that you might be joined to another, to Him who was raised from the dead, that we might bear fruit for God. For while we were in the flesh, the sinful passions, which were aroused by the Law, were at work in the members of our body to bear fruit for death. (see note Romans 7:4-5) (Comment: Regenerate and unregenerate men are contrasted, in the unregenerate “the passions of sins,” or the sinful impulses bearing fruit unto death, as these activities arise out of a state of alienation from God. In the regenerate man the power of the indwelling Spirit Who unites the soul with the risen Lord bears fruit unto God = good fruit or Good Deeds)

In this same chapter of Colossians Paul in reference to the gospel...

which has come to you, just as in all the world also it is constantly bearing fruit and increasing, even as it has been doing in you also since the day you heard of it and understood the grace of God in truth (Col 1:6-note)

Karpophereo is used 8 times in the NT

Mt 13:23; Mark 4:20, 28; Lk 8:15; Ro 7:4, 5; Col 1:6, 10

There is one use of Karpophereo in the Septuagint (LXX) in Habakkuk 3:17...

Though the fig tree should not blossom (bear no fruit - karpophoreo), And there be no fruit on the vines, Though the yield of the olive should fail, And the fields produce no food, Though the flock should be cut off from the fold, And there be no cattle in the stalls...

Lord, on our souls Thy Spirit pour;
The moral waste within restore;
O let Thy love our springtide be,
And make us all bear fruit to Thee
--Henry Lyte (Play hymn)

Precious Jesus, I beseech Thee,
May Thy words take root in me;
May this gift from heav’n enrich me
So that I bear fruit for Thee!
(Play hymn)

Almighty Father, bless the Word,
Which through Thy grace we now have heard.
O may the precious seed take root,
Spring up, and bear abundant fruit.
(Play hymn)

Every Good work - Not just "some" but "every" work that is "good". See study on Good Deeds

Good (18) (agathos) (click discussion of good deeds) means intrinsically good, inherently good in quality but with the idea of good which is also profitable, useful, benefiting others, benevolent (marked by or disposed to doing good).

The meaning of kalos (2570) is also discussed in this topic. The basic meaning of kalos  describes that which is inherently excellent or intrinsically good, providing some special or superior benefit. Kalos is good with emphasis (as discussed below) on that which is beautiful, handsome, excellent, surpassing, precious,   commendable, admirable. Kalos describes that which is inherently excellent or intrinsically good and/or that which provides some special or superior benefit.  In classical Greek kalos was originally used to describe that which outwardly beautiful. Other secular uses of kalos referred to the usefulness of something such as a fair haven, a fair wind or that which was auspicious such as sacrifices. Kalos referred to that which was "morally beautiful" or noble and hence virtue was called "the good" (to kalon). The New Testament uses of kalos are similar to the secular Greek -- outwardly fair, as the stones of the temple (Lk 21:5); well adapted to its purpose, as salt ("salt is good" Mk 9:50); competent for an office, as deacons ("good servant of Christ Jesus" 1Ti 4:6); a steward ("serving one another, as good stewards of the manifold grace of God", see note 1 Peter 4:10); a good soldier (note 2 Timothy 2:3); expedient, wholesome ("it is better for you to enter life crippled" Mk 9:43, 45, 47); morally good, noble, as works ("Let your light shine before men in such a way that they may see your good works" see note Matthew 5:16); conscience ("we are sure that we have a good conscience", see note Hebrews 13:18). The phrase it is good, i.e., a good or proper thing ("It is good not to eat meat or to drink wine", see note Romans 14:21). In the Septuagint (LXX) kalos is the most commonly used word for good as opposed to evil (e.g., see Ge 2:17; 24:50; Isaiah 5:20).

Agathos is used 102 times in 91v the NT (Mt 5:45; 7:11, 17f; 12:34f; 19:16f; 20:15; 22:10; 25:21, 23; Mark 3:4; 10:17f; Luke 1:53; 6:45; 8:8, 15; 10:42; 11:13; 12:18f; 16:25; 18:18f; 19:17; 23:50; John 1:46; 5:29; 7:12; Acts 9:36; 11:24; 23:1; Rom 2:7, 10; 3:8; 5:7; 7:12f, 18f; 8:28; 9:11; 10:15; 12:2, 9, 21; 13:3f; 14:16; 15:2; 16:19; 2 Cor 5:10; 9:8; Gal 6:6, 10; Eph 2:10; 4:28f; 6:8; Phil 1:6; Col 1:10; 1Th 3:6; 5:15; 2Th 2:16, 17; 1 Tim 1:5, 19; 2:10; 5:10; 2 Tim 2:21; 3:17; Titus 1:16; 2:5, 10; 3:1; Philemon 1:6, 14; Heb 9:11; 10:1; 13:21; Jas 1:17; 3:17; 1 Pet 2:18; 3:10f, 13, 16, 21; 3 John 1:11) and is translated generous, 1; good, 81; good man, 2; good thing, 6; good things, 6; goodness, 1; goods, 2; kind, 1; kindly, 1; kindness, 1

Kalos is used 102 times in 91v the NT (Matt 3:10; 5:16; 7:17, 18, 19; 12:33; 13:8, 23f, 27, 37f, 45, 48; 15:26; 17:4; 18:8f; 26:10, 24; Mark 4:8, 20; 7:27; 9:5, 42f, 45, 47, 50; 14:6, 21; Luke 3:9; 6:38, 43; 8:15; 9:33; 14:34; 21:5; John 2:10; 10:11, 14, 32f; Acts 25:10; 27:8; Rom 7:16, 18, 21; 12:17; 14:21; 1 Cor 5:6; 7:1, 8, 26; 9:15; 2 Cor 8:21; 13:7; Gal 4:18; 6:9; 1Thess 5:21; 1 Tim 1:8, 18; 2:3; 3:1, 7, 13; 4:4, 6; 5:10, 25; 6:12f, 18f; 2 Tim 1:14; 2:3; 4:7; Titus 2:7, 14; 3:8, 14; Heb 5:14; 6:5; 10:24; 13:9, 18; Jas 2:7; 3:13; 4:17; 1 Pet 2:12; 4:10) and is translated  beautiful, 1; better, 2; commendable manner, 1; excellent, 1; fair, 1; fine, 2; good, 79; high, 1; honest, 1; honorable, 1; right thing, 1; sound, 1; treasure, 1; what is right, 2.

Agathos is one whose goodness and works of goodness are transferred to others. Good and doing good is the idea. Agathos describes that which is beneficial in addition to being good.

Agathos is that which is  good in its character, beneficial in its effects and/or  useful in its action.

Agathos is used in the New Testament primarily of spiritual and moral excellence. Paul uses agathos to describe the gospel as the “glad tidings of good things” (see note Romans 10:15). The writer of Hebrews uses it in the same way, of “the good things to come” of which “Christ appeared as a high priest” (see note Hebrews 9:11) and of which the law was “only a shadow” (see note Hebrews 10:1).

The precise meaning of agathos can be difficult to appreciate and distinguish from kalos (2570)  an adjective that is also translated good. An attempt is made in the following discussion to bring out the difference, but in some verses where both are used, this distinction can be difficult to appreciate.

Agathos describes that which is perfect, producing pleasure, satisfaction, and a sense of well-being, for example describing a good conscience in (1Ti 1:5).

But the goal of our instruction is love from a pure heart and a good (agathos) conscience and a sincere faith.

A good (agathos) conscience is that which has been cleansed from guilt, through the blood of Christ, and as a result of this, responds to the claims of the Lord to exercise love, as being the aim of the charge Paul gives to Timothy in this verse.

Agathos describes the believer's deeds that remain withstand being tested by fire at the Judgment Seat of Christ (1Cor 3:12, 13)

The words of saints are to be agathos (good for edification) (see note Ephesians 4:29)

Paul uses agathos in his prayer in second Thessalonians writing...

Now may our Lord Jesus Christ Himself and God our Father, Who has loved us and given us eternal comfort and good (agathos) hope by grace, comfort and strengthen your hearts in every good work and word. (2Thes 2:16-17) (Comment: Here the hope is classified as intrinsically good because of its cheering and sustaining effect on the believer who cherishes it.)

In reference to God (as in Mt 19:16) agathos conveys the sense of perfect.

Agathos is distinguished from kalos in that while agathos is inherently, morally, or practically good, kalos takes that a step further and adds the idea of aesthetically good, beautiful, fair and appealing to the eye. Thus kalos is used to describe a qualification of an elder as

one who manages his own household well (kalos not agathos)" (1Ti 3:4).

In other words  an elder must be one whose leadership in the home is not only intrinsically good (which it should be = agathos), but also visibly good (kalos = because he as leader will be watched closely by the sheep under him and by the pagan outside the flock). Agathos is good in the sense of useful, kalos good in the sense of beautiful, although the distinction is subtle.

This distinction between agathos and kalos is brought out to a degree in Romans 12:17 (note) where Paul instructs believers to...

Never pay back evil for evil to anyone. Respect what is right (kalos) in the sight of all men. (Comment: Agathos refers to intrinsic goodness, and kalos here, to exterior goodness, or goodness that is seen on the exterior of a person, the outward expression of an inward goodness. When this outward expression conforms to the inward goodness, then that expression which a Christian gives of himself is an honest one, one conforming to the inner facts. The word could be translated in a connection like this by the word “seemly,” seemly in that the expression is fitting. But if the Christian assumes an outward expression which is patterned after this age, that expression not representing what he is, a child of God, but giving the beholder the impression that he is a person of the world, that expression is a dishonest one. - from Wuest - Reference or Logos)

Agathos refers to intrinsic goodness, but in Romans 12:17 Paul uses kalos to describe exterior goodness, or goodness that is seen on the exterior of a person, the outward expression of an inward goodness. Such exterior goodness (which is beautiful, fair, virtuous) is necessary because what we do as Christians is observed by those around us, and it is important that our conduct, which is open to “the eyes of everybody,” brings honor to our God and corresponds to our profession.

Vine notes that

The word kalos, “good,” signifies the absolute worth of a thing, agathos denotes what is beneficial...kalos...describes that which is intrinsically good, that which is well adapted to the purpose intended; in 1Timothy 5:10, 25, 6:18 it describes that which is ethically good, right, noble, honorable; it is to be distinguished from agathos, good in character or constitution and beneficial in effect, as in 1Timothy 1:5, 19; 2:10; 5:10. (Vine, W. Collected writings of W. E. Vine. Nashville: Thomas Nelson or Logos)

And so we encounter both kalos and agathos in 1Timothy 5:10...

(widows) having a reputation for good (kalos) works; and if she has brought up children, if she has shown hospitality to strangers, if she has washed the saints' feet, if she has assisted those in distress, and if she has devoted herself to every good (agathos) work.

Vine commenting on the use of both kalos and agathos in 1Timothy 5:10 writes that...

Some would regard these adjectives as merely interchangeable in this connection. Kalos, however, directs attention to that which is fair, noble, honorable or beautiful, outwardly and visibly, agathos to that which, being good in character or constitution, is beneficial in effect. The distinctive meanings are well exemplified here: in the first case the word lays stress upon that which, being noble and honorable, bears a favorable report (not that it is not at the same time beneficial); in the second case the stress is on the beneficial character of the work. (Ibid or Logos)

In 1Timothy 6:18 good occurs twice, once as agathos and once as kalos...

Instruct them to do good, (agahoergeo - from agathos) to be rich in good (kalos) works, to be generous and ready to share. (Comment: Here Paul teaches that the liberal use of one’s means, while beneficent in effect (agathos), is intrinsically honorable, fair, beautiful (kalos).

In Romans 7:18 (note) Paul uses both agathos and kalos writing...

For I know that nothing good (agathos - here referring to nothing capable of accomplishing good. It is incapable of acting in a beneficial way) dwells in me, that is, in my flesh; for the wishing is present in me, but the doing of the good (kalos - that which is wholly admirable, fair) is not.

Comment: Denney says that kalos  suggests the moral beauty of the law, agathos  its beneficial purpose.

As Vine emphasizes that

while the difference between the words (agathos, kalos) may be thus generally stated, they are not always readily distinguishable (Vine, W. Collected writings of W. E. Vine. Nashville: Thomas Nelson or Logos)

Barclay writes that...

There are two Greek words for good. Agathos simply describes a thing as good. Kalos means that a thing is not only good but looks good; it has a winsome attractiveness about it. Real Christianity is a lovely thing. There are so many people who are good but with their goodness possess a streak of unlovely hardness. (note on Acts 3:1)...Now in Greek, there are two words for good. There is agathos which simply describes the moral quality of a thing; there is kalos which means that in the goodness there is a quality of winsomeness which makes it lovely. When Jesus is described as the good shepherd, the word is kalos. In him there is more than efficiency and more than fidelity; there is loveliness. Sometimes in a village or town people speak about the good doctor. They are not thinking only of the doctor’s efficiency and skill as a physician; they are thinking of the sympathy and the kindness and the graciousness which he brought with him and which made him the friend of all. In the picture of Jesus as the Good Shepherd there is loveliness as well as strength and power. (note on John 10:16)... In Greek there are two words for good. There is agathos which describes a thing which is morally good; and there is kalos which describes a thing which is not only good but lovely. A thing might be agathos, and yet be hard, stern, austere, unattractive. But a thing which is kalos is winsome and lovely, with a certain bloom of charm upon it. (note on Mark 14:10) (Barclay, W: The Daily Study Bible Series. The Westminster Press or Logos)

Richards writes that...

There are two basic words for "good" found in the NT: agathos and kalos. Agathos indicates the good as useful and came to have a strong ethical and religious emphasis. On the other hand, the other word meaning "good," kalos, stresses the aesthetic. The person or thing that is kalos is beautiful, fine, noble, and praiseworthy. As a thing of beauty, such a person or object is pleasing to God and to his people and is a source of joy. This happy tone in kalos is captured in Jesus' words about the woman called Mary who washed his feet and anointed him just before he was betrayed: "She has done a beautiful thing to me," he said (Mt 26:10; Mark 14:6).

Because of their link with the good, kalos and agathos are often used synonymously and usually both are translated "good." Thus the aspect of beauty found in goodness and revealed in the Greek language is often lost in our English translations.

Agathos views the good as useful or profitable and is the word chosen when moral goodness is being considered. Kalos tends to stress the aesthetic aspect of good. Good is not only beneficial but also beautiful. (Richards, L O: Expository Dictionary of Bible Words: Regency)

MacArthur commenting on the fruit of the Spirit which includes goodness writes that the word is agathos which...

has to do with moral and spiritual excellence that is known by its sweetness and active kindness. Paul helped define this virtue when he observed that “one will hardly die for a righteous man; though perhaps for the good man someone would dare even to die” (see note Romans 5:7). A Christian can be morally upright but still not manifest the grace of goodness. He may be admired and respected for his high moral standards and might even have a friend who would risk his life for him. But the upright person who also has goodness is much more likely to have serf-sacrificing friends...(Agathos) is the internal goodness produced by the Spirit in the hearts of obedient believers, which then finds expression in external goodness spoken by his mouth and performed by his hands. It is also good that is unqualified and unrestricted, to be shown all men, including unbelievers (see Gal 6:10) (MacArthur, J. Galatians. Chicago: Moody Press or Logos)

In Mark 10:17 (also Luke 18:18 describing a certain ruler) we read of the man who came to Jesus...

And as He was setting out on a journey, a man ran up to Him and knelt before Him, and began asking Him, "Good Teacher, what shall I do to inherit eternal life?"

Mark and Luke both use agathos for good, which implies that the questioner saw the Lord as good in nature and in essence. The writers would have used the word kalos if the questioner's intent was to denote strictly external goodness or good form. In saying “good teacher” the questioner was not just calling Jesus a capable teacher but  was affirming belief in the Lord’s essential (agathos) goodness.

Wuest adds that...

agathos  which speaks of intrinsic goodness, and kalos  which speaks of goodness as it is seen from without. The word kalos  has also the idea of “beautiful.” It was used by the Greeks of anything so distinguished in form, excellence, goodness, usefulness, as to be pleasing. Hence, it can refer to anything which is handsome, useful, excellent, suitable, commendable, excellent in its nature and characteristics, and therefore well adapted to its ends...Kalos (is) a goodness seen on the outside as it strikes the eye, a beautiful, pleasing goodness. It was a work that as Swete says, possessed true moral beauty....Agathos  always includes a corresponding beneficent relation of the subject of it to another subject...Kalos speaks of goodness as seen from the outside by a spectator. (Wuest, K. S. Wuest's Word Studies from the Greek New Testament: Eerdmans or Logos)

Saints are made adequate and equipped for good (agathos) works by God's Word...

All Scripture is inspired by God and profitable for teaching, for reproof, for correction, for training in righteousness that the man of God may be adequate, equipped for every good (agathos) work." (see notes 2 Timothy 3:16-17). 

Consider the fruit tree. It is not "conscious" of the bearing process. We are to be like the fruit tree for it is God Who is causing fruit be borne in good works which blossom and ripen as we are walk obedient to His revealed will.

Vine comments that every good work

"signifies every kind of activity undertaken for the name of Christ; everything so undertaken is a means of fruitfulness, and the operating power is the indwelling Holy Spirit, upon whom the believer is entirely dependent." (Vine, W. Collected writings of W. E. Vine. Nashville: Thomas Nelson )

One way to think of this is as a process, so that in salvation God does work for us, in sanctification He does work in us and in service He does work through us and bears fruit that remains. God builds character before He calls to service. He must work in us before He can work through us. God spent 25 years working in Abraham before He gave him the promised son Isaac. Remember too that although we are not saved by good works, we are saved unto good works.

Theologian John Calvin wrote,

“It is faith alone that justifies, but faith that justifies can never be alone.”

We are not saved by faith plus good works, but by a faith that works. Any declaration of faith that does not result in a changed life and good works is a false declaration. True saving faith can never be by itself for it always brings life, and life produces good works. The person with dead faith has only an intellectual experience. In his mind, he knows the doctrines of salvation, but he has never submitted himself to God and trusted Christ for salvation. He knows the right words, but he does not back up his words with his works. Faith in Christ brings eternal life right now (John 3:16), and where there is life there must be growth and fruit. (cf James 2:17)

Are you bearing fruit in every good work? Dearly beloved, be encouraged for Paul wrote that

"we are (God's) workmanship, created in Christ Jesus for good works, which God prepared beforehand, that we should walk in them." (see note Ephesians 2:10)

Many believers minimize the place of good works in the Christian life reasoning that because we are not saved by good works, then good works are something to be shunned.  But our Lord reminds us that our incredible privilege is to

"Let your light shine before men in such a way that they may see your good works, and glorify your Father Who is in heaven.” (see note Matthew 5:16)

It is not only by words that we give testimony to the greatness of God, but also by our works. Our good works in fact pave the way for witness with good words. If our walk contradicts our words, we lose our testimony. Our “walk” and our “talk” must agree. Good works and good words must come from the same yielded heart. Too many believers today emphasize guarding the truth, but downplay living the truth. One of the best ways to guard the truth is to put it into practice. It is good to be defenders of the faith, but we must not forget to be demonstrators of the faith by letting them see our good works!

You are writing a Gospel,
A chapter each day,
By the deeds that you do
And the words that you say.
Men read what you write,
Whether faithful or true:
Just what is the Gospel
According to you?
                        --- Author unknown

When doing good works, also remember that the following question is irrelevant "Does this person deserve my good works?" We are to "abound to every good work" (NIV, 2Cor 9:8).

Paul reminded Titus (and us) that Jesus

"gave Himself for us, that He might redeem us from every lawless deed and purify for Himself a people for His own possession, zealous (afire, ardent, fervent, eager, enthusiastic) for good deeds." (see note Titus 2:14)

The writer of Hebrews exhorts believers "do not neglect doing good and sharing; for with such sacrifices God is pleased" (Heb 13:16 - note) so that good works are actually “spiritual sacrifices” that we offer to God!

Please do not misunderstand. Believers do not manufacture these good works but instead they are the fruit of God's Spirit working in our heart for as Paul reminds us in (see note Philippians 2:13)

it is God Who is at work in you, both to will and to work for His good pleasure.

Paul acknowledges that the key to his good works was the grace of God which made him adding that God's "grace toward me did not prove vain; but I labored even more than all of them, yet not I, but the grace of God with me." (1Cor 15:10). Peter writes "Keep your behavior excellent among the Gentiles, so that in the thing in which they slander you as evildoers, they may on account of your good deeds, as they observe them, glorify God in the day of visitation." (se note 1 Peter 2:12). Thus our good works serve as testimonies to the lost and even win us the right to be heard.

In sum, all of these truths about good works indicate that God has a plan for our lives and that we should walk in His will and fulfill His plan. If you'd like some additional study on the topic of "good works (deeds)" click the following links for all of the 24 passages on (good works, good deeds).

INCREASING IN THE KNOWLEDGE OF GOD: kai auxanomenoi (PPPMPN) te epignosei tou theou:  (1Pe 2:2, 2Pet 3:18, Col 2:19; Isaiah 53:11; Da 12:4; Hab 2:14; Jn 17:3; 2Cor 2:14; 4:6; 9:8; Eph 1:17; 4:13; 2Pet 1:2,3; 1Jn 5:20)

The Amplified version emphasizes that the growth is in (the sphere of) and by (the instrumentality of) the full and true knowledge of God (in contrast to the knowledge of the false philosophies which "stunt" growth and even lead to "death" if persisted therein).

Spurgeon writes...

“Fruitful in every good work”-what then? “increasing in the knowledge of God.” Look at that. It seems, then, that holiness is the road to knowledge.

God has made it so. If any man will do his will he shall know of the doctrine. If you read and study, and cannot make out the meaning of Scripture, get up and do something, and it may be, in the doing of it, you shall discover the secret.

Holiness of heart
shall increase the illumination of your mind.

Will you kindly observe that this knowledge rises in tone? for Paul first prayed that they “might be filled with the knowledge of God’s will”; but now he implores for them an increase in the knowledge of God Himself. Oh, blessed growth, first to know the law, and then to know the Lawgiver! first to know the precept, and then to know the mouth from which it comes! This is the height of knowledge, to see Christ and know the Father, and learn how to say from the heart,

“Truly our fellowship is with the Father, and with his Son Jesus Christ.”

I would call your willing attention to another thought. The apostle, if he is to be judged according to his outward language, often utters impossible things, and yet his every sentence is not only full of deep meaning, but is strictly correct. Notice his language here: in the ninth verse he says,

“that ye might be filled with the knowledge of his will.”

Can anything go beyond this? The vessel is filled right up to the brim, what can it have more? Yet the apostle says,

“increasing in the knowledge of God.”

What can that mean? If the mind is full to the brim, how can it receive more? If the man is full of knowledge, how can his knowledge increase? Can there be any increase after that? I propose to you the riddle.

Here is the answer of it: Make the vessel larger, and then there can be an increase. This solution of the difficulty requires no great wit to discover it. So that Paul plainly teaches us here that, if we have so increased in knowledge as to be full, he would have us increased in capacity to know yet more; he would have our manhood enlarged, our powers of reception increased, that we might grow from being children to be young men, and from young men to be fathers, and so may be filled--filled, always filled with all the fullness of God!

The Lord grant unto us to perceive with humility, that if we are already full of knowledge, we can still advance, for we “have not yet attained.” Let no man think that he can go no further.

“There is,” says Augustine, “a certain perfection according to the measure of this life, and it belongs to that perfection that such a perfect man should know that he is not yet perfect.”

To that I heartily subscribe. There is a certain fullness to be found in this life according to the measure of a man, and it belongs to that fullness that the man should know that he can yet increase in knowledge. Holy Bernard says

“he is not good at all who doth not desire to be better.”

I also subscribe to that saying. Some might become good if they were not puffed up with the fancy of their own perfection. Others are somewhat commendable, but will never grow because they judge themselves to be full-grown already. I would have you filled, and yet have room for more: filled with all knowledge, filled with all holiness, filled with the indwelling Spirit, filled with God, and yet increasing in knowledge, in holiness, in likeness to God, and in all good things evermore to His glory. The Lord add His blessing for Jesus’ sake. Amen. (See the full sermon - Spiritual Knowledge: It's Practical Results)

Increasing (837)(auxano)  means to cause to grow or cause to become greater in extent, size, state, or quality and in the current verse pictures the believer's continual (present tense) spiritual growth (note passive voice = saint is acted upon by God's Spirit Who produces the growth) "in (the sphere of, circumscribed by, encircled by, surrounded by - the "air" a believer "breaths" in and is enabled to live and grow spiritually is called "grace" and "true knowledge") the grace and knowledge of our Lord and Savior Jesus Christ" (2Pe 3:18-note) as we obey (Jn 7:17) and as we walk worthy (cf Php 1:27-note).

Auxano - 23x times in 23v -- Matt. 6:28; 13:32; Mk. 4:8; Lk. 1:80; 2:40; 12:27; 13:19; Jn. 3:30; Acts 6:7; 7:17; 12:24; 19:20; 1 Co. 3:6f; 2 Co. 9:10; 10:15; Eph. 2:21; 4:15; Col. 1:6, 10; 2:19; 1 Pet. 2:2; 2 Pet. 3:18.  NAS = causes the growth(1), causing the growth(1), full grown(1), grew(1), grow(8), growing(2), grows(2), increase(2), increased(2), increasing(2), spreading(1).

Auxano - 34x in the Septuagint (LXX) - Gen 1:22, 28; 8:17; 9:1, 7; 17:6, 20; 21:8, 20; 25:27; 26:22; 28:3; 30:30; 35:11; 41:52; 47:27; 48:4; 49:22; Ex 1:7; 23:30; Lev 26:9; Num 24:7; Josh 4:14; Jdg 5:11; 1 Chr 14:2; 17:10; 23:17; 2 Chr 11:23; Job 42:10; Ps 105:24; Isa 61:11; Jer 3:16; 22:30; 23:3

Note especially the vitally inherent in the Word of God - Acts 6:7; 12:24; 19:20 - So what? Preach the Word in season and out if you want to see your congregation grow in grace and the knowledge of our Lord and Savior Jesus Christ. There are no shortcuts.

Paul used auxano in this same chapter of spiritual growth, describing the gospel which had come to and transformed the lives of the Colossians "just as in all the world also it (the gospel) is constantly bearing fruit and increasing, even as it has been doing in you also since the day you heard of it and understood the grace of God in truth." (Col 1:6-note)

Paul later warned the Colossian saints to beware of defrauders who were "not holding fast to the head, from whom the entire body, being supplied and held together by the joints and ligaments, grows (auxano) with a growth (auxesis) which is from God." (see note Colossians 2:19).

There is no spiritual growth for the body (the church) apart from union with the Head, Christ. Using auxano with a similar meaning, Paul wrote to the Corinthian church:

"I planted, Apollos watered, but God was causing the growth.  So then neither the one who plants nor the one who waters is anything, but God who causes the growth." (1Cor 3:6-7)

Increasing or growth predicates an object having the element of life within itself and being acted upon by an outside power or force to produce either natural growth (eg, "lilies of the field grow" - Mt 6:28-note) or, in the metaphorical sense, spiritual growth, as used by John the Baptist in his reference to Jesus, declaring "He must continually increase (auxano) and I must continually decrease." (Jn 3:30) In (2Cor 10:15) Paul writes to the Corinthians expressing his hope that their "faith grows" (literally - is continually being grown) 

Another picture of spiritual growth is found in Luke's three descriptions of the Gospel as "the word of God ( which) kept on spreading (increasing, growing) and the number of the disciples continued to increase greatly in Jerusalem, and a great many of the priests were becoming obedient to the faith." (Acts 6:7), "the Word of the Lord continued to grow and to be multiplied." (Acts 12:24), and "the Word of the Lord was growing mightily and prevailing." (Acts 19:20).

How important for pulpits everywhere to ensure and facilitate conditions which maximize the "growth" of the Word of the Lord in the "garden" of the local body of Christ,

in Whom the whole building, being fitted together is (continually) growing (auxano) into a holy temple in the Lord." (Ep 2:21-note)

Paul exhorts believers at Ephesus

 Enfolded in love, let us grow up (auxano) in every way and in all things into Him Who is the Head, [even] Christ (the Messiah, the Anointed One)." (Eph 4:15-note, Amplified)

And in one of the most foundational truths in the New Testament regarding spiritual growth, Peter says that after

putting aside all malice and all guile and hypocrisy and envy and all slander, like newborn babes, long for the pure (unadulterated, no additives, no artificial substitutes) milk of the Word, that (purpose clause) by it you may grow (auxano) in respect to salvation (into conformity to the image of Christ). (see notes 1 Peter 2:1; 2:2)

Warren Wiersbe comments that

"It is sad when Christians have no appetite for God’s Word, but must be ‘fed’ religious entertainment instead. As we grow, we discover that the Word is milk for babes, but also strong meat for the mature (He 5:11, 12, 13, 14-see notes Heb 5:11-12; 13-14). It is also bread (Mt. 4:4) and honey (Ps 119:103)." (Wiersbe, W: Bible Exposition Commentary. 1989. Victor)

The point is that their is no spiritual growth in a believer who does not personally imbibe the milk of the living and active Word of God. 

Dear child of God, these truths about auxano beg the question

"Beloved, beloved, tell me beloved, how does your garden grow? (modified from the familiar nursery rhyme)

Knowledge of God - Not just becoming smarter sinners (smug and sacrosanct), but becoming more like the Savior (submissive and serving).

Knowledge (1922) (epignosis [word study] from gnosis = knowledge gained by experience + epi = here used to  intensify the meaning) full, perfect, precise knowledge thus signifying a more complete, more thorough, larger knowledge than that found in gnosis. Epignosis as used by Paul  stresses a true knowledge of God and His will. It was also, generally, the appropriate term for personal rather than intellectual knowledge. Epignosis  thus implies a more intimate and personal relationship than gnosis. The learner exhibits a more thorough participation in the acquiring of knowledge.