THEREFORE I SHALL ALWAYS BE READY: dio melleso (1SFAI) aei:

Note that the KJV derived from the Greek Textus Receptus reads

"Wherefore I will not be negligent to put you always in remembrance

Most textual critics feel that this represents a scribal error as it is not found in more modern Greek manuscripts.

Therefore (1352) (dio) marks a close connection with the truths Peter had just mentioned (a faith same kind as Peter's, everything necessary for life & godliness, God's precious & magnificent promises, partakers of the divine nature as manifest in 7 godly traits, escapees from the world's corruption). Peter knows that the best defense against false teaching is true living and that a church filled with saints maturing in the faith is not likely to fall prey to false teachers pushing their counterfeit brand of "Christianity". They find it easy to deceive people who do not know the Word of God and who instead are more desirous of subjective experiences. This sounds very relevant to our modern American church doesn't it? As Peter will show in the next chapter building one's spiritual house on subjective experiences alone while ignoring God's objective revelation is a surefire formula for disaster.  And so for the remainder of the chapter Peter seeks to exhort and equip his readers concerning the inerrant authority of God's revealed Word.

Be ready (3195) (mello) means to be about to, to be on the point of doing something. Mello was used in classical Greek, with a sense of certainty conveying the idea "I shall be sure". The idea is that "I shall take care to remind you...".  When?

Always (104) (aei) means always or ever and thus Peter is saying that he will be perpetually, incessantly, invariably ready to remind his readers and was thus not a passing fancy nor a fad. The sense in the Greek is, “I will be intending to remind you always.”

Why? Because it was Peter's call...to feed the sheep (Jn 21:15-17) ...to strengthen the brethren (Luke 22:32). So Peter remained ready at any & every occasion to remind them of these things. Peter knew as do all God's anointed preachers & teachers that even where knowledge and establishment exist, there is always a need for motivation and exhortation.

Spurgeon writes that...

He who exhorts others to be diligent must not himself be negligent, and Peter most appropriately writes, “Wherefore I will not be negligent to put you always in remembrance of these things”

We are not merely to preach new truths which people do not know, but we are also to preach the old truths with which they are familiar. The doctrines in which they are well established are still to be proclaimed to them. Every wise preacher brings forth from the treasury of truth things both new and old;-new, that the hearers may learn more than they knew before; old, that they may know and practice better that which they do already know in part.

TO REMIND YOU: humas hupomimneskein (PAN) :

Remind (5279)  (hupomimnesko from hupó = under + mimnesko = to remind) (Click word study of hupomimnesko) means to put another in mind of something, to cause one to remember, bring to one's mind, remind (remind suggests a jogging of one’s memory by an association or similarity).

The English word memorial refers to a structure or statue established in memory of a person or event. Hupomimnesko conveys the idea of making a memorial of what God is doing in your life and what is the hope set before you! 

Encourage others to make similar memorials because the way you think affects the way you behave, remembering that we are called out to be holy (wholly devoted) to Him. The sense in the Greek is, “I will be intending to remind you always.” Even where knowledge and establishment exist, there is still need for motivation and exhortation.

Albert Barnes writes that...

It was important for Peter to bring known truths to remembrance. Believers are apt to forget them, and then they do not exert the influence that they ought. Amid the cares, the business, the amusements, and the temptations of the world, the ministers of the gospel render us an essential service, even if they do nothing more than remind us of truths which are well understood, and which we have known before. A pastor need not always aim at originality; he renders an essential service to mankind when he reminds them of what they know but are prone to forget. He endeavors to impress plain and familiar truths on the heart and conscience, for these truths are most important for mankind. Though we may be very firm in our belief of the truth, yet it is appropriate that the grounds of our faith should be stated to us frequently, that they may be always in our remembrance. (Barnes NT Notes)

Peter knowing his days were numbered was committed to a "ministry of remembrance" and greatly desired for his readers to retain the truths that they already knew (you cannot remind one of something they don't already know) and so 3x in only 4 verses he expressed this desire to remind them (see notes 2 Peter 1:12, 1:13, 1:15). Later in not to mention a similar statement in (see note 2 Peter 3:1) we find a similar statement. Peter himself knew the tragic consequences of forgetting what you know, having deserted his Lord even though forewarned it would happen. In fact if one were to survey both the Old and New Testaments, he would find that "remembering & forgetting" are important concepts throughout Scripture. Just prior to entering into the Promised Land God warned Israel

"Beware that you do not forget the LORD your God by not keeping His commandments and His ordinances and His statutes which I am commanding you today" for when they were satisfied and content "then your heart will become proud and you will forget the LORD your God who brought you out from the land of Egypt, out of the house of slavery." (Dt 8:11,14).

OF THESE THINGS EVEN THOUGH YOU ALREADY KNOW THEM: peri touton kaiper eidotas (RAPMPA):

Know (1492) (eido, oida - eido is used only in the perfect tense = oida) literally means perception by sight (perceive, see) as in Mt 2:2 where the wise men "saw His star". The meaning of eido is somewhat difficult to convey but in general this type of "knowing" is distinguished from ginosko (and epiginosko, epignosis), the other major NT word for knowing, because ginosko refers to knowledge obtained by experience or "experiential knowledge" whereas eido often refers to more intuitive knowledge, although the distinction is not always crystal clear.

Eido (oida) then is not so much by experience as an intuitive insight that is "drilled into your heart". In spiritual terms, eido is that perception, that being aware of, that understanding, that intuitive knowledge that only the Holy Spirit of God can give. It is an absolute knowledge, a knowledge that is without a doubt. Oida describes absolute, positive, beyond a peradventure of a doubt, knowledge.

Know (oida) then carries the idea of having the "know how" , the knowledge or skill necessary to accomplish a desired goal. It means to see with the mind’s eye, and signifies a clear and primarily mental perception.

In sum eido/oida describes the divinely given intuitive knowledge which Peter's readers had received when they were born again and became partakers of the divine nature (see note 1 Peter 1:18). Human beings simply cannot know divine truth intuitively unless they become members of God's family.

The readers also would already know them these things because they had received Peters first letter (First Peter) and this gave them a background for this second epistle. Many of the things discussed in 2 Peter are also found in 1 Peter.

What are these things? (see 1 Peter 1:3-11) The things before this verse and the things after this verse. The whole chapter is a list of things that we are never to forget. Though we already know them and are already established in them, unless we continue to exercise our minds and exercise our wills in those things, they will slip from our grasp.

AND HAVE BEEN ESTABLISHED: kai esterigmenous (RPPMPA):

Established (4741) (sterizo) (Click word study of sterizo) means to set up, establish (make firm or stable, put beyond doubt), to strengthen, to fix firmly in a place, to cause to be inwardly firm or committed or to (confirm = the removing of doubts by an authoritative statement or indisputable fact). strengthen. The basic idea is that of stabilizing something by providing a support or buttress (a projecting structure of masonry or wood for supporting or giving stability to a wall or building), so that it will not totter. Vine feels that stērízō is derived from stērix, a prop (something that sustains or supports

Perfect tense indicates they were established in the truth in the past and continue into the present in that state. The perfect tense indicates settled state of solid grounding in the truth.

Wuest adds

These saints had become stabilized in the truth and were in a state of being set fast, placed firmly on it. Their knowledge of the Word and the cardinal doctrines of the Christian faith were set in their thinking. (Wuest, K. S. Wuest's Word Studies from the Greek New Testament: Eerdmans or Logos)

Sterizo is the same word used by the Lord Jesus Christ in His exhortation to Peter that

once you have turned again, strengthen (aorist imperative = Do it now! Do it effectively! Sense of urgency) your brothers. (Luke 22:32)

IN THE TRUTH WHICH IS PRESENT WITH YOU: en te parouse (PAPFSD) aletheia:

In the present truth (the truth present to you).

In a parallel passage that speaks of the value of truth, Paul like a commanding general instructs his troops to...

Stand firm (aorist imperative) therefore, HAVING GIRDED YOUR LOINS WITH TRUTH, and HAVING PUT ON THE BREASTPLATE OF RIGHTEOUSNESS, (see note Ephesians 6:14)

Truth (225) (aletheia from a = without + lêthô = that which is hidden or concealed, the combination meaning out in open) is the  the unconcealed reality lying at the basis of and agreeing with an appearance; the manifested, the veritable essence of matter.

AND I CONSIDER IT RIGHT: dikaion de hegoumai (1SPMI):

Consider (2233) (hegeomai) (present tense = continually) primarily signifies to lead, then, to consider (give thought to in order to reach a suitable conclusion, opinion, or decision). Hegeomai was a mathematical term conveying the idea "Think about it and come to a conclusion." Considering involves careful thought, not quick decision. Peter considers this to be his solemn duty or "right" -- “I consider it my duty” (see notes Philippians 3:1; Ephesians 6:1) 

Right (1342) (dikaios from dike = right, just) defines that which is in accordance with or conforming to high standards of moral integrity or morally correct behavior. It is that which is in right relation to another and so in reference to persons defines the one who is morally and ethically righteous, upright or just.

Dikaios means keeping the commands of God, guiltless and is used to describe the person whose way of thinking, feeling, and acting is wholly conformed to the will of God. In the present context it is better thought of that which is proper and fitting.

Dikaios refers to that which is expected as duty and which is claimed as a right because of one’s conformity to the rules of God. It was Peter's duty to admonish them. It was the right, fitting and proper thing for him to do. He bore a personal responsibility as an apostle who had personally been instructed by Jesus to strengthen his brethren. (Lu 22:32)

AS LONG AS I AM IN THIS DWELLING: eph oson eimi (1SPAI) en touto to skonomati:

Dwelling (4638) (skenoma from skenóo = to pitch a tent <> from skenos = tent, tabernacle) refers to a tabernacle, booth or tent which was pitched & which conveyed the picture of a temporary, transitory dwelling.

Peter uses the related root word skene in (Mt 17:4) where he speaks of making three tents. Here Peter uses skenoma as a figurative expression for his body just as Paul used (skenos) describing his body as a "tent" in (2Cor 5:1, 4). These bondservants of Christ Jesus were fully aware of the brevity of their earthly life and both were desirous to fulfill the stewardship allotted to them (cf Moses "prayer" in Ps 90:12). All God's saints need to remind themselves that their bodies are pilgrims passing through, "tents" temporarily placed on earth for a purpose, perched on the edge of eternal bliss and should order their steps accordingly!

TO STIR YOU UP: diegeirein (PAN) humas:

Spurgeon writes...

Stir up (1326) (diegeiro from dia = through + egeiro = awaken, raise, rouse) in the active voice means to cause to wake up or to awaken (as in Lu 8:24) and in the passive voice to become awake. Figuratively it was used of a of a calm sea become stormy or turbulent, a picture the author would have been quite familiar with.  Another figurative use is in reference not to the sea but to mental activity to be roused or stirred up (as in the present verse).

Diegeiro is used 7 times in the NT in the NASB...

Matthew 1:24 And Joseph arose from his sleep, and did as the angel of the Lord commanded him, and took her as his wife,

Mark 4:37 And there arose a fierce gale of wind, and the waves were breaking over the boat so much that the boat was already filling up. 38 And He Himself was in the stern, asleep on the cushion; and they awoke Him and said to Him, "Teacher, do You not care that we are perishing?" 39 And being aroused, He rebuked the wind and said to the sea, "Hush, be still." And the wind died down and it became perfectly calm.

Luke 8:24 And they came to Him and woke Him up (diegeiro), saying, "Master, Master, we are perishing!" And being aroused (egeiro), He rebuked the wind and the surging waves, and they stopped, and it became calm.

John 6:18 And the sea began to be stirred up because a strong wind was blowing.

2 Peter 1:13 (note) And I consider it right, as long as I am in this earthly dwelling, to stir you up by way of reminder,

2 Peter 3:1 (note) This is now, beloved, the second letter I am writing to you in which I am stirring up your sincere mind by way of reminder,

Rienecker says the preposition "dia" in this compound is "perfective" conveying the idea to stir up or wake up thoroughly.

Kenneth Wuest agrees writing that

"the prefixed preposition (dia) adds the idea of doing a thorough  piece of work in arousing their minds". (Wuest, K. S. Wuest's Word Studies from the Greek New Testament: Eerdmans or Logos

In sum, diegeiro means to awaken out of literal sleep. Figuratively as used twice by Peter, diegeiro means to arouse or stimulate to mental action. And so it means to stimulate one's thinking or to refresh their memory.

Peter knew that our minds have a tendency to get accustomed to truth and then to take it for granted. We forget what we ought to remember and remember what we ought to forget! We are in a spiritual war, stakes are high & we face a deadly deceptive foe. Peter says it is duty (cf Luke 22:32) to continually (present tense) shake his readers out of their lethargy, to agitate them and arouse them fully out of their somnolent state. There is a similar idea in Peter's first epistle...

Therefore, gird your minds for action, keep sober in spirit, fix your hope (aorist imperative - do it now!) completely on the grace to be brought to you at the revelation of Jesus Christ.  (see note 1 Peter 1:13)

Be of sober spirit (aorist imperative - do it now!) be on the alert. (aorist imperative - do it now!) Your adversary, the devil, prowls about like a roaring lion, seeking someone to devour. (see note 1 Peter 5:8) 

Paul issues similar calls to stir up believers...

And this do, knowing the time, that it is already the hour for you to awaken (egeiro) from sleep; for now salvation is nearer to us than when we believed. (see note Romans 13:11).

For this reason it says, "Awake (egeiro - present imperative), sleeper, and arise (aorist imperative - do it now!) from the dead, And Christ will shine on you." (see note Ephesians 5:14)

BY WAY OF REMINDER: en hupomnesei:

Reminder (5280) (hupomnesis from hupó = under + mimnesko = to remind) is the act of calling something to mind or remembering. It means to think about again (active) or be caused to think about again (passive).

Thayer says that hupomnesis refers to a remembrance prompted by another whereas a closely related word anamnesis denotes an unassisted recalling (although he goes on to state these two words are easily interchangeable in Classical Greek).

In the active sense (reminding) it represents a definite act of the person's will.  In the passive sense it refers to a recollection or reminder.