AND WE DESIRE THAT EACH ONE OF YOU SHOW THE SAME DILIGENCE: epithumoumen (1PPAI) de hekaston humon ten auten endeiknusthai (PMN) spouden:

We desire (1937) Earnestly long for, have strong desire for (1Ti 3:1)

Lust (1937) (epithumeo from epí = upon, used intensively + thumós = passion) (Click for in depth study of related noun epithumia) means literally to fix the desire upon (whether things good or bad). It means to have a strong desire to do or secure something. Note that the preposition "epi" can  express motion toward! And so it means to have one's passions or affections directed toward something (good or bad).

That is, we desire (continually - present tense) that each of you exhibit the same diligence to develop your hope, which is in danger of failing, into full assurance, unto the end of the present season of trial with its happy consummation....It is practically the same whether it is translated full development or full assurance. The two meanings coalesce. Hope develops into full assurance.

Each (1538) (hekastos from hékas = separate) every single one. This idea of separation or singling out is expressed still more strongly by heís hékastos. It means each and every one of you. The writer gets very personal and does not want to leave anyone out.

Show (1731) (endeíknumi from preposition en = in, to + deíknumi = to show) means to point out, to demonstrate, to put on display, to prove, to show proof, to show forth, to show oneself, to give visible proof, to show in anything and implies an appeal to facts. The preposition (in) in the compound suggests more than the simplest demonstration. It is like laying the index finger, as it were, on the object. It means to to show something in someone. It can mean to do something to someone, as Alexander the coppersmith "did" (endeíknumi) Paul much harm (see note 2 Timothy 4:14). In the papyri it could have a quasi-legal sense of proving a petition or charge or of proving that a charge was wrong. Josephus used endeíknumi to describe Herod Agrippa’s display of generosity to those of other nations (Josephus, Antiquities, 19:330).

The present tense calls for the saints to continually demonstrate this diligence demonstrated by the patriarchs (he illustrates this diligence with "father" Abraham - see notes Hebrews 6:13; 6:14; 6:15 ). The middle voice indicates that we ourselves must each consciously initiate this action (empowered by the Spirit of course) so that we continually show forth or demonstrate a zealous urgency. 

Diligence  (4710) (spoude from speudo = hasten, make haste) refers to eagerness, earnestness,  willingness or zeal. It denotes quick movement or haste accompanying the eagerness, etc, in the interest of a person or cause. Thus spoude can refer to swiftness of movement or action and means haste or speed (like our expression "in a hurry"). It can refer to an earnest commitment in discharge of an obligation or experience of a relationship.

Spoude was often used in Greek and Roman literature and found on inscriptions in reference to extraordinary commitment to civic and religious responsibilities, which were frequently intertwined, and also of concern for personal moral excellence or optimum devotion to the interests of others.

Spoude describes zeal (eagerness and ardent interest in pursuit of something), passion (passion applies to an emotion that is deeply stirring-- how wonderful to so fully be in love with Christ so as to be fully governed by His Spirit).

Note that assurance comes from diligence. If we are diligent in living for Christ, our hearts are filled with assurance. If we are not diligent, then we cannot be assured that all things will be well. Living an up and down life—sometimes living for Christ and other times not living for Christ, sometimes living in sin and sometimes living in righteousness—causes doubt, questioning, and wondering about salvation. And it should. We should fear lest we fall away from Christ and His Word.

Here is an incredible illustration of diligence...

The Proceedings of the U.S. Naval Institute: The USS Astoria (CA-34) was the first U.S. cruiser to engage the Japanese during the Battle of Savo Island, a night action fought 8-9 August 1942. Although she scored two hits on the Imperial flagship Chokai, the Astoria was badly damaged and sank shortly after noon, 9 August.

About 0200 hours a young midwesterner, Signalman 3rd Class Elgin Staples, was swept overboard by the blast when the Astoria's number one eight-inch gun turret exploded. Wounded in both legs by shrapnel and in semi-shock, he was kept afloat by a narrow lifebelt that he managed to activate with a simple trigger mechanism.

At around 0600 hours, Staples was rescued by a passing destroyer and returned to the Astoria, whose captain was attempting to save the cruiser by beaching her. The effort failed, and Staples, still wearing the same lifebelt, found himself back in the water. It was lunchtime. Picked up again, this time by the USS President Jackson (AP-37), he was one of 500 survivors of the battle who were evacuated to Noumea.

On board the transport Staples, for the first time, closely examined the lifebelt that had served him so well. It had been manufactured by Firestone Tire and Rubber Company of Akron, Ohio, and bore a registration number.

Given home leave, Staples told his story and asked his mother, who worked for Firestone, about the purpose of the number on the belt. She replied that the company insisted on personal responsibility for the war effort, and that the number was unique and assigned to only one inspector. Staples remembered everything about the lifebelt, and quoted the number. It was his mother's personal code and affixed to every item she was responsible for approving.

Fifty years ago, a mother's unheralded diligence in an anonymous wartime job assured her soon-to-be shipwrecked son's survival. But how much greater are the stakes in eternal matters, and how much greater is the challenge to diligence in eternal matters! "We want [literally, we long for] each one of you," says the writer in v11, "to show this same diligence to the very end, in order to make your hope sure."

SO AS TO REALIZE THE FULL ASSURANCE OF HOPE UNTIL THE END: pros ten plerophorian tes elpidos achri (until) telousn:

See result of Abraham's faith and patience in  Romans 4:21 (see notes)

The expression full assurance is used three times in the NT.

(1) Full assurance of faith—we rest on God’s word, His testimony to us (see note Hebrews 10:22).

(2) Full assurance of understanding—we know and are assured (see note Colossians 2:2).

(3) Full assurance of hope—we press on with confidence as to the outcome (Hebrews 6:11).

How does one in fact "realize the full assurance of (the) hope"? It is thru faith and patience and so the writer gets very pragmatic, reminding his predominantly Jewish audience of one they would be very familiar with (Abraham) and in fact quoting directly from the Lxx of Ge 22:17, as probably the ultimate example of Abraham's faith...he had believed God in Ge 15:6 but God's call to sacrifice his son Isaac was the ultimate test of Abraham's faith (obedience) by which he became the father of all those who believe.

Only as we apply zeal and apply faith and patience can we have an assurance that we will one day "inherit the promises". Without them, we become sluggish, and as such expose ourselves to the danger of apostasy. This idea of applying diligence is very important if you desire to sense "spiritual security".  Peter describes this need for diligence (see notes 2 Peter 1:5;  1:10;  1:11)

Note hope is modified by the definite article the (tes") in the Greek so this is a very specific hope, not some generalization or "pie in the sky by and by". This reflects the absolute certainty of future good, because as taught below Jesus has entered thru the veil and will be there as our High Priest forever. That is a sure & steadfast anchor for our souls when storms of life assail us, which are in fact guaranteed if we are truly His children (see note Philippians 1:29, Jn 16:33)

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 or as Peter Anderson put it "Hope is faith in the future tense." 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.

I like John Blanchard's definition of the Christian's hope...

'Hope' is biblical shorthand for unconditional certainty.

When hope animates us there is a vigour in the whole body.

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

“Abandon all hope, you who enter here!”

"looking for the blessed hope and the appearing of the glory of our great God and Savior, Christ Jesus."  (see note Titus 2:13).

"God has not destined us for wrath but for obtaining salvation through our Lord Jesus Christ" (1Th 5:8).

End (5056) (telos) refers to the goal. It is used 5x in Heb 3:6 3:14 6:8 6:11 7:3.

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