When Jesus said "Father forgive them, for they know not what they do", raised the questions of what the age of accountability for sin was at this time, or was it always a particular age predetermined by our Heavenly Father?
There is only one example that I can think of from the Old Testament where a sepcific age was given. The age was for those who couldn't go into the promised land (except Joshua and Caleb), meaning those younger were not prohibited from entering.
"Your carcases shall fall in the wilderness; and all that were numbered of you, according to your whole number, from twenty years old and upward which have murmured against me. Doubtless ye shall not come into the land, concerning which I sware to make you dwell therein, save Caleb the son of Jephunneh, and Joshua the son of Nun. But your little ones, which ye said should be a prey, them will I bring in, and they shall know the land which ye have despised." Numbers 14:29-31 (KJV)
The next scripture refers to the same group of persons, but refers more to their awarness/knowledge of right and wrong not specifically an age:
"Moreover your little ones, which ye said should be a prey, and your children, which in that day had no knowledge between good and evil, they shall go in thither, and unto them will I give it, and they shall possess it." Deuteronomy 1:39 (KJV)
Another scripture that I am aware of also speaks more of there being a point when awareness of right and wrong is learnt, but no age is specifically given:
"Butter and honey shall he eat, that he may know to refuse the evil and choose the good. For before the child shall know to refuse the evil and choose the good, the land that thou abhorest shall be forsaken of both their kings." Isaiah 7:15-16
In terms of the people who were calling for Jesus' to be crucified and then jeering him when he was dying on the cross, those people (whilst being a part of fulfilling God's plan) were not doing the right thing, in terms of their attitude in their hearts towards Jesus - they had murdered him in their hearts.
Paul say in Acts:
Men and brethren, children of the stock of Abraham, and whosoever among you feareth God, to you is the word of salvation sent. For they that dwell at Jerusalem, and their rulers, because they knew him not, nor yet the voices of the prophets which are read every sabbath day, they have fulfilled them in condemning him. Acts 13:26-27
In John, to some of the Pharisees, who thought they could "see" and discern right from wrong, Jesus said:
...For judgement I am come into this world, that they which see not might see; and they which see might be made blind. And some Pharisees which were with him heard these words, and said unto him, Are we blind also? Jesus said unto them, If ye were blind, ye should have no sin: but now ye say, We see; therefore your sin remaineth." John 9:39-41 (KJV)
By Jesus asking the Father to "forgive them", it was not because of the age of the people, Jesus was following his own example of what he taught his followers:
"Forgive us our sins, for we also forgive everyone who sins against us." Luke 11:2 (NIV) "But I say unto you, Love your enemies, bless them that curse you, do good to them that hate you, and pray for them which despitefully use you, and persecute you;" Matthew 5:44 (KJV)
Whether those people were forgiven for what they had in their hearts would be another question for posting, unless it has already been asked before.
Proverbs 20:11 KJB "Even a child is known by his doings, whether his work be pure, and whether it be right."
Personally, I have seen children as young 1-1.5 be able to discern right and wrong and make these choices. I believe once you can discern right and wrong you become accountable for your actions.
It seems to me that once you have the ability to do something, you are also given the discernment whether that action is right or wrong.
Answer: very young
There is no simple answer to this question as the Bible presents an extremely mature, and nuanced view of the complexity of humanity. It is true that even young children can discern some right from wrong but many older people cannot understand why some things are sinful. Here is a sample:
- Ps 51:5 suggests that we are all sinful from birth. Ps 58:3 says something similar
- Bar mitzvah was (and still is) held at age 12 because such people are supposed to have developed some sense of right and wrong.
- The reference in the people excluded from judgement in the desert wanderings, 20 years and younger suggests another age where greater maturity has developed. Ex 30:14, 38:26, Num 1:3, etc. While this may have been as much to do with army service, it required enough moral discernment to understand the subtle difference between murder and killing, as a soldier requires.
- Luke 23:34 is most significant because it discuss older people, teachers of the law and soldiers who could not understand the significance of their actions and that they were so wrong. See John 9:39-41 for another tricky example.
Therefore, I conclude that there are "sins and sins" - some are simple (eg stealing cookies from the cookie jar) and others much more complex and subtle whose sinfulness is not immediately obvious even to older people. There is everything in between too.
We mature at different rates and in different ways. I am sure that we all have sinned in various ways that we have been unaware of sometimes we found out later; and many sins we do not even know about. God is gracious to us all.
No such scripture in the bible as age of accountability for sin, that came about by bewitched and carnal minded preachers who is using vain deceit to get at your pocketbook. Man from day one comes out of their mother's womb under sin. I used to be a sinner and used to fall short of the glory of God which is Christ in you the hope of glory. When I was a sinner I was doing the will of the devil 1st John 3:8. Jesus told us man are full of pride, deceit, an evil eye etc from day one. The only way a baby can be saved is when one of or your both parents are living holy. Ask Noah or Lot by their sanctification their family was saved. Otherwise, man no matter what church they attend still continue in their sin they are not saved. I sure was no angel when I was born for 21 years of my life I lived like the devil despite going to church when I was younger that told me all sorts of lies and vain deceit and no truth. When I got born of God through Christ 25 years ago I became a man and put away childish things and gave up my sin got in my bible and washed by the blood words John 15:3. We sin no more in Christ Jesus 1st John 3:9. Why Christians wants to go on in their sin walking hand in hand with the devil and don't want to stop until they hit hell fire and brimstone I guess I will never know why. Jesus told us to go and sin no more John 5:14. When man does not want to clean up and get in their bible instead of the church social they will burn. I am an ex-sinner saved by grace an ex-sinner is a saved sinner and a saved sinner is a righteous person Romans 6:18. In Christ Jesus we are no longer sinners we are now called the righteous. It pays to sin, it pays to serve the devil, your wage or payment is called death hell fire and brimstone.
Job 14:1] Man that is born of a woman is of few days, and full of trouble.  He cometh forth like a flower, and is cut down: he fleeth also as a shadow, and continueth not.
Mark 7:21] For from within, out of the heart of men, proceed evil thoughts, adulteries, fornications, murders,  Thefts, covetousness, wickedness, deceit, lasciviousness, an evil eye, blasphemy, pride, foolishness:  All these evil things come from within, and defile the man.
1st Cor 7:14] For the unbelieving husband is sanctified by the wife, and the unbelieving wife is sanctified by the husband: else were your children unclean; but now are they holy.
John 5: Afterward Jesus findeth him in the temple, and said unto him, Behold, thou art made whole: sin no more, lest a worse thing come unto thee.
John 9: [ 31 ] Now we know that God heareth not sinners: but if any man be a worshipper of God, and doeth his will, him he heareth.
Galations 2: 16 ] Knowing that a man is not justified by the works of the law, but by the faith of Jesus Christ, even we have believed in Jesus Christ, that we might be justified by the faith of Christ, and not by the works of the law: for by the works of the law shall no flesh be justified. [ 17 ] But if, while we seek to be justified by Christ, we ourselves also are found sinners, is therefore Christ the minister of sin? God forbid. [ 18 ] For if I build again the things which I destroyed, I make myself a transgressor. [ 19 ] For I through the law am dead to the law, that I might live unto God. [ 20 ] I am crucified with Christ: nevertheless I live; yet not I, but Christ liveth in me: and the life which I now live in the flesh I live by the faith of the Son of God, who loved me, and gave himself for me. [ 21 ] I do not frustrate the grace of God: for if righteousness come by the law, then Christ is dead in vain.
1st Cor 6:9] Know ye not that the unrighteous shall not inherit the kingdom of God? Be not deceived: neither fornicators, nor idolaters, nor adulterers, nor effeminate, nor abusers of themselves with mankind,  Nor thieves, nor covetous, nor drunkards, nor revilers, nor extortioners, shall inherit the kingdom of God.  And such were some of you: but ye are washed, but ye are sanctified, but ye are justified in the name of the Lord Jesus, and by the Spirit of our God.
Hebrews 10: [ 26 ] For if we sin wilfully after that we have received the knowledge of the truth, there remaineth no more sacrifice for sins, [ 27 ] But a certain fearful looking for of judgment and fiery indignation, which shall devour the adversaries. [ 28 ] He that despised Moses' law died without mercy under two or three witnesses: [ 29 ] Of how much sorer punishment, suppose ye, shall he be thought worthy, who hath trodden under foot the Son of God, and hath counted the blood of the covenant, wherewith he was sanctified, an unholy thing, and hath done despite unto the Spirit of grace? [ 30 ] For we know him that hath said, Vengeance belongeth unto me, I will recompense, saith the Lord. And again, The Lord shall judge his people. [ 31 ] It is a fearful thing to fall into the hands of the living God.
1st John 3:4] Whosoever committeth sin transgresseth also the law: for sin is the transgression of the law.  And ye know that he was manifested to take away our sins; and in him is no sin.  Whosoever abideth in him sinneth not: whosoever sinneth hath not seen him, neither known him.  Little children, let no man deceive you: he that doeth righteousness is righteous, even as he is righteous.  He that committeth sin is of the devil; for the devil sinneth from the beginning. For this purpose the Son of God was manifested, that he might destroy the works of the devil.  Whosoever is born of God doth not commit sin; for his seed remaineth in him: and he cannot sin, because he is born of God.
1st Peter 4:18] And if the righteous scarcely be saved, where shall the ungodly and the sinner appear?
Rev 21: But the fearful, and unbelieving, and the abominable, and murderers, and whoremongers, and sorcerers, and idolaters, and all liars, shall have their part in the lake which burneth with fire and brimstone: which is the second death.
1st Timothy 6: If any man teach otherwise, and consent not to wholesome words, even the words of our Lord Jesus Christ, and to the doctrine which is according to godliness;  He is proud, knowing nothing, but doting about questions and strifes of words, whereof cometh envy, strife, railings, evil surmisings,  Perverse disputings of men of corrupt minds, and destitute of the truth, supposing that gain is godliness: from such withdraw thyself.
Ezekiel 18:4] Behold, all souls are mine; as the soul of the father, so also the soul of the son is mine: the soul that sinneth, it shall die.
Proverbs 11: 31 ] Behold, the righteous shall be recompensed in the earth: much more the wicked and the sinner.
Rev 1:3] Blessed is he that readeth, and they that hear the words of this prophecy, and keep those things which are written therein: for the time is at hand.  John to the seven churches which are in Asia: Grace be unto you, and peace, from him which is, and which was, and which is to come; and from the seven Spirits which are before his throne;  And from Jesus Christ, who is the faithful witness, and the first begotten of the dead, and the prince of the kings of the earth. Unto him that loved us, and washed us from our sins in his own blood,  And hath made us kings and priests unto God and his Father; to him be glory and dominion for ever and ever. Amen.
1st Peter 3: 18 ] For Christ also hath once suffered for sins, the just for the unjust, that he might bring us to God, being put to death in the flesh, but quickened by the Spirit: [ 19 ] By which also he went and preached unto the spirits in prison; [ 20 ] Which sometime were disobedient, when once the longsuffering of God waited in the days of Noah, while the ark was a preparing, wherein few, that is, eight souls were saved by water.
Romans 6: 1 ] What shall we say then? Shall we continue in sin, that grace may abound? [ 2 ] God forbid. How shall we, that are dead to sin, live any longer therein? [ 3 ] Know ye not, that so many of us as were baptized into Jesus Christ were baptized into his death? [ 4 ] Therefore we are buried with him by baptism into death: that like as Christ was raised up from the dead by the glory of the Father, even so we also should walk in newness of life. [ 5 ] For if we have been planted together in the likeness of his death, we shall be also in the likeness of his resurrection: [ 6 ] Knowing this, that our old man is crucified with him, that the body of sin might be destroyed, that henceforth we should not serve sin. [ 7 ] For he that is dead is freed from sin. [ 8 ] Now if we be dead with Christ, we believe that we shall also live with him: [ 9 ] Knowing that Christ being raised from the dead dieth no more; death hath no more dominion over him. [ 10 ] For in that he died, he died unto sin once: but in that he liveth, he liveth unto God. [ 11 ] Likewise reckon ye also yourselves to be dead indeed unto sin, but alive unto God through Jesus Christ our Lord. [ 12 ] Let not sin therefore reign in your mortal body, that ye should obey it in the lusts thereof. [ 13 ] Neither yield ye your members as instruments of unrighteousness unto sin: but yield yourselves unto God, as those that are alive from the dead, and your members as instruments of righteousness unto God. [ 14 ] For sin shall not have dominion over you: for ye are not under the law, but under grace. [ 15 ] What then? shall we sin, because we are not under the law, but under grace? God forbid. [ 16 ] Know ye not, that to whom ye yield yourselves servants to obey, his servants ye are to whom ye obey; whether of sin unto death, or of obedience unto righteousness? [ 17 ] But God be thanked, that ye were the servants of sin, but ye have obeyed from the heart that form of doctrine which was delivered you. [ 18 ] Being then made free from sin, ye became the servants of righteousness. [ 19 ] I speak after the manner of men because of the infirmity of your flesh: for as ye have yielded your members servants to uncleanness and to iniquity unto iniquity; even so now yield your members servants to righteousness unto holiness. [ 20 ] For when ye were the servants of sin, ye were free from righteousness. [ 21 ] What fruit had ye then in those things whereof ye are now ashamed? for the end of those things is death. [ 22 ] But now being made free from sin, and become servants to God, ye have your fruit unto holiness, and the end everlasting life. [ 23 ] For the wages of sin is death; but the gift of God is eternal life through Jesus Christ our Lord.
Augustine was challenged by the question that philosophers inevitably posed to Christians: “How could sin have entered the world, if God is good?” Augustine sought to answer this challenge and in so doing adopted many of the philosophers’ ideas.
The result, as evidenced by his writings, was that Augustine reinterpreted the Bible in light of philosophy. With respect to original sin, he understood the account of Adam and Eve as a description of humanity’s fall from grace. They sinned and were punished by God, and thus all subsequent humanity, being at that time biologically present within Adam, was party to the sin. The idea of innate sin and guilt became a widespread doctrine, as is shown by the following words from a popular American schoolbook used in the 17th and 18th centuries: “In Adam’s fall, we sinned all.”
But Augustine did not devise the concept of original sin. It was his use of specific New Testament scriptures to justify the doctrine that was new. The concept itself had been shaped from the late second century onward by certain church fathers, including Irenaeus, Origen and Tertullian. Irenaeus did not use the Scriptures at all for his definition; Origen reinterpreted the Genesis account of Adam and Eve in terms of a Platonic allegory and saw sin deriving solely from free will; and Tertullian’s version was borrowed from Stoic philosophy.
Though Augustine was convinced by the arguments of his earlier patristic peers, he made use of the apostle Paul’s letters, especially the one to the Romans, to develop his own ideas on original sin and guilt. Today, however, it is accepted that Augustine, who had never mastered the Greek language, misread Paul in at least one instance by using an inadequate Latin translation of the Greek original.
In Romans 5, Paul addresses the matter of sin. In verse 12 he states, “Therefore . . . sin came into the world through one man, and death came through sin, and so death spread to all because all have sinned” (NRSV). Later in the chapter, Paul juxtaposes the sin of Adam with the righteousness of Christ: “Just as by the one man’s disobedience the many were made sinners, so by the one man’s obedience the many will be made righteous” (Romans 5:19). In contrast to his contemporary theologians, Augustine drew from his reading of these scriptures that sin was passed biologically from Adam to all his descendants through the sexual act itself, thus equating sexual desire with sin. But why should he have reached this interpretation when marital sexual relations in Jewish society at the time of Christ and Paul were considered honorable and good?
Augustine’s outlook on sex was distorted by ideas from the world outside the Bible. Because so much philosophy was based on dualism, in which the physical was categorized as evil but the spiritual as good, some philosophers idealized the celibate state. Sexual relations were physical and therefore evil.
Augustine’s association with Neoplatonic philosophers led him to introduce their outlook within the church. This had its effect in the development of doctrine. For example, Jesus was considered immaculately conceived—without sin in that His Father was God. But because His mother, Mary, had a human father, she suffered the effect of original sin. In order to present Jesus Christ as a perfect offspring without any inherited sin from either parent, the church had to find a way to label Mary as sinless. They did this by devising the doctrine of her immaculate conception, though this inevitably leads to further questions.
Other babies were not so fortunate. Some eight centuries later the Catholic theologian Anselm extended the implications of Augustine’s concept of original sin and claimed that babies who died, did so as sinners; as sinners, they had no access to eternal life but were condemned to eternal damnation.
The world from which Paul came had a very different view of sexual relations, especially within marriage. Sex was not evil; it was part of the physical creation that God had decreed was good (Genesis 1:31). The writer of the Epistle to the Hebrews supports this view in describing the marital bed as “undefiled”—that is, pure or sacred; in other words, the sexual act did not impair a person’s relationship with God (Hebrews 13:4). The apostle Paul takes the idea further in his First Epistle to the Corinthians, where he instructs married couples not to defraud one another but to render appropriate conjugal dues. He states that in the sexual relationship each partner should focus on providing benefit to the other, not just on his or her own satisfaction. Hence Augustine’s view of sex as sin does not match New Testament teaching. Nor does it coincide with the Old Testament statement that a child does not carry its father’s sin (Ezekiel 18:19–20).
Further, Paul would have rejected Augustine’s idea of biological transmission. Paul presents a scenario in which humanity is held captive by a spirit being who enslaves them to sin (2 Corinthians 4:4–6; Ephesians 2:1–2). According to Paul, the entire world is held captive to “the prince of the power of the air,” or Satan. Paul mentions that the human spirit can be subject to either the spirit of the world or the Spirit of God (1 Corinthians 2:6–14). He also warns Christians that their battle with sin is against spiritual, not physical, forces (Ephesians 6:10–18).
When Paul speaks of sin “entering” the world, he is addressing the fact that Adam willingly submitted himself to Satan’s already sinful nature, something that Jesus Christ also confronted but rejected (Matthew 4:3–11; Romans 5:19). By this act Adam ensured that his progeny would be under Satan’s rulership and influence. Hence in Psalm 51 the author speaks of being conceived in sin. It was not that the act of conception was sin but rather that as a result of conception, he was to enter a world in slavery to sin.
So Paul saw sin within a spiritual domain rather than a biological one. This is reinforced later in his Epistle to the Romans, where he describes humanity as being in a state of bondage to spiritual forces (Romans 6:13–23). The choice for Christians is to become servants of Jesus Christ, something that can be done only through God’s Holy Spirit. It is an individually chosen responsibility rather than a hereditary one.
In his commentary titled The Mystery of Romans, Mark Nanos contrasts the action of Jesus Christ with that of Adam, stating that “unlike Adam [Jesus] did not embrace the voice of the tempter, he did not ‘eat,’ as it were. He heard the word of God, believed, and obeyed.”
Jesus Christ came to replace Satan as the ruler of the world, so that sin, by which humanity is enslaved, could be removed (Romans 16:20). Such freedom is accorded to those God draws to His Son now, but it will be accorded to all who are willing after the return of Jesus Christ. This was one reason the early Church eagerly anticipated Christ’s return—so that all humanity could benefit.
Clearly Augustine’s Neoplatonic, dualistic concept of physical being evil and spiritual being good does not coincide with Paul’s view. This leads us to a second influential idea of Augustine’s relating to sin. He proposed the concept of the “fall of man” as a result of sin. In Augustine’s view, humanity lost its spiritual relationship with its Creator and thus fell to a lower state. Is this an idea that finds support in Paul’s writings?
Paul certainly recognized the lack of a spiritual relationship and saw sin resulting in death (Romans 6:15–18). He saw the world alienated from its Creator (Ephesians 2:12; 4:18), a condition that could be corrected only by the intervention of God. But Paul also saw an opportunity for humanity to be restored to a right relationship with God after losing access to Him in the Garden of Eden. However, this could happen only by becoming a “new creation” in God’s hands. Rather than describing the human condition as “fallen,” Paul may well have thought of the situation as a failure to “rise” to what God had offered. He describes those who reject the truth once they have had a relationship with God as having fallen away (Galatians 5:4, NRSV).
Paul’s view corresponds with the rest of the biblical account in that Genesis records that Adam and Eve were denied access to the tree of life, which would have afforded them eternal life. Thus, although they were cut off or alienated from God because of sin and driven from the Garden of Eden, they had never really engaged the relationship with God that He desired, which would have been accomplished only by eating of the tree of life.
Tragically, Augustine’s misreading and misinterpretation of sin based on looking at Scripture through the prism of dualism is accepted as dogma by most contemporary Christian theologians. The doctrine of original sin owes more to Augustine’s desire to emulate the philosophers than it does to the Scriptures.