Some folks who hold to a nearly dogmatic form of rugged individualism do not like the idea of federal headship, especially when it comes to punishments. I much more rarely hear people complain that they will be judged righteous for the deeds of their federal head. It is when guilt and punishment are concerned that the objections seem to come in. There are several rebuttals.
1. General Revelation - Nature Itself
The general revelation of nature should make it apparent that the children receive what comes from their parents, as a general rule. An unborn child (fetus, if you will, though that sounds so dehumanizing) obtains nourishment from its mother via the marvelously designed placenta. The infant obtains nourishment from the mother's breast. The children generally eat the grown/hunted/gathered or purchased by their parents even once they could hypothetically fend for themselves.
Children of poor parents are usually also poor, and children of rich parents are usually well off. To describe it in statistical terms, there is a high correlation between the state of a child and the state of a child's parents - not only socioeconomically, but genetically. A child of two short parents is unlikely to be tall, and a child of two tall parents is unlikely to be short.
c. Human Justice
The laws of men too bare testimony to the fact that children are punished for their parents' sins. Most societies have laws whereby evildoers are punished in their persons or property. If a father is imprisoned or fined for a crime, his children generally suffer financially: even more so if justice is rendered against the father in a capital case. It is not that the law sets out to punish the children of law-breakers: it just happens that way.
d. Fornication / Adultery
When men and women engage in extramarital sexual relationships, it often results in procreation. The children of such unions are often stigmatized, but even more significantly they often come into the world without a father to provide for them, or without a mother that wants them. In ancient Rome, such children were sometimes murdered through exposure to the elements after birth. In modern societies, such children are often murdered by their mothers in ways that sicken at least this author. Even if a child survives birth, its a statistical observation that such children tend to have a more difficult time in life.
2. Special Revelation - Scripture
a. Examples of Children being punished for the sins of their parents.
(i) The Great Deluge
We are not specifically told that there were any infants in Noah's day, but God brought the Flood on account of the sinfulness of the world 120 years prior to the Flood. Men lived longer in those days, but they did have children, and they did not give up their usual marital relations in view of Noah's preaching.
Luke 17:27 They did eat, they drank, they married wives, they were given in marriage, until the day that Noe entered into the ark, and the flood came, and destroyed them all.
1And it came to pass, when men began to multiply on the face of the earth, and daughters were born unto them, 2That the sons of God saw the daughters of men that they were fair; and they took them wives of all which they chose. 3And the LORD said, My spirit shall not always strive with man, for that he also is flesh: yet his days shall be an hundred and twenty years. 4There were giants in the earth in those days; and also after that, when the sons of God came in unto the daughters of men, and they bare children to them, the same became mighty men which were of old, men of renown. 5And GOD saw that the wickedness of man was great in the earth, and that every imagination of the thoughts of his heart was only evil continually. 6And it repented the LORD that he had made man on the earth, and it grieved him at his heart. 7And the LORD said, I will destroy man whom I have created from the face of the earth; both man, and beast, and the creeping thing, and the fowls of the air; for it repenteth me that I have made them.
(ii) Sodom and Gomorrah
Especially considering the form of sexual immorality for which Sodom is famous, we cannot be absolutely sure that there were young infants in the city, nevertheless, there is no particular reason to suppose that they had been so exclusively consumed by illicit lust that there were none. The fire God sent against the city, however, did not discriminate according to age.
24Then the LORD rained upon Sodom and upon Gomorrah brimstone and fire from the LORD out of heaven; 25And he overthrew those cities, and all the plain, and all the inhabitants of the cities, and that which grew upon the ground.
(iii) Firstborn of Egypt - 10th Plague
You may recall that the tenth plague, the plague that permitted the Israelites not only to leave but to plunder the Egyptians, was the death of the firstborn of all the Egyptians. This plague is couched in such universal terms that we may safely assume that it included infants and not only the firstborn that had grown somewhat.
4And Moses said, Thus saith the LORD, About midnight will I go out into the midst of Egypt: 5And all the firstborn in the land of Egypt shall die, from the firstborn of Pharaoh that sitteth upon his throne, even unto the firstborn of the maidservant that is behind the mill; and all the firstborn of beasts. 6And there shall be a great cry throughout all the land of Egypt, such as there was none like it, nor shall be like it any more.
(iv) Ham's Mockery
As you may recall, our grandfather Noah got drunk and lay naked in his tent. His son Ham found him in this inebriated condition and mocked him, calling his brothers Shem and Japheth. They, however, did not join his mockery but took a sheet with them and walked backwards into the tent covering Noah in the process. When Noah discovered what had happened, he cursed Ham, but especially Ham's son, Canaan.
24And Noah awoke from his wine, and knew what his younger son had done unto him. 25And he said, Cursed be Canaan; a servant of servants shall he be unto his brethren. 26And he said, Blessed be the LORD God of Shem; and Canaan shall be his servant. 27God shall enlarge Japheth, and he shall dwell in the tents of Shem; and Canaan shall be his servant.
(v) The Unborn Child of the Middianitish Woman
You may recall that the women of Moab were a temptation to the men of Israel. So much so that they began to go after the false gods of Moab. God was angry against Israel for this unfaithfulness to Him, and smote them with a plague. But what stopped the plague was the action of Phinehas, the grandson of Aaron, who killed one of the most open philanderers with a javelin. He skewered the man and the woman - in her case, the Bible specifies that it was through her belly, from which may infer that she had a belly - i.e. was pregnant.
1And Israel abode in Shittim, and the people began to commit whoredom with the daughters of Moab. 2And they called the people unto the sacrifices of their gods: and the people did eat, and bowed down to their gods. 3And Israel joined himself unto Baalpeor: and the anger of the LORD was kindled against Israel. 4And the LORD said unto Moses, Take all the heads of the people, and hang them up before the LORD against the sun, that the fierce anger of the LORD may be turned away from Israel. 5And Moses said unto the judges of Israel, Slay ye every one his men that were joined unto Baalpeor. 6And, behold, one of the children of Israel came and brought unto his brethren a Midianitish woman in the sight of Moses, and in the sight of all the congregation of the children of Israel, who were weeping before the door of the tabernacle of the congregation. 7And when Phinehas, the son of Eleazar, the son of Aaron the priest, saw it, he rose up from among the congregation, and took a javelin in his hand; 8And he went after the man of Israel into the tent, and thrust both of them through, the man of Israel, and the woman through her belly. So the plague was stayed from the children of Israel. 9And those that died in the plague were twenty and four thousand.
(vi) Achan's Theft
You may recall Achan. He was passing through the wreckage and rubble of Jericho, a city that was cursed by God. He decided that despite God's specific prohibition, he would take several items of value that he found in Jericho. He took the items and hid them in his tent. God then defeated Israel at the hands of the tiny forces of Ai.
The fact that others were punished for Achan's sin became a sort of by-word among Israel, at least for a time:
Joshua 22:20 Did not Achan the son of Zerah commit a trespass in the accursed thing, and wrath fell on all the congregation of Israel? and that man perished not alone in his iniquity.
More to the point, however, when Joshua had discovered that Achan the son of Zerah had disobeyed God, the punishment was his death, but not only his death. Also executed were his family, and even his cattle.
24And Joshua, and all Israel with him, took Achan the son of Zerah, and the silver, and the garment, and the wedge of gold, and his sons, and his daughters, and his oxen, and his asses, and his sheep, and his tent, and all that he had: and they brought them unto the valley of Achor. 25And Joshua said, Why hast thou troubled us? the LORD shall trouble thee this day. And all Israel stoned him with stones, and burned them with fire, after they had stoned them with stones. 26And they raised over him a great heap of stones unto this day. So the LORD turned from the fierceness of his anger. Wherefore the name of that place was called, The valley of Achor, unto this day.
His children were killed with him, though we are not explicitly told that any of them were infants.
(vii) Solomon's Older Brother
Solomon's older brother is not named in Scripture. He is the child of the adultery of David with Bathsheba. As you may recall, David's seduction of Bathsheba and murder of her husband greatly displeased God, and God punished David for this. God spared David's own life, but he cursed David's line, such the sword would not depart from it, and more relevant to the point of this article, he slew David's infant son.
2 Samuel 12:7-23
7And Nathan said to David, Thou art the man. Thus saith the LORD God of Israel, I anointed thee king over Israel, and I delivered thee out of the hand of Saul; 8And I gave thee thy master's house, and thy master's wives into thy bosom, and gave thee the house of Israel and of Judah; and if that had been too little, I would moreover have given unto thee such and such things. 9Wherefore hast thou despised the commandment of the LORD, to do evil in his sight? thou hast killed Uriah the Hittite with the sword, and hast taken his wife to be thy wife, and hast slain him with the sword of the children of Ammon. 10Now therefore the sword shall never depart from thine house; because thou hast despised me, and hast taken the wife of Uriah the Hittite to be thy wife. 11Thus saith the LORD, Behold, I will raise up evil against thee out of thine own house, and I will take thy wives before thine eyes, and give them unto thy neighbour, and he shall lie with thy wives in the sight of this sun. 12For thou didst it secretly: but I will do this thing before all Israel, and before the sun. 13And David said unto Nathan, I have sinned against the LORD. And Nathan said unto David, The LORD also hath put away thy sin; thou shalt not die. 14Howbeit, because by this deed thou hast given great occasion to the enemies of the LORD to blaspheme, the child also that is born unto thee shall surely die. 15And Nathan departed unto his house. And the LORD struck the child that Uriah's wife bare unto David, and it was very sick. 16David therefore besought God for the child; and David fasted, and went in, and lay all night upon the earth. 17And the elders of his house arose, and went to him, to raise him up from the earth: but he would not, neither did he eat bread with them. 18And it came to pass on the seventh day, that the child died. And the servants of David feared to tell him that the child was dead: for they said, Behold, while the child was yet alive, we spake unto him, and he would not hearken unto our voice: how will he then vex himself, if we tell him that the child is dead? 19But when David saw that his servants whispered, David perceived that the child was dead: therefore David said unto his servants, Is the child dead? And they said, He is dead. 20Then David arose from the earth, and washed, and anointed himself, and changed his apparel, and came into the house of the LORD, and worshipped: then he came to his own house; and when he required, they set bread before him, and he did eat. 21Then said his servants unto him, What thing is this that thou hast done? thou didst fast and weep for the child, while it was alive; but when the child was dead, thou didst rise and eat bread. 22And he said, While the child was yet alive, I fasted and wept: for I said, Who can tell whether GOD will be gracious to me, that the child may live? 23But now he is dead, wherefore should I fast? can I bring him back again? I shall go to him, but he shall not return to me.
This list of examples is not exhaustive. For example, we could also add Korah (Numbers 16), Saul's sons (2 Samuel 21), or Jericho both a first (Joshua 6) and a second time (1 Kings 16), but perhaps the seven examples above suffice to prove the point.
b. God's Own Self-Description
God does not hesitate to describe himself as a God who punishes the fathers by also punishing their children. We may subsume within that description of course the specific instances where God killed or had killed the children of those who sinned, for the sins of their fathers.
On top of those, we may list the four times God specifically states that he visits the iniquity of the fathers upon the children:
(i) Exodus 20:5 Thou shalt not bow down thyself to them, nor serve them: for I the LORD thy God am a jealous God, visiting the iniquity of the fathers upon the children unto the third and fourth generation of them that hate me;
(ii) Exodus 34:7 Keeping mercy for thousands, forgiving iniquity and transgression and sin, and that will by no means clear the guilty; visiting the iniquity of the fathers upon the children, and upon the children's children, unto the third and to the fourth generation.
(iii) Numbers 14:18 The LORD is longsuffering, and of great mercy, forgiving iniquity and transgression, and by no means clearing the guilty, visiting the iniquity of the fathers upon the children unto the third and fourth generation.
(iv) Deuteronomy 5:9 Thou shalt not bow down thyself unto them, nor serve them: for I the LORD thy God am a jealous God, visiting the iniquity of the fathers upon the children unto the third and fourth generation of them that hate me,
3. General Revelation 2 - Conscience, Culture, and Reason
Perhaps this is a bit redundant, but children generally feel responsible for their parent's failures. Some children respond to this by working twice as hard to avoid doing what their parents did, and other children respond to this by fatalistically resigning themselves to follow in their parents' footsteps. While the latter approach is wrong, both approaches implicitly recognize a principle of the children being in some way held responsible for what their parents have done.
Culture to a degree reinforces this. The sometimes popular "reparations" movement among descendants of former slaves in America has it its roots a view that the descendants of slave owners should be responsible for what their ancestors did. Slavery itself (in many cultures the result of some personal failure) was passed on to children in many places. Likewise, a degree of cultural opposition to Jews (especially religious Jews) is based on (in some places and at some times in history) on the fact that their ancestors killed Christ (who, in fact, did call down God's wrath on themselves and their children, Matthew 27:25).
Furthermore, Reason applying itself to culture commends the same. For culture generally permits inheritances of goods to children (as Scripture confirms to be proper). Reason, favoring symmetry, suggests that not only positive things but negative things should be transmitted from parents to children, thus favoring the idea that guilt too may be inherited.
For all these reasons, it should be clear that it is just for children to be punished for their parents' sins. It may violate the principles on which modern pluralistic society is built - specifically the value of rugged individualism - but it is Scriptural, it is in accordance with the light of nature, and it is in accordance with the light of conscience and reason. Thus, we properly affirm it.