For the promise is unto you, and to your children, and to all that are afar off, even as many as the Lord our God shall call.
But Mr. Barnes, though of that school himself, has says of this expression, "It does not refer to children as children, and should not be adduced to establish the propriety of infant baptism, or as applicable particularly to infants. It is a promise, indeed, to parents, that the blessings of salvation shall not be confined to parents, but shall be extended also to their posterity."
As can be demonstrated again by the phrase unto all generations meaning that what is in view here is the extend of this promise. A promise to all generations and all people. As you see that makes much more contextual sense.
What is he saying? Hes saying, "This isnt isolated to the crowd todaythis is for anybody who comes into the future." Right? This is for your children, and your childrens children, and your childrens childrens children
Hes simply saying this promise goes on and on and on, and for all who are far off, its for Gentiles too. So hes saying, "For your children, Jews in the future, and for Gentiles as well in the future." Anybody who repents of sin, anybody who believes in the Lord Jesus Christ, anybody who receives the forgiveness of sin and the gift of the Holy Spiritthat promise is fulfilled to anybody whether theyre Jew or Gentile.
Similar promises occur in Isa 44:3, "I will pour my Spirit upon thy seed, and my blessing upon thine offspring,"
Exactly to what they were alluding to with the receive the gift of the Spirit in Acts and then further this with alluding to the time that Isaiah says, in which he tells us that blessing to his offspring, or future generations- to put it contemporary language.