Because an aborted baby is not baptized, it is believed that it cannot go to Heaven.
What I am wondering is where Jesus says  "Unless a man be born again..." John 3:3

An aborted baby has not been born so is there any argument, doctrines, biblical or ecclisiastical teaching that can support the above statement that aborted babies go to Heaven?

To be born again doesn't refer to physical birth but to spritual birth. An unborn baby still has a soul. It has been conceived in sin (meaning that it has Adam's sin on its soul) so, inorder to be become a child of God, its soul must be cleansed through baptism.

But maybe Jesus gives the soul of the unborn baby a chance to accept Him through baptism of desire, just as He saved the Holy Innocents. Which means that an unborn child could possibly go to Heaven. We don't know what the mercy of God will allow.

I have the book My Catholic Faith and it confirms what Songbird says.  Those children have not been baptized but do not go to hell.  This limbo they would go to is a sort of a unknowing happy place.  

Why be open to life?  What do you mean?

Maybe Limbo is actually what is best for them according to God's infinite mercy in that if they lived a "full" life, then they may have ended up in a much hotter part of hell. If abortion sent babies to heaven, then the devil most assuredly would not promote it. The abortion will send my baby to heaven, so I might as well abort my child logic could be used.

Well with sufficient prayers for baptism of their child even in the case of miscarriage God can intervene.

So for Christian parents, properly taught of the necessity of baptism, there is this hope.

It would be a fallback existing alongside Limbo, rather than doing away with it as some would have done, which is frankly, against the writings of the saints and Revelations of Our Lord Himself.

Generally however, they should be taught as in the paper here:

http://saintsworks.net/Papers%20and%20Information.htm

"How to Baptize in the Case of Miscarriage"

Something which I read is supposed to be standard Catholic teaching for parents.

Which is why I always hope that people will spread the information to other parents.

From the Revelations of St. Bridget:

'First question: Again he appeared on his ladder as before, saying: ”O Judge, I ask you: Why does one infant emerge alive from the mother's womb and obtain baptism, while another, having received a soul, dies in the mother's belly?”
Answer to the first question. The Judge answered: ”Friend, your inquiries are not made out of love but are made through my permission. So I answer you through the likeness of words.

You ask why one infant dies in the mother's belly while another emerges alive. There is a reason. All the strength of the child's body comes, of course, from the seed of its father and mother; however, if it is conceived without due strength, because of some weakness of its father or mother, it dies quickly. As a result of the negligence or carelessness of the parents as well as of my divine justice, many times it happens that what was joined together comes apart quickly.

Yet a soul is not brought to the harshest punishment for this reason, however little time it had for giving life to the body, but, rather, it comes to the mercy that is known to me. Just as the sun shining into a house is not seen as it is in its beauty - only those who look into the sky see its rays - so too the souls of such children, though they do not see my face for lack of baptism, are nevertheless closer to my mercy than to punishment, but not in the same way as my elect.'

And then Pope Sixtus V:

'For who would not detest a crime as execrable as this — a crime whose consequence is that not just bodies, but — still worse! — even souls, are, as it were, cast away? The soul of the unborn infant bears the imprint of God's image! It is a soul for whose redemption Christ our Lord shed His precious blood, a soul capable of eternal blessedness and destined for the company of angels! Who, therefore, would not condemn and punish with the utmost severity the desecration committed by one who has excluded such a soul from the blessed vision of God? Such a one has done all he or she could possibly have done to prevent this soul from reaching the place prepared for it in heaven, and has deprived God of the service of this His own creature.'

I think Clare your statement:

"The idea that unbaptised infants who die are given a chance to accept God is nice. But it means they may also reject Him. In which case they would go to the fiery part of Hell, rather than the outskirts which are more pleasant."

Is very strikingly and reminds me of some of what I have read in the past, but do not have sufficient information on.

Maybe Limbo is actually what is best for them according to God's infinite mercy in that if they lived a "full" life, then they may have ended up in a much hotter part of hell. If abortion sent babies to heaven, then the devil most assuredly would not promote it. The abortion will send my baby to heaven, so I might as well abort my child logic could be used.

I have always understood Limbo to be a pious theological opinion, not a dogma, and have generally not believed in it.  However, this is a really good argument for it, and I will have to rethink my position.

I once set myself to gathering a good deal of quotes on the subject after listening to an Audio Sancto sermon on Limbo which basically condemned the ITC and its paper on the matter.

Limbo is the lighter view, in many ways, historically. It is better than Hell proper.

Here from my notes, I have not looked at these in awhile so do not recall much, I have some of the source citations second hand I think, but do not doubt them, fwif:

'Whoever says that infants are alive in Christ even when they depart this life without being baptized is really both opposing the Apostolic preaching and condemning the whole Church which runs hastily with infants to the baptismal font because it is believed without any doubt that otherwise these infants cannot possibly be alive in Christ.'

St. Augustine, Father and Doctor of the Church, 'Doctor of Grace'  (a letter to St. Jerome (no. 27))

'The common teaching of the scholastic theologians is the within the earth there are four inner chambers: one for the damned, another for those being purged of sin, a third for those infants who have died without receiving Baptism, and a fourth which is now empty but once held those just men who died before the passion of Christ.'

St. Robert Bellarmine (1542-1621), Doctor of the Church

'It will happen, I believe . . . that those last mentioned [infants dying without baptism] will neither be admitted by the just judge to the glory of Heaven nor condemned to suffer punishment, since, though unsealed [by baptism], they are not wicked. . . . For from the fact that one does not merit punishment it does not follow that one is worthy of being honored, any more than it follows that one who is not worthy of a certain honor deserves on that account to be punished.'

St. Gregory Nazanzien, Father and Doctor of the Church, [Orat., xl, 23]

'If you want to be a Catholic do not believe, do not say, do not teach that infants carried off by death before being baptized can obtain the remission of original sin."

St. Augustine, Father and Doctor of the Church 'Doctor of Grace' (III de Anima)

Q. Where do infants go who die without baptism?
A. Infants who die without baptism go to Limbo, where they do not enjoy the sight of God but also do not suffer, this is because having original sin and this alone they do not merit Heaven but neither do they merit purgatory or Hell.

- Catechism of Christian Doctrine

'For there be some that are withdrawn from the present light, before they attain to shew forth the good or evil deserts of an active life. And whereas the Sacraments of salvation do not free them from the sin of their birth, at the same time that here they never did aright by their own act; there they are brought to torment. And these have one wound, viz. to be born in corruption, and another, to die in the flesh. But forasmuch as after death there also follows, death eternal, by a secret and righteous judgment "wounds are multiplied to them without cause." For they even receive everlasting torments, who never sinned by their own will. And hence it is written, Even the infant of a single day is not pure in His sight upon earth. Hence "Truth" says by His own lips, Except a man be born of water and of the Spirit, he cannot enter into the kingdom  of God.  Hence Paul says, We were by nature the children of wrath even as others.  

He then that adding nothing of his own is mined by the guilt of birth alone, how stands it with such an one at the last account, as far as the calculation of human sense goes, but that he is "wounded without cause?" And yet in the strict account of God it is but just that the stock of mortality, like an unfruitful tree, should preserve in the branches that bitterness which it drew from the root. Therefore he says, For He shall break me with a tempest, and multiply my wounds without cause. As if reviewing the woes of mankind he said in plain words; "With what sort of visitation does the strict Judge mercilessly slay those, whom the guilt of their own deeds condemns, if He smites for all eternity even those, whom the guilt of deliberate choice does not impeach?"'

Pope St. Gregory the Great


.. Basically, I see the current climate an extrapolation of the universal or near universal salvation theme in regards to Limbo.

First one gets rid of the place, then one extends mercy to the extent it does not exist as a state of being, and condemns the past saints and popes statements as antiquated and lacking in hope and mercy.

But, it has struck me that if infants by default went to Heaven, we would have heard about it long before now. Who would not wish to say it -- if it could be said?