My guess would be if the conjoined twins both have different fully developed brains, and hearts, they are two people with two souls.  Some of them have been successfully separated.  

If by chance one of the twins developed without a fully developed brain and is only kept "alive" because they share the same heart, blood flow, then it would only be one person.   However this is just a guess of mine.  

However since the soul is infused at the time of conception, and the twin that did not develop and is only kept "alive" as described above, it would also be my guess that at some point the soul left the body, as any fetus who died in the womb, and resides in Limbo.  In other words the body is being kept "alive" artificially, and the soul is absent from it.  Again, it is only a guess, but interesting to think about.  

This is an interesting medical ethics question and has been dealt with in many books on the subject, but it remains controversial. The best example of this ethical dilemma is the case of conjoined twins, but where one twin has not developed beyond the size of a small lump on the forehead of the other twin. The two are genetically separate, but the tiny twin depends completely on the larger twin for survival, because it has no heart, and no developed brain, but on cell sampling is shown, for example, to be of a different sex on genetic analysis. Is it morally acceptable to remove the lump? If the lump was an 'identical' twin, we would not know, because unless it had its own separate anatomy, it would be otherwise indistinguishable by any genetic test we have. Is it immoral then to remove the lump?

One solution is to treat the two as we do a mother and fetus, which can be defined as two genetically distinct beings, and therefore the lump cannot be touched, but deserves Baptism and its own name. This is more or less the Catholic approach. The counter argument to this is that it is possible for a mother to have a fetus which is her genetic clone (albeit not naturally, but identical twins are precisely such clones). Are they two different people with two different souls? The obvious answer is yes, but it raises the question of what is human life, and what is not.

Cancers, for example, are autonomous forms of life that have developed a genetic dissimilarity to the host at some stage beyond that of the zygote and take on a parasitic existence. Is the cancer part of the person? Is it human? Probably not, but again one can ask, what does it take to be human? Can you be a twenty year old lump on someone else's forehead, and be human? I think in most cases we never know it's human and it gets removed inadvertently. This is morally neutral because a sin requires knowledge and consent.

So, my answer is that, for practical purposes, a twin has its own soul once it is clear to the observer that it is a distinct genetic or otherwise autonomous entity that is nonetheless human (conjoined though it may be). We have an obligation to treat it as a person once this becomes obvious. There is also an obligation to answer to the question definitively once a suspicion is raised that some appendage to a person may in fact be the person's twin.

If one of the characters of the human soul is rationality, and since mentally retarded people do not have the ability to reason, would that mean mentally retarded people are not human, and possess irrational souls?

No. A foetus that has no measurable rationality has an immortal, fully human soul.

Quote from: Maizar

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If one of the characters of the human soul is rationality, and since mentally retarded people do not have the ability to reason, would that mean mentally retarded people are not human, and possess irrational souls?

No. A foetus that has no measurable rationality has an immortal, fully human soul.

Why is it that animals, who cannot reason, have irrational souls, but the mentally retarded, who also cannot reason, have immortal, rational, human souls? Is there a definitive answer?

The answer to this is given in Thomas Aquinas' Summa Theologica, but my own rather different answer is that what is contained in Divine Revelation does not cover every possible question, but covers the necessary questions needed for practical purposes, being the salvation of human souls. Animals have souls, yes, and their fate is not the same as that of human souls. The destiny of human souls is not uniform either, but dependent on the context of in which the person dies. The severely retarded person who dies young cannot be judged or awarded merit in the same way that a fully healthy person who dies old is judged and rewarded. However no one pretends to know exactly what God's mind is and how His perfect justice works. We are more concerned with how we behave towards the infirm and the disabled and the dignity we afford them.

Another way to explain why this kind of question is not answered directly in the Bible or elsewhere is that Christianity does approach moral and theological problems from the point of view of 'rights' but instead discusses 'obligations', which is in contrast to modern thinking. It's not our business to worry about what happens to an animal soul. What is our business is how we should behave towards animals, who are also God's creatures over which we have stewardship.