There is a subtle but very important difference between being alive and living. Very few people ever consider this in an argument about abortion, particularly those who are against legalized abortion.
Every single cell is alive, from sperms to liver cells, they are living organisms but they do not live. To actually live a brain is required, but no other organs are inherently required.
By definitions, science considers one who has sentience to be living, for humans this occurs about 3 years after birth. Sentience is not a side effect of the brain, though the brain is required.
Sentience happens after enough information has been formed and stored by the brain, when the brain becomes aware of it's own existence. This is a side effect of the information it records.
Without sentience, the brain can even utilize the information in logic and decisions, but it inevitably becomes aware by doing this. Fetuses have no brains, they do have some parts of the brain in later stages of development.
The brain develops in the fetus in much the same way it evolved, from the basic nerve response clusters on through the logic centers, ending in the memory centers. This is why at mid to late stages the fetus appears to respond to pain, it is an autonomic response to nerve stimuli.
It is the same "flinching" response to pain we all experience, which happens before the pain even registers in our brains. Our memory of the pain is what actually makes it pain.
The simple fact of the matter is that human fetuses do not feel pain during abortions, anymore than a mollusk does when it is cooked. Without the memory of the information created by the nerves, pain is not pain.