Persons have certain rights in the law. One month old children have certain rights in the law. Therefore, one month old children are persons.
Interesting syllogistic argument, and I agree wholeheartedly from an ethical perspective (that is at a societal level). Law needs to reflect pragmatic boundaries and implement legislation that allows for the individuals in the society to hold their own liberties - this includes alternative views of what constitutes personhood. In this regard, the system must reflect a pro-choice status and set a limit to the point a genetically human entity can be terminated.
The argument that personhood is defined by conscious capacity is a strong argument, and pragmatically viable - but in some instances, it is possible to have areas of law that reflect the idea that separation between two organisms is what counts as a person; take for instance manslaughter cases. Endowment of rights is purely a value judgement, arbitrary but pragmatic in having a functional society.
However, morally this is a different story. Our personal conception (no pun was intended) of personhood has to coincide with law to be legal. You are entitled to think conception is when a personhood is present, and that natural viability is enough grounds to grant moral reasoning that that is a life that is protected by your morals - ethicality seeks to remain pragmatic and set an absolute line of when they consider aforementioned entity legally a person.
In a perfect society, we would have people who loving come together, are careful about how and who they have sexual intercourse with and take responsibility for their actions. There would also be no rape and incestuous unions, nor birth defect and economical strife to second guess what is our own seed. Abortion is a sad reality and is perpetuated by both ignorance, brutality and, in most cases, irresponsibility. Law recognises this lack of idealised conditions and seeks to set parameters that are functional. I disagree with a lot of legal statutes at a personal level and we are all entitled to alternative opinion and moral reasoning.
I think my main point is that we need to recognise the distinctive separation between the two subsets of code of behaviour:
- Ethics (ethicality) is concerned with society and is created by legislative bodies and is enforceable by a court system.
- Morals (morality) is concerned with an individual and is created by the individual. Such a code of behaviour is enforced by that individual. Please note, for your moral code to be legal it must fall within the parameters of the above - ethics. To some degree, ethicality arbitrates morality and sets the "bare minimum" moral views.
There is also an extension to your above argument of that legally defined persons have responsibilities and these responsibilities are relative - they are not absolute, despite the law masquerading such. A murderer (that is someone who has committed an unlawful killing) can be exempt of complete responsibility because of mental impairment and therefore be assigned to a rehabilitation program. Personhood endows one both rights and responsibilities but they are of course relative to the capacities of the individual. The defining capacity is seen as ultimately self-perception and sensorium by law in most instances. Arbitrary but can be defended - but most things are.
This is of course only with regards to the biological side of "personhood" and the distinction between ethics and morality.