> You could start with the first case I mentioned: opposition to contraception, which is something American right-wingers are increasingly trying to class as abortion even though there are nothing more than unimplanted cells at that point.

Which forms of contraception are you talking about? Which "American right-wingers"? (And why pick on Americans? You seem to be at least partially talking about the moral views of conservative Roman Catholics, whose views are largely the same everywhere and have nothing to do with whether they are Americans or not.)

Some people believe that the moral status of an individual human being begins at conception. Some forms of contraception may prevent the implantation of a fertilized egg. If you believe a fertilized egg has the moral status of a person – a belief which is neither "scientific" nor "unscientific", but rather beyond the scope of the natural sciences to judge – then forms of contraception which prevent the implantation of a fertilized egg are plausibly immoral. Everyone can choose which moral beliefs they want to accept and which they want to reject, but either way moral beliefs are outside the proper domain of the natural sciences.

There is some controversy over whether particular forms of emergency contraception do indeed prevent implanatation or not. Some people have taken positions in that controversy which may not be supported by the scientific evidence, and so on that limited issue may be "unscientific", although I don't think anyone can fairly deny that it is at least possible that some forms of emergency contraception do sometimes prevent implantation. Similarly, although for IUDs the primary method of action happens pre-fertilization, my understanding of the scientific evidence is that IUDs do sometimes prevent implantation.

Quite separately, some religious people – in particular conservative Roman Catholics – believe methods of contraception which only act prior to conception, such as condoms, to be immoral. That's a moral belief, so (like all other moral beliefs) I can't see how it can be "scientific" or "unscientific"; and that moral belief is a separate topic from abortion. (Nobody claims condoms are a form of abortion, not even conservative Catholics who believe that condom use is immoral.)

> Most dictionaries define baby as starting at birth.

I don't agree. Which dictionaries are you talking about?

I've always considered the OED to be the most prestigious English dictionary, and it currently defines "baby" as "An unborn or newly born human being; a fetus, an infant" (sense I.1.a). That definition clearly includes the unborn in its scope, although possibly not the embryo. (And indeed, I myself would not call an embryo a "baby", although it is important to note that dictionaries are descriptive not prescriptive, so if somebody else does call an embryo a "baby", you can't argue they are wrong simply on the basis of a dictionary.)

> Where science comes into this is answering questions about development: when the brain is a handful of cells, without the major developments which start on the path to cognition it’s not what almost anyone would call a “baby”

It is not the job of the biological sciences to determine the meaning of the word "baby" in everyday use.

It is not the job of the biological sciences to answer moral questions, such as when does an individual gain the moral status of a person.

Embryology tells us that, at the point of implantation, the embryo contains around 200-300 cells, which are still largely undifferentiated. Nobody disputes that.

The question of whether those 200-300 cells constitute a "baby" (when that word is meant as a term of everyday language) or whether they have the moral status of a person, is not a question within the proper scope of the science of embryology to answer.

> As for the case you mentioned, I can see that’s a favorite talking point of Australian anti-abortion groups who are trying to portray it as common.

I've never heard anyone try to portray it as common. Everyone I've heard talking about it has presented it as a single case (out of around 14,000 abortions performed in Victoria in that year). (And, as far as I know, has not been repeated since.) The argument, however, is that whatever you think about those 14,000 as a whole (of which a mere 378 were performed post 20 weeks), surely you can agree there is something wrong with this particular case, and with laws which legally allow it. I think a lot of people who have no problem at all with abortion early in pregnancy – something which I personally support being legally readily available – think abortion of a healthy baby at 37 weeks should not be legal (and yet, under Victoria's laws, it is).

> Given that it’s a single record for common medical procedure my first thought would be that we don’t have enough information to know that it wasn’t a data entry or classification error.

So, it is in an official government report, prepared by a committee, whose members include specialist obstetricians, paediatricians, professors of midwifery, etc. Don't you think they would have noticed an outlier like this, and investigate it? The committee that prepared the report has access to the identifying details of the case (name of hospital, full name of patient, patient's date of birth, date of procedure, medical record numbers, etc). They certainly have the ability to inquire with their colleagues at the hospital where it was performed (we don't know that detail, but they do) and double check it is correct (Australian medical privacy laws have an exception for collection of government statistics, so that would not have been issue). Furthermore, there was enough controversy about it after the report's release, they surely would have investigated that data point afterwards if they hadn't already done so beforehand. If it was something as simple as a data entry error, I'm sure they would have been happy to publicly announce that. Given all of this, I think your suggestion is unlikely.

> The narratives portraying these situations as doctors happily killing viable babies have a long history of turning out to be gross misrepresentations of very painful medical situations.

I'm sure there is some very painful story behind it. My own guess is it is probably something like a young teenager (such as a 13 year old) pregnant due to rape/incest and who is actively suicidal. Obviously that's a very horrible situation, but even if my guess is right, I don't think it should be permissible to kill a healthy >=37 week baby, whether pre-birth or post-birth, even in such a horrible situation.

I think they really should have released more details about it – of course they can't publicly release any personally identifying details, but a few extra details might put the data point in greater context.