Hi!
Thanks again for your very important work!
These are the three issues that I thought you might want to adress in your "kappa" and further work:
1)
Making clear that the premises are just premises, some of which need further empirical investigation. This is, I believe, a very tricky thing about using the "empirical side" as an inspiration. This is both a methodological issue and, as we are dealing with what you describe as a group vulnarable to stigmatization and discrimination, also an ethical issue.
Some of your premises (perhaps especially in "Living the categorical imperative") not only need further empirical investigation, but are actually empirically problematic* - unless you are very clear about dealing with "ideal types" or stereotypes that may not apply to real people (other than to some extent and more as a tendensy on a group level that could be discussed as a principle for the sake of argument rather than as an empirical fact).
Personally, I think it would also be a good idea to problematize and critically reflect on the stereotypes in relation to empirical data that might be available - not to come to any conclusions, but to open the for the possibility that some premisses might be wrong. That may be beyond the scope of your philosophical aim, and irrelevant for the journals in which you publish your articles, but could nevertheless be relevant to adress in your "kappa" for the sake of a wider audience (professionals in health care and education, autists, parents, spouses, colleagues of autists...).
It could also be useful to discuss to what extent your conclusions might have bearing regardless of the truth of some claims. Wouldn't it be possible that there are some advantages to the differently wired brain even if it does not involve being extremely male, for instance? There are very well-known positive criteria for Asperger that you could refer to:
http://www.autismforum.se/gn/opencms/web/AF/Leva_med_autism/styrkor_och_utmaningar/aspie_kriterierna/aspie-originaltext/index.html*) p. 275: "Persons with Autism cannot disregard a particular truth for the 'truth' of the whole";
p. 276: "The ethics of care perspective will make little sense to moral agents with Autism".
I could show you endless discussions on internet fora proving you wrong - UNLESS you mean that people with autism on a group level are more likely to have difficulties in these areas. In fact, many aspergians have made it their continuing mission to educate or debate with other aspergians in these areas. Quite possibly they are more likely to succeed than the average neurotypical running the same mission (as neurotypicals on a group level are "weak empathizers" when it comes to understanding autistic ways of thinking and feeling, and also lack persistance).
2)
This issue has to do with static conceptions of abilities (to empathize, for instance). You may need to adress this for the sake of your own argument (besides the fact that it can be questioned empirically). If there is no capability for cognitive empathy at all, how could you then learn to lie in any other way than a very rule-based one? And it is possible to learn. I know that for a fact. It can be very energy-consuming, and one might wonder to what extent it should be necessary when it comes to some matters (Wouldn't it even be nice to know that your hair cut really looks good? With neurotypicals you never know... so why bother asking them? If the compliment merely means "I want you to think of me as a nice and polite person", it is useless as a compliment; if it means "It's nice to see you, and I notice you and want you to be happy", why not just say so?), but it is nevertheless possible at least for many mild autists.
3)
Inconsistencies: assuming deficits/disability in some places and neurodiversity in others. You mention the question whether persons with Autism should inform of their condition in order for neurotypicals not to be hurt by their 'rude' remarks. One might also raise the question whether neurotypicals should rely less on their fasades and white lies and stop playing games. Could obsession with face-saving games be viewed as a neurotypical disability? Or is it just a natural variation?

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One more thing: I have a problem with the terms "weak empathizer" and "hypo-empathizer" as they do not distinguish between cognitive and emotional empathy. I am under the impression that many (well, at least more than what is usually assumed) aspergians/autists (not all, though) are even stronger emotional empathizers than the average neurotypical. That is of course an empirical question - and I believe there is a huge variety here - but if that is actually the case, then I would say it is highly problematic to use terms that do not take these different aspects of empathy into account.