I'm interested in very problematic biological categories (for example is a cell "alive" or "dead"). See discussion on researchgate.net https://www.researchgate.net/topic/Evolutionary_Biology/post/What_are_the_necessary_and_sufficient_conditions_defining_life

Many of the comments - on and off the web - dispute the topic - claiming for example that these sort of categories are inventions of the human mind....or that transitional states nullify categorical distinctions, or that looking at the problem in another way sheds new light on it and therefore nullifies the discussion, etc. I certainly understand problems of classification in biology - and value of prototypes, ideal types, natural kings, etc.... I wanted some guidance going back to Aristotle on how to manage the sort of objections raised above.

It is a very interesting question. Going back to Aristotle you may try to identify what type of opposition is there between Life and Death. In the Book of Categories Aristotle identify 4 types of oppositions in chapter X (11b15-13b35): the opposition in a relation (like half and double), the opposition of the contraries, the opposition of privation and possession, and the opposition like in the affirmative and negative. Only one kind of contraries admit intermediaries : ex : black and white, or valorous and coward. The others like sick and in good health don't admit any intermediate. Here might be the ambiguity : in the fact that we spontaneously consider that "alive" and "dead" are simple contraries. Whether we think that there are intermediate states between these two "contraries" or not, we will have differents points of view.. Maybe another option is possible by considering that life might be a kind of possession, or ability, and death, a privation...The chapter of the Categories about opposition and especially about possession and privation might of help here. To go deeper into this concept, you might read also the chapter VIII of the Book of Categories about quality since the ability is a kind of quality. I do not have enough time to develop this more, but I hope these small indications will help you.

A remark : dead and non-living are not equivalent... Death is only a negative concept. So, the "in-between", "on the margins", and so on, may refer to very different things... and might not be so "on the boundaries"...

Yes, dead and non-living are not equivalent. And thanks for the comments and suggestions. Much to read.

My colleague and I are coming at this problem from a particular vantage. We are trying to clarify what makes something "alive." Our interest - from a biological vantage - is in the nature of aliveness (rather than, say, in the origins of life). We propose five criteria: 1. Necessarily, living things constantly act in order to sustain their ongoing existence. 2. individual living things are separate from their enviroment but at the same time maintain an openness to it and engage in transactions with it (metabolism). 3. Organisms are sensitive to their environment. 4. Organisms undergo constant change while always maintaining a "sameness" throughout this change. (Hence the identity of the organism is in its organizational structure rather than in its changing components.) 5. An organism's activities are directed towards its own future being (hence the return of teleology to biology).

You've been given an excellent answer from the Physics, which I don't mean to contradict; but I'd like to expand on the question a bit more.

If you're talking about death, the relevant question for Aristotle is whether the thing you are examining is going through a "substantial change." "Substances" for Aristotle are things that, among other qualities, reproduce themselves. Thus, a human cell may continue to belong to a human being even though it is in some sense 'dead'; but if it continues to be ordered and used by the human substance, it is still essentially human. Alternatively, if it were (say) eaten by a grizzly bear, it would undergo a substantial change: a new substantial form would be ordering the matter into the substance of a bear.

Of course you understand that Aristotle has a system built around "form" and "matter." Both terms mean different things than they do in modern science, but there is actually a very close analog to form in living beings: things like DNA do take kinds of matter and order and structure them so that a human being can be formed and supported. A lot of the question of where the cell is thus falls under the heading of what form is ordering it: if it is still the human form, then it is still essentially human. (The form of a living creature is its anima, as discussed e.g. in De Anima).

By the way, there are certain qualities that don't fit in the Aristotelian catagories. One of them is "being," so if you are talking not about a cell that is living or dead, but one that "is" or "is not," you're talking about the question of being. Things like being -- along with "good" and a few others -- are called transcendentals. Particularly later Aristotelian thinkers use the transcendentals to deal with certain kinds of questions that apply across categories. That doesn't seem to be the issue here, but it's another way that 'in between' things can be handled by the system.