you quoted what an intensional definition is, and are using it in your approach. Is an extensional definition off the table? Why?
You might actually try reading that article. Generally a bad idea to let others do your thinking for you, to too slavishly follow the herd.
In particular, try reading the section on extensional definitions:
An extensional definition gives meaning to a term by specifying its extension, that is, every object that falls under the definition of the term in question.
For example, an extensional definition of the term "nation of the world" might be given by listing all of the nations of the world, or by giving some other means of recognizing the members of the corresponding class. An explicit listing of the extension, which is only possible for finite sets and only practical for relatively small sets, is a type of enumerative definition.
If you tried to create extensional definitions for the sexes then, technically at least, you'd probably have to specify every individual member of each category. For an example of a binary, consider the even and odd numbers. An intensional definition gives the criteria for each category: evenly divisible by two, and not evenly divisible by two. Extensional definitions would have to specify exactly which numbers qualified for each of them. Even: {2, 4, 6, 8, ....}; Odd: {1, 3, 5, 7, ....}
What are these principles for creating categories (as opposed to types of definitions, intensional and extensions)?
Good question, one which is a bit thorny and has bedeviled much of philosophy for the last 2500 years. Though, as a preliminary, intensional definitions, in particular, create categories. "teenager", for example. The necessary and sufficient condition to qualify as a member of that category is to be 13 to 19. No "teenager" membership card for those outside that range.
But see:
The problem of universals is an ancient question from metaphysics that has inspired a range of philosophical topics and disputes: "Should the properties an object has in common with other objects, such as color and shape, be considered to exist beyond those objects? And if a property exists separately from objects, what is the nature of that existence?"
https://en.wikipedia.org/wiki/Problem_of_universals
Though too many philosophers have made a mess of that "problem" -- muddying the waters to make them seem deep according to Nietzsche.
But, more particularly, categories are defined by the properties that must be present for any entity to qualify as a referent of the term being defined. Don't exhibit or manifest the property "produces gametes" then not a member of the sex categories. Easy peasy.
Though that kind of leaves hanging the question as to which properties are the ones that justify creating a category to encompass those entities which possess them. But that question is more or less answered by the concept of "natural kinds", the sexes being biggies as far as biology is concerned -- foundational to the field:
"Natural kind" is an intellectual grouping, or categorizing of things, in a manner that is reflective of the actual world and not just human interests. Some treat it as a classification identifying some structure of truth and reality that exists whether or not humans recognize it. Others treat it as intrinsically useful to the human mind, but not necessarily reflective of something more objective. Candidate examples of natural kinds are found in all the sciences, but the field of chemistry provides the paradigm example of elements.
https://en.wikipedia.org/wiki/Natural_kind
The
Stanford Encyclopedia of Philosophy has a decent synopsis of the idea as well, although they go off into the weeds pretty quickly:
Scientific disciplines frequently divide the particulars they study into kinds and theorize about those kinds. To say that a kind is natural is to say that it corresponds to a grouping that reflects the structure of the natural world rather than the interests and actions of human beings.
https://plato.stanford.edu/entries/natural-kinds/
The philosopher Muhammad Ali Khalidi has, more or less successfully, argued in favour of that "thesis" with his "
Are sexes natural kinds?":
https://philpapers.org/rec/KHAASN
And I've used the Stanford Encyclopedia of Philosophy article on "
Mechanisms in Science" to argue pretty much the same point:
https://humanuseofhumanbeings.substack.com/p/rerum-cognoscere-causas
https://plato.stanford.edu/Archives/win2021/entries/science-mechanisms/#toc