I'm extremely familiar with the concept of necessary and sufficient conditions. I'm quite confident that I have a better understanding of it than you do.
Really doesn't look like it all. You apparently refuse to address what I've quoted about them in the context of intensional definitions and how the apply to the standard biological definitions.
In fact, I've explicitly addressed your arguments from that perspective a number of times, which you seem to have ignored. Specifically... the active production of a specific gamete is a SUFFICIENT condition to be categorized as either male or female... but it is NOT a NECESSARY condition. One can be male while not actively producing sperm. One cannot be a fertile male without actively producing sperm, but one can still be male.
The NECESSARY condition is the presence of the anatomical organs associated with the production of gametes.
You don't quite seem to get that that is based on your own quite idiosyncratic definition for the sexes. Do show us
any dictionary definition, do show us any reputable journal that says anything of the sort. For bonus points, show how it - if it exists - refutes the standard biological definition, a salient example of which is the Lexico definition:
male (adjective): Of or denoting the sex that produces gametes, especially spermatozoa, with which a female may be fertilized or inseminated to produce offspring.
https://www.lexico.com/definition/male
You see ANYTHING at all there about ANY anatomical organs? Much less any "associated with the production of gametes"?
I've made several good faith arguments and analogies attempting to address your misunderstandings. So far, you've either completely ignored those posts... or you've responded with condescension and arrogance even when the topic is outside of your area of expertise and well inside mine.
What a joke; you might try going back and look for my responses to you - which I have yet to see you address. Hard not to express some exasperation in the face of such pigheadedness.
Your entire reasoning is pseudomath. It's completely and irrevocably wrong.
We cannot say "clown suit" > "book". It's not a thing. It's so far from a thing that it's not even wrong.
I generally put the terms in quotes to suggest that they really weren't commensurable - as my argument underlined; which you might try unbunching your knickers long enough to actually read and think about.
Discrete spectrum, yes. However, it's important to note that the variable under consideration is the number of wheels... and numbers are unquestionably ordinal. 1 < 2 < 3 < 4 < 6 < 18... etc.
So are the positions in the ordered set {apple, book, clown suit, picture}, i.e., {1,2,3,4}
Position of clown-suit > position of book.
And one can do the same sort of thing with properties that determine membership in other polythetic categories - as in Regenmortel's example. We can give a binary representation to the sets of sufficient but not necessary properties that define the category which encompasses individuals 1 through 4:
A-B-C = 1110
A-B-D = 1101
A-C-D = 1011
B-C-D = 0111
Even if the properties are categorical, even if there's diddly-squat that allows us to say they're commensurable, we can still arbitrarily order them. The 4 sets of mutually exclusive - and orderable - combinations constitute and define entities in a discrete spectrum. Necessary property set A-B-D has a mapped index of 1101 which is greater than the mapped index (1011) of property set A-C-D.
https://www.researchgate.net/figure...n-the-case-of-8-individuals-18_fig1_309889266