I read your wall of text. You make some interesting points. But I will be honest with you: I also used to think like you, in these long convoluted ways where I was trying to explain everything I saw via programming and all sorts of mathematical extrapolations, and I for a time I believed my own b
it. But then I realised: it was all c
p and youthful arrogance.
In a nutshell, you are nitpicking. You can always define an arbitrary scale at which nothing matters: you used time in your rabbit example very effectively to discount the usefulness of the "rabbit category". Or you used these XX males as a counter example to a rigid definition of gender. You even yourself realise that this way of thinking is completely useless as you yourself say that the category of species is extremely useful:
> So strictly logically speaking, this definition is useless. Nevertheless, the concept of species is clearly a useful concept that helps us communicate things about the real world. How do we explain this?
I can explain this for you: you are thinking life is logical and "discreet" because you are a programmer and this is what you were taught. It is not: life is... continuous! Like the integral: each point has measure 0 but when you "add" a transfinite amount of 0 measure points you get... non-zero area! This resolves your rabbit paradox: each generation of rabbit is a point with measure 0 since its "difference" is so small with the generation before and after that it we can model it as 0...
Or second model: Rabbit_n = 0.9999 * Rabbit_{n+1}
After 100 generations: similarity is already 0.99
After 1000 generations: similarity is 0.90
After 10000 generations: similarity is 0.36
Tadaa: problem solved. So don't think so hard about this, use your common sense and realise that most people are men and most people are women and a few edge cases do not matter for practical purposes. And this is the crux of the matter: we need to make decisions. Hence we do what you very well describe: we categorise the particle soup around us and we act. So the usefulness of categories/abstractions CAN ONLY EVER BE MEASURED BY THEIR USEFULNESS FOR DECISION MAKING (sorry for caps I but want to emphasize). When I say decision making I mean almost everything: from deciding what sandwich to eat to deciding on how to prove Fermat's last theorem. If categories help you to do things, they are useful. End of story (for me, you can go write a book about this, make sure to send me a free copy).
Finally, this is also all bs so don't take it too seriously: I am a person on the internet.
In a nutshell, you are nitpicking. You can always define an arbitrary scale at which nothing matters: you used time in your rabbit example very effectively to discount the usefulness of the "rabbit category". Or you used these XX males as a counter example to a rigid definition of gender. You even yourself realise that this way of thinking is completely useless as you yourself say that the category of species is extremely useful:
> So strictly logically speaking, this definition is useless. Nevertheless, the concept of species is clearly a useful concept that helps us communicate things about the real world. How do we explain this?
I can explain this for you: you are thinking life is logical and "discreet" because you are a programmer and this is what you were taught. It is not: life is... continuous! Like the integral: each point has measure 0 but when you "add" a transfinite amount of 0 measure points you get... non-zero area! This resolves your rabbit paradox: each generation of rabbit is a point with measure 0 since its "difference" is so small with the generation before and after that it we can model it as 0...
Or second model: Rabbit_n = 0.9999 * Rabbit_{n+1}
After 100 generations: similarity is already 0.99
After 1000 generations: similarity is 0.90
After 10000 generations: similarity is 0.36
Tadaa: problem solved. So don't think so hard about this, use your common sense and realise that most people are men and most people are women and a few edge cases do not matter for practical purposes. And this is the crux of the matter: we need to make decisions. Hence we do what you very well describe: we categorise the particle soup around us and we act. So the usefulness of categories/abstractions CAN ONLY EVER BE MEASURED BY THEIR USEFULNESS FOR DECISION MAKING (sorry for caps I but want to emphasize). When I say decision making I mean almost everything: from deciding what sandwich to eat to deciding on how to prove Fermat's last theorem. If categories help you to do things, they are useful. End of story (for me, you can go write a book about this, make sure to send me a free copy).
Finally, this is also all bs so don't take it too seriously: I am a person on the internet.