Another possible metaphor is to think of infinities as second class citizens. For example, in our world dragons don’t exist, but if they existed they wouldn’t be able to ride the subway as easily as humans, because that would pose practical problems for both dragons and humans. Same for infinities—in the world of numbers they don’t really exist, but if they existed, it’s not clear how we could extend them equal rights of addition and so on. It’s up to politicians/mathematicians to imagine a world where dragons/infinities can live on equal terms with humans/numbers, and maybe such a world just can’t be imagined in a way that makes sense.
Argument from lack of imagination isn’t really convincing. And I do happen to think that surreal addition does make sense. Social reasons why not be interested in surreal numbers would be lack of applicability or unnaturalness reasonings. But lack of coherence really isn’t one. I do agree that the onus of responcibilty of making things workable is on the mathematician.
If you did have “flying pedestrians” that would mean human piloted cars would not be adequate first-line law enforcement. But just assuming that anything flying is a brid that can’t be criminally liable doesn’t mean that worlds outside of that assumtion are unthinkable.
And giving an ethnicity second-class citizen status just because you are uncomfortable sitting next to them in a bus is not a defensible “practical problem”.
Another possible metaphor is to think of infinities as second class citizens. For example, in our world dragons don’t exist, but if they existed they wouldn’t be able to ride the subway as easily as humans, because that would pose practical problems for both dragons and humans. Same for infinities—in the world of numbers they don’t really exist, but if they existed, it’s not clear how we could extend them equal rights of addition and so on. It’s up to politicians/mathematicians to imagine a world where dragons/infinities can live on equal terms with humans/numbers, and maybe such a world just can’t be imagined in a way that makes sense.
Argument from lack of imagination isn’t really convincing. And I do happen to think that surreal addition does make sense. Social reasons why not be interested in surreal numbers would be lack of applicability or unnaturalness reasonings. But lack of coherence really isn’t one. I do agree that the onus of responcibilty of making things workable is on the mathematician.
If you did have “flying pedestrians” that would mean human piloted cars would not be adequate first-line law enforcement. But just assuming that anything flying is a brid that can’t be criminally liable doesn’t mean that worlds outside of that assumtion are unthinkable.
And giving an ethnicity second-class citizen status just because you are uncomfortable sitting next to them in a bus is not a defensible “practical problem”.