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> Consider the set of all even integers Nope, don't: Mathematical approaches to infinity do not work. Because all mathematical approaches are limited. And the

> Consider the set of all even integers Nope, don't: Mathematical approaches to infinity do not work. Because all mathematical approaches are limited. And the infinite cannot be expressed by using the finite. Infinity must contain everything that exists and their antithesis in it. If even one thing is missing, the infinity won't be infinite. > but it is also not terribly interesting that it contains "contradictions" It's terribly interesting. Because: > the propositions "2 is even The infinity must contain the antithesis of a proposition. The antithesis of 2. The antithesis of even. The antithesis of everything involved in making that proposition. If it doesn't, then its not infinite because it is missing something.

jerf 4y ago
So, you have your idiosyncratic definition of infinity. You are welcome to it. But you are making the very common mistake of thinking you can play games with definitions and thereby somehow affect the real world. Along with failing to change anything with your definitions, you also sever yourself from any ability to communicate with anyone else in the world using a more conventional definition. I see this sort of approach a lot. It may give you a lot of warm fuzzy mystical feelings, but it's sterile. It can't go anywhere beyond that. You've locked yourself in a tiny little box with your fuzzy feelings and mixed up definitions, and you think you've got a hold of something amazing, but you're just... locked in a tiny box, with nowhere to go, with nothing allowed to come in and affect you and no ability to put anything out into the world. What's more, if you came out into the greater world with the rest of us, you'd find that your content-free mystical feelings are really just a counterfeit of the wonder that is available in the real world. More complicated, more substantial, more interesting, and as far as I can see, an infinite (heh) vista of things to discover and communicate, rather than a tiny little concept posing as a large one. Throw away your attachment to your idiosyncratic definition and join the rest of us on the real voyage of discovery. It may hurt a bit at first, and it certainly requires more work, but the pay off is worth it.

jerf 4y ago

So, you have your idiosyncratic definition of infinity. You are welcome to it. But you are making the very common mistake of thinking you can play games with definitions and thereby somehow affect the real world. Along with failing to change anything with your definitions, you also sever yourself from any ability to communicate with anyone else in the world using a more conventional definition. I see this sort of approach a lot. It may give you a lot of warm fuzzy mystical feelings, but it's sterile. It can't go anywhere beyond that. You've locked yourself in a tiny little box with your fuzzy feelings and mixed up definitions, and you think you've got a hold of something amazing, but you're just... locked in a tiny box, with nowhere to go, with nothing allowed to come in and affect you and no ability to put anything out into the world. What's more, if you came out into the greater world with the rest of us, you'd find that your content-free mystical feelings are really just a counterfeit of the wonder that is available in the real world. More complicated, more substantial, more interesting, and as far as I can see, an infinite (heh) vista of things to discover and communicate, rather than a tiny little concept posing as a large one. Throw away your attachment to your idiosyncratic definition and join the rest of us on the real voyage of discovery. It may hurt a bit at first, and it certainly requires more work, but the pay off is worth it.