>>12700171How do they imply infinitism?
>>12700724I agree. I'm a finitist and also a Platonist. I don't think it's possible to understand mathematics without being a platonist. Natural numbers can be implemented or defined as strokes on a blackboard, but they are not identical with them. They're merely one of our ways of approaching, dealing with an ideal concept of a number. There are a lot of seemingly different implementations of our concept of rational number, that means the concept of rational number is not identical with any of the implementations.
I'm not an infinitist because we have no coherent way of approaching completed infinite objects. If anyone offered a coherent way of dealing with them, I would convert in an instant, but so far we only have what boils down to sleight of hand tricks that only obfuscate the matter.
>>12700896Wouldn't you say our concept of a rational number and their arithmetic is evidence of this reality?
>>12700957Why can't a finitist believe in induction?
