>>12454052>For any number N, there exists a number M such that M>N.This is true, just take M=N+1.
>There are finitely many numbersNow you have to be very careful with what you mean by this. I didn't actually assert that there are finitely many numbers, just that you cannot put all numbers in a completed whole, and that there is no "set of natural numbers", i.e. it's a fantasy.
The concept of a "cardinality" and assigning a number representing the size of my version of natural numbers already presupposes that the natural numbers form a completed whole, an object in which lies all the numbers, a premise that I already rejected.
You may try to find a contradiction in my conception of the naturals but you won't be able to, because it's based on reality and has a model, thus is consistent, unlike your fantasy fairytale you tell yourself about the completed infinite.
>>12454056Do you reject the premise that it's possible to draw a stroke on a whiteboard?
>>12454066I see what you mean (I used to be an infinitist Platonist like you a while ago). However you are misunderstanding my point. Completing the infinite here means collecting a nonending number of things into one object and declaring it a definite object. You can admit the existence of each member of some ongoing sequence, for example the sequence of prime numbers, but that alone is not enough to justify the conception of a "set of prime numbers" as a definite mathematical object.
Another example is a Cauchy sequence. An example of completing the infinite is taking the algorithm k-> 1+ 1/2! + ... + 1/k!, which can input a number k and return you some rational number, and declaring that you can put all the values into one object, a completed (Cauchy) sequence representing e. In my opinion, this is completely unjustified and a source of a lot of confusion in mathematics.
