Le 14-juil.-06, à 18:52, Tom Caylor a écrit :
> Here is where I believe the crux is: "..." means you can continue to > add the "I" as many times as you want. Actually, this is equivalent > to: "..." means you can continue to add the "I" as many times as you > want and you can. It's just a little redundant to say it that way. > Now A and B *know*, as well as anyone can even know, what finite means. True, but unprovable. With comp you are betting here. > All they have to do is perform some experimentation to get the idea > that, after a while of adding "I" they eventually get tired and/or > loose interest, so they have to *stop*. Yes but my friend B, which is an angel, a cousin of the analytical second order arithmetic with the omega rule. He is tired after counting up to number like |||...|||...|||... ...||||||||. > What's so difficult about > understanding what stopping is? I am not denying we have some intuition of that. Just pointing that mathematicians can show we cannot define what finite means through first order logic, and then second order logic builds on that intuition, so that really "finite" is not a notion we can define in any finite way. Nor can we define "NOT finite", that is what "infinite" means. > Even the word "finite" has "fin" in > it, i.e. "end". The notion is defined by invariance. Relative one. You can imagine something stopping compare to something which does not stop. > Something > similar (invariant) is happening (adding "I" at one step is considered > the same action as adding "I" in another step) Actually adding | at the end of ||||..... giving |||....| is different from adding | at the end of |||. > and then the invariance > disappears, i.e. the adding of the "I" is no longer happening. Yes but when? I know you and me know that. The point is that we cannot explain it without admitting at the start that we know that. "that" has the type of a quale. Bruno http://iridia.ulb.ac.be/~marchal/ --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---
