Re: infinitely many nn's = infinite nn's?

Chris Menzel wrote:
On Mon, 05 Mar 2007 07:35:24 GMT, Phil <toob-headman@xxxxxxxxxxxxx>
said:

...
Unfortunately, as you say, people are not yet willing to have
completely open-minded, honest discussions on the internet, perhaps
because in such discussions, our beliefs become completely vulnerable,
open to attack or even destruction. Usually, we are simply not willing
to risk losing our beliefs, even if science states that we should,
from time to time, re-examine our beliefs in just such a vulnerable,
open manner. Of course, this applies just as much to the cranks as to
the true-believers.


Unfortunately, often as not, cranks who can't follow a simple
mathematical argument, or who are just hopelessly confused, misinterpret
their interlocutors' unwillingless to acknowledge the "soundness" of
their cranky arguments as proof that their interlocutors are simply
dogmatic true believers who don't want to risk losing their beliefs.

Ah yes, the "filibuster logical proof" method. When re-examining some belief, in order to determine whether any errors exist, we simply state, oever and over, the belief in question. That "refutes" any possible errors brought to light in the re-examination. You know, I think I'll try that on my bank account. It DOES have $10,000, it REALLY DOES have $10,000, any IDIOT KNOWS that it has $10,000... According to you, it should now have $10 K! Thanks! No need to examine the criticisms, or the paradox, or the bank statement. And here I thought that the filibuster method was mainly a crank method.

I don't suppose you could come up with a logical train of thought that shows why we CAN mix-and-match potential and actual infinity? That would save me the time of writing it up, and I will publicly thank you and acknowledge your superior intellect if you do so. Remember, so I don't waste YOUR time, I have no disagreement with either the argument proving infinitely many numbers, nor the argument proving they are all finite. It's the combination that I think violates the rules of mathematics, specifically the one that says we cannot combine results from two mutually exclusive premises (in this case, potential and actual infinity).

I just want to make sure that (1) using potential infinity in the argument proving infinitely many numbers will indeed now prove finitely many numbers (or if you prefer, "potentially infinite numbers"), (2) using actual infinity in the argument proving every number is finite will now prove that some (infinitely many but not all) are infinite "numbers" (or however we refer to such beasts), and (3) that using "mix-and-match" systems, such as, there are finitely many numbers, some of which are infinite" -- or its inverse, the current beliefs for natural numbers -- produces contradictions/paradoxes.

Thanks in advance for giving a valid correction, and not merely a "filibuster" correction!

But who am I kidding? As George says, the only option here is to publish, so that I won't have to listen to idiotic "responses." What's really going to piss me off then is that these same idiots, who are now blasting me, will then blast anyone who dares to question the latest "Holy Belief" of the "Holy Experts," namely that there CANNOT be infinitely many numbers, all of which are finite. Then, the comments will be, "Who could be stupid enough to think that a finite number of digits -- necessary, if all numbers are finite -- could possibly be used to create infinitely many numbers???" Sheesh ...

Phil
.

Relevant Pages

  • Re: infinitely many nns = infinite nns?
    ... simply not willing to risk losing our beliefs, ... I thought you meant that I was just a crank, who could not follow the simple arguments that prove there are infinitely many natural numbers, and the equally simple argument that they are all finite, and that simply restating these arguments was your method of "proving" that my paradox was flawed. ... Anyway, briefly, the argument was that if there are infinitely many numbers, then there must exist at least one number x, such that there are infinitely many numbers preceeding x on the natural number line. ... the natural numbers themselves have access to actual infinity, making it possible for infinitely many of them to exist). ...
    (sci.logic)
  • Re: Does a potential infinity actually exist?
    ... axioms with it or 'potential infinity' defined from primitives, ... I argue that the ultimate purpose of mathematics is to ... "solutions" the cranks come up with. ...
    (sci.math)
  • Re: infinitely many nns = infinite nns?
    ... Well I must say, it was VERY nice, given that you had previously said that you thought I was in general confused, to have you stand up and say that you couldn't figure out what was wrong with this particular paradox, even though you thought that it probably was wrong, somewhere. ... Usually, we are simply not willing to risk losing our beliefs, even if science states that we should, from time to time, re-examine our beliefs in just such a vulnerable, open manner. ... naturals, every one of which is finite. ... Mathematicians implicitly used actual infinity in their proof showing that there are infinitely many numbers, but then implicitly used potential infinity in the proof showing that all numbers are finite. ...
    (sci.logic)
  • Re: how to list all of the real numbers
    ... "cranks" way too much credit. ... even if they aren't actually espousing alternate axiom sets ... I still find alternate axiomatizations interesting. ... in Z (which has the ordinary axiom of infinity as currently used, ...
    (sci.math)
  • Re: "Set Theory: Constructive and Intuitionistic ZF" on SEP
    ... HERE of people who presume to defend "potential infinity"! ... He has not said anything about "potential infinity" - or rather ... logic had wrongly been extrapolated from the mathematics of finite ... "Understanding Godel isn't about following his formal proof. ...
    (sci.logic)
Quantcast