On Wednesday, January 30, 2013 3:07:07 AM UTC-8, quasi wrote: > david petry wrote:
> >Doron Zeilberger wrote the following in an opinion piece on his >website:
> >"Read Wolfgang Mueckenheim's fascinating book ! I especially > >like the bottom of page 112 and the top of page 113, that prove, > >once and for all, that (at least) the actual infinity is pure > >nonsense."
> Proves once and for all?
> By that wording, Zeilberger appears to be affirming the validity > of Mueckheim's claimed "proof" of some theorem or other which > supposedly yields the conclusion that "infinity is pure nonsense".
> Of course, in the same blog, a few months later, Zeilberger > awkwardly tries to retract the claim of "proof", asserting > that his earlier post was only intended as an offering of > philosophical support.
> However, in my opinion, that's a blatant copout.
> Worse, I regard Zeilberger's attempted "clarification" as > deceitful, as evidenced by his posted statement:
> "I have no expertise, or interest, in checking any possible > technical claims that he [Muckemheim] may have made."
> Insufficient expertise? A straight-out lie, in my opinion. [...]
I'm going to defend Zeilberger here, because I would be inclined to say exactly the same thing he has said: I have no expertise, or interest, in checking any possible technical claims that he [Muckemheim] may have made.
Any "proof" that infinity is pure nonsense must be based on an appeal to common sense. I wish that Mueckenheim would put more effort into identifying and clarifying the common sense principles he is basing his technical arguments on. Obviously, if we don't know exactly what those common sense principles are, we must admit that we have neither the expertise nor interest in checking those technical arguments.
I'd like to suggest to Mueckenheim that he consider the notion of falsifiability. Falsifiability is part of common sense logic, and it is not compatible with the actual infinite. It is emminently reasonable to accept falsifiability as part of the underlying logic of mathematics. Certainly it is part of the intuitively understood underlying logic of the mathematics that has applications in science.