"John" <Man@the.keyboard> wrote in message news:firstname.lastname@example.org... > On Sun, 23 Feb 2014 17:21:35 -0000, "Julio Di Egidio" > <email@example.com> wrote: <snip> >>Indeed. To reiterate, mine was not an objection to the notion of 1-to-1 >>mappings, e.g. I have no qualms with the idea that there are as many even >>natural numbers as there are natural numbers: both collections are simply >>*endless*. It is the idea that the natural numbers form a set, i.e. a >>complete totality that is, as I am contending, untenable. > > Why? > I don't see the contradiction between "endless" and "set". Am I > missing something?
Yes, quite simply the "i.e. a complete totality". But never mind: see below.
<snip> >>if we have 1, 2, 3, >>etc. up to (allegedly) *all* natural numbers, there is just no natural >>number missing that we can add to the lot. > > Y'know that *sounds* convincing, logically, in English and probably > in many other natural, human languages, but a lot of things that > *sound* convincing just are not.
Sometimes that's even true, but one thing is word salads, another is that it's rather a pity that informal reasoning, which is no less rigorous than the formal one, just requires much more solid logical foundations, has been expunged from academia. But that's rather a problem with our educational system, and even before that, of the general politics that want us dumb executors of instructions rather than critical thinkers. But we get OT here: if you are uncomfortable with informal reasoning, for whichever reason, that's just fine for me, you are rather welcome to engage with the more recent post of mine which did contain two mathematical statements in apparent contradiction one another. See if you can find it...