Virgil
Posts:
8,833
Registered:
1/6/11


Re: The selfcontradictory infinite hotel
Posted:
Feb 23, 2014 4:12 PM


In article <ledjeu$ocp$1@dontemail.me>, "Julio Di Egidio" <julio@diegidio.name> wrote:
> "John Gabriel" <thenewcalculus@gmail.com> wrote in message > news:3555f9e21deb486f9ce51ae0437b3251@googlegroups.com... > > On Sunday, 23 February 2014 19:29:20 UTC+2, Julio Di Egidio wrote: > >> "Julio Di Egidio" <julio@diegidio.name> wrote in message > >> > slightly more rigorously, 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. > > > > You can never have *all* the natural numbers. So, the second part of your > > statement is predicated on the assumption in your first sentence. > > Well, of course: it's the whole idea behind an ifthen, i.e. the notion of > logical consequence, that *if* the premise were true, it would then > *necessarily* (i.e. by logical necessity) follow so and so. And I did say > "allegedly" not per chance, indeed to reinforce the fact that I am talking > about something that I believe just falls apart. > > >> If, for all n, room n+1 is occupied already, the hotel is just full and > >> no > >> more guests can be accommodated. > > > > Not true. A proposition about n does not say anything about a proposition > > involving infinity. > > But there is no mention of "infinity" in that proposition. Indeed, as long > as you concede to the validity of an inductive definition for the collection > of natural numbers (i.e. 0 in N, and n in N => n+1 in N), the above sentence > as well as the subsequent one are perfectly wellformed. > > >> If, conversely, the hotel is never fully occupied, there always exists n > >> such that n+1 is not occupied. > > > > Your argument would be sound if you accepted that finite propositions can > > be used to establish results about an illformed and nonexistent > > concept  infinity. There is no such thing as infinity. It is a myth. > > But you have to show why/how infinity is an illformed and nonexistent > concept (which is what I am trying to do), there is no point in just stating > it without justification. And while I am contending that there is no such > thing as the set of all natural numbers (i.e. that there is no such thing as > potential infinity in mathematics as an endless and yet complete totality, a > pure contradiction in terms), I do not agree that there is no infinity at > all: there is in logic and there is in mathematics, just try and answer the > question where exactly Achilles catches the tortoise. This is a real and > fundamental question, as it is a fact of life that Achilles does catch the > tortoise: so should our mathematics fail to capture that result, that would > be a failure in our mathematics, obviously not in our reality. (Well, even > to this last statement one could in fact take exception, but we need > arguments.) > > Julio >
Thre is no point in trying to chop logic with "John Gabriel" <thenewcalculus@gmail.com> because he hasn't any. 

