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Re: The selfcontradictory infinite hotel
Posted:
Feb 23, 2014 7:10 PM


On 2/23/2014 3:12 PM, Virgil wrote: > 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. >
It is symmetrical.

