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Replies: 62   Last Post: Feb 24, 2014 10:17 PM

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 fom Posts: 1,968 Registered: 12/4/12
Posted: Feb 23, 2014 7:10 PM

On 2/23/2014 3:12 PM, Virgil wrote:
> In article <ledjeu\$ocp\$1@dont-email.me>,
> "Julio Di Egidio" <julio@diegidio.name> wrote:
>

>> "John Gabriel" <thenewcalculus@gmail.com> wrote in message

>>> 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
>>>>> 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 if-then, 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 well-formed.
>>

>>>> 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 ill-formed and non-existent
>>> concept - infinity. There is no such thing as infinity. It is a myth.

>>
>> But you have to show why/how infinity is an ill-formed and non-existent
>> 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.