Date: Apr 4, 2013 2:57 PM
Author: William Hughes
Subject: Re: Matheology § 224
On Apr 4, 8:30 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

> On 4 Apr., 19:45, William Hughes <wpihug...@gmail.com> wrote:

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> > On Apr 4, 6:37 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

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> > > On 4 Apr., 18:13, William Hughes <wpihug...@gmail.com> wrote:

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> > > > On Apr 4, 5:15 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

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> > > > > On 4 Apr., 16:01, William Hughes <wpihug...@gmail.com> wrote:

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> > > > <snip>

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> > > > > > If you remove "every finite line"

> > > > > > your are removing an infinite thing

> > > > > > "an infinite collection of finite things"

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> > > > > If an infinite collection of infinite things exists actually, i.e., IF

> > > > > it is not only simple nonsense, to talk about an actually infinite set

> > > > > of finite numbers, then I can remove this infinite thing because it

> > > > > consists of only all finite things for which induction is valid.

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> > > > Nope. The fact that the collection contains only things for which

> > > > induction is valid, does not mean induction is valid for the

> > > > collection.

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> > > And you believe that, therefore, always elements must exists which in

> > > principle are subject to induction but in fact are not subjected to

> > > induction?

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> > Nope, just that you can have a collection where everything in the

> > collection

> > is subject to induction, but where the collection itself is not

> > subject to

> > induction.

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> If the collection is something else than all its elements, then you

> may be right.

No, a collection is no more and no less than "all its elements".

Note the "no less". A collection need not share a property

that every one of its elements has. In this case

every one of the elements of the collection has the property

that it can be removed without changing the union.

The collection does not have this property.

[This holds for the "collection of all finite lines"

other collections, e.g. a "collection of three lines"

do have the property that they can be removed without

changing the union]