Date: Feb 15, 2013 1:06 AM
Author: fom
Subject: Re: Matheology § 222 Back to the root<br> s
On 2/14/2013 5:53 PM, Virgil wrote:

> In article

> <edc41700-d86f-4db5-8928-62768ed77a36@z9g2000vbx.googlegroups.com>,

> William Hughes <wpihughes@gmail.com> wrote:

>

>> On Feb 14, 8:26 am, WM <mueck...@rz.fh-augsburg.de> wrote:

>>> On 13 Feb., 23:22, William Hughes <wpihug...@gmail.com> wrote:

>>>

>>>> On Feb 13, 9:03 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

>>>> <snip>

>>>

>>>>> You cannot discern that two potentially infinity sequences are equal.

>>>>> When will you understand that such a result requires completeness?

>>>

>>>> Nope

>>>

>>>> Two potentially infinite sequences x and y are

>>>> equal iff for every natural number n, the

>>>> nth FIS of x is equal to the nth FIS of y

>>>

>>

>> So we note that it makes perfect sense to ask

>> if potentially infinite sequences x and y are equal,

>> we have cases where they are not equal and cases

>> where they are equal. We also note that no

>> concept of completed is needed, so equality can

>> be demonstrated by induction.

>>

>> So WMs statements are

>>

>> there is a line l such that d and l

>> are equal as potentially infinite sequences.

>>

>> there is no line l such that d and l

>> are equal as potentially infinite

>> sequences.

>

> Thus WM accepts

> 'P and not P' but rejects 'Tertium Non Datur'.

>>

>>

>>

>>

>>

>>

>>> And just this criterion is satisfied for the system

>>>

>>> 1

>>> 12

>>> 123

>>> ...

>>>

>>> For every n all FISs of d are identical with all FISs of line n.

>

> For every n there is an (n+1)st fison of d not identical to any FIS of

> line n.

>

And, because WM is basing his arguments on

the structure of the naturals as a directed

set, it is that (n+1)st fison that grounds

comparability of the terms of its proper

initial sequence.

Laughably, WM complains about reversal of

quantifiers. His use of the directed

set properties is comparable to what is

manipulated in formulating the forcing

language for models of set theory. In

that context, a complete Boolean algebra

less its 0 (bottom) is the basic structure,

and the forcing language is expressly

constructed in terms of the inverted

order.