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Topic: ZFC is inconsistent
Replies: 54   Last Post: Mar 23, 2013 9:02 PM

 Messages: [ Previous | Next ]
 fom Posts: 1,968 Registered: 12/4/12
Re: ZFC is inconsistent
Posted: Mar 17, 2013 5:54 AM

On 3/16/2013 4:57 PM, WM wrote:
> On 16 Mrz., 16:13, fom <fomJ...@nyms.net> wrote:
>

>> Where we come to the question of
>> how you refer to points without
>> an implicit use of infinity.

>
> All points that you can define geometrically, belong to a finite
> collection.

>>
>> This, of course, comes back to
>> how you refer singularly without
>> an implicit use of infinity.

>
> A unit can be defined without referring to infinity. I think it is one
> of the silliest arguments of matheology that infinity is required to
> define finity. It is simply insane.

No. It is merely respectful -- something of
which you seem incapable.

============================================

"A point is that which has no part."

Euclid

"For when we spoke of things in a subject,
we did not mean things belonging in
something as parts"

Aristotle

"What St. Thomas affirms on this point
here every individual is a lowest
species') is true of all substances,
provided one takes the specific
difference in the way that geometers
take it with regard to their figures."

Leibniz

"If m_1, m_2, ..., m_v, ... is any
countable infinite set of elements
of [the linear point manifold] M of
such a nature that [for closed
intervals given by a positive
distance]:

lim [m_(v+u), m_v] = 0 for v=oo

then there is always one and only one
element m of M such that

lim [m_(v+u), m_v] = 0 for v=oo"

Cantor to Dedekind

"If x is any object of the domain,
there exists a set {x} containing
x and only x as element"

"The question whether x=y or not
is always definite since it is
equivalent to the question whether
or not xe{y}"

Zermelo

"A unit is that by virtue of which
each of the things that exist is
called one"

Euclid

"The more I have thought the matter
over, the more convinced I have become
that arithmetic and geometry have
developed on the same basis -- a
geometrical one in fact -- so that
mathematics in its entirety is
really geometry"

Frege

"In whatever manner and by whatever
means a mode of knowledge may relate
to objects, intuition is that through
which it is in immediate relation
to them, and to which all thought
as a means is directed."

"Objects are given to us by means
of sensibility, and it alone yields
us intuitions"

"By means of outer sense, a property
of our mind, we represent to ourselves
objects as outside us, and all without
exception in space"

"Geometry is a science which determines
the properties of space synthetically,
and yet a priori."

Kant

"..., I shall deal first with projective
geometry. This, I shall maintain, is
necessarily true of any form of
externality, and is, since some such
form is necessary to experience,
completely a priori."

"We can distinguish different parts
of space, but all parts are qualitatively
similar, and are distinguished only
by the immediate fact that they
lie outside one another"

"Analysis, being unable to find
any earlier halting-place, finds
its elements in points, that is,
in zero quanta of space"

"A point must be spatial, otherwise
it would not fulfill the function
of a spatial element; but again,
it must contain no space, for any
finite extension is capable of
further analysis. Points can
never be given in intuition,
which has no concern for the
infinitesimal."

Russell

A1:
If P is a part of object Q, then Q is not a
part of object P

A2:
If P is a part of object Q, and Q is a part of object R,
then P is a part of object R

D1:
P is an ingredient of an object Q when and only when,
P is the same object as Q or is a part of object Q

D2:
P is the class of objects p, when and only when the
following conditions are fulfilled:

a)
P is an object

b)
every p is an ingredient of object P

c)
for any Q, if Q is an ingredient of object P, then
some ingredient of object Q is an ingredient of
some p

Lesniewski

And, to put Lesniewskian ideas into a form
that is related to ZF and compatible with
the deductive calculus of first-order predicate
logic,

with model theoretic considerations

news://news.giganews.com:119/5bidnemPpsnq13zNnZ2dnUVZ_sOdnZ2d@giganews.com

and a construction of Dedekind cuts

news://news.giganews.com:119/M5qdncGgG5a-VbvMnZ2dnUVZ_rCdnZ2d@giganews.com

as well as a geometric basis for the
logical language

news://news.giganews.com:119/Jr2dnbdYvtfPdlrNnZ2dnUVZ_t-dnZ2d@giganews.com

news://news.giganews.com:119/IqudndogJ8-VB1zNnZ2dnUVZ_qydnZ2d@giganews.com

news://news.giganews.com:119/zsCdnW9U7v4BOlzNnZ2dnUVZ_hmdnZ2d@giganews.com

news://news.giganews.com:119/AuqdnYcXm8eaLVzNnZ2dnUVZ_h-dnZ2d@giganews.com

news://news.giganews.com:119/EsqdnX0_NvwwKlzNnZ2dnUVZ_o-dnZ2d@giganews.com

news://news.giganews.com:119/Jr2dnbZYvtc2dlrNnZ2dnUVZ_t-dnZ2d@giganews.com

news://news.giganews.com:119/dbydnS9OZYESWFzNnZ2dnUVZ_uidnZ2d@giganews.com

news://news.giganews.com:119/Jr2dnbFYvtcHcVrNnZ2dnUVZ_t-dnZ2d@giganews.com

news://news.giganews.com:119/Jr2dnbBYvtedcFrNnZ2dnUVZ_t-dnZ2d@giganews.com

news://news.giganews.com:119/Jr2dnbNYvtf9cFrNnZ2dnUVZ_t-dnZ2d@giganews.com

news://news.giganews.com:119/Jr2dnbNYvtf9cFrNnZ2dnUVZ_t-dnZ2d@giganews.com

Date Subject Author
3/13/13 byron
3/13/13 Inverse 18 Mathematics
3/13/13 byron
3/13/13 YBM
3/23/13 Jesse F. Hughes
3/13/13 Frederick Williams
3/14/13 byron
3/15/13 mueckenh@rz.fh-augsburg.de
3/15/13 YBM
3/15/13 Virgil
3/15/13 fom
3/16/13 mueckenh@rz.fh-augsburg.de
3/16/13 fom
3/16/13 mueckenh@rz.fh-augsburg.de
3/16/13 Virgil
3/17/13 mueckenh@rz.fh-augsburg.de
3/17/13 Virgil
3/18/13 fom
3/18/13 fom
3/17/13 fom
3/17/13 mueckenh@rz.fh-augsburg.de
3/17/13 Virgil
3/17/13 fom
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 Virgil
3/17/13 Virgil
3/18/13 fom
3/16/13 Virgil
3/16/13 mueckenh@rz.fh-augsburg.de
3/16/13 fom
3/16/13 mueckenh@rz.fh-augsburg.de
3/16/13 Virgil
3/17/13 mueckenh@rz.fh-augsburg.de
3/17/13 Virgil
3/17/13 mueckenh@rz.fh-augsburg.de
3/17/13 Virgil
3/17/13 fom
3/17/13 fom
3/17/13 mueckenh@rz.fh-augsburg.de
3/17/13 fom
3/17/13 mueckenh@rz.fh-augsburg.de
3/17/13 Virgil
3/18/13 fom
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 Virgil
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 fom
3/18/13 Virgil
3/18/13 Virgil
3/18/13 fom
3/18/13 Virgil
3/18/13 fom
3/18/13 fom
3/17/13 Virgil
3/16/13 Virgil