Matheology § 095

[WM]

Matheology § 095


Dr. D.F.M. Strauss, is professor of philosophy at the University of
the Free State in Bloemfontein, South Africa.

In Chapter II Strauss addresses various philosophical problems in
mathematics.
Mathematics is concerned with number and space, the first two
modalities. The prime issue in mathematics is how to treat infinity.
Strauss discusses three main foundational crises in the history of
mathematics: (1) the discovery of irrationals, (2) infinitesimal
calculus, and (3) modern set theory. All three involve the relation
between potential and actual infinity. Much attention is devoted to
the conflict between Cantor's treatment of actually infinite sets and
the intuitionists' rejection of actual infinity.
The Dutch mathematician L.E.J. Brouwer (1882-1966), an ardent
promoter of intuitionism, lived in Amsterdam at the same time as
Dooyeweerd and had some influence on Dooyeweerd. Dooyeweerd
acknowledged only the potential infinite; he found the idea of the
actual infinite unacceptable. {{Obviously there are many people
sharing this opinion. Unfortunaltely modern censorship cares that
these people rarely get a chance to write in mathematical journals.
Compare the situation with Hilbert, who fired Brouwer from the board
of the Mathematische Annalen, starting what Einstein called the war of
the frogs and the mice. For this Machtergreifung in 1928 Hilbert had
less authorization than Hiltler had for his in 1933.}} Strauss,
however, argues that Dooyeweerdian philosophy actually provides
grounds for both types of infinity. Strauss distinguishes between the
successive infinite and the at once infinite. The successive infinite
is associated with numbers and determines every denumerable, endless
succession of numbers (e.g., the integers or rational numbers). The at
once infinite, on the other hand, is associated with the continuous
extension of space. The latter represents a higher order of infinity;
it cannot be reduced to a successive infinity since space cannot be
reduced to number {{that's why uncountable sets are an absurdity.}}

Review: D.F.M. Strauss "Paradigms in Mathematics, Physics and Biology:
Their Philosophical Roots", Tekskor Bk, Danhof, South Africa, (2001,
revised 2004), 177 pp.

Regards, WM

[Zuhair]

Are you saying that mathematicians nowadays will turn the blind eye
for anyone who have ideas like Dooyeweerdian? Why is that? I don't
think this is the case, i.e. I don't think they object to merely
having those ideas, I don't know however, but I think what
mathematicians want is non trivial new results, if Dooyeweerdian's
intuitions can be stated clearly on informal level as to admit
faithful formalization of them with a consistent formal system and if
that formal system showed success in interpreting ordinary mathematics
as well as opening the doors for further mathematical investigation,
then I don't think a single mathematician of this time would object to
that just because of the philosophical opinions of Dooyeweerdian or
others as regards those subjects you alluded to.

Second acceptance or rejection of actual infinity as opposed to
potential infinity is just a matter of opinion about what is
convenient to mathematics that is grounded in ones intuitions about
the physical reality of such matters, something that mathematics in my
own personal opinion should not involve itself with. A mathematical
theory explaining part of physics might fail to do so yet it remains a
piece of mathematics isn't it? I think mathematics is free to engage
in all possible matters as far as its speaking in a consistent manner,
what we think is far fetched might turn to be a reality, for who's to
know what reality is? I don't think that mathematics should take parts
in such debates that I personally qualify as extracurricular!

Let those having opinion like Dooyeweerdian put up fruitful
mathematical work and I don't think any mathematician now and then
would object to it. And I think what is said about potential infinity
and all formalizations related to them can be interpreted in many
existing formal works and I don't think anybody would object to
further workup with non trivial new advancements in that field!

There is nothing against working with the ideas you are promoting in
this Usenet provided that they lead to consistent formalizations
brewing further non trivial results and advancements. But the point
that I object to in your posts is that you ridicule the other side?
why? The other side to you (which is the standard one nowadays)
promote ideas that are "far fetched", "ridiculous", "fantasies", "non
realistic", "detached" etc... , while in fact those ideas made
advancements in consistent formalization and in understanding many
aspects of mathematics itself, possibly they might not find any
application soon because they are detached far from our customary
conception of reality as you said but who's to know what the future
brings. I personally think all of those ideas you condemn are
justified to investigate on mathematical grounds, actually they are
very interesting on to themselves even without any application.

Zuhair

[WM]

On 23 Jul., 21:39, Zuhair <zaljo...@gmail.com> wrote:

> Second acceptance or rejection of actual infinity as opposed to
> potential infinity is just a matter of opinion

No. Please look carefully into § 092, for instance, or § 062.

Do you know that, according to set theory, the limit of the sequence
0
1, 2
3, 4, 5, 6
...

is the empty set? But this limit makes the paths in the Binary Tree
being actually infinite!!!

>
>
> There is nothing against working with the ideas you are promoting in
> this Usenet provided that they lead to consistent formalizations
> brewing further non trivial results and advancements. But the point
> that I object to in your posts is that you ridicule the other side?

That is but a bit of irony and sarcasm, to make my texts more
attractive. The other side strikes harder.

> The other side to you (which is the standard one nowadays)
> promote ideas that are "far fetched", "ridiculous", "fantasies", "non
> realistic", "detached" etc... , while in fact those ideas made
> advancements in consistent formalization and in understanding many
> aspects of mathematics itself, possibly they might not find any
> application soon because they are detached far from our customary
> conception of reality as you said but who's to know what the future
> brings.

Since these ideas are selfcontradictory, future cannot make them
interesting.

Regards, WM

[Graham Cooper]

All you have "advanced" is a THEORY of IN-CONSISTENCY which interrupts
EVERY SINGLE LOGIC TEXT.

WM and many others have been trying to post more fundamental theories
for decades that are not "STOOPID".

You wouldn't call this a MISSING ROW would you??

0.xoooo..
0.oooxo..
0.ooxoo..
0.oxooo..
0.oooox..
..


but you call this a missing row!
A WITNESS TO SIZE > INFINITY!!

0.xoooo..
0.oxooo..
0.ooxoo..
0.oooxo..
0.oooox..
..


Why don't you ADDRESS the NUMEROUS OBVIOUS BLATANT FLAWS

based on your MISCONCEPTION that

ALL(F):N->R E(r):R ALL(n):N r =/= F(n)

is somehow mysteriously proven in FOL!


Before you waste your time making 20 more equivalent theories to ZFC
that actually prove this in 2OL since you are quantifying over all
lists or functions..

Try addressing your oversights!

*****************************************************
*****************************************************

Q1
What are 2 missing reals from this List using Cantor's method?

LIST
0.100..
0.000..
0.001..
..
LIST'
0.000.. (Old Row 2)
0.100.. (Old Row 1)
0.001..
..

*****************************************************
*****************************************************


Q2
Why is this GODEL NUMBER BARRED from a theory?

20032104211598200321042105
a00(a10,a11)=!a00(a10,a10)
x e y <-> NOT(x e x)
RUSSELL'S SET

*****************************************************
*****************************************************

Q3
And this GODEL NUMBER is a prerequisite of all theories > PA?

8203215
!a0(a1)
NOT(PROOF(GN#))
GODEL'S STATEMENT

*****************************************************
*****************************************************

Q4
How can there be uncountable many GODEL NUMBERS like this?

20130415
a01(0,1)
MIDPOINT(0,1)
A CHOICE FUNCTION

*****************************************************
*****************************************************

Q5
Which 1 of these does not hold?

a) N <-BIJECTS-> GODEL NUMBERS
b) GODEL NUMBERS <-BIJECT-> FUNCTIONS
c) CHOICE FUNCTIONS <-BIJECT-> SETS
d) |SETS| > |N|


*****************************************************
*****************************************************


Q6
Does this Anti-Diagonal Method produce any unique digit segment not
listed?

AD METHOD
Choose the number 0.a_1a_2a_3...., where a_i = 1 if the i-th
number in your list had zero in its i-position, a_i = 0 otherwise.

LIST
R1= < <314><15><926><535><8979><323> ... >
R2= < <27><18281828><459045><235360> ... >
R3= < <333><333><333><333><333><333> ... >
R4= < <888888888888888888888><8><88> ... >
R5= < <0123456789><0123456789><01234 ... >
R6= < <1><414><21356><2373095><0488> ... >
....


*****************************************************
*****************************************************




G. Cooper (BInfTech)
--

http://tinyURL.com/BLUEPRINTS-THEOREM
http://tinyURL.com/BLUEPRINTS-TURING
http://tinyURL.com/BLUEPRINTS-GODEL
http://tinyURL.com/BLUEPRINTS-PROOF
http://tinyURL.com/BLUEPRINTS-MATHS
http://tinyURL.com/BLUEPRINTS-LOGIC
http://tinyURL.com/BLUEPRINTS-BRAIN
http://tinyURL.com/BLUEPRINTS-REAL
http://tinyURL.com/BLUEPRINTS-SETS
http://tinyURL.com/BLUEPRINTS-HALT
http://tinyURL.com/BLUEPRINTS-P-NP
http://tinyURL.com/BLUEPRINTS-GUT
http://tinyURL.com/BLUEPRINTS-AI

LOGIC AXIOM - The Closure Of Tautologies
E(Y) Y={x|f(x)} <-> PROOF( E(Y) Y={x|f(x)} )

MATHEMATICS AXIOM - The Examination of Theories
E(Y) Y={x|f(x)} <-> !PROOF( !E(Y) Y={x|f(x)} )

PROOF(C) :- C
PROOF(C) :- DERIVE(A,B,C)
DERIVE(A,B,C) :- PROOF(A), PROOF(B), TAUT(A,B,C)

8203215 = GODEL NUMBER
!A0(A1) = NOT(PROOF(8203215)) <-/-> E(Y) Y={x|f(x)}

10 IF HALT(this-program-ref) THEN GOTO 10
ORIGINS OF CHAITAN'S OMEGA AND |R|>|N|

************
| 5GL / WHY? WHEN?
| 4GL / WHAT? not HOW! ?person(P)
| 3GL / FUNCTION STACK proc(a,b)
| 2GL / MNEMONICS LDA 0101
| 1GL/ MACHINE CODE 101 0101
===
CPU

[Zuhair]

They are not self contradictory! Some have been formalized by rigorous
formal systems and PROVED to be consistent! Whether they are TRUE or
not, this is another question, but anyhow being consistent is
something on its own.

Zuhair

[Virgil]

In article
<6e5193e9-303c-4fdb...@8g2000vbu.googlegroups.com>,

WM <muec...@rz.fh-augsburg.de> wrote:

> Compare the situation with Hilbert, who fired Brouwer from the board
> of the Mathematische Annalen, starting what Einstein called the war of
> the frogs and the mice. For this Machtergreifung in 1928 Hilbert had
> less authorization than Hiltler had for his in 1933.

WM has now descended to accusing his opponents of Hitlerism!

Such is the evil of WMatheology!
--

[FredJeffries]

http://www.acmsonline.org/journal/2005/strauss%20review.pdf

[Zuhair]

On Jul 23, 4:55 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 23 Jul., 21:39, Zuhair <zaljo...@gmail.com> wrote:
>
> > Second acceptance or rejection of actual infinity as opposed to
> > potential infinity is just a matter of opinion
>
> No. Please look carefully into § 092, for instance, or § 062.
>
> Do you know that, according to set theory, the limit of the sequence
> 0
> 1, 2
> 3, 4, 5, 6
> ...
>

Honestly I don't know what you mean by that, I don't see a sequence of
naturals that can serve as a limit for this sequence of sequences
(tuples), so there is NO limit in that sense, this doesn't mean that
the limit is the empty set!

But if we use Transfinites then the limit is simply:

w,w+1,w+2,....

and this is not the empty set!

Zuhair

[Zuhair]

On Jul 23, 11:55 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 23 Jul., 21:39, Zuhair <zaljo...@gmail.com> wrote:
>
> > Second acceptance or rejection of actual infinity as opposed to
> > potential infinity is just a matter of opinion
>
> No. Please look carefully into § 092, for instance, or § 062.
>
> Do you know that, according to set theory, the limit of the sequence
> 0
> 1, 2
> 3, 4, 5, 6
> ...

Hmmm, now that I read the previous posting of yours, yes there is NO
limit for this series at all. So the limit is not the empty set at
all.

Zuhair

[FredJeffries]

On Jul 23, 11:25 am, WM <mueck...@rz.fh-augsburg.de> wrote:
> Matheology § 095
>

> Review: D.F.M. Strauss "Paradigms in Mathematics, Physics and Biology:
> Their Philosophical Roots", Tekskor Bk, Danhof, South Africa, (2001,
> revised 2004), 177 pp.

Professor Strauss's works are available at his web site:

http://daniestrauss.com/index.php

Of interest might be:
"Introduction to a Philosophy of the Infinite"
http://daniestrauss.com/DS%20Best%20OytputPrior%20to%20Last%208%20Years%20Phil-Inf.pdf

"Philosophical Reflections on Continuity"
http://daniestrauss.com/DS%20Best%20Output%20Prior%20to%20Last%208%20Years%20Continuity.pdf

"Mathematics and Physics"
http://daniestrauss.com/2008%20-%20Maths%20and%20Physics%20-%20Monograph.pdf
which includes a discussion of Cantor's Diagonal Proof in Appendix I

"Is a Christian Mathematics Possible?"
http://daniestrauss.com/DS%202003%20Christian%20Mathematics%20JOURNAL%20FOR%20CHRISTIAN%20SCHOLARSHIP.pdf

"How 'Rational' is 'Rationality'?"
http://daniestrauss.com/DS%20Other%20Output%202003%20How%20Rational%20is%20Rationality.pdf

[Virgil]

In article
<a4a44498-c3c6-461d...@m2g2000pbv.googlegroups.com>,

Then WM needs to learn how to present those theories in non-stupid ways
and with non-stupid arguments, which so far he has bee totally unable to
do.

>
> You wouldn't call this a MISSING ROW would you??

What "this"?

>
> 0.xoooo..
> 0.oooxo..
> 0.ooxoo..
> 0.oxooo..
> 0.oooox..
> ..
>

From the above, 0.oxoxo.. is one thing missing.

>
> but you call this a missing row!
> A WITNESS TO SIZE > INFINITY!!
>
> 0.xoooo..
> 0.oxooo..
> 0.ooxoo..
> 0.oooxo..
> 0.oooox..

From the above 0.ooooo.. is is one thing missing.

> ..
>
>
> Why don't you ADDRESS the NUMEROUS OBVIOUS BLATANT FLAWS
>
> based on your MISCONCEPTION that
>
> ALL(F):N->R E(r):R ALL(n):N r =/= F(n)
>
> is somehow mysteriously proven in FOL!
>
>
> Before you waste your time making 20 more equivalent theories to ZFC
> that actually prove this in 2OL since you are quantifying over all
> lists or functions..
>
> Try addressing your oversights!
>
> *****************************************************
> *****************************************************
>
> Q1
> What are 2 missing reals from this List using Cantor's method?
>
> LIST
> 0.100..
> 0.000..
> 0.001..
> ..
> LIST'
> 0.000.. (Old Row 2)
> 0.100.. (Old Row 1)
> 0.001..
> ..

0.010.., AND 0.111.. and 0.110.. and 0.011.., and 0.101..
--

[Virgil]

In article
<0a9bf2e9-451e-4a59...@d6g2000vbe.googlegroups.com>,

WM <muec...@rz.fh-augsburg.de> wrote:

> On 23 Jul., 21:39, Zuhair <zaljo...@gmail.com> wrote:
>
> > Second acceptance or rejection of actual infinity as opposed to
> > potential infinity is just a matter of opinion
>
> No. Please look carefully into � 092, for instance, or � 062.
>
> Do you know that, according to set theory, the limit of the sequence
> 0
> 1, 2
> 3, 4, 5, 6
> ...
>
> is the empty set? But this limit makes the paths in the Binary Tree
> being actually infinite!!!

If you mean the sets {0}, {1,2}, {3.4.5.6}, ..., then it is the well
defined definition of the limit of a sequence of sets which makes the
limit equal to {}.

And since a path in a complete infinite binary tree must be an endless
sequence of nodes, its being actual is quite normal.

> >
> >
> > There is nothing against working with the ideas you are promoting in
> > this Usenet provided that they lead to consistent formalizations
> > brewing further non trivial results and advancements. But the point
> > that I object to in your posts is that you ridicule the other side?
>
> That is but a bit of irony and sarcasm, to make my texts more
> attractive. The other side strikes harder.

When presented with nonsense, one is permitted to cal it nonsense.

>
> > The other side to you (which is the standard one nowadays)
> > promote ideas that are "far fetched", "ridiculous", "fantasies", "non
> > realistic", "detached" etc... , while in fact those ideas made
> > advancements in consistent formalization and in understanding many
> > aspects of mathematics itself, possibly they might not find any
> > application soon because they are detached far from our customary
> > conception of reality as you said but who's to know what the future
> > brings.
>
> Since these ideas are selfcontradictory, future cannot make them
> interesting.

They are only "self contradictory" in WMytheology, since most
mathematicians use them quite freely without any of the problems WM
claims must follow.
>
> Regards, WM
--

[Virgil]

In article
<cc681d9c-09ea-4333...@w24g2000vby.googlegroups.com>,

In WMytheology notation, apparently a line-feed/carraige-return can act
as a set separator, making one set to each line.

In which case the sequence of sets apparently would be
S_n = { m in |N: 2^n-1 <= m < 2^(n+1) -1}, for |N = {0,1,2,...}
which are pairwise disjoint, and for which
LimSup S_n = Lim_Inf S_n = Lim S_n = {}.
--

[WM]

On 24 Jul., 01:31, Zuhair <zaljo...@gmail.com> wrote:
> On Jul 23, 4:55 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > On 23 Jul., 21:39, Zuhair <zaljo...@gmail.com> wrote:
>
> > > Second acceptance or rejection of actual infinity as opposed to
> > > potential infinity is just a matter of opinion
>
> > No. Please look carefully into § 092, for instance, or § 062.
>
> > Do you know that, according to set theory, the limit of the sequence
> > 0
> > 1, 2
> > 3, 4, 5, 6
> > ...
>
> Honestly I don't know what you mean by that, I don't see a sequence of
> naturals that can serve as a limit for this sequence of sequences

I use to write the terms below each other because electronic "paper"
is not expensive, and so we get a clearer picture.

> (tuples), so there is NO limit in that sense, this doesn't mean that
> the limit is the empty set!

Set theory gives the limit empty set. Cp. Tristram Shandy.

Regards, WM

[Zuhair]

I don't know what you mean by that, I think you are confusing NO LIMIT
for a limit that is empty, there is a difference you know.

Zuhair

[LudovicoVan]

"Zuhair" wrote in message
news:47d05b95-438f-460f...@m3g2000vbl.googlegroups.com...

> On Jul 24, 11:23 am, WM <mueck...@rz.fh-augsburg.de> wrote:

> > Set theory gives the limit empty set. Cp. Tristram Shandy.
>

> I don't know what you mean by that, I think you are confusing NO
> LIMIT for a limit that is empty, there is a difference you know.

Right, but the problem with those definitions (*) rather is that we get an
empty limit-set in both cases: when the limit does not exist and when the
limit is divergent. That is why I have been claiming that those definitions
are simply inadequate (but could be fixed, I think).

(*) So that nobody gets confused, we are talking specifically of:
<http://en.wikipedia.org/wiki/Limit_superior_and_limit_inferior#Special_case:_discrete_metric>

-LV

[Virgil]

In article
<5a237c27-e542-44ff...@n16g2000vbn.googlegroups.com>,

If what WM means is the sequence of sets {0},{1,2}, {3,4,5,6}, ...,
then there is a limit, the empty set, at least according to standard set
definitions, but if WM means anything else, like, for example, ordered
sets, (0), (1,3), (3,4,5,6), ..., then he must prove his claim using
some accepted definition of a limit of appropriate type.
--

[WM]

On 24 Jul., 21:03, Virgil <vir...@ligriv.com> wrote:
> In article
> <5a237c27-e542-44ff-bb23-281c9117f...@n16g2000vbn.googlegroups.com>,

>
> If what WM means is the sequence of sets {0},{1,2}, {3,4,5,6}, ...,
> then there is a limit, the empty set, at least according to standard set
> definitions, but if WM means anything else, like, for example, ordered
> sets, (0), (1,3), (3,4,5,6), ..., then he must prove his claim using
> some accepted definition of a limit of appropriate type.

Consider this again:
> > ((1, 1))
> > ((2, 1), (3, 2))
> > ((4, 1), (5, 2), (6, 3))
> > ...

If the first coordinates have a limit and the second coordinates have
a limit, then the set of pairs must have a limit too, at least in case
set theory consistently describes infinite sets. But that is here not
the case. Therefore set theory does not describe infinite sets
consistenly.

Regards, WM

[WM]

On 24 Jul., 16:11, Zuhair <zaljo...@gmail.com> wrote:
> On Jul 24, 11:23 am, WM <mueck...@rz.fh-augsburg.de> wrote:
>
>
>
>
>
> > On 24 Jul., 01:31, Zuhair <zaljo...@gmail.com> wrote:
>
> > > On Jul 23, 4:55 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > > > On 23 Jul., 21:39, Zuhair <zaljo...@gmail.com> wrote:
>
> > > > > Second acceptance or rejection of actual infinity as opposed to
> > > > > potential infinity is just a matter of opinion
>
> > > > No. Please look carefully into § 092, for instance, or § 062.
>
> > > > Do you know that, according to set theory, the limit of the sequence
> > > > 0
> > > > 1, 2
> > > > 3, 4, 5, 6
> > > > ...
>
> > > Honestly I don't know what you mean by that, I don't see a sequence of
> > > naturals that can serve as a limit for this sequence of sequences
>
> > I use to write the terms below each other because electronic "paper"
> > is not expensive, and so we get a clearer picture.
>
> > > (tuples), so there is NO limit in that sense, this doesn't mean that
> > > the limit is the empty set!
>
> > Set theory gives the limit empty set. Cp. Tristram Shandy.
>

> I don't know what you mean by that, I think you are confusing NO LIMIT
> for a limit that is empty, there is a difference you know.

Please learn to calculate the limit of a sequence of sets M_k:
LimSup (M_n) = /\(n = 1 ... oo)[\/(k = n ... oo) M_k]
LimInf (M_n) = \/(n = 1 ... oo)[/\(k = n ... oo) M_k]

If both exist, there is a limit.

Regards, WM

[Virgil]

In article
<809cbf4c-ac0f-4b0d...@6g2000vbv.googlegroups.com>,

That limit definition only applies to a sequence of sets, and does not
necessarily apply to sequences requiring any other structure beyond mere
sethood.
--

[Virgil]

In article
<9bac84e9-0352-4e86...@n16g2000vbn.googlegroups.com>,

WM <muec...@rz.fh-augsburg.de> wrote:

> On 24 Jul., 21:03, Virgil <vir...@ligriv.com> wrote:
> > In article
> > <5a237c27-e542-44ff-bb23-281c9117f...@n16g2000vbn.googlegroups.com>,
>
> >
> > If what WM means is the sequence of sets {0},{1,2}, {3,4,5,6}, ...,
> > then there is a limit, the empty set, at least according to standard set
> > definitions, but if WM means anything else, like, for example, ordered
> > sets, (0), (1,3), (3,4,5,6), ..., then he must prove his claim using
> > some accepted definition of a limit of appropriate type.
>
> Consider this again:

> > > ((1, 1)) = S_1
> > > ((2, 1), (3, 2)) = S_2
> > > ((4, 1), (5, 2), (6, 3)) = S_3
> > > ...
>

Is LimInf S_n = LimSup S_n ?

If not, then no limit exists!

> If the first coordinates have a limit and the second coordinates have
> a limit, then the set of pairs must have a limit too, at least in case
> set theory consistently describes infinite sets.

Wrong! The only relevant definition for a limit to a
sequence of sets, S_n, is the common value, if there is one,
of LimInf S_n and LimSup S_n.

And since S_n /\ S_m = {} whenever m =/= n, that common value is {}, if
it exists at all.
--

[FredJeffries]

On Jul 23, 12:39 pm, Zuhair <zaljo...@gmail.com> wrote:
>
> Are you saying that mathematicians nowadays will turn the blind eye
> for anyone who have ideas like Dooyeweerdian? Why is that? I don't
> think this is the case, i.e. I don't think they object to merely
> having those ideas, I don't know however, but I think what
> mathematicians want is non trivial new results, if Dooyeweerdian's
> intuitions can be stated clearly on informal level as to admit
> faithful formalization of them with a consistent formal system and if
> that formal system showed success in interpreting ordinary mathematics
> as well as opening the doors for further mathematical investigation,

Ah, that's where it all breaks down. As much sympathy as I have for
a Dooyeweerd/Strauss non-reductionistic system or any other non-
standard
foundation (or non-foundation), I have yet to come across any that
actually solve a mathematical problem.

Few mathematicians care about foundational matters. They just want
to do their jobs. Unless you show them something with impact, like
irrational numbers, analytic geometry, set theory..., your work will
just gather dust on some forgotten library shelf. Whatever happened
to fuzzy logic and catastrophe theory?

[Virgil]

In article
<6f8e16c9-cb6f-4deb...@f9g2000pbd.googlegroups.com>,

Both are alive and well as forms of applied mathematics.
Fuzzy logic has about 2.7 million Google hits and
catastrophe theory about 12.7 million.
--

[Michael Press]

In article
<6f8e16c9-cb6f-4deb...@f9g2000pbd.googlegroups.com>,
FredJeffries <fredje...@gmail.com> wrote:

Or wavelets? Or string theory?

Fuzzy logic should never have gotten off the ground.
It could never have done anything that probability
already does.

Catastrophe theory is a bunch of good examples of
bad engineering and how to avoid fabricating another one.

Optimizing a structure for strength and weight is not
enough. Suppose a structure has a buckling mode, that
buckles suddenly, but continuously so that it does not
immediately collapse. Now suppose the engineer puts in
two such buckling modes and fully optimizes. The
composite structure might collapse without warning.

Example. A vertical rod pinned at its base to rotate in
a vertical plane, held vertical with a spring. Adding
weight to the top will eventually make the rod sag to
one side or another, but not collapse. Support the
vertical rod with a ball and socket joint at its base.
Hold it up with equal springs in the x-z and y-z
planes. Now start adding weight and it will go from
vertical to collapse immediately. (Some find this
calculation amusing.)

Imperfection sensitivity is another example. Oft times
buckling load is not a smooth function of the
imperfection parameter

Catastrophe theory gathers and categorizes these analyses.
That it does not seem to lead any further is not an
indictment of CT. It had to be done.

--
Michael Press

[Graham Cooper]

On Jul 31, 1:33 am, FredJeffries <fredjeffr...@gmail.com> wrote:
> On Jul 23, 12:39 pm, Zuhair <zaljo...@gmail.com> wrote:
>
>
>
> > Are you saying that mathematicians nowadays will turn the blind eye
> > for anyone who have ideas like Dooyeweerdian? Why is that? I don't
> > think this is the case, i.e. I don't think they object to merely
> > having those ideas, I don't know however, but I think what
> > mathematicians want is non trivial new results, if Dooyeweerdian's
> > intuitions can be stated clearly on informal level as to admit
> > faithful formalization of them with a consistent formal system and if
> > that formal system showed success in interpreting ordinary mathematics
> > as well as opening the doors for further mathematical investigation,
>
> Ah, that's where it all breaks down. As much sympathy as I have for
> a Dooyeweerd/Strauss non-reductionistic system or any other non-
> standard
> foundation (or non-foundation), I have yet to come across any that
> actually solve a mathematical problem.
>
> Few mathematicians care about foundational matters. They just want
> to do their jobs. Unless you show them something with impact, like

Innovation peters out, a new smart phone button every few years is all
that's left.

All that remains now is a colossal set of hard problems... most of
which will fall under the one hammer, automated semantics.

1971
Person: HAD YOU TOUCHED ANY PYRAMID BEFORE YOU PUT THE GREEN ONE ON
THE LITTLE CUBE?
Computer: YES, THE GREEN ONE.

Person: WHEN DID YOU PICK IT UP?
Computer: WHILE I WAS STACKING UP THE RED CUBE, A LARGE RED BLOCK AND
A LARGE GREEN CUBE.

Person: WHY?
Computer: TO GET RID OF IT.

Person: WHY DID YOU DO THAT?
Computer: TO CLEAN OFF THE RED CUBE.

Person: WHY DID YOU CLEAR OFF THAT CUBE?
Computer: TO PUT IT ON A LARGE GREEN CUBE.

Person: WHY DID YOU DO THAT?
Computer: TO STACK UP THE RED CUBE , A LARGE RED BLOCK AND A LARGE
GREEN CUBE.

Person: WHY DID YOU DO THAT?
Computer: BECAUSE YOU ASKED ME TO.

Person: HOW DID YOU DO IT?
Computer: BY PUTTING A LARGE...

Person: HAVE YOU PICKED SUPERBLOCK UP SINCE WE BEGAN?
Computer: YES.

Person: WHY DID YOU DROP IT?
Computer: BY "IT", I ASSUME YOU MEAN THE SUPERBLOCK.
I CAN'T EXPLAIN A NON-EXISTENT EVENT.

http://en.wikipedia.org/wiki/SHRDLU
One was that SHRDLU's world was so simple that the entire set of
objects and locations could be described by including as few as
perhaps 50 words: nouns like "block" and "cone", verbs like "place on"
and "move to", and adjectives like "big" and "blue". The possible
combinations of these basic language building blocks were quite
simple, and the program was fairly adept at figuring out what the user
meant.

Herc
--
www.microPROLOG.com