FAQFAQ   SearchSearch   MemberlistMemberlist   UsergroupsUsergroups 
 ProfileProfile   PreferencesPreferences   Log in to check your private messagesLog in to check your private messages   Log inLog in 
Forum index » Science and Technology » Math
Set Theory: Should you believe?
Post new topic   Reply to topic Page 1 of 31 [457 Posts] View previous topic :: View next topic
Goto page:  1, 2, 3, ..., 29, 30, 31 Next
Author Message
Karl Malbrain
science forum beginner


Joined: 27 Jun 2006
Posts: 17

PostPosted: Wed Jul 12, 2006 10:56 pm    Post subject: Re: Set Theory: Should you believe? Reply with quote

Norman Wildberger wrote:
Quote:
I have posted an article at http://web.maths.unsw.edu.au/~norman/views.htm
that has caused a bit of discussion in some logic circles.

My claims in short: 1) most of `elementary mathematics' is not sufficiently
well understood by the mathematical establishment, leading to weaknesses in
K12 and college curriculum, 2) the current theory of `real numbers' is a
joke, and sidesteps the crucial issue of understanding the computational
specification of the continuum, and 3) `infinite sets' are a metaphysical
concept, and unnecessary for correct mathematics.

Analysts and set theorists are welcome to send me reasoned responses.

Assoc Prof N J Wildberger
School of Maths
UNSW

I've added sci.logic to your posting. karl m
Back to top
Gonšalo Rodrigues
science forum beginner


Joined: 31 May 2005
Posts: 22

PostPosted: Thu Jul 13, 2006 1:43 am    Post subject: Re: Set Theory: Should you believe? Reply with quote

On Thu, 13 Jul 2006 08:37:51 -0700, "Norman Wildberger"
<wildberger@pacific.net.au> fed this fish to the penguins:

Quote:
I have posted an article at http://web.maths.unsw.edu.au/~norman/views.htm
that has caused a bit of discussion in some logic circles.

My claims in short: 1) most of `elementary mathematics' is not sufficiently
well understood by the mathematical establishment, leading to weaknesses in
K12 and college curriculum, 2) the current theory of `real numbers' is a
joke, and sidesteps the crucial issue of understanding the computational
specification of the continuum, and 3) `infinite sets' are a metaphysical
concept, and unnecessary for correct mathematics.

Analysts and set theorists are welcome to send me reasoned responses.


I have read it all and I have survived. I will not offer any reasoned
response because you have not written a reasoned article. While at
some points your position is tenable and understandable, there are
just too many blunders, confusions and errors to try to answer it.

With my best regards,
G. Rodrigues
Back to top
Peter Webb
science forum Guru Wannabe


Joined: 05 May 2005
Posts: 192

PostPosted: Thu Jul 13, 2006 2:11 am    Post subject: Re: Set Theory: Should you believe? Reply with quote

<malbrain@yahoo.com> wrote in message
news:1152744973.140793.242750@h48g2000cwc.googlegroups.com...
Quote:
Norman Wildberger wrote:
I have posted an article at
http://web.maths.unsw.edu.au/~norman/views.htm
that has caused a bit of discussion in some logic circles.


Well, the discussion that I have seen - on this newsgroup (sci.math or
sci.logic, I can't remember) - is that it is bullshit. Much of it admittedly
from me.

Quote:
My claims in short: 1) most of `elementary mathematics' is not
sufficiently
well understood by the mathematical establishment, leading to weaknesses
in
K12 and college curriculum,

I don't know about the "mathematical establishment" (as a whole) not
understanding "elementary mathematics", but your own writings on set theory
and the axiomatic method don't fill me with confidence.

2) the current theory of `real numbers' is a
Quote:
joke, and sidesteps the crucial issue of understanding the computational
specification of the continuum, and

This is pure crank stuff. Describing a huge and extremely rigorously defined
area such as the construction of the Reals as a "joke" without any
mathematical justification is flakey at best; the phrase "computational
specification of the continuum" (a phrase that gets exactly zero matches on
Google) is crank babble.


3) `infinite sets' are a metaphysical
Quote:
concept, and unnecessary for correct mathematics.

No, infinite sets are a mathematical concept, not unlike perfect circles and
the exact value of the sqrt(2).

Tell me, is the set of all natural numbers finite or infinite? Or if you
can't form the set, why not?

What about the set of all points on a perfect circle (ie all solutions to
x^2 + y^2 = 1). Finite or infinite? Or don't you believe that I can define a
set as being all points on the unit circle. If not, why not? What is wrong
with {(x,y) | x^2 + y^2 = 1} as a set? Infinite or finite?

Your paper has no mathematical content, and is pure crank stuff. The stuff
about Axioms somehow being irrelevant to mathematics is just your own
philosophical ramblings. Surprising, since you seem to accept the axioms of
group theory, but not set theory (because they are too complicated and too
abstract for your liking)? Do groups with an infinite number of elements
exist, by the way?

I would have ignored this post - and previous posts on your "mathematical
insights" - in much the same way that I ignore posts about "Einstein was
wrong" or "Cantor's diagonal proof is flawed" - as pure crank material. The
only reason I haven't, is that you are a mathematics teacher, and it worries
me that somebody (eg your students) may be being taught this stuff about set
theory.

Tell me, do you accept that there are models for the ZF Axioms if we drop
Axiom 6 ? Do you accept that there is a model for the ZF axioms if we
include an additional axiom:

Exists S such that { } is an element of S, and x elements of S implies x
union {x) is an element of S ???
(informally known as the axiom of infinity)

If you don't, I can certainly show you a model (the von-Neumann construction
of N).

How is this axiom fundamentally different from the other axioms?



Quote:

Analysts and set theorists are welcome to send me reasoned responses.

Assoc Prof N J Wildberger
School of Maths
UNSW

I've added sci.logic to your posting. karl m
Back to top
Gene Ward Smith
science forum Guru


Joined: 08 Jul 2005
Posts: 409

PostPosted: Thu Jul 13, 2006 2:16 am    Post subject: Re: Set Theory: Should you believe? Reply with quote

Norman Wildberger wrote:
Quote:
I have posted an article at http://web.maths.unsw.edu.au/~norman/views.htm
that has caused a bit of discussion in some logic circles.

Your paper starts out saying a lot of things that are blatanly false.
This is not a good way to make a reasoned argument.

You say, for instance, that "the Academy" has consistently refused to
get serious about foundational questions, whereas doing that has been a
major theme of twentieth century mathematics, and many great
mathematicians have made it their life's work. You claim physicists
have trouble with string theory because they make use of set theory,
which is simply nonsense. I suspect you don't know much about string
theory. You claim the axioms of set theory have not been questioned,
which is drivel. You sneer at people who do what you claim you think
should be done, namely study the foundations of mathematics, and put
the word "supposedly" before "difficult", indicating that you think set
theory and logic are dead easy. But do you know any serious set theory?
You claim that most mathematicians could not define a vector or a
function, as if you possessed the secret decoder ring which made you
smarter than the rest of us.

In short, you sound, just in your opening few paragraphs, altogether
too much like the kind of people we constantly come across here on
sci.math. You sound like a crank. I think you *are* a crank. I suggest
you stick to subjects you've studied, and not sound off on topics you
don't understand.
Back to top
david petry
science forum Guru


Joined: 18 May 2005
Posts: 503

PostPosted: Thu Jul 13, 2006 2:54 am    Post subject: Re: Set Theory: Should you believe? Reply with quote

Norman Wildberger wrote:

Quote:
My claims in short: 1) most of `elementary mathematics' is not sufficiently
well understood by the mathematical establishment, leading to weaknesses in
K12 and college curriculum, 2) the current theory of `real numbers' is a
joke, and sidesteps the crucial issue of understanding the computational
specification of the continuum, and 3) `infinite sets' are a metaphysical
concept, and unnecessary for correct mathematics.

Here's two relevant quotes:

"ordinary mathematical practice does not require an enigmatic
metaphysical universe of sets" (Nik Weaver)

"the actual infinite is not required for the mathematics of the
physical world" (Feferman)

Most mathematicians working in the field of foundations understand and
accept those quotes, but the average mathematician may not.

What I have suggested is that mathematics needs a reality check;
mathematics can and should be treated as a science in which testable
consequences are required. I suspect that is what you are getting at,
although I don't think you've said it especially clearly.


Quote:
Analysts and set theorists are welcome to send me reasoned responses.

"Send" them to you? Why would anyone do that?
Back to top
Gene Ward Smith
science forum Guru


Joined: 08 Jul 2005
Posts: 409

PostPosted: Thu Jul 13, 2006 3:07 am    Post subject: Re: Set Theory: Should you believe? Reply with quote

david petry wrote:

Quote:
Most mathematicians working in the field of foundations understand and
accept those quotes, but the average mathematician may not.

Most mathematicians are not enthusiastic about being forced to work
only in terms of first-order arithmetic, or even second-order
arithmetic, either. Because it would be a big, fat pain and accomplish
nothing they see as necessary. On the other hand, they might very well
be interested in the question of whether, and to what extent, what they
are doing can be done using weaker assumptions--so long as you don't
try to *make* them do it that way.
Back to top
lesterzick@cableone.net
science forum beginner


Joined: 12 Jul 2006
Posts: 3

PostPosted: Thu Jul 13, 2006 3:15 am    Post subject: Re: Set Theory: Should you believe? Reply with quote

On Thu, 13 Jul 2006 12:11:34 +1000, "Peter Webb"
<webbfamily-diespamdie@optusnet.com.au> wrote:

Quote:

malbrain@yahoo.com> wrote in message
news:1152744973.140793.242750@h48g2000cwc.googlegroups.com...
Norman Wildberger wrote:
I have posted an article at
http://web.maths.unsw.edu.au/~norman/views.htm
that has caused a bit of discussion in some logic circles.


Well, the discussion that I have seen - on this newsgroup (sci.math or
sci.logic, I can't remember) - is that it is bullshit. Much of it admittedly
from me.

My claims in short: 1) most of `elementary mathematics' is not
sufficiently
well understood by the mathematical establishment, leading to weaknesses
in
K12 and college curriculum,

I don't know about the "mathematical establishment" (as a whole) not
understanding "elementary mathematics", but your own writings on set theory
and the axiomatic method don't fill me with confidence.

2) the current theory of `real numbers' is a
joke, and sidesteps the crucial issue of understanding the computational
specification of the continuum, and

This is pure crank stuff. Describing a huge and extremely rigorously defined
area such as the construction of the Reals as a "joke" without any
mathematical justification is flakey at best; the phrase "computational
specification of the continuum" (a phrase that gets exactly zero matches on
Google) is crank babble.


3) `infinite sets' are a metaphysical
concept, and unnecessary for correct mathematics.

No, infinite sets are a mathematical concept, not unlike perfect circles and
the exact value of the sqrt(2).

Tell me, is the set of all natural numbers finite or infinite? Or if you
can't form the set, why not?

What about the set of all points on a perfect circle (ie all solutions to
x^2 + y^2 = 1).

Well technically of course all solutions you point out define a
perfect sphere not a perfect circle.

Quote:
Finite or infinite? Or don't you believe that I can define a
set as being all points on the unit circle. If not, why not? What is wrong
with {(x,y) | x^2 + y^2 = 1} as a set? Infinite or finite?

Your paper has no mathematical content, and is pure crank stuff. The stuff
about Axioms somehow being irrelevant to mathematics is just your own
philosophical ramblings. Surprising, since you seem to accept the axioms of
group theory, but not set theory (because they are too complicated and too
abstract for your liking)? Do groups with an infinite number of elements
exist, by the way?

I would have ignored this post - and previous posts on your "mathematical
insights" - in much the same way that I ignore posts about "Einstein was
wrong" or "Cantor's diagonal proof is flawed" - as pure crank material. The
only reason I haven't, is that you are a mathematics teacher, and it worries
me that somebody (eg your students) may be being taught this stuff about set
theory.

Tell me, do you accept that there are models for the ZF Axioms if we drop
Axiom 6 ? Do you accept that there is a model for the ZF axioms if we
include an additional axiom:

Exists S such that { } is an element of S, and x elements of S implies x
union {x) is an element of S ???
(informally known as the axiom of infinity)

If you don't, I can certainly show you a model (the von-Neumann construction
of N).

How is this axiom fundamentally different from the other axioms?




Analysts and set theorists are welcome to send me reasoned responses.

Assoc Prof N J Wildberger
School of Maths
UNSW

I've added sci.logic to your posting. karl m


~v~~
Back to top
Virgil
science forum Guru


Joined: 24 Mar 2005
Posts: 5536

PostPosted: Thu Jul 13, 2006 3:37 am    Post subject: Re: Set Theory: Should you believe? Reply with quote

In article <ggebb2dj42j589uhhsojj0gbr0ddgec2u1@4ax.com>,
lesterzick@cableone.net wrote:

Quote:
What about the set of all points on a perfect circle (ie all solutions to
x^2 + y^2 = 1).

Well technically of course all solutions you point out define a
perfect sphere not a perfect circle.

With only two variables, x and y, there is no need to presume three
dimensions, but if one does, one gets a right circular cylinder, not a
sphere.

If one doesn't assume three (or more) dimensions, one does get a circle.
Back to top
Gerry Myerson
science forum Guru


Joined: 28 Apr 2005
Posts: 871

PostPosted: Thu Jul 13, 2006 4:02 am    Post subject: Re: Set Theory: Should you believe? Reply with quote

In article <44b5abd7$0$1207$afc38c87@news.optusnet.com.au>,
"Peter Webb" <webbfamily-diespamdie@optusnet.com.au> wrote:

Quote:
malbrain@yahoo.com> wrote in message
news:1152744973.140793.242750@h48g2000cwc.googlegroups.com...
Norman Wildberger wrote:
I have posted an article at
http://web.maths.unsw.edu.au/~norman/views.htm
that has caused a bit of discussion in some logic circles.


Well, the discussion that I have seen - on this newsgroup (sci.math or
sci.logic, I can't remember) - is that it is bullshit.

Ad hominem.

Quote:
My claims in short: 1) most of `elementary mathematics' is not
sufficiently well understood by the mathematical establishment,
leading to weaknesses in K12 and college curriculum,

I don't know about the "mathematical establishment" (as a whole) not
understanding "elementary mathematics", but your own writings on set theory
and the axiomatic method don't fill me with confidence.

Ad hominem.

Quote:
2) the current theory of `real numbers' is a
joke, and sidesteps the crucial issue of understanding the computational
specification of the continuum, and

This is pure crank stuff. Describing a huge and extremely rigorously defined
area such as the construction of the Reals as a "joke" without any
mathematical justification is flakey at best; the phrase "computational
specification of the continuum" (a phrase that gets exactly zero matches on
Google) is crank babble.

The mathematical justification for describing the current theory of
real numbers as a joke is given in the paper. You may not find it
convincing - I may not find it convincing - but it's there.

"Crank babble" is ad hominem.

Quote:
3) `infinite sets' are a metaphysical
concept, and unnecessary for correct mathematics.

No, infinite sets are a mathematical concept, not unlike perfect circles and
the exact value of the sqrt(2).

Tell me, is the set of all natural numbers finite or infinite? Or if you
can't form the set, why not?

I think Norm would say, 1) you can't form the set (and Norm's reasons
are given in the article), and 2) you don't need to - there's no good
mathematics you can do with the completed infinite set that you can't
do without it.

Quote:
What about the set of all points on a perfect circle (ie all solutions to
x^2 + y^2 = 1). Finite or infinite? Or don't you believe that I can define a
set as being all points on the unit circle. If not, why not? What is wrong
with {(x,y) | x^2 + y^2 = 1} as a set? Infinite or finite?

Again, I think Norm is arguing against the completed infinite. For
reasons discussed in some detail in the article, you can't (he contends)
sensibly write about the set of all natural numbers, or any of these
other sets that most mathematicians are quite happy with - moreover,
you don't lose anything valuable if you discard them.

Quote:
Your paper has no mathematical content, and is pure crank stuff. The stuff
about Axioms somehow being irrelevant to mathematics is just your own
philosophical ramblings. Surprising, since you seem to accept the axioms of
group theory, but not set theory (because they are too complicated and too
abstract for your liking)? Do groups with an infinite number of elements
exist, by the way?

More ad hominem. Norm accepts the axioms of group theory as the
definition of what a group is, and has no problem with them because
he can construct (finite) models of them. He argues that the axioms
of set theory (in particular, ZFC) don't define what a set is and
don't lead to sensible constructions of infinite sets.

Quote:
I would have ignored this post - and previous posts on your "mathematical
insights" - in much the same way that I ignore posts about "Einstein was
wrong" or "Cantor's diagonal proof is flawed" - as pure crank material. The
only reason I haven't, is that you are a mathematics teacher, and it worries
me that somebody (eg your students) may be being taught this stuff about set
theory.

I'm not sure how you think your method of not ignoring Norm's post
will prevent his students from being taught his ideas.

Quote:
Tell me, do you accept that there are models for the ZF Axioms if we drop
Axiom 6 ? Do you accept that there is a model for the ZF axioms if we
include an additional axiom:

Exists S such that { } is an element of S, and x elements of S implies x
union {x) is an element of S ???
(informally known as the axiom of infinity)

If you don't, I can certainly show you a model (the von-Neumann construction
of N).

How is this axiom fundamentally different from the other axioms?

It seems to me Norm is making several points, two of which are
that ZFC sucks and that mathematics doesn't need axioms in the first
place. Your suggestions may or may not have any bearing on the first
point, but they don't address the second.

I'm dismayed by the level of vituperation in some of the posts in
this thread. Norm is not presenting a high-school algebra proof of
Fermat's Last Theorem, nor is he insisting that the reals are countable
because you can always take that real number that you left off your
list and stick it on at the end. He's adopting a finitistic, or
constructivist, or computational view of mathematics. It's an unpopular
view, it doesn't particularly appeal to me, but I don't see the need
to go ballistic in response.

--
Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email)
Back to top
Gene Ward Smith
science forum Guru


Joined: 08 Jul 2005
Posts: 409

PostPosted: Thu Jul 13, 2006 6:04 am    Post subject: Re: Set Theory: Should you believe? Reply with quote

Gerry Myerson wrote:

Quote:
I'm dismayed by the level of vituperation in some of the posts in
this thread.

Norm starts out his paper, which I didn't read because the beginning
was so extremely unpromising, in what seems to me to be a very
insulting way. If he has ideas he wants to be taken seriously I suggest
he remove the sneers directed at set theorists, who apparently are
beneath contempt, and wild remarks about physics and the like. Present
a reasoned argument in a reasonable way and people are likely to react
more positively, and less likely to conclude that you are an idiot and
simply quit reading.

Quote:
He's adopting a finitistic, or
constructivist, or computational view of mathematics.

He's also spitting on people who don't. I think it is terribly arrogant
to dismiss people like
Shelah or Woodin with such utter contempt like this, and I didn't see
any signs, as far as I had gotten, that he even knows anything about
modern set theory. Does he?
Back to top
Gene Ward Smith
science forum Guru


Joined: 08 Jul 2005
Posts: 409

PostPosted: Thu Jul 13, 2006 6:34 am    Post subject: Re: Set Theory: Should you believe? Reply with quote

Gerry Myerson wrote:

Quote:
I think Norm would say, 1) you can't form the set (and Norm's reasons
are given in the article), and 2) you don't need to - there's no good
mathematics you can do with the completed infinite set that you can't
do without it.

Norm is also opposed to axioms. Without axioms, how do we know when we
are "forming" an infinte set? If I state Euclid's theorem on the
infinitude of primes, am I "forming" a set? Am I forming a set just by
referencing the integers at all? If Norm won't give a set of axioms he
finds acceptable, we can't very well say that measureable cardinals
contradict his foundations for mathematics, because he hasn't really
given a foundation. He has, in fact, claimed that infinite sets are
metaphysics; but if they are metaphysics, he's not talking mathematics
at all, but metaphysics. In which case, so what? What do his
metaphysical beliefs have to do with mathematics?

Quote:
More ad hominem. Norm accepts the axioms of group theory as the
definition of what a group is, and has no problem with them because
he can construct (finite) models of them.

In which case, he can hardly say he is rejecting axioms, and ought to
step forward and say what his proposed axioms are. Would ditching the
axiom of infinity do it? If not, what would?
Back to top
Gerry Myerson
science forum Guru


Joined: 28 Apr 2005
Posts: 871

PostPosted: Thu Jul 13, 2006 7:06 am    Post subject: Re: Set Theory: Should you believe? Reply with quote

In article <1152772442.981716.222160@m73g2000cwd.googlegroups.com>,
"Gene Ward Smith" <genewardsmith@gmail.com> wrote:

Quote:
Gerry Myerson wrote:

I think Norm would say, 1) you can't form the set (and Norm's reasons
are given in the article), and 2) you don't need to - there's no good
mathematics you can do with the completed infinite set that you can't
do without it.

Norm is also opposed to axioms. Without axioms, how do we know when we
are "forming" an infinte set? If I state Euclid's theorem on the
infinitude of primes, am I "forming" a set? Am I forming a set just by
referencing the integers at all? If Norm won't give a set of axioms he
finds acceptable, we can't very well say that measureable cardinals
contradict his foundations for mathematics, because he hasn't really
given a foundation. He has, in fact, claimed that infinite sets are
metaphysics; but if they are metaphysics, he's not talking mathematics
at all, but metaphysics. In which case, so what? What do his
metaphysical beliefs have to do with mathematics?

All these questions are better directed to Norm than to me,
but I'll make believe I know what he is on about, and answer
thus:

If I remember right, Euclid never said "there's an infinitude of
primes." He just said, "given any prime, there's a bigger one."
You and I are accustomed to interpreting the second as meaning
the same thing as the first, but I think that until quite recent
times, mathematicians didn't. They didn't accept "the completed
infinity," and they were still able to develop the theory of
numbers, prove the quadratic reciprocity theorem, the four squares
theorem, etc. If you state the theorem the way Euclid did,
you are not forming an infinite set, and you can get on perfectly
well that way.

As for measureable cardinals, I'm guessing the question of their
existence doesn't interest Norm one way or the other, on the
grounds that the stability or otherwise of the Sydney Harbor
Bridge is unlikely to depend on the outcome. The real world
questions mathematics sprang from do not depend on these
abstractions, nor on the axiom systems in which they are debated.

Quote:
More ad hominem. Norm accepts the axioms of group theory as the
definition of what a group is, and has no problem with them because
he can construct (finite) models of them.

In which case, he can hardly say he is rejecting axioms, and ought to
step forward and say what his proposed axioms are. Would ditching the
axiom of infinity do it? If not, what would?

I don't know, and if you really want to know, you could try
asking him. But perhaps he is only saying, "the axioms
of group theory define an interesting set of structures, which
I can construct, and which help me answer questions about physics,
while the axioms of set theory only help me study set theory,
which is not where the real value of mathematics is."

--
Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email)
Back to top
Gene Ward Smith
science forum Guru


Joined: 08 Jul 2005
Posts: 409

PostPosted: Thu Jul 13, 2006 7:07 am    Post subject: Re: Set Theory: Should you believe? Reply with quote

Norman Wildberger wrote:
Quote:
I have posted an article at http://web.maths.unsw.edu.au/~norman/views.htm
that has caused a bit of discussion in some logic circles.

Here's a quote from the paper, which I think shows how confused
Wildberger is about axioms:

"In ordinary mathematics, statements are either true, false, or they
don't make sense. If you have an elaborate theory of 'hierarchies upon
hierarchies of infinite sets', in which you cannot even in principle
decide if there is something between the first and second 'infinity' on
your list, there's a time to admit you are no longer doing
mathematics."

Of course, the statement about not being able to decide if there is a
cardinal between aleph_0 and aleph_1 is absurd, but leave that aside
and look instead at the statement that there is a cardinal between
aleph_0 and 2^aleph_0. How does this differ from the statement that the
sum of the angles of a triangle cannot be determined in absolute
geometry?

Suppose, when faced with the fact that not everyone found the parallel
postulate to be intuituively true, the Greek geometers had simply
removed it from consideration. They could then be attacked with the
sneer that they were not doing mathematics at all, because they could
not answer so basic a question as whether the sum of the angles of a
triangle was less than, equal to, or greater than two right angles. Yet
I think it is clear they *would* be doing geometry. For that matter a
group theorist who cannot tell you if a generic group is abelian or
nonabelian, since it might be either, is not failing to do mathematics.

The difference is that we've given up on the idea that there is a
single correct geometry, but still feel (and that's nothing but
intuition speaking) that there is a single true set theory, just as we
think there is a single true number theory. But our intution is not
strong enough to settle all the questions as to what this true set
theory actually is. This is really a meta problem for mathematics, and
not a question which can allow a person to conclude that set theorists
are not mathematicians, any more than the existence of nonstandard
models for first-order arithmetic would prove number theorists are not
mathematicians. As to rigor, the mechanically verified proofs of the
Mizar project are more rigorous than mere mortals like you, me, or
Wildberger do, and they are based on set theory with (if needed)
inacessible cardinals. The rigor argument is clearly therefore baloney,
and Wildberger cannot seem to separate mathematics from metaphysics for
the rest of it.
Back to top
Gerry Myerson
science forum Guru


Joined: 28 Apr 2005
Posts: 871

PostPosted: Thu Jul 13, 2006 7:13 am    Post subject: Re: Set Theory: Should you believe? Reply with quote

In article <1152770679.597975.88170@p79g2000cwp.googlegroups.com>,
"Gene Ward Smith" <genewardsmith@gmail.com> wrote:

Quote:
I didn't see any signs, as far as I had gotten, that he even knows
anything about modern set theory. Does he?

I don't know.

I reject astrology, even though I don't know anything about modern
astrology (I don't even know if there is such a thing). I reject
"creation science" and "intelligent design," even though I haven't
read any recent writings of their advocates. I don't have to; I
know where they're going, and I know they're never going to get
anywhere useful, going in that direction.

I personally don't put set theory in the same category as astrology
or creation science. Maybe Norm does. I don't know.

--
Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email)
Back to top
Russell Easterly
science forum Guru Wannabe


Joined: 27 Jun 2005
Posts: 199

PostPosted: Thu Jul 13, 2006 7:14 am    Post subject: Re: Set Theory: Should you believe? Reply with quote

"Gene Ward Smith" <genewardsmith@gmail.com> wrote in message
news:1152770679.597975.88170@p79g2000cwp.googlegroups.com...
Quote:

Gerry Myerson wrote:

I'm dismayed by the level of vituperation in some of the posts in
this thread.

Norm starts out his paper, which I didn't read because the beginning
was so extremely unpromising, in what seems to me to be a very
insulting way. If he has ideas he wants to be taken seriously I suggest
he remove the sneers directed at set theorists, who apparently are
beneath contempt, and wild remarks about physics and the like. Present
a reasoned argument in a reasonable way and people are likely to react
more positively, and less likely to conclude that you are an idiot and
simply quit reading.

He's adopting a finitistic, or
constructivist, or computational view of mathematics.

He's also spitting on people who don't. I think it is terribly arrogant
to dismiss people like
Shelah or Woodin with such utter contempt like this, and I didn't see
any signs, as far as I had gotten, that he even knows anything about
modern set theory. Does he?

I think he is all too familiar with modern set theorists.
Set theorists have written the book on how to treat
others with contempt.

Most branches of mathematics will accept any reasonable proof.
Set theorists demand proofs in set theory.
This is like the Catholic Church requiring Mass be given in Latin.
It is a method of guaranteeing only the priests (the true
believers) know the Church's doctrines.
It is designed to prevent skeptics (non-believers) from being
able to question Church doctrine, since you need to know
a dead language to have any idea what that doctrine is.

Imagine if Einstein had been told he had to prove relativity
in Newtonian physics before anyone would consider his ideas.


Russell
- 2 many 2 count
Back to top
Google

Back to top
Display posts from previous:   
Post new topic   Reply to topic Page 1 of 31 [457 Posts] Goto page:  1, 2, 3, ..., 29, 30, 31 Next
View previous topic :: View next topic
The time now is Wed Oct 18, 2017 5:32 am | All times are GMT
Forum index » Science and Technology » Math
Jump to:  

Similar Topics
Topic Author Forum Replies Last Post
No new posts unified theory gb6724 New Theories 4 Fri Jul 21, 2006 5:25 am
No new posts Signal Nonlocality Loophole in Quantum Theory? Jack Sarfatti Math 0 Thu Jul 20, 2006 1:59 am
No new posts A Combinatorics/Graph Theory Question mathlover Undergraduate 1 Wed Jul 19, 2006 11:30 pm
No new posts A Combinatorics/Graph Theory Question mathlover Math 2 Wed Jul 19, 2006 11:02 pm
No new posts A Combinatorics/Graph Theory Question mathlover Combinatorics 0 Wed Jul 19, 2006 10:58 pm

Copyright © 2004-2005 DeniX Solutions SRL
Other DeniX Solutions sites: Electronics forum |  Medicine forum |  Unix/Linux blog |  Unix/Linux documentation |  Unix/Linux forums  |  send newsletters
 


Powered by phpBB © 2001, 2005 phpBB Group
[ Time: 0.0443s ][ Queries: 16 (0.0056s) ][ GZIP on - Debug on ]