Re: Completeness & consistency, was: A sad thread

Previous thread: the snapshot way by Mihai Popescu B. S. on Sunday, January 6, 2008 - 5:00 pm. (3 messages)

Next thread: Great OS, thanks by Doug Milam on Sunday, January 6, 2008 - 6:14 pm. (1 message)
To: <misc@...>
Date: Sunday, January 6, 2008 - 4:37 pm

Hello,

I came to the misc@ list from Journal links just to see what is the real
discussion about RMS and OpenBSD.
From the start I have to tell the list that I'm sad. I have read sad things and
now I think I should not read those things. In fact someone should put a waring
label like "Read with caution" or "Rude language and affecting text inside".

Normally, I am just a common user of OpenBSD and I know that the project runs
with some ideas and some peopel which I respect and I think they are good for
the purpose of the project. What I will say next should be taken as an user
feedback and nothing more.

A. "License" thing

Once I asked a lawyer why do people need lawyers in court since we have very
clear laws state the rules for us.
The man was in difficulty to answer, but eventually he tried and told me that
the laws are not very clear like I used to think.
Of course, the next question was why don't you make them clear... this way you
know when some did something wrong and you know what the punishment is.
This time the man was in real trouble answering me and he looked at me and
said: "I really don't see what you are trying to find out, but what I've
learned in school is that the law is always questionable. As a lawyer, it is
your job to use it in your client advantage."
Later, I found out that our human language is too weak to define laws in
absolute and clear terms.
Having this said, I have read the BSD licence. Basically I understood that you
can do anything with the code, the only request is to put the copyright text
inside the source code files. ( If what I understood is not right, maybe some
details and examples can be added to the web page.)
The GPL licence I never got with it to some understanding. I thing it is very
confusing and I was lost in many DOs and DON'Ts. I don't know what GPL allows
you and what it doesn't. Basically, I like an example with variations.

Of course you need licences, but don't try to be so absolute on defining them
because you can't. I think...

From: L <L@...>
To: Mihai Popescu B. S. <mihaipbs@...>
Cc: <misc@...>
Date: Sunday, January 6, 2008 - 7:36 pm

Stallman continually keeps repairing and admitting to a small amount of
his errors... and this entire thread has made progress. The only reason
stallman started admitting to anything, was because people were so
persistent and tough on him.

How often I have to beat these quotes below into people I don't know:

/"...a philosopher who did not hurt anybody's feelings was not doing his
job."
--Plato (source: Wikipedia)/

/"...a programmer who did not hurt anybody's feelings was not doing his
job."
--L505 (source: Z505)/

/"..one of the men who brings legal charges against Socrates, Anytus,
warns him about the trouble he may get into if he does not stop
criticizing important people."
--Wikipedia/

Everyone is so nicey nicey huggy huggy with stallman in other communties
and they never speak up about any of his philosophies because they
believe everything he says blindly. Linus once in a while speaks up
about Stallman and everyone gets mad at Linus. Do you see a pattern
here? There is nothing wrong with speaking up once in a while. I'm
growing a hatred toward people who are scared of speaking up.. they have
no guts and they try and STOP ME from speaking up. They are speaking up
themselves, about me speaking up. Hypocrisy?

The fact that Stallman himself is replying, shows that he wants to be
here. If it was so bad for him, he would have left. He is learning
something about freedom.. but he won't admit to it. I have personally
taught the man more than anyone else here, as we all know.

As for the language? Why can't people just get a sense of humor? Stop
being so sensitive about such things. This is email and laughing is
healthy. Foul language is not always nice, but at times it is extremely
hilarious.. and anyone who whines about being hurt from foul language
should really learn to cope with it.. because humans by nature should
not be perfectly nice all the time. If we were all nice we'd all believe
in the tooth fairy.

To: OpenBSD <misc@...>, Mihai Popescu B. S. <mihaipbs@...>
Date: Sunday, January 6, 2008 - 7:16 pm

Mr Stallman says he cannot browse the web, we respect that and are helping him!

I do think we shouldn't respond to his croonies.

+++chefren

To: <misc@...>
Cc: Mihai Popescu B. S. <mihaipbs@...>
Date: Sunday, January 6, 2008 - 10:38 pm

Not true. Language can define the laws of of physics or of mathematics
in extremely clear, precise, and absolute terms.

Bringing the discussion back to operating systems, I think that the our
legal system is a giant complicated mess for the same reason that
Microsoft Windows is a giant complicated mess: a cleanly-organized
system was simply not a priority for its creators.

To: Matthew Szudzik <mszudzik@...>
Cc: <misc@...>, Mihai Popescu B. S. <mihaipbs@...>
Date: Sunday, January 6, 2008 - 11:21 pm

Many if not most physicists and mathematicians would dispute that
statement. There are numerous important debates in the fields of
physics and mathematics about what fundamental rules mean and how they
may and may not be used. (There are also multiple useful,
mutually-inconsistent formal systems in both fields.)

In math, physics, or software licensing, one must ask whether problems
of clarity are the result of the language and how it is used, or the
result of people not knowing quite what they mean when they use the
language. Imprecise language is valuable when one wants to communicate

A cleanly-organized legal system would operate efficiently and
consequently be extremely powerful. Horrible atrocities would result.
The US legal system was designed for the express purpose of limiting
its own efficiency. I doubt the creators of Microsoft Windows made a
bad operating system to empower the people who would be most directly
affected by it. While not everything about Microsoft is bad, I
wouldn't give them so much credit as to compare their products to a
poorly functioning government.

-Eliah

To: <degeneracypressure@...>
Cc: Matthew Szudzik <mszudzik@...>, <misc@...>, Mihai Popescu B. S. <mihaipbs@...>
Date: Monday, January 7, 2008 - 3:37 am

On Sun, 6 Jan 2008 22:21:14 -0500

Provably so?

Dhu

To: Duncan Patton a Campbell <campbell@...>
Cc: Matthew Szudzik <mszudzik@...>, <degeneracypressure@...>, <misc@...>, Mihai Popescu B. S. <mihaipbs@...>
Date: Monday, January 7, 2008 - 1:02 pm

Yes. For example, in intuitionistic analysis every real-valued
function of a real-valued variable is continuous, whereas
classically most of them (e.g., in the sense of cardinality) are
not. (To anticipate (the substance of) a remark: Yes, e.g., there
is no Heaviside function in intuitionistic analysis and no, that
does not prevent intuitionistic analysis from being able to do
the work in applications that the Heaviside function does for
classical analysis (just somewhat differently).)
The full picture is more complicated, however. There are
translations between the formal systems (or perhaps of one into
an expansion by imaginaries, higher types and/or modal operators
of (possibly a reduct of) the other). Semantically, this often
corresponds to a construction in one formal system of a structure
that faithfully (perhaps only relative to certain formulae) models
the other formal system.
Examples: classically one can verify the foregoing result of
intuitionistic analysis, e.g., by interpreting it in a gros topos
of subcanonical sheaves on a category of spaces (an extension[1]
of Cohen's method of forcing for constructing models of set theory);
Klein's model of the hyperbolic plane and the (essentially)
Grassmann construction of projective space, each of which is a
construction on (part of) an euclidean space.

Observe that this does not contradict Matthew's original remark;
if anything, it reveals some of the depth of that remark.
Matthew knows what he is talking about.

[1] This word conceals a lengthy description of an involved
relationship; I am sure that some would dispute its aptness.

To: William Boshuck <boshuk@...>
Cc: Matthew Szudzik <mszudzik@...>, <degeneracypressure@...>, <misc@...>, Mihai Popescu B. S. <mihaipbs@...>
Date: Monday, January 7, 2008 - 5:14 pm

On Mon, 7 Jan 2008 12:02:08 -0500

?intuitionistic?

Dhu

To: <degeneracypressure@...>, Duncan Patton a Campbell <campbell@...>
Cc: Matthew Szudzik <mszudzik@...>, <misc@...>, Mihai Popescu B. S. <mihaipbs@...>
Date: Monday, January 7, 2008 - 4:02 am

+1

I'd love an example of Math being inconsistent. Quite frankly, I'd be
surprised if this is true.

best regards,
Reid Nichol

President Bush says:

War Is Peace
Freedom Is Slavery
Ignorance Is Strength

____________________________________________________________________________________
Be a better friend, newshound, and
know-it-all with Yahoo! Mobile. Try it now. http://mobile.yahoo.com/;_ylt=Ahu06i62sR8HDtDypao8Wcj9tAcJ

To: Eliah Kagan <degeneracypressure@...>, Duncan Patton a Campbell <campbell@...>, Reid Nichol <rnichol_rrc@...>
Cc: <misc@...>
Date: Monday, January 7, 2008 - 3:24 pm

Eliah has beautifully demonstrated this for both Mathematics
and Physics. What is flabbergasting me about such questions
is that these are extremely old facts - essentially, known for
more than 70 years - and many people still believe that formal
science can be both complete and consistent.

http://en.wikipedia.org/wiki/Nicolas_Bourbaki
- nicely narrating how the attempt to transform mathematics
into a single unified and consistent theory miserable failed

http://wiki/G%C3%B6del%27s_incompleteness_theorem
- explaining why

http://en.wikipedia.org/wiki/Kurt_G%C3%B6del (1906-1978)
- "One of the most significant logicians of all time, GC6el's work
has had immense impact upon scientific and philosophical thinking
in the 20th century, a time when many, such as Bertrand Russell,
A. N. Whitehead and David Hilbert, were attempting to use logic
and set theory to understand the foundations of mathematics."

Still, many people appearantly never heard of the problems he
described, even though we are now well into the 3rd millenium...

Reply-To: poster set, we are *terribly* off-topic.

To: Eliah Kagan <degeneracypressure@...>, Duncan Patton a Campbell <campbell@...>, <schwarze@...>
Cc: <misc@...>
Date: Monday, January 7, 2008 - 8:47 pm

Setting the record straight because I can't in good conscience have
such nonsense sitting in public not refuted.

You haven't pointed to an instance of an inconsistency in Mathematics.
Which, I'll point out, was what I explicitly asked for.

Basically, you're referencing a choice in Mathematics that we have,
that we can go for either consistent OR complete. And you seem to be
saying that Mathematics is neither? You don't seem to understand the
issues involved and/or have incomplete knowledge/understanding of the
history of Mathematics.

"What is flabbergasting me" is that you haven't a clue and/or lack the
attention to detail to answer questions that were explicitly asked.

Point of fact, Mathematics has been proven to have the option to be
either consistent OR complete. From what I've learned, we've chosen to
be consistent. Which, IMO, was a very very wise decision. If you
don't agree, point to a specific instance of an inconsistency in modern
Mathematics.

Eliah Kagan wrote:
"""
Tony Abernethy's example of non-Euclidean geometries being
inconsistent with Euclidean geometry is a good one.
"""

This is so very wrong it isn't even funny. You deserve to be ridiculed
publicly into oblivion for making such nonsensical statements.

I mean seriously, Euclidean geometry assumes a perfectly flat plain
whereas non-Eucliden geometry does not. Do you think they'll go in
different directions? Do you think that it is even remotely reasonable
to compare the conclusions after such a divergence without considering
limiting cases?

Though a couple of the statements you make after the above statement
are reasonable, you take it in a direction and make conclusions that
aren't (meaningless?!?!?). This mixture of reasonable with
unreasonable, including such logic makes such statements erroneously
compelling, which is very dangerous for those learning this stuff for
the first time. Please stay away from making any statements on the
foundations of Mathematics in the future as you s...

To: 'Eliah Kagan' <degeneracypressure@...>, 'Duncan Patton a Campbell' <campbell@...>, <schwarze@...>, 'Reid Nichol' <rnichol_rrc@...>
Cc: <rms@...>, <misc@...>
Date: Tuesday, January 8, 2008 - 3:17 am

Axioms:
Empty set -- this is consistent.
There is nothing there to be inconsistent.

Foo and NOT-Foo -- this is complete
From these two little axioms all true statements can be derived.
(and all the false ones too)

So what?
Going from those trivial cases to the whole of 19th century math is more
than fits into one mind.
This is now the 21st century.

Cc: Eliah Kagan <degeneracypressure@...>, Duncan Patton a Campbell <campbell@...>, <misc@...>, Reid Nichol <rnichol_rrc@...>
Date: Monday, January 7, 2008 - 9:14 pm

I would be little bit more careful about dragging the incompletness
theorem into the discussion without properly understanding
the statement of the theorem, its meaning, and corollaries.
The connections that you are trying to make between the incompletness
theorem and Burbaki project are very shallow at best and I certainly
have not heard them before.

Kind Regards,

Predrag

Department of Mathematics
University of Arizona

P. S. I am no expert on mathematical logic but definitely know little
bit better than your average bystander.

To: <schwarze@...>
Cc: Duncan Patton a Campbell <campbell@...>, <misc@...>, Reid Nichol <rnichol_rrc@...>
Date: Monday, January 7, 2008 - 9:09 pm

For the record, I do not believe that there is necessarily no complete
and entirely correct *physical* theory "out there" to be discovered.
Such a theory, when formalized mathematically, would have to allow
well-formed undecidable statements. But those statements would not
necessarily be *about* physical reality, any more than an applied
system that modestly extends Zermelo-Frankel set theory (with or
without the Axiom of Choice) to contain axioms about voter
demographics is incomplete with respect to classification of voters
due to the undecidability of the Continuum Hypothesis. In other words,
the "complete physics" would actually use only part of the
mathematical framework used to formalize it.

It's also possible that a complete and correct theory of physics will
be discovered and be accepted, and still not be formalized
mathematically. Quantum Electrodynamics is probably the most
successful scientific theory ever (in terms of the number,
consistency, and precision of its predictions), and yet as far as I
know it has still not been formalized in the mathematical sense.

-Eliah

To: <degeneracypressure@...>
Cc: <misc@...>, <schwarze@...>, Reid Nichol <rnichol_rrc@...>
Date: Tuesday, January 8, 2008 - 3:41 am

On Mon, 7 Jan 2008 20:09:47 -0500

Is it not the case that you can show that you cannot prove a system
both complete and consistent? ---> doesn't mean there is no "God"
just that you cannot prove it.

Dhu

To: <degeneracypressure@...>, 'Duncan Patton a Campbell' <campbell@...>, 'Reid Nichol' <rnichol_rrc@...>
Cc: 'Matthew Szudzik' <mszudzik@...>, <rms@...>, <misc@...>, 'Mihai Popescu B. S.' <mihaipbs@...>
Date: Monday, January 7, 2008 - 6:18 am

System A being inconsistent with System B
(that's what the "mutually-inconsistent formal systems" means)

System RMS being self-inconsistent
(that's this thread)

To: Reid Nichol <rnichol_rrc@...>
Cc: Matthew Szudzik <mszudzik@...>, <rms@...>, Duncan Patton a Campbell <campbell@...>, <misc@...>, Mihai Popescu B. S. <mihaipbs@...>
Date: Monday, January 7, 2008 - 5:22 am

Tony Abernethy's example of non-Euclidean geometries being
inconsistent with Euclidean geometry is a good one.

The statement "Mathematics is consistent," is not false. It is
meaningless. At least if you try to consider it mathematically. It is
sort of like saying, "the public library is consistent." In
mathematics, there are mathematical systems. Mathematical systems have
axioms. Axioms are statements that, within a particular system, are
accepted without proof. Using a mathematical system doesn't mean you
believe the axioms--it just means that you are willing to see what
happens when you suppose that they are true.

A set of statements is consistent if the conjunction of all the
statements in the set is not a contradiction. (Also, the empty set is
consistent.) Otherwise the set is inconsistent. A mathematical system
is itself consistent if the set containing all and only axioms of that
system is consistent. Otherwise the system is inconsistent. Two or
more mathematical systems are mutually consistent if the union of
their sets of axioms is consistent, and mutually inconsistent
otherwise.

Statements A and B are dependent if and only if either provably
follows from the other. Otherwise they are independent.

The axioms of Euclidean Geometry are provably consistent. The Parallel
Postulate, which states that parallel lines intersect nowhere, is
provably independent of the other axioms of Euclidean Geometry. Adding
in the Parallel Postulate gives you a geometry describing a flat
space. Adding in its negation or statements stronger than its negation
(i.e. statements from which its negation follows, but which do not
follow from its negation) give you geometries describing other spaces.
Both Euclidean and non-Euclidean geometries (such as those in which
the parallel postulate does not hold) are used by mathematicians.

A similar situation exists where ZFC (accepting the Axiom of Choice)
and ZF-C (accepting the negation of the Axiom of Choice) systems are
mutually inconsistent ...

To: <degeneracypressure@...>
Cc: <mszudzik@...>, <campbell@...>, <misc@...>, <mihaipbs@...>, <rnichol_rrc@...>
Date: Monday, January 7, 2008 - 1:15 pm

You have done a pretty good job of summarizing my position.
The sex education analogy is quite clear and valid.
(I'm in favor of teaching people how to use contraception,
because I'm in favor of encouraging sex.)
Thank you for helping to explain.

In this discussion I have stuck to correcting misstatements about my
views, and refuting criticism. I have defended and explained my
ethical views in response to attacks, and only for that reason.
If others let that question drop, so will I.

To: <degeneracypressure@...>, 'Duncan Patton a Campbell' <campbell@...>
Cc: 'Matthew Szudzik' <mszudzik@...>, <misc@...>, 'Mihai Popescu B. S.' <mihaipbs@...>
Date: Monday, January 7, 2008 - 4:00 am

Euclidean and ono-Euclidian geometries should suffice.

To: <degeneracypressure@...>, 'Duncan Patton a Campbell' <campbell@...>, <tony@...>
Cc: 'Matthew Szudzik' <mszudzik@...>, <misc@...>, 'Mihai Popescu B. S.' <mihaipbs@...>
Date: Monday, January 7, 2008 - 4:26 am

Google (including scholar.g) gave nothing of value (I see 4 results
when I search for ono-Euclidean on g and nothing on scholar.g). Any
specific references? Or something else that would yield results.

best regards,
Reid Nichol

President Bush says:

War Is Peace
Freedom Is Slavery
Ignorance Is Strength

____________________________________________________________________________________
Never miss a thing. Make Yahoo your home page.
http://www.yahoo.com/r/hs

To: Reid Nichol <rnichol_rrc@...>
Cc: 'Matthew Szudzik' <mszudzik@...>, <degeneracypressure@...>, <misc@...>, <tony@...>, 'Mihai Popescu B. S.' <mihaipbs@...>
Date: Monday, January 7, 2008 - 5:18 am

On Mon, 7 Jan 2008 00:26:35 -0800 (PST)

ono-Euclidian appears to reference something by Omar Kayam, an 11th c
Iranian _POET_. If we are to allow the arg. that Creationism is science,
we might allow that such an "inconsistency" has meaning.

To: 'Duncan Patton a Campbell' <campbell@...>, 'Reid Nichol' <rnichol_rrc@...>
Cc: 'Matthew Szudzik' <mszudzik@...>, <degeneracypressure@...>, <misc@...>, 'Mihai Popescu B. S.' <mihaipbs@...>
Date: Monday, January 7, 2008 - 5:41 am

oops: NON-Euclidean
(still more accurate than a lot of ... on this thread)

To: 'Matthew Szudzik' <mszudzik@...>, <misc@...>
Cc: 'Mihai Popescu B. S.' <mihaipbs@...>
Date: Sunday, January 6, 2008 - 11:51 pm

First the obvious: If it can, then why doesn't it?

Second, seems like mathematics has "axioms" not "laws".

There are a few things you can define with pretty good rigor,
not all that easy to do a lot with 'em though.
That glib a statement is only made by people who have no
concept of clear or of precise or of absolute.

To: <misc@...>
Cc: <rms@...>
Date: Sunday, January 6, 2008 - 9:23 pm

[...]

+1

I'm a Debian GNU/Linux and OpenBSD user. I'm a FSF member and I buy
OpenBSD stuff to support the project, and I try to help Debian, GNU,
Linux and OpenBSD projects as far my capabilities allow me.

And I don't understand how important people that I admire can fall down
in so childish discussion. I'm ashamed as free software supporter and I
feel insulted by members of two communities. In the beginning I think
clearly who was right and who wasn't, but now it is not important.

So now you can continue flaming yourselves and flame me too everybody.
Maybe I'm too old to still believe in peace.

--
Francisco J. Tsao Santmn
http://tsao.enelparaiso.org

To: Francisco J. Tsao Santin <tsao@...>
Cc: <rms@...>, <misc@...>
Date: Tuesday, January 8, 2008 - 1:48 pm

Maybe because those people are not so thoughtful and thus important as

It is very important to make clear that some "interesting" statements
are just lies.

All freedom-claims of Richard Stallman are dubious and is main point
in life, the DRM part he added to BSD to make it GPL is enslaving

Mr Stallman is not peaceful at all he tries to enslave programmers for
no reason and he lies to his followers.

That's very sad.

+++chefren

Previous thread: the snapshot way by Mihai Popescu B. S. on Sunday, January 6, 2008 - 5:00 pm. (3 messages)

Next thread: Great OS, thanks by Doug Milam on Sunday, January 6, 2008 - 6:14 pm. (1 message)