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Science Forum Index » Mathematics Forum » What is Mathematics?
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| Benj |
 Posted: Tue Apr 29, 2008 6:40 am |
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On Apr 26, 1:34 pm, Lester Zick <dontbot...@nowhere.net> wrote:
Quote: On Sat, 26 Apr 2008 12:14:21 GMT, Aatu Koskensilta
So if someone demonstrates he was, in fact, at home yesterday that's
mathematics?
If he can demonstrate the proposition exhaustively, yes. Usually such
things are demonstrated inexhaustively, through testimony and so on.
Typically if the proposition can be demonstrated exhaustively as a
necessary truth, the result is mathematical regardless of how trivial.
No. Mathematics is NEVER "true" which is to say conforms to reality.
There is a great error out there today in science which states that
somehow mathematics is MORE real than reality. This is a COMPLETE
misunderstanding of what mathematics is!
Mathematics are logical models which may or may not relate or
approximately describe (predict) reality. Beyond that mathematics has
NO connection with reality. People like to assume that mathematics
comes out of reality like 1 + 1 = 2. But that is not where it comes
from. Indeed that is a APPLICATION of just ONE mathematical system as
a model ONTO reality!
So do parallel lines meet at "infinity" or do they not meet there?
Mathematics doesn't give a damn which. What mathematics cares about is
that one STARTS with a given premise and then logically develops a
SYSTEM based upon that premise. The "correctness" of mathematics has
ONLY to do with how carefully and correctly the steps used to develop
the system were done. Whether or not the final system is a model of
ANYTHING is irrelevant! When one says 1+1 = 2 is "true",
mathematically one only means that the logic and rules followed to
develop arithmetic were followed precisely and correctly. It has
NOTHING to do with the existence of two separate apples creating a
pair! But oddly enough we find that one particular system of
arithmetic seems to work pretty well as a MODEL to predict what
happens when I've got several boxes of apples and start arranging them
in groups!
Therefore ANY practical matter such as being home or not at home has
NOTHING to do with mathematics! The logical system you might use to
"prove" a given fact of reality is mathematics, but truth is that
mathematics can NEVER "prove" reality because mathematics itself is
not "real".
Once those in our science departments figure this out science will
make a great leap forward! |
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| Aatu Koskensilta |
| Posted: Tue Apr 29, 2008 10:50 am |
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On 2008-04-29, in sci.logic, Occidental wrote:
Quote: But a list is not a criterion; is the criterion itself one of the
things about which we must remain silent?
Alas Wittgenstein was never very explicit on this issue in his
writing. The closest he comes is on p. 342 of the Hello-Kitty book --
so named because his notes were at the time circulated in the form of
indecipherable scribbling in a Hello-Kitty notebook -- where he
says, in Heikki Nyman's translation:
127. It might happen that someone asks us a question about our own
past work. Suppose, for example, that someone asks you "Why did
you choose gardening?". Just how are we to answer? We are
naturally drawn to certain ways of answering, but thinking of
that gives me a strange tingly feeling in my toe. Here we must
ask: why the toe? Why should the question give rise to such a
strange occurrence specifically in the toe? (NB. Consider the
claim "The dog is nowhere to be seen but my toe feels quite
tingly indeed". Why would anyone ever say such a thing?)
--
Aatu Koskensilta (aatu.koskensilta@xortec.fi)
"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus |
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| Lester Zick |
| Posted: Tue Apr 29, 2008 11:08 am |
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On Mon, 28 Apr 2008 10:47:06 GMT, Aatu Koskensilta
<aatu.koskensilta@xortec.fi> wrote:
Quote: The reason choice is
accepted as true is that most people find it utterly compelling, quite
unable to imagine how it could fail, a principle pleasing to the
intellect that allows them to make mathematical use of the idea of
sets as arbitrary extensional collections.
Assumptions of truth are often plausibly incorrect as readers of these
newsgroups should readily appreciate.
~v~~ |
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| Aatu Koskensilta |
| Posted: Tue Apr 29, 2008 10:04 pm |
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On 2008-04-29, in sci.math, Chris Menzel wrote:
Quote: Easily as cogent and persuasive as anything in the post-Tractatus
Wittgensteinian corpus!
It's probably safe to say the old Witters was having a bad day when
writing the quoted passage. There is much value to Wittgenstein's
later work, though not necessarily in the sense Wittgenstein
enthusiasts would have it.
Take for example Wittgenstein's writings on the philosophy of
mathematics. There is little point, outside of history of philosophy
and Wittgenstein studies, to try to tease out of them any systematic
philosophical doctrine -- even a casual inspection reveals most of his
remarks are simply not relevant to modern mathematics, and are instead
concerned almost entirely with elementary arithmetic. What is of value
are the occasionally highly penetrating observations and insights, and
the fact that it is only in these writings we find an actual example
of a consistently anti-realist interpretation of the whole of
mathematics. (This is something Torkel used to blather about now and
then.)
Even intuitionists are extravagantly realist in the sense relevant
here, in taking it to be a definite matter of fact whether a number is
prime or not, and going on about, in an uncompromisingly realistic
manner, the antics of a mystical creature, the idealised
mathematician, capable of fantastic feats such as normalising
arbitrarily complex intuitionistic proofs to obtain numeric witnesses
for existential statements and so on. Perhaps intuitionistic
mathematics is not the mathematics of God, but it is mathematics of a
superbly powerful semi-deity. In exploring such matters, much
inspiration might be gleaned from Wittgenstein.
--
Aatu Koskensilta (aatu.koskensilta@xortec.fi)
"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus |
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| T.H. Ray |
| Posted: Thu May 01, 2008 2:59 am |
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Quote: In article
17336283.1208809303160.JavaMail.jakarta@nitrogen.math
forum.org>,
T.H. Ray <thray123@aol.com> wrote:
LauLuna
"Mathematics is what mathematicians do".
I'd prefer something a bit less sociological. What
about "mathematics
is any theoretical activity which can rely on
theorem proving" ?
THR
Then mathematics could not be distinguished from
philosophy.
Tom
Regards
No, philosophers do all sorts of speculation, and
come up with conjectures, or what they would like
to be true. Provability or often truth does not
enter into their conclusions.
I have seen the following definition:
A philosopher is someone who is looking for
a black cat, in a totally dark room, which
isn't there, and finds it!
If a mathematician were in this situation, it would
be
a proof that mathematics is inconsistent, and we
would
then have to go back and find an adequate weaker
system
of axioms.
We have different memories of that quote about black
cats. I am fairly sure the correct one is from
Charles Darwin: "A mathematician is a blind man in a dark
room looking for a black cat which isn't there." The
reason I am fairly sure is that I once made the
mistake of attributing it to Bertrand Russell.
Nevertheless, your point is well taken. A philosopher
may well find truth that was never there, while the
terms of existence are a mathematician's sine qua non.
Tom
Quote: --
This address is for information only. I do not claim
that these views
are those of the Statistics Department or of Purdue
University.
Herman Rubin, Department of Statistics, Purdue
University
hrubin@stat.purdue.edu Phone: (765)494-6054
FAX: (765)494-0558 |
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| Occidental |
| Posted: Thu May 01, 2008 4:07 am |
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On May 1, 9:01 am, Wolf Kirchmeir <wolf...@sympatico.ca> wrote:
Quote: Aatu Koskensilta wrote:
On 2008-04-29, in sci.math, Chris Menzel wrote:
Easily as cogent and persuasive as anything in the post-Tractatus
Wittgensteinian corpus!
It's probably safe to say the old Witters was having a bad day when
writing the quoted passage. There is much value to Wittgenstein's
later work, though not necessarily in the sense Wittgenstein
enthusiasts would have it.
[...]
You don't recognise satre when you read it.
--
wolf k.
Are you referring to Jean-Paul Satire? |
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| Wolf Kirchmeir |
| Posted: Thu May 01, 2008 8:01 am |
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Guest
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Aatu Koskensilta wrote:
Quote: On 2008-04-29, in sci.math, Chris Menzel wrote:
Easily as cogent and persuasive as anything in the post-Tractatus
Wittgensteinian corpus!
It's probably safe to say the old Witters was having a bad day when
writing the quoted passage. There is much value to Wittgenstein's
later work, though not necessarily in the sense Wittgenstein
enthusiasts would have it.
[...]
You don't recognise satre when you read it.
--
wolf k. |
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| Wolf Kirchmeir |
| Posted: Thu May 01, 2008 11:04 am |
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Guest
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Occidental wrote:
Quote: On May 1, 9:01 am, Wolf Kirchmeir <wolf...@sympatico.ca> wrote:
Aatu Koskensilta wrote:
On 2008-04-29, in sci.math, Chris Menzel wrote:
Easily as cogent and persuasive as anything in the post-Tractatus
Wittgensteinian corpus!
It's probably safe to say the old Witters was having a bad day when
writing the quoted passage. There is much value to Wittgenstein's
later work, though not necessarily in the sense Wittgenstein
enthusiasts would have it.
[...]
You don't recognise satre when you read it.
--
wolf k.
Are you referring to Jean-Paul Satire?
B'ding!
Good one! Clusmy typits, me. ;-)
--
wolf k. |
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| Lester Zick |
| Posted: Thu May 01, 2008 11:10 am |
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Guest
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Yeah, I can't really tell what you're talking about here. Basically it
appears you're using a variety of terms without any real definitions.
On Tue, 29 Apr 2008 09:40:35 -0700 (PDT), Benj <bjacoby@iwaynet.net>
wrote:
Quote: On Apr 26, 1:34 pm, Lester Zick <dontbot...@nowhere.net> wrote:
On Sat, 26 Apr 2008 12:14:21 GMT, Aatu Koskensilta
So if someone demonstrates he was, in fact, at home yesterday that's
mathematics?
If he can demonstrate the proposition exhaustively, yes. Usually such
things are demonstrated inexhaustively, through testimony and so on.
Typically if the proposition can be demonstrated exhaustively as a
necessary truth, the result is mathematical regardless of how trivial.
No. Mathematics is NEVER "true" which is to say conforms to reality.
There is a great error out there today in science which states that
somehow mathematics is MORE real than reality. This is a COMPLETE
misunderstanding of what mathematics is!
Mathematics are logical models which may or may not relate or
approximately describe (predict) reality. Beyond that mathematics has
NO connection with reality. People like to assume that mathematics
comes out of reality like 1 + 1 = 2. But that is not where it comes
from. Indeed that is a APPLICATION of just ONE mathematical system as
a model ONTO reality!
So do parallel lines meet at "infinity" or do they not meet there?
Mathematics doesn't give a damn which. What mathematics cares about is
that one STARTS with a given premise and then logically develops a
SYSTEM based upon that premise. The "correctness" of mathematics has
ONLY to do with how carefully and correctly the steps used to develop
the system were done. Whether or not the final system is a model of
ANYTHING is irrelevant! When one says 1+1 = 2 is "true",
mathematically one only means that the logic and rules followed to
develop arithmetic were followed precisely and correctly. It has
NOTHING to do with the existence of two separate apples creating a
pair! But oddly enough we find that one particular system of
arithmetic seems to work pretty well as a MODEL to predict what
happens when I've got several boxes of apples and start arranging them
in groups!
Therefore ANY practical matter such as being home or not at home has
NOTHING to do with mathematics! The logical system you might use to
"prove" a given fact of reality is mathematics, but truth is that
mathematics can NEVER "prove" reality because mathematics itself is
not "real".
Once those in our science departments figure this out science will
make a great leap forward!
~v~~ |
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