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Definition of Mathematics (3)
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Zuhair
Mar 8, 2012, 1:37:12 AM3/8/12
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In prior two posts by the same title, I tried to define mathematics,
there were some pitfalls to those definitions; here is the latest of
my attempts:
"Mathematics is the class of all Cores of consistent formal systems".
In symbols:
Def.) Math = {x| x={M| Exist T. T is a consistent formal system & M is
a model of T}}
The idea of this definition is clear, the "Core" of any formal theory
is the entity that decided the choice of the primitives and axioms of
that theory; the axioms of the formal theory are nothing but
characterizations of the Core of it. Now the class of all models of a
formal theory is an object that stands for the Core of that theory,
every formal theory has one Core that is represented by the class of
all models of it. But one Core can be formalized by different equi-
interpretable formal systems.
Def.) Formal mathematics is the class of all consistent formal
systems.
Now a formal empirical theory is just a particular model of an
element of formal mathematics in which every element in the domain of
that model is verifiable to exist on empirical bases, it must not be
confused with the core of that formal system.
Whether or not we may consider the core of a formal physical theory
to have physical existence is something more related to philosophy of
mathematics than it to mathematics.
Zuhair
there were some pitfalls to those definitions; here is the latest of
my attempts:
"Mathematics is the class of all Cores of consistent formal systems".
In symbols:
Def.) Math = {x| x={M| Exist T. T is a consistent formal system & M is
a model of T}}
The idea of this definition is clear, the "Core" of any formal theory
is the entity that decided the choice of the primitives and axioms of
that theory; the axioms of the formal theory are nothing but
characterizations of the Core of it. Now the class of all models of a
formal theory is an object that stands for the Core of that theory,
every formal theory has one Core that is represented by the class of
all models of it. But one Core can be formalized by different equi-
interpretable formal systems.
Def.) Formal mathematics is the class of all consistent formal
systems.
Now a formal empirical theory is just a particular model of an
element of formal mathematics in which every element in the domain of
that model is verifiable to exist on empirical bases, it must not be
confused with the core of that formal system.
Whether or not we may consider the core of a formal physical theory
to have physical existence is something more related to philosophy of
mathematics than it to mathematics.
Zuhair
Rupert
Mar 8, 2012, 10:41:07 AM3/8/12
to
Do all formal systems include classical first-order logic? Or is some
broader range of logics allowed? And presumably all formal systems are
recursively enumerable?
In my view a satisfactory definition of mathematics would have to be
able to explain why mathematicians are interested in some consistent
formal systems more than others.
Zuhair
Mar 8, 2012, 1:20:10 PM3/8/12
to
your mind is another concept! you can call it: Effective Mathematics,
or something like that sort, in which we may add further
specifications to the definition.
Zuhair
Zuhair
Mar 9, 2012, 2:43:41 AM3/9/12
to
On Mar 8, 6:41 pm, Rupert <rupertmccal...@yahoo.com> wrote:
MoeBlee
Mar 10, 2012, 2:24:41 PM3/10/12
to
On Mar 8, 12:37 am, Zuhair <zaljo...@gmail.com> wrote:
> Math = {x| x={M| Exist T. T is a consistent formal system & M is
> a model of T}}
Why do write it that way when it's just:
> Math = {x| x={M| Exist T. T is a consistent formal system & M is
> a model of T}}
{{M | ET(T is a consistent theory and M is a model of T)}}
But every model is a model of some consistent theory.
What you've written is the singleton whose only member is the class of
all models. But the class of all models is a proper class. In what
theory do you allow a proper class to be member of a singleton?
And I really don't see that mathematics is equal to a singleton.
Mathematics is a subject matter. It's not, by any ordinary notion,
some particular singleton set.
MoeBlee
Zuhair
Mar 10, 2012, 3:32:32 PM3/10/12
to
Math = {x| Exist T. x={M| M is a model of T} }
Thanks!
Zuhair
MoeBlee
Mar 10, 2012, 3:51:06 PM3/10/12
to
On Mar 10, 2:32 pm, Zuhair <zaljo...@gmail.com> wrote:
> Ok, you are right actually, it should be
>
> Math = {x| Exist T. x={M| M is a model of T} }
>
> Thanks!
But who in the world would regard mathematics as a particular
> Ok, you are right actually, it should be
>
> Math = {x| Exist T. x={M| M is a model of T} }
>
> Thanks!
singleton?
And it doesn't even make sense for a proper class (the class of all
models, since every model is a model of some theory T) to be a member
of another set or class. And why even nest it in a singleton? Why not
just refer to the class of all models? Even so, though, who in the
world would regard mathematics as the class of all models?
MoeBlee
Zuhair
Mar 10, 2012, 4:09:57 PM3/10/12
to
On Mar 10, 11:51 pm, MoeBlee <modem...@gmail.com> wrote:
> On Mar 10, 2:32 pm, Zuhair <zaljo...@gmail.com> wrote:
>
> > Ok, you are right actually, it should be
>
> > Math = {x| Exist T. x={M| M is a model of T} }
>
> > Thanks!
>
> But who in the world would regard mathematics as a particular
> singleton?
>
No this is not a particular singleton at all, why you think it is
> On Mar 10, 2:32 pm, Zuhair <zaljo...@gmail.com> wrote:
>
> > Ok, you are right actually, it should be
>
> > Math = {x| Exist T. x={M| M is a model of T} }
>
> > Thanks!
>
> But who in the world would regard mathematics as a particular
> singleton?
>
singleton.
Zuhair
Zuhair
Mar 10, 2012, 4:23:39 PM3/10/12
to
On Mar 10, 11:51 pm, MoeBlee <modem...@gmail.com> wrote:
discovered a typo in my definition. Your last replay is not speaking
about my definition at all!
Zuhair
MoeBlee
Mar 10, 2012, 5:42:54 PM3/10/12
to
On Mar 10, 3:09 pm, Zuhair <zaljo...@gmail.com> wrote:
> No this is not a particular singleton at all, why you think it is
> singleton.
I overlooked how you changed it.
> No this is not a particular singleton at all, why you think it is
> singleton.
Anyway, I don't think mathematics is a class of classes of models.
MoeBlee
Transfer Principle
Mar 11, 2012, 12:26:37 AM3/11/12
to
On Mar 7, 10:37 pm, Zuhair <zaljo...@gmail.com> wrote:
> In prior two posts by the same title, I tried to define mathematics,
> there were some pitfalls to those definitions; here is the latest of
> my attempts:
The de facto definition of "mathematics" on sci.math is:
> In prior two posts by the same title, I tried to define mathematics,
> there were some pitfalls to those definitions; here is the latest of
> my attempts:
-- Mathematics is what one posts to sci.math oneself.
-- Non-mathematics is what one's opponent posts to sci.math.
Of course, no one will ever admit that this is the definition of
mathematics that he uses, but we see time and time again that no
poster ever gives his opponent credit for doing mathematics.
> "Mathematics is the class of all Cores of consistent formal systems".
the majority doesn't consider it to be mathematics. If the system
lacks formal rigor or consistency, the poster is criticized (and
accused of not fully understanding "mathematics"). But otherwise
if the system is sufficiently rigorous, the poster is ignored. In
neither case does the majority acknowledge that the OP is doing
mathematics that just happens to be nonstandard.
FredJeffries
Mar 11, 2012, 12:14:23 PM3/11/12
to
On Mar 10, 10:26 pm, Transfer Principle <david.l.wal...@lausd.net>
wrote:
mathematics and things like algebra, geometry, calculus, ... are non-
mathematics.
wrote:
>
> The de facto definition of "mathematics" on sci.math is:
>
> -- Mathematics is what one posts to sci.math oneself.
> -- Non-mathematics is what one's opponent posts to sci.math.
Therefore your crying and whining and self-righteousness is
> The de facto definition of "mathematics" on sci.math is:
>
> -- Mathematics is what one posts to sci.math oneself.
> -- Non-mathematics is what one's opponent posts to sci.math.
mathematics and things like algebra, geometry, calculus, ... are non-
mathematics.
Fabrizio J Bonsignore
Mar 11, 2012, 2:13:25 PM3/11/12
to
That s an extensive definition, so begin adding cartoons and drawings
here to call it math, can you tell me what function gives a Human face
profile continuous plot on (x,y) and some angles? You are making
Origami with symbols and ideas.
Danilo J Bonsignore
here to call it math, can you tell me what function gives a Human face
profile continuous plot on (x,y) and some angles? You are making
Origami with symbols and ideas.
Danilo J Bonsignore
Fabrizio J Bonsignore
Mar 11, 2012, 2:21:17 PM3/11/12
to
The true meaning of mathematics is... to find the set of all equal
objects under the maximum number of equality classes.
Danilo J Bonsignore
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Edward Green View profile
More options Nov 19 2010, 9:20 pm
Newsgroups: sci.math, sci.physics, sci.econ
From: Edward Green <spamspamsp...@netzero.com>
Date: Fri, 19 Nov 2010 17:20:59 -0800 (PST)
Local: Fri, Nov 19 2010 9:20 pm
Subject: Re: A math definition of mathermatics!
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On Nov 19, 7:01 pm, Fabrizio J Bonsignore <synto...@gmail.com> wrote:
> The true meaning of mathematics is... to find the set of all equal
> objects under the maximum number of equality classes.
Would you mind explaining that a little more fully?
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Efftard K. Donglemeier View profile
More options Nov 20 2010, 2:17 am
Newsgroups: sci.math, sci.physics, sci.econ
From: "Efftard K. Donglemeier" <c...@clownpenis.fart>
Date: Fri, 19 Nov 2010 22:17:45 -0800
Local: Sat, Nov 20 2010 2:17 am
Subject: Re: A math definition of mathermatics!
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Lern hau two speling teh mathematics, you google-posting dago.
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jmfbahciv View profile
More options Nov 20 2010, 10:09 am
Newsgroups: sci.math, sci.physics, sci.econ
From: jmfbahciv <See.ab...@aol.com>
Date: 20 Nov 2010 14:09:44 GMT
Local: Sat, Nov 20 2010 10:09 am
Subject: Re: A math definition of mathermatics!
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Efftard K. Donglemeier wrote:
> Lern hau two speling teh mathematics, you google-posting dago.
He knows how to spell google. He's making a mess of his
ASCII English on purpose.
/BAH
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Fabrizio J Bonsignore View profile
More options Nov 23 2010, 10:18 pm
Newsgroups: sci.math, sci.physics, sci.econ
From: Fabrizio J Bonsignore <synto...@gmail.com>
Date: Tue, 23 Nov 2010 18:18:41 -0800 (PST)
Local: Tues, Nov 23 2010 10:18 pm
Subject: Re: A math definition of mathermatics!
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On Nov 19, 8:20 pm, Edward Green <spamspamsp...@netzero.com> wrote:
> Would you mind explaining that a little more fully?
But that is the point!
Danilo J Bonsignore
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Fabrizio J Bonsignore View profile
More options Nov 23 2010, 10:19 pm
Newsgroups: sci.math, sci.physics, sci.econ
From: Fabrizio J Bonsignore <synto...@gmail.com>
Date: Tue, 23 Nov 2010 18:19:59 -0800 (PST)
Local: Tues, Nov 23 2010 10:19 pm
Subject: Re: A math definition of mathermatics!
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On Nov 20, 9:09 am, jmfbahciv <See.ab...@aol.com> wrote:
> Efftard K. Donglemeier wrote:
> > Lern hau two speling tehmathematics, you google-posting dago.
> He knows how to spell google. He's making a mess of his
> ASCII English on purpose.
> /BAH
Mather(ma(tics)) Sorry...
Danilo J Bonsignore
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Fabrizio J Bonsignore View profile
More options Dec 13 2010, 10:30 am
Newsgroups: sci.math, sci.physics, sci.econ
From: Fabrizio J Bonsignore <synto...@gmail.com>
Date: Mon, 13 Dec 2010 06:30:23 -0800 (PST)
Local: Mon, Dec 13 2010 10:30 am
Subject: Re: A math definition of mathermatics!
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No one minded that it is a self recursive and asymptotic definition?
Computable.
Danilo J Bonsignore
objects under the maximum number of equality classes.
Danilo J Bonsignore
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Edward Green View profile
More options Nov 19 2010, 9:20 pm
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From: Edward Green <spamspamsp...@netzero.com>
Date: Fri, 19 Nov 2010 17:20:59 -0800 (PST)
Local: Fri, Nov 19 2010 9:20 pm
Subject: Re: A math definition of mathermatics!
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On Nov 19, 7:01 pm, Fabrizio J Bonsignore <synto...@gmail.com> wrote:
> The true meaning of mathematics is... to find the set of all equal
> objects under the maximum number of equality classes.
Would you mind explaining that a little more fully?
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Efftard K. Donglemeier View profile
More options Nov 20 2010, 2:17 am
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From: "Efftard K. Donglemeier" <c...@clownpenis.fart>
Date: Fri, 19 Nov 2010 22:17:45 -0800
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Subject: Re: A math definition of mathermatics!
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Lern hau two speling teh mathematics, you google-posting dago.
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jmfbahciv View profile
More options Nov 20 2010, 10:09 am
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From: jmfbahciv <See.ab...@aol.com>
Date: 20 Nov 2010 14:09:44 GMT
Local: Sat, Nov 20 2010 10:09 am
Subject: Re: A math definition of mathermatics!
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Efftard K. Donglemeier wrote:
> Lern hau two speling teh mathematics, you google-posting dago.
He knows how to spell google. He's making a mess of his
ASCII English on purpose.
/BAH
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Fabrizio J Bonsignore View profile
More options Nov 23 2010, 10:18 pm
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From: Fabrizio J Bonsignore <synto...@gmail.com>
Date: Tue, 23 Nov 2010 18:18:41 -0800 (PST)
Local: Tues, Nov 23 2010 10:18 pm
Subject: Re: A math definition of mathermatics!
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On Nov 19, 8:20 pm, Edward Green <spamspamsp...@netzero.com> wrote:
> Would you mind explaining that a little more fully?
But that is the point!
Danilo J Bonsignore
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Fabrizio J Bonsignore View profile
More options Nov 23 2010, 10:19 pm
Newsgroups: sci.math, sci.physics, sci.econ
From: Fabrizio J Bonsignore <synto...@gmail.com>
Date: Tue, 23 Nov 2010 18:19:59 -0800 (PST)
Local: Tues, Nov 23 2010 10:19 pm
Subject: Re: A math definition of mathermatics!
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On Nov 20, 9:09 am, jmfbahciv <See.ab...@aol.com> wrote:
> Efftard K. Donglemeier wrote:
> > Lern hau two speling tehmathematics, you google-posting dago.
> He knows how to spell google. He's making a mess of his
> ASCII English on purpose.
> /BAH
Mather(ma(tics)) Sorry...
Danilo J Bonsignore
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Fabrizio J Bonsignore View profile
More options Dec 13 2010, 10:30 am
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From: Fabrizio J Bonsignore <synto...@gmail.com>
Date: Mon, 13 Dec 2010 06:30:23 -0800 (PST)
Local: Mon, Dec 13 2010 10:30 am
Subject: Re: A math definition of mathermatics!
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No one minded that it is a self recursive and asymptotic definition?
Computable.
Danilo J Bonsignore
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