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| John Jones... |
 Posted: Fri Oct 30, 2009 7:02 pm |
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To begin this definition of a set I will describe the difference between
"necessary" and "sufficient" conditions:
Being a frog is a sufficient condition for being an amphibian, while a
set of legs, three-chambered heart, etc, are necessary conditions for
being an amphibian.
PROPOSALS
A minimal definition of a set is that it is a totality of necessary
conditions or elements . There is no possibility for the set "the set of
unnecessary elements". If we expand the compressed name for the set "the
set of unnecessary elements" we have "the set A of unnecessary elements
for the set B".
A necessary condition is an element in a set, and the set is a name for
a totality of necessary conditions. The totality of necessary conditions
is not a subset of a sufficient condition but is given as a possibility
of it.
DISCUSSION
That is, "sufficient conditions" identify objects, but "necessary
conditions" do not identify objects, except through a sufficient
condition. A stand-alone set is, accordingly, not re-identifiable and is
not an object. It follows that subsets, and sets of sets are also not
objects until their possibility is given through a sufficient condition. |
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| Peter Webb... |
| Posted: Fri Oct 30, 2009 9:47 pm |
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Dear Musatov now posting as Mr Jones:
"John Jones" <jonescardiff at (no spam) btinternet.com> wrote in message
news:hcg2av$pan$1 at (no spam) news.eternal-september.org...
[quote]To begin this definition of a set I will describe the difference between
"necessary" and "sufficient" conditions:
Being a frog is a sufficient condition for being an amphibian, while a set
of legs, three-chambered heart, etc, are necessary conditions for being an
amphibian.
[/quote]
This a a maths newsgroup. "Neccesary" and "sufficient" are already well
defined terms, known I suspect by almost everybody here, and such knowledge
is not dependent upon the reader knowing the number of heart chambers that
salamanders and newts have (which I don't know).
I will assume that you are using the normal mathematical definitions of
"neccessary" and "sufficient" and this stuff about frogs is completely
irrelevant to any mathematical argument you may wish to advance.
[quote]
PROPOSALS
A minimal definition of a set is that it is a totality of necessary
conditions or elements .
[/quote]
Ok, give me your definition (as a totality of necessary conditions or
elements) of the set {{}}.
[quote]There is no possibility for the set "the set of unnecessary elements".
[/quote]
Whilst mathematics provides a standard definition of "neccessary", I know of
no mathematical definition of "unnecessary" (as opposed to "not neccesary")
let alone "unnecessary elements". You need to define this.
[quote]If we expand the compressed name for the set "the set of unnecessary
elements" we have "the set A of unnecessary elements for the set B".
[/quote]
Still don't know what an "uneccesary element" is.
[quote]A necessary condition is an element in a set,
[/quote]
Maybe you do have some completely different meaning for the word
"neccesary". In mathematics, the word "neccesary" in this sort of context
refers to statements that can have truth values, not elements of sets. Thus
it is neccesary that primes greater than 2 are odd, but "7" is not a
"neccesary" element of a set of prime numbers.
[quote]and the set is a name for a totality of necessary conditions.
[/quote]
Again, what then is the name of {{}} ?
[quote]The totality of necessary conditions is not a subset of a sufficient
condition but is given as a possibility of it.
[/quote]
So "conditions" are sets? And what does "totality" mean here exactly? The
union of some things indexed by something else? What things exactly?
Hopefully one day your interest in mathematics may cause you to study it at
University or at least at some level more sophisticated than junior high
school. When you do that, you will learn that unless you define your terms,
your conclusions based on those terms are meaningless. Like everything you
have posted above. |
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| Jim Burns... |
| Posted: Sat Oct 31, 2009 7:23 am |
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John Jones wrote:
[...]
[quote]A minimal definition of a set is that it is
a totality of necessary conditions or elements .
[...]
and the set is a name for
a totality of necessary conditions.
[...][/quote]
:
:'You are sad,' the Knight said in an anxious tone:
:'let me sing you a song to comfort you.'
:
:'Is it very long?' Alice asked, for she had heard
:a good deal of poetry that day.
:
:'It's long,' said the Knight, 'but very, VERY beautiful.
:Everybody that hears me sing it--either it brings the
:TEARS into their eyes, or else--'
:
:'Or else what?' said Alice, for the Knight had made
:a sudden pause.
:
:'Or else it doesn't, you know. The name of the song
:is called "HADDOCKS' EYES."'
:
:'Oh, that's the name of the song, is it?' Alice said,
:trying to feel interested.
:
:'No, you don't understand,' the Knight said, looking
:a little vexed. 'That's what the name is CALLED.
:The name really IS "THE AGED AGED MAN."'
:
:'Then I ought to have said "That's what the SONG is
:called"?' Alice corrected herself.
:
:'No, you oughtn't: that's quite another thing!
:The SONG is called "WAYS AND MEANS": but that's only
:what it's CALLED, you know!'
:
:'Well, what IS the song, then?' said Alice, who was
:by this time completely bewildered.
:
:'I was coming to that,' the Knight said. 'The song
:really IS "A-SITTING ON A GATE": and the tune's
:my own invention.'
:
http://www.gutenberg.org/files/12/12.txt
/Through the Looking-Glass/, by Lewis Carroll,
from CHAPTER VIII. 'It's my own Invention' |
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| John Jones... |
| Posted: Sat Oct 31, 2009 7:38 pm |
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Guest
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Peter Webb wrote:
[quote]Dear Musatov now posting as Mr Jones:
"John Jones" <jonescardiff at (no spam) btinternet.com> wrote in message
news:hcg2av$pan$1 at (no spam) news.eternal-september.org...
To begin this definition of a set I will describe the difference
between "necessary" and "sufficient" conditions:
Being a frog is a sufficient condition for being an amphibian, while a
set of legs, three-chambered heart, etc, are necessary conditions for
being an amphibian.
This a a maths newsgroup. "Neccesary" and "sufficient" are already well
defined terms, known I suspect by almost everybody here, and such
knowledge is not dependent upon the reader knowing the number of heart
chambers that salamanders and newts have (which I don't know).
[/quote]
If you had written any academic essays on the philosophy or foundations
of logic and mathematics, then you would know that you begin by stating
the commonly understood before moving on to related themes.
[quote]I will assume that you are using the normal mathematical definitions of
"neccessary" and "sufficient" and this stuff about frogs is completely
irrelevant to any mathematical argument you may wish to advance.
[/quote]
Don't be stupid Peter. It looks like you are saying that there is a
complete, irreconcilable, severance between common terms and
understandings, and mathematics. I don't think you will get far
academically, or publicly, holding that position.
[quote]A minimal definition of a set is that it is a totality of necessary
conditions or elements .
Ok, give me your definition (as a totality of necessary conditions or
elements) of the set {{}}.
[/quote]
A set has elements as necessary conditions, i.e. they are necessarily
"in" the set. Why? As mathematics has no contingent possibilities it
follows that for any mathematical set, its elements are necessarily in
the set.
[quote]
There is no possibility for the set "the set of unnecessary elements".
Whilst mathematics provides a standard definition of "neccessary", I
know of no mathematical definition of "unnecessary" (as opposed to "not
neccesary") let alone "unnecessary elements". You need to define this.
[/quote]
Unnecessary elements are contingent elements.
[quote]
A necessary condition is an element in a set,
Maybe you do have some completely different meaning for the word
"neccesary". In mathematics, the word "neccesary" in this sort of
context refers to statements that can have truth values, not elements of
sets.
[/quote]
A truth value, and a variable, I would remind you, are not mathematical
descriptions until they are fixed, non-mathematically, as a value.
[quote]Thus it is neccesary that primes greater than 2 are odd, but "7"
is not a "neccesary" element of a set of prime numbers.
[/quote]
You are treating the appearance of "7" as if it is a numeral. But the
appearances of the number "7" are necessary.
[quote]
and the set is a name for a totality of necessary conditions.
Again, what then is the name of {{}} ?
[/quote]
The subset isn't a set. The name of the set you have already given. And
there is only one set. It is {{}}. The inner brackets show elements, not
sets. I would have thought that that was fairly obvious.
[quote]
The totality of necessary conditions is not a subset of a sufficient
condition but is given as a possibility of it.
So "conditions" are sets?
[/quote]
Yes you right. That's lazy of me. A set is comprised of elements, each
and every one of which is a necessary condition.
[quote]And what does "totality" mean here exactly?
[/quote]
A Totality is a count of elements. Whereas a whole, or sufficient
condition, manifests or collects the elements. The set is the name, not
of the elements, but of the sufficient condition.
[quote]The union of some things indexed by something else? What things exactly?
[/quote]
A set is not identified or indexed through its elements or necessary
conditions. The elements of a set are identified through a necessary
condition. The name of that necessary condition is the name of the set.
Otherwise, the set of elements becomes an element itself.
[quote]
Hopefully one day your interest in mathematics may cause you to study it
at University or at least at some level more sophisticated than junior
high school. When you do that, you will learn that unless you define
your terms, your conclusions based on those terms are meaningless. Like
everything you have posted above.
[/quote]
I write how I was taught to write for my MA in analytic philosophy.
What's the point of getting centric about it? |
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| Aatu Koskensilta... |
| Posted: Sat Oct 31, 2009 9:15 pm |
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Guest
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John Jones <jonescardiff at (no spam) btinternet.com> writes:
[quote]I write how I was taught to write for my MA in analytic
philosophy.
[/quote]
You're too modest.
--
Aatu Koskensilta (aatu.koskensilta at (no spam) uta.fi)
"Wovon mann nicht sprechen kann, darüber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus |
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| John Jones... |
| Posted: Sun Nov 01, 2009 7:08 am |
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Guest
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John Jones wrote:
[quote]Peter Webb wrote:
Dear Musatov now posting as Mr Jones:
"John Jones" <jonescardiff at (no spam) btinternet.com> wrote in message
news:hcg2av$pan$1 at (no spam) news.eternal-september.org...
To begin this definition of a set I will describe the difference
between "necessary" and "sufficient" conditions:
Being a frog is a sufficient condition for being an amphibian, while
a set of legs, three-chambered heart, etc, are necessary conditions
for being an amphibian.
This a a maths newsgroup. "Neccesary" and "sufficient" are already
well defined terms, known I suspect by almost everybody here, and such
knowledge is not dependent upon the reader knowing the number of heart
chambers that salamanders and newts have (which I don't know).
If you had written any academic essays on the philosophy or foundations
of logic and mathematics, then you would know that you begin by stating
the commonly understood before moving on to related themes.
I will assume that you are using the normal mathematical definitions
of "neccessary" and "sufficient" and this stuff about frogs is
completely irrelevant to any mathematical argument you may wish to
advance.
Don't be stupid Peter. It looks like you are saying that there is a
complete, irreconcilable, severance between common terms and
understandings, and mathematics. I don't think you will get far
academically, or publicly, holding that position.
A minimal definition of a set is that it is a totality of necessary
conditions or elements .
Ok, give me your definition (as a totality of necessary conditions or
elements) of the set {{}}.
A set has elements as necessary conditions, i.e. they are necessarily
"in" the set. Why? As mathematics has no contingent possibilities it
follows that for any mathematical set, its elements are necessarily in
the set.
There is no possibility for the set "the set of unnecessary elements".
Whilst mathematics provides a standard definition of "neccessary", I
know of no mathematical definition of "unnecessary" (as opposed to
"not neccesary") let alone "unnecessary elements". You need to define
this.
Unnecessary elements are contingent elements.
A necessary condition is an element in a set,
Maybe you do have some completely different meaning for the word
"neccesary". In mathematics, the word "neccesary" in this sort of
context refers to statements that can have truth values, not elements
of sets.
A truth value, and a variable, I would remind you, are not mathematical
descriptions until they are fixed, non-mathematically, as a value.
Thus it is neccesary that primes greater than 2 are odd, but "7" is
not a "neccesary" element of a set of prime numbers.
You are treating the appearance of "7" as if it is a numeral. But the
appearances of the number "7" are necessary.
and the set is a name for a totality of necessary conditions.
Again, what then is the name of {{}} ?
The subset isn't a set. The name of the set you have already given. And
there is only one set. It is {{}}. The inner brackets show elements, not
sets. I would have thought that that was fairly obvious.
The totality of necessary conditions is not a subset of a sufficient
condition but is given as a possibility of it.
So "conditions" are sets?
Yes you right. That's lazy of me. A set is comprised of elements, each
and every one of which is a necessary condition.
And what does "totality" mean here exactly?
A Totality is a count of elements. Whereas a whole, or sufficient
condition, manifests or collects the elements. The set is the name, not
of the elements, but of the sufficient condition.
The union of some things indexed by something else? What things exactly?
A set is not identified or indexed through its elements or necessary
conditions. The elements of a set are identified through a necessary
condition. The name of that necessary condition is the name of the set.
Otherwise, the set of elements becomes an element itself.
[/quote]
That should read "sufficient", and not "necessary" condition. So the
elements of a set are NAMED as necessary conditions, and are IDENTIFIED
through a sufficient condition. |
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| Tegiri Nenashi... |
| Posted: Mon Nov 02, 2009 2:02 pm |
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Guest
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On Oct 31, 5:38 pm, John Jones <jonescard... at (no spam) btinternet.com> wrote:
[quote]Peter Webb wrote:
Ok, give me your definition (as a totality of necessary conditions or
elements) of the set {{}}.
A set has elements as necessary conditions, i.e. they are necessarily
"in" the set. Why? As mathematics has no contingent possibilities it
follows that for any mathematical set, its elements are necessarily in
the set.
[/quote]
What about negative set (the one that has elements removed)? Are those
removed elements "necessarily in the set", or outside the set? |
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| Tegiri Nenashi... |
| Posted: Tue Nov 03, 2009 3:03 pm |
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On Nov 3, 2:34 pm, John Jones <jonescard... at (no spam) btinternet.com> wrote:
[quote]Tegiri Nenashi wrote:
On Oct 31, 5:38 pm, John Jones <jonescard... at (no spam) btinternet.com> wrote:
Peter Webb wrote:
Ok, give me your definition (as a totality of necessary conditions or
elements) of the set {{}}.
A set has elements as necessary conditions, i.e. they are necessarily
"in" the set. Why? As mathematics has no contingent possibilities it
follows that for any mathematical set, its elements are necessarily in
the set.
What about negative set (the one that has elements removed)? Are those
removed elements "necessarily in the set", or outside the set?
The elements are in the set, where "absence of elements" goes proxy for
them. There's no ontological priorities in mathematics.
[/quote]
Well, unlike your writings demonstration that there can't be "negative
set" (I was kidding) is nothing short of elegance.
For any set x we have
x v {} = x <--- from definition of empty set
x v x = x <--- idempotence
x v (-x) = {} <--- the alleged negative set definition
Then we come to contradiction:
(x v x) v (-x) = {}
x v (x v (-x)) = x
P.S. "idempotence"... Why am I posting in these impotent threads? |
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| John Jones... |
| Posted: Tue Nov 03, 2009 5:34 pm |
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Tegiri Nenashi wrote:
[quote]On Oct 31, 5:38 pm, John Jones <jonescard... at (no spam) btinternet.com> wrote:
Peter Webb wrote:
Ok, give me your definition (as a totality of necessary conditions or
elements) of the set {{}}.
A set has elements as necessary conditions, i.e. they are necessarily
"in" the set. Why? As mathematics has no contingent possibilities it
follows that for any mathematical set, its elements are necessarily in
the set.
What about negative set (the one that has elements removed)? Are those
removed elements "necessarily in the set", or outside the set?
[/quote]
The elements are in the set, where "absence of elements" goes proxy for
them. There's no ontological priorities in mathematics. |
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| John Jones... |
| Posted: Wed Nov 04, 2009 2:37 pm |
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Tegiri Nenashi wrote:
[quote]On Nov 3, 2:34 pm, John Jones <jonescard... at (no spam) btinternet.com> wrote:
Tegiri Nenashi wrote:
On Oct 31, 5:38 pm, John Jones <jonescard... at (no spam) btinternet.com> wrote:
Peter Webb wrote:
Ok, give me your definition (as a totality of necessary conditions or
elements) of the set {{}}.
A set has elements as necessary conditions, i.e. they are necessarily
"in" the set. Why? As mathematics has no contingent possibilities it
follows that for any mathematical set, its elements are necessarily in
the set.
What about negative set (the one that has elements removed)? Are those
removed elements "necessarily in the set", or outside the set?
The elements are in the set, where "absence of elements" goes proxy for
them. There's no ontological priorities in mathematics.
Well, unlike your writings demonstration that there can't be "negative
set" (I was kidding) is nothing short of elegance.
For any set x we have
x v {} = x <--- from definition of empty set
x v x = x <--- idempotence
x v (-x) = {} <--- the alleged negative set definition
Then we come to contradiction:
(x v x) v (-x) = {}
x v (x v (-x)) = x
P.S. "idempotence"... Why am I posting in these impotent threads?
[/quote]
I would point out that terms like "empty" or "absent" have no place in
mathematics except as a technical jargon. Otherwise we read them as
ontological terms, and mathematics doesn't deal with ontology (the type
of space, or the way in which things exist).
Whether p is here, there, somewhere else, hidden, "absent but here in
thought", etc etc., makes no difference. It's still p. |
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