Numerals

[James Malone]

Hi IAOers,

I'm trying to align some IAO work with some software projects we have.
You have the class numeral (I presume instead of number) but you also
have classes that have as part of their name the word "number", e.g.
lot number, serial number, version number. Is that intentional or
will they be changed to serial numeral, lot numeral, telephone numeral
and so on? I would love to hear that "number" is indeed a class in
reality but I suspect that is not what I'm going to hear :)

James


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[Frank Gibson]

On Thu, Dec 3, 2009 at 5:34 PM, James Malone <james....@gmail.com> wrote:

Hi IAOers,

I'm trying to align some IAO work with some software projects we have.
You have the class numeral (I presume instead of number) but you also
have classes that have as part of their name the word "number", e.g.
lot number, serial number, version number.  Is that intentional or
will they be changed to serial numeral, lot numeral, telephone numeral
and so on? I would love to hear that "number" is indeed a class in
reality but I suspect that is not what I'm going to hear :)

Number and Numeral are used interchangeable as synonyms, wether you agree with that or not. Excluding one over the other will just cause confusion in the real world for your users. In addition, you say that a numeral is a symbol for a number, but if numbers dont exits then you cant use them in the definition either.

Frank




 

James


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[Barry Smith]

'Number' and 'numeral' should not be used as synonyms. A numeral (I
think) is the name of a number in the mathematical sense. But not
everything that is called 'number' is a number in the mathematical
sense. Thus as credit card number is not a number in the mathematical
sense. The test of whether an X number is a number in the
mathematical sense is: does it makes sense to add two of them together.
BS

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[Pat Hayes]

On Dec 4, 2009, at 5:25 AM, Frank Gibson wrote:

On Thu, Dec 3, 2009 at 5:34 PM, James Malone <james....@gmail.com> wrote:

Hi IAOers,

I'm trying to align some IAO work with some software projects we have.
You have the class numeral (I presume instead of number) but you also
have classes that have as part of their name the word "number", e.g.
lot number, serial number, version number.  Is that intentional or
will they be changed to serial numeral, lot numeral, telephone numeral
and so on? I would love to hear that "number" is indeed a class in
reality but I suspect that is not what I'm going to hear :)

Number and Numeral are used interchangeable as synonyms, wether you agree with that or not.

Its nothing to do with who agrees with what. As a matter of plain fact, numerals are not numbers. Now, people in the 'real' world often use the term "number" to refer to a numeral, and perhaps, though more rarely, the opposite: but that linguistic quirk does not make numbers into numerals, any more than calling a whale a fish stops it being a mammal. 

Excluding one over the other will just cause confusion in the real world for your users.

I agree that we are unlikely to change linguistic habits like this and should not attempt to do so. However, the *ontology* had better keep the distinction clear. 

Pat Hayes

In addition, you say that a numeral is a symbol for a number, but if numbers dont exits then you cant use them in the definition either.

Frank




 

James


--
European Bioinformatics Institute,
Cambridge, CB10 1SD,
United Kingdom
Tel numeral: + 44 (0) 1223 494 676
Fax numeral: + 44 (0) 1223 492 468

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[Albert Goldfain]

I agree with Barry that numbers and numerals should not be used as
synonyms. Here are some differences/points to be made:

(1) A numeral is a constituent of a larger numeration system (e.g.,
binary digits 00101, Roman numerals XVIII, Arabic numerals 234, tally
marks IIII, etc) which includes a syntactic rules for representing
arbitrarily large numbers ( See
http://en.wikipedia.org/wiki/Numeral_system and
http://books.google.com/books?id=uxMEi6kp0JkC ) and sometimes a way to
represent the distinctions between cardinals, ordinals, and nominals.

(2) A number is that which is represented by numerals. There are
different views in the phil of mathematics about what Barry called the
"mathematical sense of number"...I happen to like the structural
realist perspective (see http://books.google.com/books?id=9xVErjy9qPQC
) which makes numbers positions in structures...the slogan is "offices
not officeholders". I would say that numbers are those things that
make sense to *count* (not 'add' as barry said).

(3) We only know numbers via concretizations (am I using this IAO term
correctly?) of finite initial segments of the natural number
progression (and mathematical extensions to this progression for
integers, reals, complex numbers)...the most important developmentally
early such concretization is the fingers.

(4) We can do mathematics successfully because we come to
intersubjective alignment with other users of numeration systems, and
those numeration systems are successful only to the degree to which
they permit this alignment. If anyone doesn't believe this, I would
invite you to do next year's taxes in roman numerals :-)

(5) Socially constructed systems of number-like things like credit
card numbers and SSNs stand in a relationship with numeration systems
that could be worked out.

I could say a lot more on these issues, but I'd better stop :-)

-Albert

[James Malone]

Ok so I understand some of the thinking, however it seems the point
still stands there is no class 'number' presently and it appears to me
from all of these explanations, this class it still valid and should
be added to IAO, although not as a synonym for 'numeral'. So can we
have the class 'number' then please, albeit with some aboutness
relation to the class numeral?

James

[Barry Smith]

The Information Artifact Ontology is designed to be an information
artifact ontology. Artifacts (like 'MDCCCLXIII') are social
creations. Numbers (like 246321) are outside time and space. They are
not social creations. Therefore they are out of scope. If there is a
good practical reason to add 'number' to IAO, in addition to
'numeral', as a stopgap until James creates something like an
Abstract Entity Ontology which would serve as its proper home, I
would not object.
BS

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[Bjoern Peters]

James, am I guessing correctly that you want to have 'number' in as a parent class of e.g. social security number etc.? If I understand Barry correctly, he would object to have 'numeral' as the parent class. I also think he would object to have 'number' as the parent class. Instead, what I think we will need is something like 'numeric identifier' which as Albert wrote should stand in some relation to 'numeral'. I would guess that a numeric identifier stands in a equivalency relation (in the mathematical sense) to a numeral which can be used for checking to numeric identifiers for identity, and for efficient searches / sorting of lists of numeric identifiers.

- Bjoern

Bjoern Peters
Assistant Member
La Jolla Institute for Allergy and Immunology
9420 Athena Circle
La Jolla, CA 92037, USA
Tel: 858/752-6914
Fax: 858/752-6987
http://www.liai.org/pages/faculty-peters

[James Malone]

Indeed, my motivation comes from trying to understand what the class
numeral encapsulated - which it appears is a deeper thought process
than the present definition describes - and how classes can exist such
as 'serial "number"' and 'lot "number"' without the class 'number'. If
i understand correctly, Barry is suggesting that what IAO is really
trying to capture is the social convention behind the use of the word
number and it's meaning relevant to this use, which is more akin to a
label. I am grateful for the responses, my understanding has been
increased, however it still begs the question where the class 'number'
lives (within or without IAO)? I agree numeric identifier sounds about
right Bjoern and seems to meet Barry et al's scope.

James

[Frank Gibson]

On Mon, Dec 7, 2009 at 10:05 AM, James Malone <james....@gmail.com> wrote:

Indeed, my motivation comes from trying to understand what the class
numeral encapsulated - which it appears is a deeper thought process
than the present definition describes - and how classes can exist such
as 'serial "number"' and 'lot "number"' without the class 'number'. If
i understand correctly, Barry is suggesting that what IAO is really
trying to capture is the social convention behind the use of the word
number and it's meaning relevant to this use, which is more akin to a
label. I am grateful for the responses, my understanding has been
increased, however it still begs the question where the class 'number'
lives (within or without IAO)? I agree numeric identifier sounds about
right Bjoern and seems to meet Barry et al's scope.

So Barry's statement that "number" is out of scope of the IAO is a fair one. It would not be productive to re-model mathematics under IAO. However, I wonder how you can explicitly define a symbol for something that is "outside of time and space" without describing that thing that the symbol represents? However, I don't believe you can avoid the use of "number" as a label for a class. For example even if you make the statement that batch_number is a numeral, you have unintentionally stated that "number" is a synonymous label for numeral.

Numerical Identifier may be a way to cope with this, saying something like a numerical_identifier has_parts(or something equivalent). However, we also need letters of the alphabet, as not all batch_numbers are completely composed of numbers. I assume the alphabet presents the same issue, that it is a symbol for something outside time and space......

In addition, a clear statement that the mathematical sense of "number" is out of scope of IAO, as Barry put forward, may be helpful if associated with the definition of numeral, as some sort of editor comment.

Frank

 

[Pat Hayes]

On Dec 7, 2009, at 4:28 AM, Frank Gibson wrote:

On Mon, Dec 7, 2009 at 10:05 AM, James Malone <james....@gmail.com> wrote:

Indeed, my motivation comes from trying to understand what the class
numeral encapsulated - which it appears is a deeper thought process
than the present definition describes - and how classes can exist such
as 'serial "number"' and 'lot "number"' without the class 'number'. If
i understand correctly, Barry is suggesting that what IAO is really
trying to capture is the social convention behind the use of the word
number and it's meaning relevant to this use, which is more akin to a
label. I am grateful for the responses, my understanding has been
increased, however it still begs the question where the class 'number'
lives (within or without IAO)? I agree numeric identifier sounds about
right Bjoern and seems to meet Barry et al's scope.

So Barry's statement that "number" is out of scope of the IAO is a fair one. It would not be productive to re-model mathematics under IAO. However, I wonder how you can explicitly define a symbol for something that is "outside of time and space" without describing that thing that the symbol represents? However, I don't believe you can avoid the use of "number" as a label for a class. For example even if you make the statement that batch_number is a numeral, you have unintentionally stated that "number" is a synonymous label for numeral.

No, you havn't. There is nothing in any ontology formalism I know of that implies any relationship between entities on the basis of a similarity of their identifying strings. "Patrick_John_Hayes" refers to me, but that does not imply any relationship between me and something called a "trick". Similarly, calling something a "batch_number" does not imply any relationship between it an things called "number". 

BTW, I think Barry would want to say that 'batch numbers' and similar things are identifiers, which are numerical identifiers by virtue of being made up from numerical characters, but are *not* numerals, in that they do not denote numbers. So for example a credit card number is, for Barry, not a numeral as it is not intended to denote a natural number. Barry, correct me if I have this wrong.

Numerical Identifier may be a way to cope with this, saying something like a numerical_identifier has_parts(or something equivalent). However, we also need letters of the alphabet, as not all batch_numbers are completely composed of numbers. I assume the alphabet presents the same issue, that it is a symbol for something outside time and space......

No. The letter "a" does not denote anything in the way that the numeral "1" does. 

Pat

In addition, a clear statement that the mathematical sense of "number" is out of scope of IAO, as Barry put forward, may be helpful if associated with the definition of numeral, as some sort of editor comment.

PS. Its going to he hard for the IAO to absolutely forswear all reference to numbers. Its almost impossible to write a formal ontology without using numerals to denote numbers *somewhere*. 

[Barry Smith]

You are right.

>>Numerical Identifier may be a way to cope with this, saying
>>something like a numerical_identifier has_parts(or something
>>equivalent). However, we also need letters of the alphabet, as not
>>all batch_numbers are completely composed of numbers. I assume the
>>alphabet presents the same issue, that it is a symbol for something
>>outside time and space......
>
>No. The letter "a" does not denote anything in the way that the
>numeral "1" does.

Indeed
(which does not denote anything, either, perforce).
BS

>> <http://en.wikipedia.org/wiki/Numeral_system>http://en.wikipedia.org/wiki/Numeral_system
>> and
>> >> > >
>> <http://books.google.com/books?id=uxMEi6kp0JkC>http://books.google.com/books?id=uxMEi6kp0JkC

>> ) and sometimes a way to
>> >> > > represent the distinctions between cardinals, ordinals, and nominals.
>> >> > >
>> >> > > (2) A number is that which is represented by numerals. There are
>> >> > > different views in the phil of mathematics about what Barry
>> called the
>> >> > > "mathematical sense of number"...I happen to like the structural
>> >> > > realist perspective (see

>> <http://books.google.com/books?id=9xVErjy9qPQC>http://books.google.com/books?id=9xVErjy9qPQC

>> >> > > ) which makes numbers positions in structures...the slogan
>> is "offices
>> >> > > not officeholders". I would say that numbers are those things that
>> >> > > make sense to *count* (not 'add' as barry said).
>> >> > >
>> >> > > (3) We only know numbers via concretizations (am I using
>> this IAO term
>> >> > > correctly?) of finite initial segments of the natural number
>> >> > > progression (and mathematical extensions to this progression for
>> >> > > integers, reals, complex numbers)...the most important
>> developmentally
>> >> > > early such concretization is the fingers.
>> >> > >
>> >> > > (4) We can do mathematics successfully because we come to
>> >> > > intersubjective alignment with other users of numeration systems, and
>> >> > > those numeration systems are successful only to the degree to which
>> >> > > they permit this alignment. If anyone doesn't believe this, I would
>> >> > > invite you to do next year's taxes in roman numerals :-)
>> >> > >
>> >> > > (5) Socially constructed systems of number-like things like credit
>> >> > > card numbers and SSNs stand in a relationship with numeration systems
>> >> > > that could be worked out.
>> >> > >
>> >> > > I could say a lot more on these issues, but I'd better stop :-)
>> >> > >
>> >> > > -Albert
>> >> > >
>> >> > > On Fri, Dec 4, 2009 at 10:30 AM, Barry Smith

>> <<mailto:phis...@buffalo.edu>phis...@buffalo.edu>

>> >> > > wrote:
>> >> > >> 'Number' and 'numeral' should not be used as synonyms. A numeral (I
>> >> > >> think) is the name of a number in the mathematical sense. But not
>> >> > >> everything that is called 'number' is a number in the mathematical
>> >> > >> sense. Thus as credit card number is not a number in the
>> mathematical
>> >> > >> sense. The test of whether an X number is a number in the
>> >> > >> mathematical sense is: does it makes sense to add two of them
>> >> > >> together.
>> >> > >> BS
>> >> > >>
>> >> > >> At 06:25 AM 12/4/2009, Frank Gibson wrote:
>> >> > >>
>> >> > >>
>> >> > >>>On Thu, Dec 3, 2009 at 5:34 PM, James Malone

>> >> > >>><<mailto:james....@gmail.com><mailto:james.malone@gmail.

>> >> > <mailto:y...@googlegroups.com>y...@googlegroups.com

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>> > Assistant Member
>> > La Jolla Institute for Allergy and Immunology
>> > 9420 Athena Circle
>> > La Jolla, CA 92037, USA
>> > Tel: 858/752-6914
>> > Fax: 858/752-6987
>> >

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