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Re: [ontolog-forum] [ontology-summit] Estimating number of all known fac

from [John Bottoms] [Permanent Link][Original]
To: ontolog-forum@xxxxxxxxxxxxxxxx
From: John Bottoms <john@xxxxxxxxxxxxxxxxxxxx>
Date: Thu, 24 May 2012 14:09:01 -0400
Message-id: <4FBE793D.7010609@xxxxxxxxxxxxxxxxxxxx>
Matthew,

Thank you. That makes sense.
I'm trying to understand the structure and content of a "fact". It appears that it is a structure made of the following, some of which are optional:
1. at its base, it is statement. Some prefer to call it a proposition.
2. it has a truth-value. I prefer something like "believability value" to be more objective about the source.  (Brute facts, unknowable and unknown statements may have unique truth-values.)
3. source information
4. some persistence qualifier(s) (The old: "The king of France is bald" issue.)
5. a context/situation
6. Self or other ownership indication (needed for duality or multi-agency)

While these elements are present in many statements, it appears that facts have unique values that enable or constrain specific processing.

-John Bottoms
 FirstStar Systems
 Concord, MA USA

On 5/24/2012 12:06 PM, Matthew West wrote:

Dear John,

 

if: 1.       The fact of the state of affairs that really exists.
then how is a fact knowable?

 

MW: Through evidence, some is more reliable and objective than others.


Russell seemed to side step the question of facts by discussing statements of fact or facts as references.

Yet it is Russell's precept (?) that analytic philosophy requires an argument for the existence of...facts.
We all know what we could do with facts; if had one.

 

MW: It does not make sense to talk about “having” facts, they just are. The difficult bit is the reliability of determining them.

 

But without an argument for the existence of fact(s) then it's turtles all the way down.

 

MW: Well as I see it there are two alternatives, either there are facts or there are not. If there are not facts then we do not even exist (that would be a fact) so we do not need to worry about it. So I prefer to go with facts existing, because then I can exist too.


JohnS, slide 64 of "Goal" says:
"Since the Tractatus consists of language about language, it does
not state facts about the world. Therefore, it too is meaningless."
and slide 93 indicates:
" Observations generate low-level facts (atoms).
   Induction derives general axioms from multiple facts"

It also appears that Dunn's "facts" and "contingent facts" side steps the issue by creating semantic entities that are not grounded, i.e. "facts describe a possible world". Do facts then only exist in the math of the homunculus?

 

MW: Possible worlds include the world we live in.

 

Regards

 

Matthew West                            

Information  Junction

Tel: +44 1489 880185

Mobile: +44 750 3385279

Skype: dr.matthew.west

matthew.west@xxxxxxxxxxxxxxxxxxxxxxxxx

http://www.informationjunction.co.uk/

http://www.matthew-west.org.uk/

 

This email originates from Information Junction Ltd. Registered in England and Wales No. 6632177.

Registered office: 2 Brookside, Meadow Way, Letchworth Garden City, Hertfordshire, SG6 3JE.

 



-John Bottoms
 FirstStar Systems
 Concord, MA USA

On 5/24/2012 5:39 AM, Matthew West wrote:

Dear Alexander,

 

Not sure I understand you correctly - why do you think that facts don't exist in the information space? (and what do you mean under an information space?)

In addition, I think I am a bit confused and there are plenty of questions I cannot find answer on. Some (I think relevant to the subject) are:

1) can a "state of affairs in the world" exists without one's perception of it?


MW: Of course, unless you do not believe in evolution. Otherwise the world did not exist before humans/life because there was no one to perceive it. Reality (facts) is not perception, reality is what perception is of.

 


2) if two different people have different perceptions and make different statements about the "state of affairs in the world", do we have 1 fact, 2 facts, or 3 facts (suppose that the statement is a fact)?

 

MW: There are 3 facts (at least)

1.      The fact of the state of affairs that really exists.

2.      The fact that person A has made a statement about the state of affairs.

3.      The fact that person B has made a statement about the state of affairs.

 

What is said in the statements is not a fact, only its being stated.



3) if one has a perception of a "state of affairs in the world" - does this perception affects the "state of affairs in the world" ?

 

That one has a perception of a state of affairs is itself a state of affairs, whether it reflects accurately the true state of affairs is something else.

 

Regards

 

Matthew West                            

Information  Junction

Tel: +44 1489 880185

Mobile: +44 750 3385279

Skype: dr.matthew.west

matthew.west@xxxxxxxxxxxxxxxxxxxxxxxxx

http://www.informationjunction.co.uk/

http://www.matthew-west.org.uk/

 

This email originates from Information Junction Ltd. Registered in England and Wales No. 6632177.

Registered office: 2 Brookside, Meadow Way, Letchworth Garden City, Hertfordshire, SG6 3JE.

 

 



Regards,
Alex



24 May 2012 09:30

Dear Alex,

Indeed, any “taking” would be making a statement, but there is some fact (state of affairs in the world) that the statement is made about. Facts do not exist in the information space (except that the existence of certain statements are facts).

 

Regards

 

Matthew West                           

Information  Junction

Tel: +44 1489 880185

Mobile: +44 750 3385279

Skype: dr.matthew.west

matthew.west@xxxxxxxxxxxxxxxxxxxxxxxxx

http://www.informationjunction.co.uk/

http://www.matthew-west.org.uk/

 

This email originates from Information Junction Ltd. Registered in England and Wales No. 6632177.

Registered office: 2 Brookside, Meadow Way, Letchworth Garden City, Hertfordshire, SG6 3JE.

 

 

 

From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Alexander Titov
Sent: 23 May 2012 21:45
To: [ontolog-forum]
Subject: Re: [ontolog-forum] [ontology-summit] Estimating number of all known facts

 

In my opinion it might be quite difficult to "take" how things are - any "taking" of it might either affect things, or be a report/statement.

Regards,
Alex Titov




23 May 2012 21:29

Dear John,

 

It seems you have a different idea of what a fact is. I would take the facts as how things are in the world. A report of how things are would be a statement rather than a fact.

 

Regards

 

Matthew West                           

Information  Junction

Tel: +44 1489 880185

Mobile: +44 750 3385279

Skype: dr.matthew.west

matthew.west@xxxxxxxxxxxxxxxxxxxxxxxxx

http://www.informationjunction.co.uk/

http://www.matthew-west.org.uk/

 

This email originates from Information Junction Ltd. Registered in England and Wales No. 6632177.

Registered office: 2 Brookside, Meadow Way, Letchworth Garden City, Hertfordshire, SG6 3JE.

 

 

 

From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of John Bottoms
Sent: 23 May 2012 16:36
To: [ontolog-forum]
Subject: Re: [ontolog-forum] [ontology-summit] Estimating number of all known facts

 

It seems to me that some questions concerning "facts" are missing.
1. Who (and when) declared some statement as a fact?
2. If someone declared something a fact, can't humans (or actor) make subjective errors?
3. What is the life duration of a specific fact?
4. In what situation was the fact true?
5. What is the audience or community for that fact?

It seems to me that facts should be treated as signals in a communication system first. They must be communicated faithfully and the communication system must be capable of communicating any signal for which the system was designed. The system should only qualify and reject signals (facts) that are beyond its capabilities to communicate. In essence, a fact communicating system contains a classifier.

When a signal is received, the information from the signal can be extracted and processed further. Facts in isolation are meaningless statements. They are intended for use by a community. Even when stored for later use, signals and facts should have information associated with them that grounds them or provides hints on their use.

If we are talking about an individual knowing or retaining facts then there is an issue of garbage collection. For a universal system, such as a knowledge web, the management of a collection of facts should be viewed differently.

-John Bottoms
 FirstStar Systems
 Concord, MA USA

On 5/23/2012 7:20 AM, Christopher Menzel wrote:

On May 23, 2012, at 12:59 AM, William Frank wrote:

 

Then they are, as you suggest, confusing facts with beliefs. But I think there are very few people in this forum who are that confused.






Another is how do you **count** facts?  For almost 40 years, in the mid last century, started by Russel and Wittgenstein's idea of an atomic fact, carried forward by Carnap, might have suggested a way.   For example, take the fact that I have 10 toes, and i know this is true, at least the last time I looked.  Then, there are other facts that I know on reflection, such as that I have at least 3 toes, and that I do not have exactly 7 toes, and that I have fewer that 11 toes.  In fact, going forward, we have an **infinite** number of facts: for each n, the fact that I have fewer than n toes, where n is greater than 10. I think the atomic facts in question are 10 in number, that I have toe 1, toe 2, etc.  The problem with this is that atomic facts are based, as Mathew Lange says, on relationships between known entities, and how do we count these?  The foot, the toes, the 26 bones in the foot, the 356 blood vessels?

 

These are all reasonable questions and observations, but they don't show that there is anything inherently vague or intractable about facts. Compare the situation in set theory. In the early history of set theory there were analogous questions: Can sets contain themselves as members? Are there infinite sets?  Is there a set of all sets?  A set of all cardinal numbers?  Can all sets be well-ordered? Relative to one or another theory of sets, all of these questions have clear answers. Likewise, if you want facts in your ontology, you need a theory of facts that will generate clear answers and serve your purposes.






 

Sez you. What's your theory of facts?  What's a beholder? What's a label? You can't just pull stuff like this out of thin air and expect it to be meaningful.

 

Chris Menzel

 







_________________________________________________________________

 

23 May 2012 16:36

It seems to me that some questions concerning "facts" are missing.
1. Who (and when) declared some statement as a fact?
2. If someone declared something a fact, can't humans (or actor) make subjective errors?
3. What is the life duration of a specific fact?
4. In what situation was the fact true?
5. What is the audience or community for that fact?

It seems to me that facts should be treated as signals in a communication system first. They must be communicated faithfully and the communication system must be capable of communicating any signal for which the system was designed. The system should only qualify and reject signals (facts) that are beyond its capabilities to communicate. In essence, a fact communicating system contains a classifier.

When a signal is received, the information from the signal can be extracted and processed further. Facts in isolation are meaningless statements. They are intended for use by a community. Even when stored for later use, signals and facts should have information associated with them that grounds them or provides hints on their use.

If we are talking about an individual knowing or retaining facts then there is an issue of garbage collection. For a universal system, such as a knowledge web, the management of a collection of facts should be viewed differently.

-John Bottoms
 FirstStar Systems
 Concord, MA USA



23 May 2012 12:20

On May 23, 2012, at 12:59 AM, William Frank wrote:

 

Then they are, as you suggest, confusing facts with beliefs. But I think there are very few people in this forum who are that confused.





Another is how do you **count** facts?  For almost 40 years, in the mid last century, started by Russel and Wittgenstein's idea of an atomic fact, carried forward by Carnap, might have suggested a way.   For example, take the fact that I have 10 toes, and i know this is true, at least the last time I looked.  Then, there are other facts that I know on reflection, such as that I have at least 3 toes, and that I do not have exactly 7 toes, and that I have fewer that 11 toes.  In fact, going forward, we have an **infinite** number of facts: for each n, the fact that I have fewer than n toes, where n is greater than 10. I think the atomic facts in question are 10 in number, that I have toe 1, toe 2, etc.  The problem with this is that atomic facts are based, as Mathew Lange says, on relationships between known entities, and how do we count these?  The foot, the toes, the 26 bones in the foot, the 356 blood vessels?

 

These are all reasonable questions and observations, but they don't show that there is anything inherently vague or intractable about facts. Compare the situation in set theory. In the early history of set theory there were analogous questions: Can sets contain themselves as members? Are there infinite sets?  Is there a set of all sets?  A set of all cardinal numbers?  Can all sets be well-ordered? Relative to one or another theory of sets, all of these questions have clear answers. Likewise, if you want facts in your ontology, you need a theory of facts that will generate clear answers and serve your purposes.





 

Sez you. What's your theory of facts?  What's a beholder? What's a label? You can't just pull stuff like this out of thin air and expect it to be meaningful.

 

Chris Menzel

 

_________________________________________________________________

22 May 2012 23:59

This is a question that could lead to a lot of different threads, that could be amusing or troublesome, and maybe some thread that might be enlightening.

One, that has been brought up below, is the fact that facts are slippery things: what people believe is true, what they are so sure about, they are willing to call it a fact, does not mean it IS true.   Back to the theory of knowlege, which does not seem to fair well in this forum, with the total relativists among us seeming to believe (inconsistently) that a fact itself is "just" what somebody believes, inconsistent, because if they assert that, and I believe different, (that a fact is a statement that is true, and a known fact being one that someone is justified in believing (i.e.,knowledge = justified true belief). then we have no argument, since all beliefs are equally true, which leads me to wonder why they bother to converse, since there are no rational grounds for any discovery of what is more likely to be true.

But this is realted to the well known (fact?) that we can't ever be *sure* what is true, so we can't count facts but only justified (and perhaps unjustifed) beliefs, and the well known (fact) that only a surprisingly small number of the statements made on the Web appear to be true.   

Another is how do you **count** facts?   For almost 40 years, in the mid last century, started by Russel and Wittgenstein's idea of an atomic fact, carried forward by Carnap, might have suggested a way.   For example, take the fact that I have 10 toes, and i know this is true, at least the last time I looked.  Then, there are other facts that I know on reflection, such as that I have at least 3 toes, and that I do not have exactly 7 toes, and that I have fewer that 11 toes.  In fact, going forward, we have an **infinite** number of facts: for each n, the fact that I have fewer than n toes, where n is greater than 10. I think the atomic facts in question are 10 in number, that I have toe 1, toe 2, etc.  The problem with this is that atomic facts are based, as Mathew Lange says, on relationships between known entities, and how do we count these?  The foot, the toes, the 26 bones in the foot, the 356 blood vessels?

So, it seems one needs an ontology of types of things, and a count of the instances of each type, and then perhaps the factorial of the sum of those counts, might be the number of possible atomic facts in the world identified by that ontology.  Then, the total number of facts would be the sum of all the atomic facts expressible in each ontology.  I suspect the fact that most of these possible atomic facts would be false would not change the order of magnitude of the answer.  It would seem that how many of these possible facts could be known depends on the availability of knowers.

This all might lead to a reasonable investigation or to a Zen moment, or both..








--
William Frank

22 May 2012 23:05

Billions is several orders of magnitude too small, to be sure--but then again you were talking about beholders, not the facts themselves...wiuch leads me to think that we perhaps could estimate a ballpark average number of facts that a beholder needs to know for various levels of sophistication in particular knowledge domains--including "common sense".
In addition to ability--Malcolm Gladwell's, 10,000 hours must be roughly translatable in terms of "knowable entities".
Just looking for ballpark here...surely someone has investigated this in terms of knowledge engineering...




23 May 2012 21:45

In my opinion it might be quite difficult to "take" how things are - any "taking" of it might either affect things, or be a report/statement.

Regards,
Alex Titov

23 May 2012 21:29

Dear John,

 

It seems you have a different idea of what a fact is. I would take the facts as how things are in the world. A report of how things are would be a statement rather than a fact.

 

Regards

 

Matthew West                           

Information  Junction

Tel: +44 1489 880185

Mobile: +44 750 3385279

Skype: dr.matthew.west

matthew.west@xxxxxxxxxxxxxxxxxxxxxxxxx

http://www.informationjunction.co.uk/

http://www.matthew-west.org.uk/

 

This email originates from Information Junction Ltd. Registered in England and Wales No. 6632177.

Registered office: 2 Brookside, Meadow Way, Letchworth Garden City, Hertfordshire, SG6 3JE.

 

 

 

From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of John Bottoms
Sent: 23 May 2012 16:36
To: [ontolog-forum]
Subject: Re: [ontolog-forum] [ontology-summit] Estimating number of all known facts

 

It seems to me that some questions concerning "facts" are missing.
1. Who (and when) declared some statement as a fact?
2. If someone declared something a fact, can't humans (or actor) make subjective errors?
3. What is the life duration of a specific fact?
4. In what situation was the fact true?
5. What is the audience or community for that fact?

It seems to me that facts should be treated as signals in a communication system first. They must be communicated faithfully and the communication system must be capable of communicating any signal for which the system was designed. The system should only qualify and reject signals (facts) that are beyond its capabilities to communicate. In essence, a fact communicating system contains a classifier.

When a signal is received, the information from the signal can be extracted and processed further. Facts in isolation are meaningless statements. They are intended for use by a community. Even when stored for later use, signals and facts should have information associated with them that grounds them or provides hints on their use.

If we are talking about an individual knowing or retaining facts then there is an issue of garbage collection. For a universal system, such as a knowledge web, the management of a collection of facts should be viewed differently.

-John Bottoms
 FirstStar Systems
 Concord, MA USA

On 5/23/2012 7:20 AM, Christopher Menzel wrote:

On May 23, 2012, at 12:59 AM, William Frank wrote:

 

Then they are, as you suggest, confusing facts with beliefs. But I think there are very few people in this forum who are that confused.





Another is how do you **count** facts?  For almost 40 years, in the mid last century, started by Russel and Wittgenstein's idea of an atomic fact, carried forward by Carnap, might have suggested a way.   For example, take the fact that I have 10 toes, and i know this is true, at least the last time I looked.  Then, there are other facts that I know on reflection, such as that I have at least 3 toes, and that I do not have exactly 7 toes, and that I have fewer that 11 toes.  In fact, going forward, we have an **infinite** number of facts: for each n, the fact that I have fewer than n toes, where n is greater than 10. I think the atomic facts in question are 10 in number, that I have toe 1, toe 2, etc.  The problem with this is that atomic facts are based, as Mathew Lange says, on relationships between known entities, and how do we count these?  The foot, the toes, the 26 bones in the foot, the 356 blood vessels?

 

These are all reasonable questions and observations, but they don't show that there is anything inherently vague or intractable about facts. Compare the situation in set theory. In the early history of set theory there were analogous questions: Can sets contain themselves as members? Are there infinite sets?  Is there a set of all sets?  A set of all cardinal numbers?  Can all sets be well-ordered? Relative to one or another theory of sets, all of these questions have clear answers. Likewise, if you want facts in your ontology, you need a theory of facts that will generate clear answers and serve your purposes.





 

Sez you. What's your theory of facts?  What's a beholder? What's a label? You can't just pull stuff like this out of thin air and expect it to be meaningful.

 

Chris Menzel

 






_________________________________________________________________

 




 
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