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

To: "mclange@xxxxxxxxxxx" <mclange@xxxxxxxxxxx>, "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
Cc: "[ontolog-summit]" <ontology-summit@xxxxxxxxxxxxxxxx>
From: Ed Barkmeyer <edbark@xxxxxxxx>
Date: Thu, 24 May 2012 15:55:52 -0400
Message-id: <4FBE9248.7070608@xxxxxxxx>
Matthew (Lange),

you wrote:
I am really feeling like my thread has been hijacked by people who like to read their own writing:> conjecture. I have purposefully avoided quoting any one person--but you know who you are.

Sitting on the sidelines, it seems to me that the thread has been hijacked by people asking two rather important questions:
 1) what is meant by "fact"?  Is a 'fact' a belief of an individual or a community, however large, or a statement whose truth value can somehow be determined objectively, or just a postulate for a 'possible world', independent of anyone's acceptance of that world as "reality" in any sense.
 2) what do you mean by "count"?  First, you have to be able to distinguish individuals: when are two "facts" different? And second, you have to tell us whether you really mean only to produce some kind of bound _expression_ for the quantity of facts of a kind, or you want a mechanism for enumeration of all possible facts, i.e., a mechanism for generating facts that guarantees to generate every fact at some point in the process.

>From a linguistic point of view, the last would imply that one could enumerate all existing 'things' and all meaningfully distinct verb concepts, and thus somehow generate all possible sentences, and then have a means of eliminating those that are false or non-determinable.  Alternatively, I suppose we might have a means of generating only provable theorems, assuming we all agreed on what the universal set of postulates is.

The point of the discussion is that all of these are hard questions.  Yes, the discussion goes down many paths in trying to answer them, and some of those paths are less rewarding than others, where "rewarding" is indeed in the eye of the beholder (or whatever the appropriate metaphor for this form of experience might be).

Perhaps folks are afraid to read/respond to my real-world examples of facts, or did my propositions just get lost in the list mud?

Here again are some examples of facts, I would be delighted if someone would attempt to bound factual knowledge so that they could be quantified--or otherwise provide succinct reasons about why my examples are not facts.
Fact examples:
  1. The earth revolves around the sun.

Yes, or at least, there have been several billion such cycles and we expect as many more.  This represents "acquired knowledge" about the universe we live in.

2.  The Greek letter Pi represents the irrational number that is the ratio between a circle's circumference and diameter.

By comparison with 1, this is true because mathematicians since Pythagoras have declared it to be so.  It is a fiat.  Others might argue that pi represents a voiceless labial stop, as in Pythogoras' name, a fiat of a different community.

3.  A calorie is the amount of energy it takes to raise the  temperature of 1cc of water 1 deg. C at sea level.

This is also a fiat -- a definition.  We define the term "calorie" to mean: the amount of energy ...

4.  Chemical X contains Y calories of available energy. (of course substituting where appropriate)

This actually makes an unstated presumption about the way in which the chemical mass will be converted to usable energy.  What X actually contains is bonding energies (about which I know nothing) and a certain amount of kinetic energy based on its temperature.  So, I think this is half a fact -- a statement that is "taken to be true scientifically" under some conditions.

Are these not facts?

Well, you tell me.  Is a representation convention a "fact"?  Is the definition of a term a "fact"?  Is the best scientific judgement about the nature of some aspect of the universe a "fact"?  I think we could safely argue that the two man-made facts about the use of symbols for concepts are "facts", because they are fiats and we control them.  It follows, I think, that one might be able to enumerate all possible usefully distinct sounds makeable by the human organs of speech, and thus all possible "word" things, but it is not at all clear to me how one could associate all possible definitions, or even all definitions in use.  Whether something similar can be done for all possible symbols I couldn't say.

Are they not countable?

If you mean "bounded", I doubt it.  If you mean "countable" in the Cauchy sense -- they can be algorithmically placed in 1-to-1 correspondence with the natural numbers -- I won't hazard a guess.

Again, aside from bending the space-time continuum, or  dismissing laws of nature like thermodynamics...I fail to see the need for relativism here...or, what am I missing? If you agree that these are facts, then let's get pragmatic and enumerate the properties/boundaries around the nature of a fact.

That is, I think, what this brainstorming session is trying to do.  Do you have some suggestion about making the session more profitable?  Do you have any idea where to start? 

I will confess the uselessness of this email by simply saying:  I have no idea how to do either.

Also, I must express my displeasure with several members' netiquette on this list:
1) In addition to Mr. West, my name is also Matthew  (this is a FACT)--please use unambiguous identifiers in responses
2) Spell Check is courteous--not a fact, but perhaps an opinion shared by many--one or two misspelled words words I can understand...but some of these posts are ridiculous.

You presume, I think, that the amount of effort expended in writing these emails is uniformly high.  I can say with certainty that that is not a fact.  :-)




Edward J. Barkmeyer                        Email: edbark@xxxxxxxx
National Institute of Standards & Technology
Systems Integration Division
100 Bureau Drive, Stop 8263                Tel: +1 301-975-3528
Gaithersburg, MD 20899-8263                Cel: +1 240-672-5800

"The opinions expressed above do not reflect consensus of NIST, 
 and have not been reviewed by any Government authority."

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