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
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.
- 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
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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