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

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Wed, 23 May 2012 13:20:39 +0200
Message-id: <F34EC7FC-1AA8-4DCC-97B4-E808FB65D641@xxxxxxxx>
On May 23, 2012, at 12:59 AM, William Frank wrote:
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,

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.

On Tue, May 22, 2012 at 2:28 PM, LaVern Pritchard <lavern@xxxxxxxxxxxx> wrote:
The number of known facts is unknowable because a fact is in the eye of the beholder or a label,

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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