First, interpret the question as "How many relations
are needed for English for one individual"? (01)
Expertise in one lifetime area involves about half our
capability, and learning approximately 12,000 things; (02)
our total capacity is therefore approximately 25,000 things,
no more than about a quarter of which can be relationships; (03)
I conclude that a method of expressing what an individual
does should take about 6,000 true relations. (04)
An exceptionally broad individual with multiple hobbies
could have less depth and about twice as many relations. (05)
Second, assume that the human race has a hundred lifetime
areas of expertise; then you need 600,000 relations for
everything that anyone would actually express in English,
of which 98 percent are seldom-used and low priority. (06)
Third, modify this for the average person,
instead of for the expert;
you would have to express less than a fifth of these
(lest you approach the reciprocal of the Feigenbaum Constant
loading factor after which your world view would tends to change,
and you would start calling yourself an expert). (07)
Therefore, for non-exert use of English, you would need
120,000 relations of which all but 2 percent are scarcely used
and low priority. (08)
To test these approximations, try them on different fields:
a seamstress, a biochemist, a translator of ancient documents,
a doctor, a taxi driver, a lawyer, a farmer, a pilot,
a carpenter, a laborer, and a marketer. (09)
Mike Brenner (010)
-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F.
Sowa
Sent: Friday, October 10, 2008 9:01 PM
To: ontolog-forum@xxxxxxxxxxxxxxxx
Subject: Re: [ontolog-forum] Axiomatic ontology (011)
Rob and Chris, (012)
RF>> How many [relations] are needed for English? (013)
CM> Good heavens, the question doesn't even make sense. (014)
The main sense I would make of it is "How many different kinds
of relations might be expressed in English?" (015)
My interpretation of that question would be: What is the set
of all possible relations that might be mentioned or defined in
any version of any formal logic or any programming language or
any similar formalism. (016)
Since any of those relations could also be mentioned or defined
in English sentences, the number for English would be the
cardinal number for the totality of all those for any formal
language. (017)
The number of relations that are possible would be uncountably
infinite, but the number that could actually be defined or
specified in a finite statement (in any natural or artificial
language) would be merely countably infinite. (018)
That is still very large. (019)
John (020)
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