On 6/29/2012 4:25 PM, ravi sharma wrote:
> How can we then state 2+2 = 4, except conceptually unless list
> items in point one above are established to be TRUE? (01)
I agree with what Doug said, but I'd like to clarify a few points. (02)
First, all definitions are conventions about how we agree to use
some words or symbols of a natural or artificial language. For
most natural languages, the conventions grew mostly by habit as
people found certain ways of using the language as more convenient
or easier to remember. (03)
You can call them verbal or conceptual conventions, if you like.
That is all any definition can be. (04)
But after you agree to some conventions, then you can prove
statements that follow from them, such as 2+2=4. (05)
The same is true of games like chess or bridge. The rules are
purely arbitrary. But if a group of players agree to abide by
the rules, then you can prove theorems about which positions
lead to a win or a loss. (06)
Those theorems are true, given the rules of the game as hypotheses.
All of mathematics is like that: you start with some definitions,
and prove some theorems that follow from those definitions. (07)
For various kinds of applications, some branches of mathematics
are more useful than others. You can use arithmetic for banking,
geometry for surveying the land, or differential equations for
fluid dynamics. But a theorem about chess or bridge is only
useful for playing that particular game. (08)
John (09)
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontologforum/
Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontologforum/
Unsubscribe: mailto:ontologforumleave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/
To join: http://ontolog.cim3.net/cgibin/wiki.pl?WikiHomePage#nid1J (010)
