Hi John, (01)
That is the difference between math and engineering. In engineering, there
is ALWAYS a rationale because there is ALWAYS a large number of ways to do
things, each way having its own practical profile. The rationale is usually
based on five factors: specifications, cost, quality, effectiveness and
reliability. There are very few real problems of any substance that can
only be solved by implementing ONE math formalism. It's the mix and
interplay of formal models bound into the embodiment of an application that
makes it useful. Another view of this reality is that each model could have
an ontology or three, but the matrix of the application must mix the
ontologies together, interface where appropriate, and construct the
realities of the application from a selection of (ontologically) math
models. (02)
Math is purely conceptual, and has no necessary mapping to reality.
Differential equations are useful because physical reality behaves in many
respects like the canonical differentials that make up such a model. But I
wouldn't expect a rationale for math other than the model making sense
logically and syntactically. It's the semantics of the application that
drives the choice of math models selected for implementing those semantics. (03)
-Rich (04)
Sincerely,
Rich Cooper
EnglishLogicKernel.com
Rich AT EnglishLogicKernel DOT com
9 4 9 \ 5 2 5 - 5 7 1 2
-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F. Sowa
Sent: Thursday, August 19, 2010 3:05 PM
To: ontolog-forum@xxxxxxxxxxxxxxxx
Subject: Re: [ontolog-forum] Triadic Sign Relations (05)
On 8/19/2010 2:07 PM, Rich Cooper wrote:
> But I see no rationale justifying the requirement that only attributive
> properties (single argument fluents) be used to form the lattice. (06)
Whenever you have a partial ordering over any domain D, you can define
a lattice over D. If you like, you can define a lattice over n-adic
relations. (07)
In pure mathematics, there is no "rationale". You just state some
definitions and axioms and prove some theorems. If you don't like
somebody's abstract theory, you can ignore it, and it won't bite you. (08)
For applications, you might have some discussion over what choice
of formalism is useful for solving the problems you need to solve.
Some formalisms are better than others according to whatever measure
of goodness you consider important. (09)
John (010)
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