Re: [ontolog-forum] Intensional relation

[joseph simpson <jjs0sbw@xxxxxxxxx>]

There appears to be an interesting point about the mathematical relations as they apply to natural language real-world relationships.

This point is associated with the attributes of a mathematical relation.... reflexive, asymmetric, transitive and so on...

When a real-world relationship is transformed to a mathematical relation, these issues become interesting...

For example...

If a system is defined as a relationship mapped over a set of objects....

When the natural language relationship is transformed to a mathematical relation ... there can be issues.

Example....

Objects 1,2,3,4, and 5 are connected to each other and create a system....

The "connected-to" real world relationship is transformed to a binary mathematical relation....

The mathematical representation of the system will exhibit different forms depending on the relation attributes...

Take care, be good to yourself and have fun,

Joe

On Fri, Jan 4, 2013 at 9:16 AM, <sowa@xxxxxxxxxxx> wrote:

There is no conflict whatsoever between being clear and precise in logic and being clear and precise in ordinary language.

It does require some work to learn any new language, natural or artificial.  But the requirements are the same:  make the point as clear as possible with a minimum  of distracting detail.

> 2013/1/3 matthew lange <mclange@xxxxxxxxxxx>

>> John: "Teaching ontology by burying the fundamental insights under the
>> trivial notation is pedagogical malpractice."
>> or
>> Leo: "The point of using mathematical (or logical) notation is to make
>> your statement precise and unambiguous."
>>
>> Cannot these perspectives be harmonized?

They most definitely can.  In a previous note, I quoted Paul Halmos as a mathematician  who could explain his ideas clearly and precisely in English and in mathematical notation.

John

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-- 
Joe Simpson

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