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Re: [ontolog-forum] axiom

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>, "rhm@xxxxxxxxxxxxx" <rhm@xxxxxxxxxxxxx>
From: "Barkmeyer, Edward J" <edward.barkmeyer@xxxxxxxx>
Date: Tue, 22 Apr 2014 16:23:45 +0000
Message-id: <acd47f139a374f469a75ebe6dd1df002@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx>



The simple definition of ‘axiom’ is “a statement/sentence that you take to be true”, usually without having any ability to prove its truth from other knowledge or assumptions.  There can be many different reasons WHY someone takes a given statement to be true – social agreement, blind faith, preponderance of evidence, hubris, etc.  That does not affect the concept ‘axiom’.


There are other vernacular uses of the term ‘axiom’, but with respect to the discipline of ontology development, an axiom is just a sentence taken to be true.


It is worthy of note that 99% of all ontologies, information models and UML models consist of nothing but terms and axioms.  Everything captured in the model is offered without any evidence for its validity.  The theorems – the statements that can be proved using the ontology – are the answers to the questions that form the use cases for the ontology.




From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Bruce Schuman
Sent: Monday, April 21, 2014 12:14 PM
To: rhm@xxxxxxxxxxxxx; '[ontolog-forum] '
Subject: Re: [ontolog-forum] axiom


What is an axiom?


For me – in this context of “semantic ontology” and computer science, where we are trying to be highly precise,  these below definitions of “axiom” are like non-sequiturs.  I don’t get this.


They might refer to things that are “axiomatic” by social convention – but the way I see it, any general statement written in abstract terms in the English language cannot be unambiguous, and therefore cannot be “axiomatic”.


Let’s say that the axiom we want to explore is “All dogs are free”.  We  might get some social agreement on that among certain groups.


But for me – trying to build an inviolate irrefutable system based on that idea, that would lead to non-controversial results – is just impossible, and based on a fundamental misunderstanding.


What do these words mean?


What is “a dog”?


What is “free”?


Maybe we know what “are” means – maybe we don’t.


Maybe we know what “all” means (if we know what “a dog” is) – and maybe we don’t.


All those terms and definitions are stipulative.  “A dog is what I say it is”.  “Freedom is what I say it is”.  And that’s the only certain meaning those words have.


And if we are a follower of some philosopher – maybe those words mean what that philosopher says they mean.  But even that is not likely to produce stable results, as the followers are very likely to start quarreling about the specific implications.  We need the philosopher/guru standing around to give us his/her authoritative “correct” answer (opinion) on any questions that arise.  We’re not going to be realizing Leibniz’s dream: “Let us calculate…”


Under any kind of “load stress” (critical examination or controversy), a proposition/axiom stated in those broad abstract terms – leads to crazy-making.  It doesn’t work.  Don’t do it.


So – for me, scratching my head and wondering why so many messages have been posted on this subject – maybe I just don’t understand something that everybody else agrees on – or maybe this concept of “axiom” needs a hard-edged definition in this “ontolog” context.


If I had my way, every natural language term would be (stipulatively) grounded (somehow) in the real number line, with exact measurements in x number of decimal places in explicit dimensions with a known error tolerance..  A “dog” is exactly this….


That’s the only way to stop the arguments and lead to stable structures.




Bruce Schuman


From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Richard H. McCullough
Sent: Sunday, April 20, 2014 10:48 PM
To: [ontolog-forum]
Subject: [ontolog-forum] axiom


The New Shorter Oxford English Dictionary gives three definitions.

1) a) An established or generally accepted principle;
b) a maxim;
c) a rule.

2) Logic. A proposition (true or false).

3) Math.
a) A self-evident truth;
b) a proposition on which an abstractly defined structure
is based.

Rand:axiom is 3a;
McCullough:axiom is 3b;
Ontolog Forum:axiom is ?;

Dick McCullough
Context Knowledge Systems
Name your propositions !

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