|To:||"[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>|
|From:||Kathryn Blackmond Laskey <klaskey@xxxxxxx>|
|Date:||Wed, 01 Aug 2007 12:26:40 -0400|
Your remark hearkens back to our discussion of what an ontology is really about.
Model theoretic semantics says there is a domain D, which is a set, and the objects, attributes and relationships defined in the ontology refer to elements of, functions defined on, and subsets of this set D.
Many people feel this is way too abstract. "But my ontology of horse racing is about horses!!! And jockeys and racetracks and betting odds! It emphatically is not about sets!"
We have had many heated discussions in this forum about whether sentences in a biology textbook are about cells in the world or about cells in a biological model of cells. Jon suggested maybe they are about both. That they can be about both is why engineering works! It's why you can get up in the morning expecting your car to start, the traffic lights to work, and the bridge not to collapse.
Engineers build a computer model of the bridge because there is a great deal less loss of life and a much greater return on the dollar from building computer simulations of cars driving across the bridge and testing out various designs before setting the cement mixers and beam layers to work. We have learned in the school of hard knocks that it is not a good idea to try out a bridge design by building it and seeing whether it collapses under the load we put on it.
The equations the engineer programs into the simulation are about the bridge model. The engineer uses this fact to debug her simulation and to test out various bridge designs by changing aspects of the computer model. Because the equations are about the model, she can be confident that changes in parameters of the model will result in changes to the simulation output that accurately reflect her intentions. The equations are also about the actual bridge that is going to be built. Well, to be precise, the equations for the discarded designs are about bridges she is considering building, and the ones in the final design are about the bridge she plans to build, but they will probably be modified somewhat by the time concrete is poured. In any case, because the equations are about both the bridge model and the bridge, she can be confident (if it's a good model) that predictions she makes on the basis of the simulation (such as how much load the bridge can bear) will be true of the actual bridge when it is built. Thus, the fact that the assertions are true both of the bridge model and the real bridge is the reason that engineers can design bridges that can carry the traffic they are designed to carry. Our lives depend on this vital characteristic of models.
Some of the very same equations could, under different circumstances, be used to model airplanes or electrical circuits or pollution in the Chesapeake Bay. That is the beauty of mathematics. There are common mathematical structures that are generally useful across a wide variety of problem domains. It is also the bane of students who are interested in nursing or robotics or baseball, but have to sit through a generic mathematics course that either uses almost no examples or requires them to do problems about applications about which they don't care a hoot. This gives rise to frequent turf wars between the math department, which is sure the psychology department or the nursing school is incapable of teaching math the way it ought to be taught, and the nursing school or psychology department, which complains that the mathematicians lose the students by teaching abstractions divorced from applications that would hold the students' interest. Probably, both are right -- that's part of the price we pay for mass-producing education. But that's a different soap-box.
At 10:31 AM -0500 8/1/07, Christopher Menzel wrote:
> The scopes and subject matters of Ontology and Logic shouldn't be
> defined by
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