These days, I participated in some interesting discussions about Visual Thinking and model, and saw the proposition on the blog of Model Practice: “essentially all models are wrong, but some are useful” by Scott E. Page in the online lecture Model Thinking, and the comment by the blogger (|=), “without being ‘wrong’ (i.e. loosing details) it would not be a model.” Which makes me think of some thoughts of mine about the notion of model, and the example I constructed carefully. See the picture.
There are three stones. Is that a model? My answer is unknown, but one can use it in some case as a model by mapping the stones to the Earth, Moon and Sun.
Thus, however, is that a good model? Some one may be said: It’s so ugly, of course it’s a poor model… but I’ll still say: unknown.
One day, I used the three stones as a model to interpreted what is a lunar eclipse, successfully. In this case, I can say, the three stones was a good enough model.
This example concerned in almost all of the secrets about that what is a model. I have been thinking about this questions over the years. So far, my answer is as follows. Borrow Wittgenstein’s definition of meaning as use, it could be said, for a large class of cases—though not for all—in which we employ the word ‘model’ it can be defined thus: a model is a role in the situation where the role carries certain properties of a thing directly or indirectly and works by the properties. In other words, we say an entity modeled the thing when it playing the role in a case as the satiation. Any entity has the properties and meets some conditions, is able to be used as a model in the situation.
 By Wittgenstein: “For a large class of cases—though not for all—in which we employ the word ‘meaning’ it can be defined thus: the meaning of a word is its use in the language”, Philosophical Investigations, cited from: Biletzki, Anat and Matar, Anat, “Ludwig Wittgenstein”, The Stanford Encyclopedia of Philosophy (Summer 2011 Edition), Edward N. Zalta (ed.), URL = http://plato.stanford.edu/archives/sum2011/entries/wittgenstein/.
(Sorry I did not well use the schedule, so, issued a draft before this version to subscribers.)
Updated on 29 February, 2012
changed “Any entity has the properties and meets some conditions, will be used as a model in the situation.”
to “Any entity has the properties and meets some conditions, is able to be used as a model in the situation.”
Updated on 30 April, 2012
Original “we say an entity modeled on the thing when it playing the role in a case as the satiation.”
Corrected “we say an entity modeled the thing when it playing the role in a case as the satiation.”
(That was a wrong expression for my thoughts: the model I discussed was NOT the thing modeled “on” another.)
Version on 7 July, 2012
There are some drawbacks of the last version of the definition. One is the “carries certain properties of a thing” may be considered somewhat ambiguous: is a transmitter carrying properties (e.g. an optical device) a model? of course no. Other is that, it is meaningless that call an object as a model just because it has a group of properties of a thing else and work with it. So, I modified the definition, use “has” to replace “carries” and add “substitute”, as below:
a model is a role in the situation where the role has certain properties of a thing directly or indirectly and works as a substitute of the thing on the properties.
Version on 12 August, 2012
I asked Dr. phil. Roland Müller for his comment to the idea of “model as use” and the last version of my definition of model. He gave me a quite positive comments that “your formula ‘the model as use’ is very convincing.” He also reminded me that “‘working as substitute’ is only one of 25 possible functions of a model.” (here is a his page related to this: http://www.muellerscience.com/ENGLISH/model.htm)
In this work, I’m trying to find a broader definition to cover the majority of the things which are called models, especially in the cases that lead to confusion, such as the differences and connections between “model” in the mathematical model theory and in many of common senses.
In the last version, I added the “substitute” to attempt to more clearly explain the nature of model. As I mentioned in the last update, it sounds not sufficient to that only says a model “carries” or “has” the properties of some thing. A model should be provided and worked in (or based on) the properties for a thing (else). I think this is a sort of “substitute” but only in the sense that providing the properties, in other words, the properties are used in the situation and provided by the model but belonged to the thing else. This is different from that says that “A is a substitute of B” in general.
However, it sounds the expression in last version is still not enough clear, so I try to give a new version again:
we call an entity model while it plays the role in the situation where the entity has and provides a set of properties directly or indirectly as the substitute for a thing else.