Editing Mathematical model (section)

====Philosophical considerations====

Many types of modeling implicitly involve claims about [[causality]].  This is usually (but not always) true of models involving differential equations.  As the purpose of modeling is to increase our understanding of the world, the validity of a model rests not only on its fit to empirical observations, but also on its ability to extrapolate to situations or data beyond those originally described in the model. One can think of this as the differentiation between qualitative and quantitative predictions. One can also argue that a model is worthless unless it provides some insight which goes beyond what is already known from direct investigation of the phenomenon being studied.

An example of such criticism is the argument that the mathematical models of [[optimal foraging theory]] do not offer insight that goes beyond the common-sense conclusions of [[evolution]] and other basic principles of ecology.<ref>{{Cite journal | last1 = Pyke | first1 = G. H. | doi = 10.1146/annurev.es.15.110184.002515 | title = Optimal Foraging Theory: A Critical Review | journal = Annual Review of Ecology and Systematics | volume = 15 | pages = 523–575 | year = 1984 | issue = 1 | bibcode = 1984AnRES..15..523P }}</ref> It should also be noted that while mathematical modeling uses mathematical concepts and language, it is not itself a branch of mathematics and does not necessarily conform to any [[mathematical logic]], but is typically a branch of some science or other technical subject, with corresponding concepts and standards of argumentation.<ref name="Edwards" />