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Clarifying the role of mathematics in theory development

Authors
Chris Donkin
University of New South Wales ~ Psychology
Aba Szollosi
UNSW, Australia
Jared Hotaling
University of New South Wales ~ School of Psychology
Abstract

Though formal implementations of theories can be useful, they are not necessarily so. So, while a good theory is one that lends itself to being implemented formally, a "good" model does not guarantee a good theory. The scope of what can be learned from a mathematical model is based on the extent to which that model is implied by its motivating theory, and, therefore, what implications the failure of a model has for that theory. We discuss common use of mathematics in psychology, such as model fitting and model selection, with these limitations in mind.

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Theory development
Discussion
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Hi Chris, I really liked your discussion of non-solutions! We need more awareness of non-solutions.

Iris van Rooij 0 comments

Very clear talk! I am very curious what you think about the relative usefulness of mathematics in finding the implications of theories compared to other methods. For example, I have been working on the debating techniques practiced by Tibetan monks (see some posters presented here) and they use a kind of Socratic reasoning to find the implications ...

Marieke Van Vugt 1 comment

Thank you for the interesting talk! I think one important point which is worth emphasizing (sort of a corollary to the precision aspect of mathematical theory in the talk) is the important of mathematics as a vehicle for communication. By developing a mathematical theory, this provide an unambiguous efficient way to communicate complex ideas in an...

Prof. Richard Golden 0 comments
"models" vs. "theories" Last updated 3 months ago

How is it any different from the old saying--maybe I am actually just making this up--that in social sciences, we only have (mathematical) models of "qualitative" theories, whereas natural sciences have "hard" (mathematical) theories? Maybe my question is: is there an example of a mathematical theory in social sciences that satisfies the condition...

Dr. Eric Cosyn 1 comment