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Is there an accurate view on the distinction between "what mathematics can model" and what it cannot?

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Not just in hard sciences. What about social, political questions? What's the accuracy of statistical research relative to "without statistics"?

What kinds of aspects are there to be considered:

  • bias or unbiasedness of conductors
  • collecting enough data
  • ...

But can one take any kind of stance for example to, whether "statistical truth" is more accurate than "non-statistical truth"? I've once read a view that suggested that "statistical truth" is a particular orientation to truth, it's not necessarily "more accurate" (since e.g. accuracy is relative to the chosen base beliefs, such as whether collective truth may override subjective truth), it's different.

Please link to references, if this is a topic that's broadly covered somewhere already. Likely not conclusively, since the world is ever-changing, but in order to e.g. follow "current view".

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closed as off-topic by David K, KReiser, Lord Shark the Unknown, Jyrki Lahtonen, KM101 Dec 14 '18 at 7:49

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is not about mathematics, within the scope defined in the help center." – David K, KReiser, KM101
If this question can be reworded to fit the rules in the help center, please edit the question.

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It is a very broad question that probably belongs much more to the Philosophy of Science as general than strictly to math. However, I'll try to give you some brief answers for further (re)search.

Is there an accurate view on the distinction between "what mathematics can model" and what it cannot?

No. E.g., there is long lasting debate about usefulness of mathematical modeling in Economics and especially in Finance. The more radical views, expressed by N. N. Taleb in his popular books, is that modelling in finance is not only not useful, but actually harmful. More moderate point of view about mathematical and statistical modelling in Social sciences as whole, can be summarized by George E. P. Box quote "All models are wrong, but some are useful".

IMHO, The main distinction between modeling in Social Sciences and in Hard Sciences is that in the latter the model is the theory, while in the first is just a mathematical formulation of some world view. For example, $E= MC ^ 2$ is not just some model of estimating the amount of required energy for so and so. It reveals an underlying truth about the structure of the world. While, e.g., some model for options pricing just gives you an $\textit{estimate}$ of the price, under such and such assumptions and even then it can be mostly wrong and has many corrections and modifications for every possible scenario.

Besides Taleb's books, you can also try "Models Behaving Badly" by Emanuel Derman and "The Physic of Wall-street" by James Owen Weatherall. Although these are popular books, they still have very rich and detailed bibliographical lists that can guide you towards others sources including huge scientific literature on this topic.

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