Re: Probability Theory--A Science?

clemenr_at_wmin.ac.uk
Date: 02/03/05 

Date: 3 Feb 2005 05:08:12 -0800

Einar Andreas Rødland wrote:
> W. Wat son wrote:
> > Mathematics is not considered a science, but is probability theory?

> > Statistics? I would lean to yes on both.
>
> Probability theory and statistics (the theory at least) are both
> branches of mathematics.
>
> In other languages, there are several distinct words for 'science'
> corresponding to different meanings of 'science'. I'll give the
> germanic terms (modulo misspellings).
>
> 1. natural science (Naturwissenschaft);
> 2. natural and mathematical sciences (Realwissenschaft);
> 3. all kinds of research including social sciences (Wissenschaft).
>
> As far as I understand, in English the term 'science' can mean either

> the study of the the physical world (i.e. 1. natural science) or
> research in general (i.e. 3.). I'm not certain if it is also used in
> sense 2. as well, though I can't find that in any of the dictionaries

> I checked.

There are quite a few books, journals, and other resources where
philosophers argue about what is science or not.

As a truncated, personal opinion, I would classify as science most
forms of study that allow us to construct theories that make
predictions about unseen cases and events, where the theories that
emerge from these studies can be objectively studied, and in particular
are falsifiable.

Significance testing is a branch of statistics that gives a theoretical
framework for analysing the results of experiments and predicting the
likelihood that these results will hold in a quantified fraction of
future cases. The theories that these significance tests are based on
are allowing us to make predictions for future cases. It would be
possible to perform the future experiments and see whether the
predictions of the underlying theory are correct. If the long-term
error rate was considerably different from that predicted, I would
consider the underlying theory to be falsified.

It is true that such experiments could not conclusively prove that the
significance tests, or the theory they are based on, is correct or
incorrect. But, neither can experimental data in biology and many other
sciences really prove anything.

Cheers,

Ross-c

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