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I am a PhD in biological sciences with some background in graduate-level probability. I am interested in questions like what does it mean for an event to have probability $x$ at a philosophical level.

I have read some of Russell's writings on the philosophy of mathematics and I am maybe looking for something in that flavor. Maybe more specifically what does it mean for a process to be random.

User1865345
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Nuri Alço
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    Check https://plato.stanford.edu/entries/probability-interpret/ – Tim Feb 22 '23 at 12:18
  • This seems a bit like an opinion question and it may be better to be more clear about what specifically you are looking for. Are you just looking for books on probability? – Shawn Hemelstrand Feb 22 '23 at 12:50
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    what does "philosophical level" mean? I doubt this forum is a good place to even discuss this subject. I haven't seen anything useful or even sensible coming out of dragging scientific concepts out of their scientific contexts. – Aksakal Feb 22 '23 at 13:15
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    https://errorstatistics.com/ for instance https://errorstatistics.com/2013/07/14/stephen-senn-indefinite-irrelevance-2/ randomness discussed in context – kjetil b halvorsen Feb 22 '23 at 13:30
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    I don't know what you want from the philosophical context, but have a look at Probability Theory: The Logic of Science by Jeynes. – User1865345 Feb 22 '23 at 13:51
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    Ian Hacking is a philosopher who has written several books on this sort of thing: e.g. The Taming of Chance, and The Emergence of Probability. – Jeremy Miles Feb 22 '23 at 17:20
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    You can't do science without doing philosophy is my opinion – Nuri Alço Feb 25 '23 at 17:57

4 Answers4

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Even though people speak about Bayesians and frequentists, as if statisticians are some sort of followers of a religion, most of statistics is very straightforward and pragmatic without bothering too much about philosophy.

Because of that there aren't many famous books about philosophy of statistics written by statisticians. I would regard instead as important statisticians' books or articles such things like

  • Fisher (1925) Statistical Methods for Research Workers
  • Kolmogorov, (1950 English)(1933 German) Foundations of the theory of probability
  • Cramér (1946) Mathematical Methods of Statistics

When you search philosophy on this forum then you may encounter some pointers in threads such as Who Are The Bayesians? or Who are frequentists? and discussions about the likelihood principle. But not much of it is more insightful than the 'against the mathematicians' written over two millennia ago.

Sextus Empiricus
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Here are a few that focus on the philosophy of statistics:

Gabbay, D. M., Thagard, P., Woods, J., Bandyopadhyay, P. S., & Forster, M. R. (2011). Philosophy of Statistics (Vol. 7). Elsevier.

Gelman, A. (2009). Bayes, Jeffreys, prior distributions and the philosophy of statistics. Statistical Science, 24(2), 176-178.

Good, I. J. (1988). The interface between statistics and philosophy of science. Statistical Science, 3(4), 386-397.

Mayo, D. G. (1979). Philosophy of statistics. University of Pennsylvania.

Robert Long
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Here are some suggestions I can provide that are mostly historical or canonical texts but ultimately have philosophical roots. My first two bullets are more specific to probability whereas the other two are more generalist texts that may be interesting. A lot of philosophical underpinnings are buried in the walls of stats books but are nonetheless important:

  • A couple of good books that serve as good documents of the historical developments of statistics as well as the philosophical arguments they were trying to tackle are The Lady Tasting Tea by Salsburg and The Unfinished Game by Devlin, preferably read back to back. Reading them gives insight on what many mathematicians and statisticians were fighting for in developing these methods. You would probably greatly appreciate the latter because it is more specific to developing probability theory, but the former also talks a lot about this and even mentions Russell in brief.
  • Fisher's book The Design of Experiments put forth a lot of the rationale behind NHST and the original Neyman-Pearson paper introduced to the Royal Society provide useful insights about the NHST paradigm. These are works that I wish I was introduced to a lot earlier, as I was not aware of the Fisher-Neyman-Pearson distinctions behind NHST until reading them. Again, because you are committed to the probability side of this, these are probably essential texts to read to understand the rationale behind their methods.
  • The Grammar of Science by Karl Pearson is another good read, which is largely conversational. Spearman's paper on IQ provides interesting insights into how psychology was far too descriptive and needed to be far more inferential (whereafter he makes the case for the methods he developed).
  • Tukey's book on exploratory data analysis (EDA) explains important parts of how exploratory data analysis is such a pivotal part of statistical inference, and this paper by Tong does a good job of elaborating more on the less coveted but equally important aspects of EDA in science.

I will say as an aside that the philosophy of statistics probably can't be easily gathered with one book or article. There are many different perspectives, largely shaped by historical and contextual factors, that really generate a larger understanding of the statistical world. You will probably have to gather a conscensus on your own from reading multiple texts where the "philosophical underpinnings" lie.

Shawn Hemelstrand
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Statistics and Truth: Putting Chance to Work, by C Radhakrishna Rao (yes, the author is the "R" in C-R Inequality and Rao-Blackwell Theorem).

User1865345
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Zhanxiong
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