The Emergence of Probability: A Philosophical Study of Early Ideas About Probability, Induction and Statistical Inference

by Ian Hacking

Historical records show that there was no real concept of probability in Europe before the mid-seventeenth century although the use of dice and other randomizing objects was commonplace. Ian Hacking here presents a philosophical critique of early ideas about probability, induction and statistical inference and the growth of this new family of ideas in the fifteenth, sixteenth and seventeenth centuries. The contemporary debate centres round such figures as Pascal, Leibniz and Jacques Bernoulli. What brought about the change in ideas? The author invokes in his explanation a wider intellectual framework involving the growth of science, economics and the theology of the period.

Genres: Philosophy, History, Mathematics, Science, Nonfiction, History Of Science, Economics

Paperback

Published August 31, 1984

About the author

Ian Hacking is Professor Emeritus of Philosophy at the University of Toronto, specialised in the History of Science.

Wikipedia entry

Reviews

[Nat]

Hacking's genealogy of probability is what reading Foucault would be like if Foucault was enjoyable to read. The first half is an account of how the idea of something being "probable" went from meaning that it was attested to by an authority to allowing the world itself to be such an authority, to then being associated with what we moderns think of as "evidence" (that is, not just the fact that someone says something is the case, but observing some testimony-independent facts). By telling this story, Hacking complicates ordinary language philosophy by quoting Gassendi (one of Descartes' contemporaries) in 1658, saying:

"We use the expressions 'to have an opinion' and 'to know' interchangeably, as the practice of everyday speech shows, and if you look at the matter carefully, knowledge and opinion can be considered synonyms".

"To know" doesn't mean what it used to.

And there's an equally interesting discussion of the emergence of the scientific method, in which Hacking distinguishes four attitudes towards experimentation:

Dissection (cutting things open to see how they work), the test (theory T predicts that x should be followed by y, so bring about x and see if it is followed by y; if it is, the theory is corroborated, if not, it is confuted), the adventure(!) (just combining stuff for the fun of it, like the alchemists, not guided by theory, seeing what happens), and the diagnosis.

I confess that the alchemist's notion of experiment as adventure sounds like the most fun to me.

[Mohamad Zolfaghari · Rating 4 out of 5]

I chose this book by mistake. As a Mathematician i expected this book to be much more mathematical but it turned out to be fully philosophical!
Considering this was my first book on philosophy, it took me a long time reading it. The Author expect the reader to have a firm knowledge of philosophy and be familiar with work of Descartes, Bacon .... which made me to have a computer on my side and search throughout my reading.
Although i admit i did not grasp all the concepts and did not fully/deeply understood all reasonings, this book had a big impact on my thoughts.
I collect some gems from this book and i believe it will be much better when i come back to this book after couple of years. Biggest gem for me, was to understand the mind of people before 1600 and how modern human have a completely different mindset. Also to understand that science is not just proves and formula, science needs a basic of philosophy supporting it and a person like Leibnitz whom i knew as a great mathematician was actually a great philosopher. Also reading a book in this level (however i did not follow everything) showed me how big problems are tackled by big people, how the border of science is fuzzy and what big scientists do in order to push these borders.

[Alexander · Rating 5 out of 5]

Hacking's Emergence of Probability is a fantastic, erudite, exquisitely written treatment of the growth of the idea of probability. I only read the early portions while poking around in the latter parts but I felt that everything I read made me smarter and better informed. Hacking just has a gift for accumulating, synthesizing, and communicating ideas and information. He is a very sensitive reader of other authors who pays careful attention to what they are saying, and why, and does an excellent job of situating his view among others and showing why his is to be preferred. The treatment of Pascal's wager is extremely good and he does a very fine job of detecting the structure of the argument and pointing out its real weak points (namely, its initial premises, rather than its formal structure, which is flawless), while showing how badly formulated most objections to the wager are. He is also a joy to read, which is quite rare in this genre. A wonderful book.

[Lourens · Rating 4 out of 5]

Hacking poses that the conceptual innoviations that underpin probability all happened in or around the 1660s. Probability emerged from the Renaissance transformation in opinion, and the evolution of "signs" from medieval superstition to evidence in the context of induction. There was a duality between epistemological chance (confidence about beliefs) and aleatory chance (concerning games), that would not be united until the late 17th century.
Two cool facts: Pascal's wager, although often dismissed as flawed, was truly novel in its conception of decision theory under uncertainty. The "expectation" of a bet was formalized before the probability of an event, and was even applied to life expectancy using mortality tables (shoutout Johan de Witt).

Expect a tough book to get through. It presumes that you have a lot of context on epistemology, probability theory, statistics, and also that you already have quite solid understanding about the the history of mathematics. That is all fine. If you're willing to do some research on the side, there are many rabbit holes to explore.

I did not enjoy the structure, both across and within chapters. It could've done with a lot more signposting: more guiding paragraphs that tell the reader what we will talk about now, and foreshadow why it is relevant. Instead, often a paragraph's relevance only becomes apparent a few paragraphs later. The first few chapters I would try and find steps of reasoning I thought I missed, before resigning to this rambling style.

Finally, and this might just be a characteristic of this academic field, but a significant part of the text is dedicated to speculating what someone was thinking. This feels a bit silly at times. But I appreciate the transparency, instead of presenting unreasonable certainty, something that would've been at odds with the subject matter itself.

[Kate · Rating 3 out of 5]

Better than I was expecting. A must-read for historians and philosophers interested in the development of probability (obviously) and evidence (not so obvious). Four stars for a disciplinary audience. Three for the general reader - while clear and a surprisingly fast read, Hacking assumes in his reader a working base of knowledge about 17th century science (and more specifically mathematics). He does not waste space summarizing Descartes' Discourse on Method or explaining Liebniz's metaphysics; he assumes you are basically comfortable with the Baconian project. Readers lacking this background may find even the less-theory-laden chapters difficult to parse. Regardless, I enjoyed it more than I was expecting.

[Ricardo Moreno Mauro · Rating 4 out of 5]

Un excelente libro que mezcla la historia con la filosofía de la ciencia La probabilidad, algo que todos estamos acostumbrados hoy en día ¿De donde viene, su origen, no solo en las matemáticoas sino que en cada instante de nuestras vidas, Muy bueno, y académico, aunque de divulgación se recomienda tener una cierta base filosófica

[Kyle Muntz · Rating 5 out of 5]

unspeakably brilliant in so many ways, especially for hacking's insights on the historical development of epistemology (leading up to Hume). also: some of the clearest theoretical prose I've ever read

[Brendan · Rating 3 out of 5]

Fine.

This book was just fine.

Definitely by an academic and for other academics. There is nothing wrong about that, but I was hoping for something with a little bit more gumption. Perhaps a bit more analysis on why probability was a practical and necessarily emergent phenomenon of a certain era. This one seemed to get bogged down into too many weedy, multi-page long details about exactly how words were defined and exactly when they were defined that way. I feel as if I just read a talented grad student's unedited first attempt at a thesis paper. There are some gems, so I leave you with my favorite quote:

I once found an original oil painting of a notable Elizabethan courtier in my college brewhouse, and was able to hang him on my wall. I looked him up and found that he had served as a senior civil servant in a succession of turbulent and contradictory reigns, now catholic, now not, each given to executing its predecessors.
'How could he do this?', I asked a conservative young historian.
'How could human society survive without such men?', he replied.
A parable: there have to be continuities or else everything will fall apart.

[David Jinkins · Rating 3 out of 5]

As you will know if you have worked in mathematics, choosing clear and parsimonious notation is one of the most important ways to make ones ideas clear. In my experience, it is difficult to even think clearly without good notation. The current common notation of probability, as I understand, was not developed until the later 19th and 20th centuries. This makes the insights of the founders of the field in the 17th and 18th centuries even more impressive. The Emergence of Probability gives the reader first-hand experience in the difficulty of understanding ideas without easily understandable notation. Here is a random page I turned to:

In this final chapter the author applies numerical measures to probability. One 'contingent event' in question is the winning of a game where each of ten players risks one coin for an even chance of getting ten back. Loss is neuf fois plus probable than gain. There are 'nine degrees of probability of losing a coin for only one of gaining nine'. These are the first occasions in print where probability, so called, is measured.

I can understand this sort of language if I puzzle over it long enough, but it is hard for me.

The book was too "in the weeds" for me, with detailed discussions of some minor figures from the early 17th century and a detailed descriptions of some important books from that time period. What I took away from the book as a whole was that probability came out of two traditions. One of them involved dice games, where the gambler is trying to determine the precise frequency of a particular even occurring. The other is about the degree of belief one has in something occurring. This latter type of probability has its basis in an earlier meaning of probable, which meant something like "according to a reliable source."

When I was a first year graduate student, my econometrics professor was a "frequentist", and thought Bayesian statistics was a joke because its results depend on a prior, and no one knows where those come from. Later I learned that "Bayesians" criticize frequentists for relying on limit theorems in a finite world. Hacking shows that this debate was baked into mathematical probability from the beginning.

[Ciaran Yates · Rating 4 out of 5]

Ok so I’m bored, I’ve got a two hour plane journey ahead of me and I’ve just finished this book - so let’s go.

This is one of those books that makes you feel stupid - but in a good way. Coming out of it you feel like you’re able to comprehend something about the world that you simply couldn’t have beforehand.

More than anything Hacking really puts into focus how radically different the inner lives of people living only four/five hundred years ago must have been. It still seems kind of crazy that an idea as simple as probability didn’t really exist, at least not as we understand it, until around 1660. Makes you wonder how many other concepts there are that are commonplace nowadays people but that back in the day simply did not have in their mental artillery?

The problem of induction (Can you really say “Swans are white” simply because you have never seen one that isn’t?) for example. To me it seems like a fairly simple idea. It’s the type of question that I think a modern person could come to raise all on their own, an inspired “shower thought” on some uneventful Thursday morning. However, as Hacking makes abundantly clear, we’re only really able to see this problem because we’re already working with an intellectual framework within which it can be clearly expressed. A framework which apparently didn’t exist, (at least in Europe) until after the 17th century.

Its kind of like cryptic crosswords. I’m personally rubbish at them - I really have no idea how they work. However, I have a friend who is truly a cryptic crossword wizard. What looks like gibberish to me looks to him like a coordinated system of signs: a mosaic organised in such a way that when perceived in the correct fashion presents a problem for him to solve. Although we could both be staring at the same broadsheet, only he knows the appropriate way to interpret what we see and, as such, only he would be able to perceive the problem at hand. To see the problem you need to know the right rules to follow.

Understanding this does inspire a certain level of gratitude that I got to grow up in a time where people have already spent a lot of time trying to, metaphorically speaking, figure out these rules. It means that I get to have thoughts in the shower that simply weren’t concretely conceivable for millennia of human civilisation. Thanks to a couple decades of philosophy, and certain contingent social and economic factors, you and I can now read the cryptic crossword! Which is kind of cool, or at least it is to me.

Reading this book also makes me think that, at least in terms of the ideas being bandied about, it’s possible that the future will look more mysterious and different, than it’s possible for us to conceive from where we stand right now. How many problems are still out there for us to solve that we, thinking about the world as we do, simply cannot perceive yet? What are the ideas that will seem obvious to someone alive 500 years from
now that we at present are completely oblivious to? Big stuff.

However, despite being very smart and cool and interesting, I will say that a major issue with this book is that there are probably only a pocketful of people who have ever lived that could possibly understand it in its entirety. Expecting the reader to already possess an in depth knowledge of not just probability theory but also of subjects ranging from epistemology to the history of medicine is asking a bit much in my opinion. Although in fairness to Hacking, I’m probably not the intended audience. So maybe this is more of a me problem.

Anyways, theres 30 mins left of the flight and I’m left wishing I had napped instead of writing this. In short, great book. Probably wouldn’t recommend it to anyone I know though.

[0xd34df00d · Rating 4 out of 5]

A wonderful little historical and philosophical excursion into the birth of the whole concept of probability, along with the frequency/epistemology duality (even if I don’t agree with every interpretation or derivation that Hacking makes). Very high signal, very high food-for-thought protein per page.

And, in addition to the main dish, it’s amazing to see how some tangential modern tropes (like mechanizing mathematics) were already present in the XVII century in Ars Combinatoria, for example.

The only problem (but I guess it’s my problem) is that I still don’t understand why exactl probability came into discourse specifically in 1660s or so — as Hacking emphasized, answering that is the goal of his work, and not just enumerating who said what and when. And I don’t have a clear answer yet that’s better than “well, it's the stars so aligned that a few thinkers thought together productively, and also the plague of 1603 provided some recorded data and a good moral reason to dig into it”, roughly.

[Matthew · Rating 5 out of 5]

So glad I followed an oomfie’s recommendation to the work of Ian Hacking bc this book fully convinced me to inaugurate a philosophy of science era… I need a new thing to be dilettantish about, semiotics and psychoanalysis have been fun but there’s definitely room for a third now that grad school is done.

Great example of my favorite kind of nonfiction book—one that takes a single idea, probability in this case, and pulls it through the eye of a needle. Functions as a history of the philosophy of statistical science, which is exactly the kind of angle I required to ~get~ any of the mathematical stuff. Major healing inner child vibes bc man did I struggle with this stuff in school… luckily the years have built a pretty healthy tolerance for abstraction. And the payoff is that I get to finally learn how to solve logic puzzles about dice games!

Hacking is a great writer btw, this book would be totally unintelligible to non-specialists (🙋🏻‍♂️) if it weren’t for the clarity of his prose.

[Adrian Manea · Rating 5 out of 5]

Very impressive, this book left me wanting for more!

I'm a mathematician, so I have some formal training in probability theory. However, I was curious about the history of the concept -- I only knew that it originated in gambling --, and its philosophical implications.

This book delivered superbly, easy to understand and with many excerpts from the most influential thinkers. Where there was some "real" math involved, the author chose examples that were simple enough for anyone to grasp, and the philosophical discussion was pleasant and easy to read (for a non-philosopher like myself).

I liked the connections that the author kept highlighting with medicine and inductive reasoning -- I haven't considered the latter, so it was illuminating.

The only criticism I have is that it was too short. I would have liked it to be at least double, so there was more room for details. Nevertheless, this is where the rich references and bibliography help.

[Pierrot Seban · Rating 5 out of 5]

It's a great book. It's practically French, philosophically-minded history of concepts. As myself a philosopher highly interested in (but not a specialist of) 17th century authors, I really learned or re-learned a lot, which doesn't happen often at this point. A great and novel entry point into fascinating parts of the works of several great authors, from Pascal to Hume. And really illuminating on what is, in my view, a true and difficult problem : the nature of probability, as a thing in the world but also as a thing in modern European thought, and the enigma of why no notion of probability emerged (apparently) before the 17th century.

I don't believe the book offers a completely satisfiying answer, I'm not even quite convinced by the way it frames it, but it is still an excellent ressource and many passages are truly truly great and will be added in my personnal list of reference texts.

[Samuel Stanton · Rating 5 out of 5]

There is a lot to like about this book. Hacking's prose is thoughtful and detailed, but always within reach. I found myself making more time in my routine to read because of my anticipation for the next development in the artfully constructed narrative involving many of the major players in late-Enlightenment philosophy and mathematics. It is truly rare to find books that are so informative and yet thoroughly enjoyable.

[Sarah · Rating 3 out of 5]

Three and a half. This wasn't at all what I was expecting (or looking for), but was interesting and thoughtful nonetheless. Hacking's work is a historical examination of the philosophical emergence of probability theory, rather than an in-depth explanation of the stages of theory development themselves.

Cited in Money: The True Story of a Made-Up Thing, ch. 4. Borrowed from NOBLE network.

[Z. · Rating 4 out of 5]

I was looking for a theory-heavy overview of historical understandings of probability. This book isn't that. What Hacking tries to do here is clarify what the right primary sources to look at for such an understanding would be, and just enough theory for the links is put down. It makes for a very good reference work as a result which is why I rated it a 4.

[Dean · Rating 5 out of 5]

Thoroughly interesting. Presumes some knowledge of probability and history of science/philosophy. Made me read "The Taming of Chance" immediately after, but also wonder about how to learn more about probability in India, referred to briefly in the first chapter.

[Anh · Rating 2 out of 5]

You can tell it was written by a philosopher. There's no clear structure or progression.

[Stephen Wong · Rating 5 out of 5]

This book draws a sharp distinction between epistemic probability (the kind that "proves" or offers grounds for belief in something) and aleatory probability (the kind that is based on a distribution, whether formal or from observations, or from chance or luck). The book also attempts to point to the originating insights into the divergence that resulted in this distinction, and the chapters on Leibniz's approach that informs his entire philosophy are welcome elucidations or contributions on Leibniz. For somebody who has studied stochastic models (in finance and risk) only after having philosophical grounding in epistemology beforehand, this book offers the link between the two, as though a trapdoor has been opened from one discrete silo to the other. The interested reader will benefit from the book's treatment of induction (said to be contra-Aristotelian) yet will appreciate how Leibniz also used the law as a model of probability and certainty. To the contemporary general reader, the book will hopefully provide some sophisticated answers to questions of scientific knowledge and moral certainty, not the what is now becoming a dogmatic leaning towards what is called "the wisdom of crowds" or "the market is never wrong" or "if it quacks like a duck". On the other hand, perhaps this book may be a commentary on the philosophy of pragmatism which I might hasten to call a constructivist probabilism or materialism. No matter, I invite the reader to use the book to expand on its insights...

[YL · Rating 4 out of 5]

An excellent history of philosophy sort of take on 'the conditions of possibility' of probability theory as 'degree of belief'. I liked this book better than Daston's more history of science book 'Classical Probability in the Enlightenment', which covers roughly the same period but seems to make a more specific argument. Where hacking argues that probability emerged in the aftermath of a new way of reading and evaluating evidence -- beyond testimony, daston has a more histor-y approach where she sets down the conditions of emergence for individual concepts, some of which have to do with evidence, some of which do not. To me, it seems like Hacking is able to give a flavour of just how monumental a change it was to be able to say 'it is probably this' without delving into details I don't give a shit about, but probably someone cares about the specific details that Daston gives, somewhere.

[Mariana · Rating 4 out of 5]

Muy filosófico, y un poco rebuscado en algunas secciones, pero también muy interesante. Me encanta el análisis del origen de una idea que hoy damos por obvia (incluso si entenderla completamente no es trivial). Creo que si supiera un poco más de filosofía y los personajes históricos hubiera podido valorar un poco más este libro.

[Ira · Rating 2 out of 5]

Primarily informed by Leibniz input, it highlights important differences between aleatory and epistemic probability. Most interesting for its historical account of the lesser known contributors to the doctrine in the 17th and 18th century.

[Zarathustra Goertzel · Rating 3 out of 5]

As advertised, my intuition for probability has increased ;).
I think the importance of the difference between aleatory and epistemic probability is a bit forced. I guess the author is covering his tracks for modern critics ^^;

[Dave Peticolas · Rating 3 out of 5]

Hacking investigates the early history of ideas concerning probability and inference from statistical data.

[Kerem Cankocak · Rating 5 out of 5]

Hacking harika bir Bilim tarihçisi....

[Dan · Rating 5 out of 5]

Is the world deterministic? Does God play dice? What is probability: frequency, opinion, perception, authority, or else?
This is a book on archeology of probability and people who tried to answer these questions.