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The Science of Conjecture: Evidence and Probability before Pascal
Before Pascal and Fermat's discovery of the mathematics of probability in 1654, how did we make reliable predictions? What methods in law, science, commerce, philosophy, and logic helped us to get at the truth in cases where certainty was not attainable? In this text, James Franklin examines how judges, witch inquisitors, and juries evaluated evidence; scientists weighed reasons for and against scientific theories; and merchants counted shipwrecks to determine insurance rates. Sometimes this type of reasoning avoided numbers entirely, as in the legal standard of proof beyond a reasonable doubt; at other times it involved rough numerical estimates, as in gambling odds or the level of risk in chance events.
512 pages, Hardcover
First published January 1, 2001
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Displaying 1 - 12 of 12 reviews
December 27, 2017
If you don't know about probability, you should read this book to learn about it. If you know about probability, you should read this book to learn that you are wrong.
The book is quite dense and hard to read (especially the parts about law), but it is well worth it. It is nice to know that in 21th century we are still capable of science and connecting the dots, not just minmaxing in one domain.
The book is quite dense and hard to read (especially the parts about law), but it is well worth it. It is nice to know that in 21th century we are still capable of science and connecting the dots, not just minmaxing in one domain.
December 21, 2017
If you have a formal science background, the only way in which you know "probability" is via assorted mathematical equations. If you work in AI, you try to apply those equations (or related things, like neural nets) to solve tasks. But if you work in AGI, you have to ask harder questions, like "how does one know if something is true?" and "what does it mean to know something?" and "how can I prove that this is true?" and for that, math is insufficient. The point is that courts of law use proofs all the time: "proof of guilt beyond a reasonable doubt" and this is NOT a statement about Bayesian inference. So what is it?
It turns out that this is the highest form of a theory of probability developed by the medieval Scholastics, and survives unmodified to this very day in our legal system. Franklin explains who the Scholastics are, why they did what they did, and why its important. Well, he actually explains/reviews much much more, but this was my favorite, most memorable part. So if you have that formal science background, this is a very refreshing and entertaining reminder that there's much more to probability than just equations, and how it is that we got to here.
p.s. turns out "Occam's Razor" is a good bit more subtle than it's current modern-day usage. It was originally a statement about the nature of probability and proof, and how God evades it, when performing miracles. The current, modern form of "Occam's Razor" was actually first stated by Aristotle; what Occam did was add the twist about God.
It turns out that this is the highest form of a theory of probability developed by the medieval Scholastics, and survives unmodified to this very day in our legal system. Franklin explains who the Scholastics are, why they did what they did, and why its important. Well, he actually explains/reviews much much more, but this was my favorite, most memorable part. So if you have that formal science background, this is a very refreshing and entertaining reminder that there's much more to probability than just equations, and how it is that we got to here.
p.s. turns out "Occam's Razor" is a good bit more subtle than it's current modern-day usage. It was originally a statement about the nature of probability and proof, and how God evades it, when performing miracles. The current, modern form of "Occam's Razor" was actually first stated by Aristotle; what Occam did was add the twist about God.
March 8, 2021
If the title of this book seems daunting to you, well, then, your instincts are sound. This is not a book for the faint of heart. However, if you're up for an amazing intellectual trek through the high-country (and some low country) of the mind, then you'll find this book a genuinely rewarding experience. I came to the book via a recommendation from Nassim Taleb, and the praise that Taleb expressed for the book proved more than accurate.
Author James Franklin is an Australian mathematician-philosopher, but this description sells him short. The breadth of learning displayed in this volume is truly astonishing. Reading it, you might guess him a linguist, a lawyer, a rhetorician, a medievalist, a scientist, and so on. As the title lets you know, his topics are broad--"evidence" and "probability"--and his account runs from the dawn of Western civ in Egypt and Mesopotamia up to the early modern period of Pascal. (Would that someone write a similar history of Indian and Chinese thought!) Pascal, along with Fermat and Huygens, and a few lesser-known figures, marked a change in thinking about probability when they developed mathematical models and algorithms for calculating the odds (probabilities) involved in stochastic games of chance, such as dice. But as Franklin notes from the beginning of this book, most thinking about probability throughout Western history, including the period after Pascal, addresses probability (and chance) by the use of ordinary language. We see this demonstrated in terms such as "more likely than not," "a preponderance of the evidence," and "beyond reasonable doubt" to give examples of common phrases still used today by lawyers, judges, and juries.
Franklin traces ideas about evidence and probability through the domain of law, which proves the most significant domain for delineating issues of evidence in general and probabilities in particular. But Franklin also addresses developments about these topics in rhetoric, philosophy, theology, moral theology and philosophy (such as the casuistry of the Jesuits), insurance and business law, and natural science. Thinking about issues of evidence and probability has its roots in Greek and Roman thought, but perhaps more noteworthy is the fact that medieval thought and practice analyzed and advanced these concepts greatly. Franklin argues adamantly against many calumnies hurled against medieval thought by modern critics. Many post-classical, pre-Renaissance thinkers receive attention and implicit praise from Franklin for their groundbreaking insights: names like Baldus, Orseme, Duns Scotus, Buridan, Ockham, John of Salisbury, and Nicholas of Autrecourt, and so on. Many of these thinkers and sources were new or only vaguely familiar to me.
There are times, I must admit, when I found the going a bit slow, although only in the relatively small section on Pascal and his peers did Franklin delve much into math as such. However, I'm quick to forgive Franklin for going a bit deep into the weeds at some points because of the importance of his overall message. Indeed, if you're pressed for time or just want to dip your toe in the get the feel, just read his prefaces (original and 2015), Conclusion, and Epilogue and you will have received a valuable reward for your time. Issues of evidence and the challenge of probabilities are as important and vital to our well-being today as they have been at any time throughout history. Indeed, given the extraordinary human powers that now threaten the entire planet and the continued well-being and survival of humankind as a species, we'd do well to do all we can to educate ourselves about these principles and thereby promote sound decision-making involving issues of evidence and probability. These terms were a part of my everyday concerns as a lawyer who practiced before trial and appellate courts (and administrative tribunals). But issues of evidence and probability have application quite as much (albeit less explicitly so) in our everyday lives. We experience these issues as individuals and as members of groups, for instance, as members of political entities that make decisions that affect our well-being from the level of our neighborhoods to the level of our nation and even now involving our entire world. For instance, we see these issues raised and discussed in great depth and with great concern in our thinking about how to best address climate change.
Conclusion: The Science of Conjecture is quite an amazing book as a work of scholarship and as a prompt to thought. I would compare in its comprehensiveness and depth to Thomas McEllivey's The Shape of Ancient Thought: Comparative Studies in Greek and Indian Philosophies. High praise indeed!
Author James Franklin is an Australian mathematician-philosopher, but this description sells him short. The breadth of learning displayed in this volume is truly astonishing. Reading it, you might guess him a linguist, a lawyer, a rhetorician, a medievalist, a scientist, and so on. As the title lets you know, his topics are broad--"evidence" and "probability"--and his account runs from the dawn of Western civ in Egypt and Mesopotamia up to the early modern period of Pascal. (Would that someone write a similar history of Indian and Chinese thought!) Pascal, along with Fermat and Huygens, and a few lesser-known figures, marked a change in thinking about probability when they developed mathematical models and algorithms for calculating the odds (probabilities) involved in stochastic games of chance, such as dice. But as Franklin notes from the beginning of this book, most thinking about probability throughout Western history, including the period after Pascal, addresses probability (and chance) by the use of ordinary language. We see this demonstrated in terms such as "more likely than not," "a preponderance of the evidence," and "beyond reasonable doubt" to give examples of common phrases still used today by lawyers, judges, and juries.
Franklin traces ideas about evidence and probability through the domain of law, which proves the most significant domain for delineating issues of evidence in general and probabilities in particular. But Franklin also addresses developments about these topics in rhetoric, philosophy, theology, moral theology and philosophy (such as the casuistry of the Jesuits), insurance and business law, and natural science. Thinking about issues of evidence and probability has its roots in Greek and Roman thought, but perhaps more noteworthy is the fact that medieval thought and practice analyzed and advanced these concepts greatly. Franklin argues adamantly against many calumnies hurled against medieval thought by modern critics. Many post-classical, pre-Renaissance thinkers receive attention and implicit praise from Franklin for their groundbreaking insights: names like Baldus, Orseme, Duns Scotus, Buridan, Ockham, John of Salisbury, and Nicholas of Autrecourt, and so on. Many of these thinkers and sources were new or only vaguely familiar to me.
There are times, I must admit, when I found the going a bit slow, although only in the relatively small section on Pascal and his peers did Franklin delve much into math as such. However, I'm quick to forgive Franklin for going a bit deep into the weeds at some points because of the importance of his overall message. Indeed, if you're pressed for time or just want to dip your toe in the get the feel, just read his prefaces (original and 2015), Conclusion, and Epilogue and you will have received a valuable reward for your time. Issues of evidence and the challenge of probabilities are as important and vital to our well-being today as they have been at any time throughout history. Indeed, given the extraordinary human powers that now threaten the entire planet and the continued well-being and survival of humankind as a species, we'd do well to do all we can to educate ourselves about these principles and thereby promote sound decision-making involving issues of evidence and probability. These terms were a part of my everyday concerns as a lawyer who practiced before trial and appellate courts (and administrative tribunals). But issues of evidence and probability have application quite as much (albeit less explicitly so) in our everyday lives. We experience these issues as individuals and as members of groups, for instance, as members of political entities that make decisions that affect our well-being from the level of our neighborhoods to the level of our nation and even now involving our entire world. For instance, we see these issues raised and discussed in great depth and with great concern in our thinking about how to best address climate change.
Conclusion: The Science of Conjecture is quite an amazing book as a work of scholarship and as a prompt to thought. I would compare in its comprehensiveness and depth to Thomas McEllivey's The Shape of Ancient Thought: Comparative Studies in Greek and Indian Philosophies. High praise indeed!
October 29, 2021
When we think of probability, it is often Enlightenment names like Pascal and Bayes, which spring to mind. The genius of this book is that it show how much we miss if we neglect the riches of medieval and pre-medieval thought.
Tthe classical era had an overwhelming interest in certainty and the deductive thought of logic and mathematics. But traders also needed to insure ships, and sailing was an extremely risky business. Although no explicit theory of probability and risk sprang up, traders inched their way towards a working theory. Sailing at different times of the year, and sailing to different destinations all led to varying rates of insurance.
When we come into the medieval period the author’s erudition opens up important ethical texts and business practices.
Probabilism was a particularly interesting ethical theory in that it argued that moral dilemmas could be settled with a course of action that was ‘probably’ moral even if it was not more probably so, than not. We can only look back on this with astonishment. If 1000 academics said that Euthanasia was murder, but a single one had said that it wasn’t, then that could produce a very low probability in favour of euthanasia as morally acceptable. Under some versions of probabilism someone facing an ethical dilemma could use that low probability and prefer it to the weight of opinion arguing the opposite case.
Unsurprisingly probabilism led to moral laxism. Almost anything could count as probable on this low threshold. What is interesting as we look back at it, is the way that contemporary thinkers could see the problems, but they did not have a vocabulary of probatility with which to express themselves.
Equally as interesting was the medieval practice of annuities. People would make pledges to abbeys in return for a fixed income for their life. The rates would vary depending on age and circumstances, once again reflecting an acute appreciation of probabilities, even though it was never articulated into a theory.
One of the interesting things about the book is the way that the author blends in-depth analytic exposition, with thoughtful commentary. On the issue of annuities he wonders why the issue was not probed more carefully by academics in the middle ages. Then he notes that those same academics were often sponsored by the Religious Orders benefiting from the trade in annuities. Could such a conflict of interest have impacted upon their academic speculations ?
The breadth of the book is exhausting. It covers 1700 years with a main focus on European thought, but it does also include asides relating developments to Jewish and Islamic thinkers. There is the occasional reference to Japanese and Chinese thinkers, although it is clearly a little tokenish in places. If there was any aread that could have been developed it was its coverage of those issues.
Overall, however, the book is full of interesting details. It is an academic book, so it is demanding in places. But the prose is readily readable and eminently rewarding, if readers are prepared to give it some time.
Tthe classical era had an overwhelming interest in certainty and the deductive thought of logic and mathematics. But traders also needed to insure ships, and sailing was an extremely risky business. Although no explicit theory of probability and risk sprang up, traders inched their way towards a working theory. Sailing at different times of the year, and sailing to different destinations all led to varying rates of insurance.
When we come into the medieval period the author’s erudition opens up important ethical texts and business practices.
Probabilism was a particularly interesting ethical theory in that it argued that moral dilemmas could be settled with a course of action that was ‘probably’ moral even if it was not more probably so, than not. We can only look back on this with astonishment. If 1000 academics said that Euthanasia was murder, but a single one had said that it wasn’t, then that could produce a very low probability in favour of euthanasia as morally acceptable. Under some versions of probabilism someone facing an ethical dilemma could use that low probability and prefer it to the weight of opinion arguing the opposite case.
Unsurprisingly probabilism led to moral laxism. Almost anything could count as probable on this low threshold. What is interesting as we look back at it, is the way that contemporary thinkers could see the problems, but they did not have a vocabulary of probatility with which to express themselves.
Equally as interesting was the medieval practice of annuities. People would make pledges to abbeys in return for a fixed income for their life. The rates would vary depending on age and circumstances, once again reflecting an acute appreciation of probabilities, even though it was never articulated into a theory.
One of the interesting things about the book is the way that the author blends in-depth analytic exposition, with thoughtful commentary. On the issue of annuities he wonders why the issue was not probed more carefully by academics in the middle ages. Then he notes that those same academics were often sponsored by the Religious Orders benefiting from the trade in annuities. Could such a conflict of interest have impacted upon their academic speculations ?
The breadth of the book is exhausting. It covers 1700 years with a main focus on European thought, but it does also include asides relating developments to Jewish and Islamic thinkers. There is the occasional reference to Japanese and Chinese thinkers, although it is clearly a little tokenish in places. If there was any aread that could have been developed it was its coverage of those issues.
Overall, however, the book is full of interesting details. It is an academic book, so it is demanding in places. But the prose is readily readable and eminently rewarding, if readers are prepared to give it some time.
Read
June 23, 2022I have a law school friend who proudly (or not proudly? I couldn't quite understand his sentiment) professed to never having thought of the word 'probability' in his entire life. I thought privately, you certainly have, although Lady Probability was dressed in different attire when you met her. This book confirms it and more. Before some people with gambles to win and too much time on their hands sat down and codified these things in mathematical language, the sense of an event being 'unlikely', 'likely', 'almost certain' or 'nigh-impossible' was present everywhere through law, governance and trade. Not much of a difference today, if you think about how these fields manifest in the 21st-century! It's interesting to read about the ingenious ways people used to predict probabilities in the absence of maths.
This is a dense read requiring much peripheral knowledge about history and religion, and I could spend up to an hour on a single page just looking up the context of the references he made, for fear that I'd entirely lose the plot by the next page. But all in all, a highly rewarding read. Incidentally, I found that James Franklin works at my university. It is highly unlikely (ha) that I'd ever meet him, but if I do, I will congratulate him on a highly illuminating book.
This is a dense read requiring much peripheral knowledge about history and religion, and I could spend up to an hour on a single page just looking up the context of the references he made, for fear that I'd entirely lose the plot by the next page. But all in all, a highly rewarding read. Incidentally, I found that James Franklin works at my university. It is highly unlikely (ha) that I'd ever meet him, but if I do, I will congratulate him on a highly illuminating book.
February 3, 2019
There is no questioning the scholarship and thoroughness of this book. The only problem is that it truly reads like a reference book. And if it were sold as such I'd easily give it 5 stars. I'm sure I'll be referring to it many times. It does not overlook nonmathematical contributions to the "science of conjecture" and that's a big strength of the book, though it also forces the author to really cover a lot of material most wouldn't normally think of as directly related probability. The closest it comes to a readable book is in the conclusion, but just enumerating the subsections (fields)in that chapter (12) can give some idea of how much is crammed into this book and its style:
Mathematics, Legal Theory, Political Theory, Economics, Psychology, Philosophy, Linguistics, Physics, Arithmetic, Geometry, Ethics, Anthropology, Hermeneutics, Knowledge Organization and Information Technology, Argument and Logic and a few others.
Mathematics, Legal Theory, Political Theory, Economics, Psychology, Philosophy, Linguistics, Physics, Arithmetic, Geometry, Ethics, Anthropology, Hermeneutics, Knowledge Organization and Information Technology, Argument and Logic and a few others.
May 4, 2022
Although this book has 'Probability' in the title it isn't really about probability at all. It's a catalogue of probabilistic thinking before its mathematical formalisation in the mid 17th century.
An affinity for probability or the history of probability is irrelevant. That's not what this book is about. Your enjoyment will be dependent on your interest in Law, Religion, Science, and Philosophy. I like some of these topics so enjoyed these sections of the book, skipping the others. I would encourage the reader to do the same; Franklin struggles to find a common thread that links chapters in a satisfying way.
But he does manage to do this in the conclusion and epilogue, the two best parts of the book.
An affinity for probability or the history of probability is irrelevant. That's not what this book is about. Your enjoyment will be dependent on your interest in Law, Religion, Science, and Philosophy. I like some of these topics so enjoyed these sections of the book, skipping the others. I would encourage the reader to do the same; Franklin struggles to find a common thread that links chapters in a satisfying way.
But he does manage to do this in the conclusion and epilogue, the two best parts of the book.
November 26, 2017
Not as entertaining or compelling a read as I expected (I'd put it down last year and picked it up again this year), but Franklin's sheer erudition is mind-blowing (his extensive, and almost exhaustive, sources include works in original Latin, Italian, German, and Spanish, for example). As the author admits, there ARE a lot of quotes, many of which could have been made less perplexing with a bit of help and orientation from the author (but then that may have gone a little against his policy of letting the quotes speak for themselves).
June 16, 2020
I'm only giving this book 4 stars, because it was so far over my head (Law-intensive)...
but I read it. haha..
It is dense.
Maybe one day I will find myself educated enough to give it another go.
but I read it. haha..
It is dense.
Maybe one day I will find myself educated enough to give it another go.
June 5, 2021
A magisterial work, one of deep clarity, convincing reason, and supreme scholarship. Set's a high bar for future discussions on probability.
August 2, 2023
Slow going, yet informative, but probably a book only a mathematician would love.
December 20, 2017
This is a great work of scholarship.
From the ancients and their ideas of credibility to not-exactly-generalizable maxims about likelihood or reasonable doubt.
Probability is the meta subject of meta subjects.
From the ancients and their ideas of credibility to not-exactly-generalizable maxims about likelihood or reasonable doubt.
Probability is the meta subject of meta subjects.
Displaying 1 - 12 of 12 reviews