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Philosophical Devices: Proofs, Probabilities, Possibilities, and Sets
This book is designed to explain the technical ideas that are taken for granted in much contemporary philosophical writing. Notions like "denumerability," "modal scope distinction," "Bayesian conditionalization," and "logical completeness" are usually only elucidated deep within difficult specialist texts. By offering simple explanations that by-pass much irrelevant and boring detail, Philosophical Devices is able to cover a wealth of material that is normally only available to specialists.
The book contains four sections, each of three chapters. The first section is about sets and numbers, starting with the membership relation and ending with the generalized continuum hypothesis. The second is about analyticity, a prioricity, and necessity. The third is about probability, outlining the difference between objective and subjective probability and exploring aspects of conditionalization and correlation. The fourth deals with metalogic, focusing on the contrast between syntax and semantics, and finishing with a sketch of Godel's theorem.
Philosophical Devices will be useful for university students who have got past the foothills of philosophy and are starting to read more widely, but it does not assume any prior expertise. All the issues discussed are intrinsically interesting, and often downright fascinating. It can be read with pleasure and profit by anybody who is curious about the technical infrastructure of contemporary philosophy.
The book contains four sections, each of three chapters. The first section is about sets and numbers, starting with the membership relation and ending with the generalized continuum hypothesis. The second is about analyticity, a prioricity, and necessity. The third is about probability, outlining the difference between objective and subjective probability and exploring aspects of conditionalization and correlation. The fourth deals with metalogic, focusing on the contrast between syntax and semantics, and finishing with a sketch of Godel's theorem.
Philosophical Devices will be useful for university students who have got past the foothills of philosophy and are starting to read more widely, but it does not assume any prior expertise. All the issues discussed are intrinsically interesting, and often downright fascinating. It can be read with pleasure and profit by anybody who is curious about the technical infrastructure of contemporary philosophy.
214 pages, Hardcover
First published October 4, 2012
104 people are currently reading
966 people want to read
About the author
David Papineau
31 books26 followersDavid Papineau ( born 1947) is a British academic philosopher, born in Como, Italy.[1] He works as Professor of Philosophy of Science at King's College London and the City University of New York Graduate Center having previously taught for several years at Cambridge University where he was a fellow of Robinson College.
Papineau was born in Italy and grew up in Trinidad, England and South Africa.[citation needed] He received a BSc in mathematics from the University of Natal and a BA and PhD in philosophy from the University of Cambridge under the supervision of Ian Hacking.
He has worked in metaphysics, epistemology, and the philosophies of science, mind, and mathematics. His overall stance is naturalist and realist. He is one of the originators of the teleosemantic theory of mental representation, a solution to the problem of intentionality which derives the intentional content of our beliefs from their biological purpose. He is also a defender of the a posteriori physicalist solution to the mind-body problem
Papineau was elected President of the British Society for the Philosophy of Science for 1993–5, of the Mind Association for 2009–10 and of the Aristotelian Society for 2013-4
His latest book Knowing the Score (2017) is written for a general readership, and looks at a number of ways in which sporting issues cast light on long-standing philosophical problems.
Papineau lives in London with his wife, Rose Wild
Papineau was born in Italy and grew up in Trinidad, England and South Africa.[citation needed] He received a BSc in mathematics from the University of Natal and a BA and PhD in philosophy from the University of Cambridge under the supervision of Ian Hacking.
He has worked in metaphysics, epistemology, and the philosophies of science, mind, and mathematics. His overall stance is naturalist and realist. He is one of the originators of the teleosemantic theory of mental representation, a solution to the problem of intentionality which derives the intentional content of our beliefs from their biological purpose. He is also a defender of the a posteriori physicalist solution to the mind-body problem
Papineau was elected President of the British Society for the Philosophy of Science for 1993–5, of the Mind Association for 2009–10 and of the Aristotelian Society for 2013-4
His latest book Knowing the Score (2017) is written for a general readership, and looks at a number of ways in which sporting issues cast light on long-standing philosophical problems.
Papineau lives in London with his wife, Rose Wild
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Displaying 1 - 30 of 37 reviews
November 28, 2017
Possibly one of those books that should be required reading for (beginning?) high-school students. Would've been nicer if some of the proofs(*cough* Godels *cough*) were more detailed and had less ... handwaving, but that is to be expected from such a short book and one that focuses more on philosophy. The author also points to other works that provide the skipped over details in those cases as well, so that is nice!
January 29, 2020
2020 re-reading: I still admire this little book, although perhaps not as much as I did when I originally read it. A strong introduction to a number of topics which are not always well explained on philosophy courses, and yet which are essential to them. A useful read for anyone entering philosophy course.
original review
This little book summarises a range of what Papineau calls "Philosophical Devices", and I think of as tools - that is the tools used in a variety of philosophical situations, and which understanding of is often taken for granted in philosophy texts. You would probably have a to read quite a few books to cover the range of materials covered in this volume. It is written in a pleasantly light and easy style, for what could be very dry materials. The explanations are all clear.
Examples of the explanations I found particularly good are de dicto and de re modal statements, conditional probabilities and the explanations of syntax and semantics. In each case I have read much longer and more technical explanations which have been far less helpful. Understanding the devices in this book could help with philosophical studies in epistemology, methodology, and metaphysics to name a few.
My one caveat, is that in the introduction Papineau says "nothing in what follows presumes any prior knowledge". This is a compact and helpful guide - but as such if you really are coming at this with absolutely no prior knowledge I think this may be a little too compact! (I could be wrong about this). On the other hand, if you have some familiarity but find yourself confused from time to time, or want to remind yourself about various fundamental devices that you did understand but have forgotten, you should find this an excellent and very accessible guide.
original review
This little book summarises a range of what Papineau calls "Philosophical Devices", and I think of as tools - that is the tools used in a variety of philosophical situations, and which understanding of is often taken for granted in philosophy texts. You would probably have a to read quite a few books to cover the range of materials covered in this volume. It is written in a pleasantly light and easy style, for what could be very dry materials. The explanations are all clear.
Examples of the explanations I found particularly good are de dicto and de re modal statements, conditional probabilities and the explanations of syntax and semantics. In each case I have read much longer and more technical explanations which have been far less helpful. Understanding the devices in this book could help with philosophical studies in epistemology, methodology, and metaphysics to name a few.
My one caveat, is that in the introduction Papineau says "nothing in what follows presumes any prior knowledge". This is a compact and helpful guide - but as such if you really are coming at this with absolutely no prior knowledge I think this may be a little too compact! (I could be wrong about this). On the other hand, if you have some familiarity but find yourself confused from time to time, or want to remind yourself about various fundamental devices that you did understand but have forgotten, you should find this an excellent and very accessible guide.
January 31, 2025
This is a succinct but significant overview of basic philosophical concepts that anyone reading current philosophy, especially contemporary analytic philosophy, need to know.
Part 1 ,2and 4 were outstanding. However part 3 was less appealing to me, it could have been better, but it was such a joyful reading that I couldn't help but give it five-stars.
Part 1 ,2and 4 were outstanding. However part 3 was less appealing to me, it could have been better, but it was such a joyful reading that I couldn't help but give it five-stars.
May 19, 2014
I wish I had known about David Papineau's Philosophical Devices when I first started studying philosophy at an academic level. So much of what makes philosophy difficult to study is bound up in concepts and principles everyone seems to have as part of their background knowledge. Many times I have gone to office hours needing tutoring on the finer points of conditionals, probability theory, set theory, the analytic and synthetic distinction, and the difference between de re and de dicto necessity. Often I left with only a little better understanding of the issues, and a vague sense of what NOT to write in a paper fearing I would say something ignorant about them. This book goes a long way in alleviating that problem, because Papineau does a wonderful job breaking these rather abstruse topics down into plain language. I was especially impressed with the clarity exposition with respect to Kripke's modal semantics and causal theory of reference, Russell's paradox, Cantor's continuum hypothesis, and Godel's incompleteness theorem. I will revisit this volume again and again to brush up on these subjects to better my understanding and that of my students if I get the chance to teach.
December 15, 2012
A very interesting little book that gives a concise overview of the key concepts in logic, epistemology, probabilistic reasoning and metalogic. Very accessible. Recommended for all those who want to get acquainted quickly with the key concepts of modern analytic philosophy.
November 5, 2017
Good primer and/or refreshment on set theory, logic, metalogic, modal logic, Bayesian probability and Gödel. Don't expect much more than basics — but the book does a good job of explaining them clearly. Must-read for anyone newly interested in modern philosophical discourse.
March 23, 2017
Great introduction to useful tools
A street-fighting introduction to some formal techniques. It goes beyond the ordinary topics of Logic 101 courses to give its readers an intuition (and some formalization) on concepts such as probability, the concept of theories, the analytic/synthetic distinction and modal logic. The author sometimes shows his own positions as less controversial than they are (especially when it comes to his defense of Bayesianism), but that does not impact significantly the book. An interesting read for those interested in logic, argumentation tools, mathematics and computing, especially for readers without much of a theoretical basis.
A street-fighting introduction to some formal techniques. It goes beyond the ordinary topics of Logic 101 courses to give its readers an intuition (and some formalization) on concepts such as probability, the concept of theories, the analytic/synthetic distinction and modal logic. The author sometimes shows his own positions as less controversial than they are (especially when it comes to his defense of Bayesianism), but that does not impact significantly the book. An interesting read for those interested in logic, argumentation tools, mathematics and computing, especially for readers without much of a theoretical basis.
September 20, 2020
This is a fantastic book that introduces and teaches technical subject matter relevant to contemporary analytic philosophy. Papineau covers briefly, but sufficiently (for a starting place), naive set theory, logic/meta-logic (also Godel's Incompleteness result(s)), probability theory, modality/possible worlds, truth, and the ideas contained in Kripke's Naming and Necessity (and more). Papineau is very easy to read, generally, and manages to give a friendly introduction to all of this in under 200 pages, exercises included.
I'm very confident that Philosophical devices would be invaluable to any undergraduate Philosophy student and *might* be useful for others if they ever want to refresh their memory. It's hard to fault this book.
I'm very confident that Philosophical devices would be invaluable to any undergraduate Philosophy student and *might* be useful for others if they ever want to refresh their memory. It's hard to fault this book.
July 13, 2016
An excellent introduction to technical Analytical Philosophy.
The book is divided into three parts,
a) Sets and Numbers
b) Analyticity, A prioricity and Necessity
c) Nature and uses of Probability
My favorite chapter was chapter 6 -–Naming and Necessity.
I learnt about Scope Distinctions, Rigid Designations.
Where else would you learn these distinctions?
There's a lot more on each topic.
Deus Vult
--Gottfried
The book is divided into three parts,
a) Sets and Numbers
b) Analyticity, A prioricity and Necessity
c) Nature and uses of Probability
My favorite chapter was chapter 6 -–Naming and Necessity.
I learnt about Scope Distinctions, Rigid Designations.
Where else would you learn these distinctions?
There's a lot more on each topic.
Deus Vult
--Gottfried
October 9, 2017
If you are looking for a good early grad student/advanced undergrad introduction to the formal methods useful for technical philosophy, this is an extremely good bet
October 15, 2020
Wish I had heard of it as an undergrad
January 31, 2025
This book is divided into four parts, each covering an interesting branch of modern philosophy.
Part 1 is about Set Theory and orders of infinity, and I found it to be fantastic, especially the chapter on the latter. The fact that infinities of different sizes exist is one of the most counterintuitive things ever. I've never been able to truly internalize this fact—it always feels like something must have gone terribly wrong in the proof. My problems with infinity probably originate from the apparent absurdity of indeterminate and determinate forms in math, where something like infinity⁰ is indeterminate, but 0^infinity = 0. Further reading necessary.
Part 2 explains terms like "analytic truth" and "essential property." Without precise definitions of these terms, following many philosophical arguments becomes nearly impossible. In this regard, this chapter was probably the most useful to me personally. Does a distinction between essential and accidental properties really exist, or should everything be considered essential? Again, further reading necessary.
Part 3 is about probability and, unfortunately, a little less engaging than the other chapters. There isn't much to dispute (which, in philosophy, is synonymous with dull), and the focus leans more on syntax and math, which doesn’t quite fit the tone of the book.
Part 4 covers logical systems, soundness, completeness, and related topics. I was already familiar with most of these concepts (having read the first few chapters of Gödel, Escher, Bach), but they are so fascinating that revisiting them is a joy. The book concludes on a masterful note with Gödel's Incompleteness Theorem, which, alongside a few ideas from quantum mechanics, I consider one of the most profound and intellectually devastating truths in our world.
To go on a cringy tangent, the pervading feelings one gets when reading about Gödel’s proof are always some variation of "How the hell do you even come up with that?" and "Sir, this is a Wendy’s." Then comes the realization that human intelligence can reach such astonishing heights—and yet, specimens of the same species are capable of blind, uncritical fanaticism, both to their own detriment and that of the species.
Part 1 is about Set Theory and orders of infinity, and I found it to be fantastic, especially the chapter on the latter. The fact that infinities of different sizes exist is one of the most counterintuitive things ever. I've never been able to truly internalize this fact—it always feels like something must have gone terribly wrong in the proof. My problems with infinity probably originate from the apparent absurdity of indeterminate and determinate forms in math, where something like infinity⁰ is indeterminate, but 0^infinity = 0. Further reading necessary.
Part 2 explains terms like "analytic truth" and "essential property." Without precise definitions of these terms, following many philosophical arguments becomes nearly impossible. In this regard, this chapter was probably the most useful to me personally. Does a distinction between essential and accidental properties really exist, or should everything be considered essential? Again, further reading necessary.
Part 3 is about probability and, unfortunately, a little less engaging than the other chapters. There isn't much to dispute (which, in philosophy, is synonymous with dull), and the focus leans more on syntax and math, which doesn’t quite fit the tone of the book.
Part 4 covers logical systems, soundness, completeness, and related topics. I was already familiar with most of these concepts (having read the first few chapters of Gödel, Escher, Bach), but they are so fascinating that revisiting them is a joy. The book concludes on a masterful note with Gödel's Incompleteness Theorem, which, alongside a few ideas from quantum mechanics, I consider one of the most profound and intellectually devastating truths in our world.
To go on a cringy tangent, the pervading feelings one gets when reading about Gödel’s proof are always some variation of "How the hell do you even come up with that?" and "Sir, this is a Wendy’s." Then comes the realization that human intelligence can reach such astonishing heights—and yet, specimens of the same species are capable of blind, uncritical fanaticism, both to their own detriment and that of the species.
July 5, 2023
Papineau's books, published from OUP, seems to contain an inordinate number of typos. Why the bad/rushed editing in every (both) cases?
This is my second Papineau book. By accident in a way. It is for a different course, and it is an introductory book - to help novice philosophers, and not cutting edge philosophy of mind that we read earlier.
It is helpful.
But he goes too fast in a lot of places. Let's say Bayes' theorem, I have studied it earlier and know what it is, but if I hadn't, or even with what I know, his way of going about it is not the most helpful.
And there were other sections - mostly the final ones on Logic, and partys of other sections as well, could have been more helpful if they went slower. And with his clear writing style, if he went slower, and thought of presenting begininnings more carefully, it could have been much more helpful.
I read, the entire book (quite scrupulously, including the footnootes, and further readings, except maybe in the first or second chapters..but did not do the exercises), printed (that's a first, I think. The other papineau was part printed and part hardcover from the library, maybe parts even in the computer).
This is my second Papineau book. By accident in a way. It is for a different course, and it is an introductory book - to help novice philosophers, and not cutting edge philosophy of mind that we read earlier.
It is helpful.
But he goes too fast in a lot of places. Let's say Bayes' theorem, I have studied it earlier and know what it is, but if I hadn't, or even with what I know, his way of going about it is not the most helpful.
And there were other sections - mostly the final ones on Logic, and partys of other sections as well, could have been more helpful if they went slower. And with his clear writing style, if he went slower, and thought of presenting begininnings more carefully, it could have been much more helpful.
I read, the entire book (quite scrupulously, including the footnootes, and further readings, except maybe in the first or second chapters..but did not do the exercises), printed (that's a first, I think. The other papineau was part printed and part hardcover from the library, maybe parts even in the computer).
May 18, 2021
This book fulfills its promises as a brief introduction to topics that lie at the intersection of mathematical logic and philosophy. It has a decent set of chapter exercises and solutions. It would be good for self-study, undergraduates, or even high-school students with the appropriate reading level and mathematical maturity.
The explanations of the key issues are clear and do a lot to demystify some topics that many students in both mathematics and philosophy would not have encountered in their previous readings. Of course, in a book this short, some of the treatments are too brief to fully do the topics justice - it was probably a mistake to go into Gödel's theorem at this level but at least it makes the readership aware of the issues involved and where to look for further details. Each chapter has references to other books that dig deeper into the material covered.
Overall, I would recommend this book to anyone interested in the topics listed in the subtitle.
The explanations of the key issues are clear and do a lot to demystify some topics that many students in both mathematics and philosophy would not have encountered in their previous readings. Of course, in a book this short, some of the treatments are too brief to fully do the topics justice - it was probably a mistake to go into Gödel's theorem at this level but at least it makes the readership aware of the issues involved and where to look for further details. Each chapter has references to other books that dig deeper into the material covered.
Overall, I would recommend this book to anyone interested in the topics listed in the subtitle.
March 18, 2025
A short read that encompasses 4 main areas essential to modern analytic philosophy. The section on analyticity and necessity expands what I've learnt back in the Kant course (de re, de dicto) while the section on causation finally answers my puzzle of how causation should be inferred from correlation. Other interesting ideas and theories are also introduced e.g. types of infinity, Russel's paradox, Godel's theorem. What I love the most is that each section includes exercises for clearing the concepts.
This might be the first analytic philosophy book that I have finished. I wish I can carry what I have equipped from this book into more analytic philosophy.
This might be the first analytic philosophy book that I have finished. I wish I can carry what I have equipped from this book into more analytic philosophy.
August 3, 2025
This is a sensational ''introduction'' to logic and many of the most fundamental ways in which philosophers talk about any other subject matter. I am confident in that, after having understood this book, anyone would be well-equipped to understand the logical steps made within philosophical arguments, and any series of thoughts in general. For those not well-versed in mathematics, some sections of the book will be challenging, at least that was my case, but the author makes excellent introductions that build up arguments over time. The effort in reading this book will be absolutely worth it. It has inspired me to keep expanding my understanding of logic. Great book!
March 17, 2021
Interesting treatment, I am not a philosopher, neither that much inclined, but the treatment of the subject, in its clarity, happens to be appealing. A lot of basics are covered in this book, unless you want to specialize I doubt you'd need much more. The reading requires concentration for the subtlety of this subject, but it is cleverly divided and concise in the slightly over one hundred pages of the book. Thank you,
October 14, 2021
This book provides a fair overview of many of the core tools required to understand the academic analytic philosophy of today. However, bear in mind that some of the more controversial and complex topics are to some extent glossed over. And some chapters I find to be over confident and dogmatic in some of the pronouncements of the domain that is covered by certain logical principles and approaches.
January 3, 2019
Books name fits it purpose but I can only guess it fullfils on its promises - since my personal profession isn't philosophy.
Succint and clear descriptions of very interesting and useful ideas.
Features exercises (with solutions) and nice list of further reading if one has the privilege to go deeper.
Succint and clear descriptions of very interesting and useful ideas.
Features exercises (with solutions) and nice list of further reading if one has the privilege to go deeper.
Want to read
February 11, 2020Philosophical Methodology
May 21, 2020
A very good introductory book for anyone interested in solid reasoning. In spite of me knowing much of the material in the book, it was still a good refreshing read.
January 15, 2021
Handy book for anyone who wants a reference book for technical ideas in philosophy. I'll surely be revisiting this text again.
June 1, 2021
Very handy to cover the core concepts of some fundamental reasoning tools and to recommend further reading
September 27, 2021
Very useful and solid explanation of main philosophical concepts used in technical papers, explained as simply as possible but no simpler than that.
September 25, 2022
Good intro to the subject.
July 27, 2023
Thanks now I can read
December 9, 2020
This book was a worthwhile read. The exercises were fun and most of the chapters are written very clearly and concisely. Overall, it offers a good introduction to some techniques used in modern philosophy. However, there is some room for improvement.
In his book, Papineau uses examples to introduce concepts. This is not bad per se, but in some chapters it was a bit irritating. For example in the chapter on naming and necessity, nearly three pages of examples of scope distinctions are presented without offering a concise definition at all.
To my mind, the nearly complete lack of formal notation is not sensible. The book is meant to be a shortcut to techniques used in contemporary philosophy, which in turn is at times heavily formalized.
In his book, Papineau uses examples to introduce concepts. This is not bad per se, but in some chapters it was a bit irritating. For example in the chapter on naming and necessity, nearly three pages of examples of scope distinctions are presented without offering a concise definition at all.
To my mind, the nearly complete lack of formal notation is not sensible. The book is meant to be a shortcut to techniques used in contemporary philosophy, which in turn is at times heavily formalized.
June 5, 2014
Nearly giving it 3 stars, frankly. Many of the chapters were confusing and/or seemingly unimportant. Also, and not that this is a reason to dislike the book, I was expecting something much different. That said, some of the chapters, particularly 5 and 6, were interesting, helpful, and useful. Besides that, the print is very poor quality and fuzzy rather than crisp. Some of the concepts appeared to be made even more confusing by either the wording, format used (e.g. propositional logic symbols are written out), or rapid-fire employment of newly introduced, specialized terms. In some cases, it may just be that the author was trying to cover too much ground in too little space (the book is quite small). Chapter 3 was particularly confusing, and chapters 11 and 12 seemed utterly useless, to be honest. Many chapters include practice questions at the end that are far too open-ended to be constructive (e.g. something like 'write out an argument that has false premises and a true conclusion'). I will (hopefully) go through the book again and write up a proper, full review, that has more targeted criticisms and points of praise. (And in fact I may lower the rating to 3 stars). Overall, I hope a second edition is soon forthcoming that fixes at least some of the minor problems, if not the content-based ones I had.
January 6, 2014
This volume largely delivers on what it promises: a quick overview of commonly used materials in technical philosophy that normally might be left to other disciplines. This particular text is useful to artificial intelligence practitioners in covering some of the semantic issues of conditional probabilities and causality, and also in laying out the difference between some closely related distinctions (analytic/synthetic, a priori/a posteriori, necessary/contingent), in particular introducing the relatively recently explicated category of necessary a posteriori, which emerges in the certain usage of names. I found this book a quick, easy, and helpful read, although I'm not sure how much I was helped by certain familiarities with the material. If I did have a complaint, it was that some materials were introduced with just not quite enough surroundings to be useful in a self-standing way, offering a tease of more difficult areas, as particularly affected the section on meta-logic. However, I'm pleased to say that I could make this complaint very rarely, and overall this book lives up to it's promise of making the devices of technical philosophy clear.
March 24, 2016
When confronted with complicated squiggles and mysterious words in a contemporary philosophical book or paper, one can often despair and give up. Papineau's little book is what you need at hand. Papineau claims that the tools philosophers use are not as complicated as one thinks. Papineau blows the lid on mysteries like set theory, probability and metalogic rendering the pesky stack of squiggles in that paper powerless to exclude.
I found Papineau's brief explanations easy to follow and eminently readable. The only shortcoming is that Papineau, for the sake of brevity, provides too few examples to show how each theory can be applied.
Nonetheless, a fine addition to my closest shelf.
I found Papineau's brief explanations easy to follow and eminently readable. The only shortcoming is that Papineau, for the sake of brevity, provides too few examples to show how each theory can be applied.
Nonetheless, a fine addition to my closest shelf.
Displaying 1 - 30 of 37 reviews