More Precisely: The Math You Need to Do Philosophy Paperback – January 29, 2009

The amazing thing about the little handful of books on Mathematical Philosophy--2 by Shapiro, Frege, Russell and of course Benacerraf and Putnam's classic, is the paucity of literature in this key field!Some will say that mathematical philosophy, or the closely related philosophy of mathematics, only began in the 1980's in earnest. But reading the "big 5" shows threads going back to antiquity. The field is far from settled, and the two aspects--the philosophy of math itself, and the closely related field of applying math and logic TO other branches of philosophy, has enough active journalized information in the mid 2014+ years to fill 50 volumes. Since thousands have been written in mainline philosophy, and even the philosophy of science as well as logic, this is not without surprise and mystery.The good news is that an invested, energetic reader can pick up this handful of keys and be in the top percent of folks on the planet with a good foundation! This is hardly true of any other field. I'd start with Shapiro's Oxford Encylopedia, study Benacerraf and Putnam's classic collection of essays, then finish with Shapiro's deep and difficult "Thinking about" and of course Russell and Frege for historic and specialized puzzle pieces.One "sleeper" I'd like to recommend that is not usually included in comparisons of books in this field is Steinhart:  More Precisely: The Math You Need to Do Philosophy .Eric helps with both math within philosophy (the basics) and tangentially helps with the math used as examples within the philosophy OF math. Beyond the issues of categorization, discovery, math as model vs. underpinning reality ala the Matrix, there of course is the whole field of logic, induction, deduction, etc. which has thousands of volumes. The six mentioned here cover logic, but are much more specific in the broader subject area of mathematics, which now includes dynamical systems and differential equations undreamt of in the past, and bringing many new mental tools to bear, from intuition to analytic, qualitative, numeric, perturbative and of course stochastic. Here are the other links to those mentioned in this survey: The Oxford Handbook of Philosophy of Mathematics and Logic (Oxford Handbooks) Thinking about Mathematics: The Philosophy of Mathematics Philosophy of Mathematics: Selected Readings The Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Concept of Number Introduction to Mathematical Philosophy Enjoy!

Amazing book. I bought this book because it was a recommended book in the book philosophical devices. I think that this should be required in philosophy programs, If they want to seriously prepare there students to read current philosophical work. In every contempory book that I have read that said you just need a little logical knowledge to read it, the logic they are using is metalogic not the basic logic you learn in undergrad. Not everyone that studies philosophy gets a course in this subject ( I haven't found a single school), and learning set theory is difficult if you are a liberal arts person. This gives you enough to read analytic philosophical text with a reasonable degree of understanding. This is necessary if you want to get anywhere in contemporary philosophy. Also, I recommend the book philosophical Devices to get a working understanding of the language of philosophy. This is what professor will expect you to know, but you don't get in most undergraduate programs.

I found this book looking for the answer: what is the difference between a set and a class? I'm happy to report that Prof. Steinhart provides a satisfying answer. I also liked what he did with relations, which are not that interesting in themselves. In particular I was drawn to his example of "The Memory Relation," which uses John Locke's memory criterion for the persistence of a person. These examples give a flavor of how Prof. Steinhart combines basic and not so basic ideas from various areas of math (machines, probability, infinity, more infinity) with a sure philosophical hand to create an interesting and well-written book.

This book is hardly thorough but what it covers is excellent. I've had a mental block with certain aspects of math for years: I see an equation and my eyes roll into the top of my head. But somehow Steinhart's treatment broke throught that. I would love to see an expanded scope. His goal is to treat the most essential concepts needed to do philosophy. He does this well. However, I think there are a number of concepts that could be brought to bear in philosophy (and other subjects) that could use his rare ability to explain. I found myself disappointed as I approached the end because I wasn't ready to quit learning mathematical concepts.

I love this book. As someone who is preparing for grad school, I really wanted to be sure that I was up to date on all of the logic and mathematics that are needed to do contemporary analytic philosophy. More Precisely is an excellent tool for reaching this goal. It is incredibly informative with great examples and is very easy to read. It painlessly teaches many essential concepts, such as set theory, Bayesian inference, and modal semantics. This book should be required for all serious philosophy students.

Extremely thin and paltry. Taught me almost nothing. I don't understand the point of the stuff on 'machines' (a 'machine' seems to mean a childish, meaningless diagram or something), and the chapter gave me no sense of any possible application; the stuff on set theory was designed for slubberdegullions (highly infantilising); the introduction to probability was ok, but you can find out this stuff anywhere; and the formal semantics was awful, particularly considering that formal semantics bears very little relation to the actual semantics of natural language, and therefore seems to just lead philosophers down long, meandering, futile paths (and what the heck has it got to do with maths?).I thought this book might actually have some mathematics in it. Maybe some Cantor, maybe some Godel, maybe some calculus, maybe some physics. Alas, no.An apology for a book on mathematics.

This is a great handbook to have. I've read and reread often; it's actually entertaining along with being informative.

Killer book. Only one of its kind that I know of. More philosophers need to read it. It's just so clear.

More precisely, the correct title of this book should be “The Math You Need To Do Post-War Analytic Philosophy”. You can get by perfectly well up to, say, The Philosophical Investigations (including the work of Frege and Russell) without knowing any of this stuff. With that caveat in mind, then the book can’t be faulted, although absolute beginners would perhaps be better off going first to David Papineau’s “Philosophical Devices”. Professor Steinhart sets out admirably and clearly all the topics – set theory, Turing Machines, algorithms, game theory, etc., - that you need to understand Quine, Davidson, possible worlds, and so on. It has made me more inclined than ever towards Wittgenstein’s view that “There is no religious denomination in which the misuse of metaphysical expressions has been responsible for so much sin as it has in mathematics”. Or, in the words of Thomas Nashe : “What is Logicke but the highe waie to wrangling, contayning in it a world of bibble babble.”

Analytische Philosophie lebt von ihrem Hang zur absoluten Genauigkeit. Dies schlägt sich gerade in der Theoretischen Philosophie in einem Formalismus nieder, der so stark in Logik, Mengenlehre und Wahrscheinlichkeitsrechnung verhaftet ist, dass es für viele Studienanfänger schwer ist, den Einstieg in dieses wunderbare Fach zu finden. Viele studieren auch Philosophie, weil sie eher weniger mit Mathematik in der Schule anfangen konnten (so erging es auch mir). Die Beschäftigung mit einer formalen Basis lohnt aber - denn hat man es geschafft, diese Werkzeuge zu meistern, können sich sehr große Möglichkeiten für Bereiche, wie Metaphysik, Epistemologie, Philosophie des Geistes und Philosophie der Wissenschaften ergeben. Weiter ist eine Beschäftigung der zeitgenössischen Literatur zu diesen Themen ohne das Handwerkzeug, das in diesem Buch vorgestellt wird, kaum zu managen.Steinhart hat es geschafft, in seinem Mathematikbuch (!), das auf die Bedürfnisse von Philosophen zugeschnitten ist, den Leser sanft an die Themen heranzuführen und deutlich zu machen. Bei mir hat es viele Aha-Effekte hervorgerufen. Ich fühle mich nun fähiger auch schwierigere philosophische Texte anzugehen.

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Great introduction. Precise language and notation (unlike other introductions). Made me a maths enthusiast.Understandable on its own, even to someone who didn't have any mathematical training worth mentioning.

Para cualquier estudiante o profesionista, muy útil.