Some other logic books attempt to summarize the broad sweep of mathematical logic systems, but this book by Curry is encyclopedic in breadth and virtuosic in depth. It should not be allowed to go out of print! It is not only historically important, but also an invaluable reference work for current working mathematicians and logicians.
This Dover book,
Foundations of Mathematical Logic
, by Haskell Brooks Curry, originally published in 1963, summarizes pretty much every approach to logic up to that time. Although there is a chapter at the end on modal logic, it's mostly concerned with the kinds of logics which are directly applicable to real-world mathematics.
At first, I found this book pointlessly abstruse, but the more I study and refer to it, the more I find it fills many gaps in the literature that the other 45 mathematical logical books on my shelf do not fill. For example, Curry presents a wide range of propositional and predicate calculus systems, classified by his very terse abbreviations, like TA for an absolute propositional algebra which uses introduction and elimination rules, and TC for a classical positive propositional algebra with similar rules, but HA for a propositional version of TA whose only rule is modus ponens, and HC for the propositional version of TC, and so forth. The axioms and rules are also systematically named, like Pe for implication elimination (i.e. modus ponens) and Pi for implication introduction (i.e. the "deduction theorem"). After a while, the dozens of such notations start to make sense.
One oddity of this book, compared to others, is how late in the book negation appears. Out of 8 chapters, it is only in chapter 6 that negation appears, and then many different kinds of negation are considered, including intuitionistic styles.
The references to the literature are truly copious. This book would be of great value if only for the thousands of references, covering every point and every point of view. The historical notes are also very valuable. Every chapter has a "supplementary topics" section of several pages where the subject and its history are surveyed, and choices of approach are explained in comparison to other possible approaches.
The eight chapter titles give an idea of the systematic progression of ideas in this book. Chapter 4 on relational logical algebra presents lattices as an underlying concept layer. Then Chapter 5 presents "the theory of implication", which deals with "systems which are assertional in character". (In other words, not all logical systems are assertional, which is somewhat different to the way many other books present logic.) Following Chapter 6 on negation is Chapter 7 on quantification, which extends the propositional systems to various forms of predicate calculus. Although most serious logic books of the 1950s and 1960s seem to have preferred to use only one a-priori rule (modus ponens) for inference, Curry describes a "T formulation of quantification" (page 342) which includes Rule G and Rule C amongst the inference rules. (These rules were given their names by
Rosser
in 1953, but Curry does not use these names.)
In conclusion, Curry's book is encyclopedic in character despite its small size, it has great historical importance (because it is cited so much by later authors as a standard text), and it synthesizes a very broad range of logics into a single unified analytical framework. So I hope very much that it will not go out of print.
Enjoy fast, free delivery, exclusive deals, and award-winning movies & TV shows with Prime
Try Prime
and start saving today with fast, free delivery
Download the free Kindle app and start reading Kindle books instantly on your smartphone, tablet, or computer - no Kindle device required.
Read instantly on your browser with Kindle for Web.
Using your mobile phone camera - scan the code below and download the Kindle app.
Something went wrong. Please try your request again later.
Frequently bought together
$29.95
Get it as soon as Thursday, May 23
Only 10 left in stock (more on the way).
+
Total price:
To see our price, add these items to your cart.
Choose items to buy together.
Similar items that may ship from close to you
Page 1 of 1 Start overPage 1 of 1
About the author
Follow authors to get new release updates, plus improved recommendations.
