Development of Modern Logic

Stephen Boydstun's picture
Submitted by Stephen Boydstun on Sun, 2009-03-29 15:10

The Development of Modern Logic
Leila Haaparanta, editor (Oxford 2009)

Table of Contents
1. Introduction - Leila Haaparanta
2. Late Medieval Logic - Tuomo Aho and Mikko Yrjönsuuri
3. Logic and Philosophy of Logic from Humanism to Kant - Mirella Capozzi and Gino Roncaglia
4. The Emergence of Symbolic Logic: the Interplay between Logic and Mathematics
The Mathematical Origins of Nineteenth Century Algebra of Logic - Volker Peckhaus
Gottlob Frege - Christian Thiel
5. The Emergence of Symbolic Logic: the Interplay between Logic and Philosophy
The Logic Question - Risto Vilkko
The Relations between Logic and Philosophy 1874-1931 - Leila Haaparanta
6. A Century of Judgement and Inference: 1837-1936
Some Strands in the Development of Logic - Göran Sundholm
7. The Development of Mathematical Logic from Russell to Tarski 1900-1935 - Paolo Mancosu, Richard Zach, and Calixto Badesa
8. Main Trends in Mathematical Logic after the 1930s
Set Theory, Model Theory, and Computability Theory - Wilfrid Hodges
Proof Theory of Classical and Intuitionistic Logic - Jan von Plato
9. Modal Logic from Kant to Possible Worlds Semantics - Tapio Korte, Ari Maunu, and Tuomo Aho
Appendix: Conditionals and Possible Worlds: On C. S. Peirce's Conception of Conditionals and Modalities - Risto Hilpinen
10. Logic and Semantics in the Twentieth Century - Gabriel Sandu and Tuomo Aho
11. The Philosophy of Alternative Logics - Andrew Aberdein and Stephen Read
12. Philosophy of Inductive Logic - Sandy Zabell
13. Logic and Linguistics in the Twentieth Century - Alessandro Lenci and Gabriel Sandu
14. Logic and Artificial Intelligence - Richmond Thomason
15. Indian Logic - J. N. Mohanty [my esteemed first Kant professor], et al.


The Development of Logic
William Kneale and Martha Kneale

From Frege to Gödel
Jean van Heijenoort


Metaphysics and Logic

More on Origins of Logic


Foundations of Logic


A is A

( categories: )


Stephen Boydstun's picture

I recall Dr. Peikoff once giving some sort of negative estimation of the worth of symbolic logic (also called mathematical logic, and more recently, called standard classical logic) in one of his recorded lectures roughly thirty-five years ago. I don’t know how much of symbolic logic he knew then, or has learned since. I don’t know if his evaluation of it has changed.

On my shelf is a book titled Classical Mathematical Logic (2006 Princeton) by Richard L. Epstein. After taking the student through the level of logic in which competence is required nowadays of every graduate student in philosophy (propositional logic, predicate logic, and their axiomatizations), the student is rewarded with two chapters on logical formalization of two areas of mathematics: group theory and linear orderings. (That second one is mighty important for a measurment-omission analysis of concepts in terms of modern measurement theory; see the section Affordance of Ordinal Measures and note 25 of “Universals and Measurement.”) Then the student is given a chapter on second-order classical predicate logic. With that equipment in hand, we are prepared for the logical formalizations of five more areas of mathematics, in five chapters: the natural numbers, the integers and rationals, the real numbers, one-dimensional geometry, and two-dimensional geometry.

I said the student is “rewarded.” My quantum mechanics professor Robert Sachs, at Chicago thirty years ago, once told a story about Hermann Weyl. Physicists attending a conference in some charming European city, would be touring the charms, but where was Weyl? He was off at the local library looking up obscure mathematical functions, seeing if there was something he could put to use. Sachs concluded: “Different folks have different pleasures.”

I certainly do disagree that symbolic logic is worthless or inimical to human knowledge. Peikoff does have a shining piece on origins of the principle of noncontradiction, which has been noticed here and will be discussed over at the thread Philosophy of Logic.


seddon's picture

Do you disagree with Peikoff (and Veatch) that symbolic is evil, or words to that effect.


Philosophy of Logic

Stephen Boydstun's picture

Reflections on philosophy of logic are here.


Ptgymatic's picture

Thanks, Stephen. I know the Kline book.
How many walls does your library occupy, anyway?



Stephen Boydstun's picture

The book Frege to Gödel is a collection of principal papers advancing logic over that period. I rely on it for original source material. The Kneales’ book is a solid classic I have turned to for many years. The new book The Development of Modern Logic, consisting of essays by various specialists in the history of logic, is not yet issued. It is sure to be tremendous.

Whether it is called history or development, these go to the story of how the discipline we call logic was discovered. Logic is discovered, just as mathematics is discovered. Counterparts for mathematics would be books such as Morris Kline’s Mathematical Thought: From Ancient to Modern Times or Carl Boyer’s History of Analytic Geometry.

Pretty abstract subject!

Ptgymatic's picture

Not logic, not the history of logic, but "development," i.e., the history of the processes that changed logic? Or am I reading too much into that one word? It is an intimidating table of contents, you have to admit.

I always, Stephen, read these reference postings of yours with great interest. Should I assume they are recommendations, that is, you have found them good?


Comment viewing options

Select your preferred way to display the comments and click "Save settings" to activate your changes.