Logical Philosophy of Science

This page will follow the development of a book that might be called Logical Philosophy of Science, or perhaps The Logic of Theories. As new chapter drafts become available, they will be posted below. The book is a highly collaborative enterprise, organized by Hans Halvorson. Contributors include Thomas Barrett, Dimitris Tsementzis, and Evan Washington. Thanks also to Neil Dewar, Laurenz Hudetz, and Sebastian Lutz for freely sharing their ideas. If you have corrections, suggestions, or would otherwise like to be involved, please email hhalvors at princeton dot edu.

Introduction to metalogic pdf
The category of sets
Includes a basic introduction to category theory
pdf
The category of propositional theories
Includes basic introductions to Boolean algebra, topology, and the Stone duality theorem
pdf
First-order logic in syntatic approach
First-order logic in semantic approach
Basic introduction to model theory. Completeness and compactness theorems. Lowenheim-Skolem theorem
Definitions and definitional equivalence
Includes an introduction to many-sorted logic, Morita equivalence, Beth's theorem, and Quine's elimination of sorts
Translations and translational equivalence
Scientific reduction
Syntactic (Nagelian) and semantic (new-wave) accounts of reduction. Supervenience versus reduction.
Implicit definition and analytic truth
In 1940, Goodman and Quine "proved" that synthetic postulates can be eliminated — thereby setting up Quine's famous argument against the analytic-synthetic distinction. Here we explain their proof, and why it doesn't quite underwrite the philosophical claims that they attempt to base upon it.
Theoretical terms and Ramsification
Symmetry
Putnam's model theoretic argument against realism
What is realism?
The realism-antirealism distinction is not as clear cut as you might think. Formulations such as "belief in a mind-independent reality" are not very helpful. I propose that we think about realism and antirealism as views about theoretical equivalence: realists have tight standards for equivalence, antirealists have more relaxed standards. Using this classification, it becomes obvious that extreme realist and antirealist views lead to absurdity.