Intro Logic Lecture Slides

I’ve put the source code for my Logic 1 lecture slides into GitHub. That’s a pretty standard intro logic course, using Language, Proof & Logic as a text.  I do have mainly computer science students in the course, and I try to make the material relevant to them as much as possible.  There are also some (I think) cool examples of logic in action in philosophy, especially a really good illustration of quantifier alternation by Mary Astell (in lecture 15).  It’s all CC0 licensed, so you can use it completely freely in your own lectures if you wish. PDFs are here, you can make print-friendly versions of each by changing the included header in each file.  I’ve been meaning to clean them up, but I won’t get to teach Logic 1 until a year from now at the earliest. So provided as-is, use with caution, etc.

Carnap’s early metatheory: Scope and limits

Georg Schiemer, Richard Zach, and Erich Reck. 2017. “Carnap’s Early Metatheory: Scope and Limits,” Synthese 194(1), 33–65

In his Untersuchungen zur allgemeinen Axiomatik (1928) and Abriss der Logistik (1929), Rudolf Carnap attempted to formulate the metatheory of axiomatic theories within a single, fully interpreted type-theoretic framework and to investigate a number of meta-logical notions in it, such as those of model, consequence, consistency, completeness, and decidability. These attempts were largely unsuccessful, also in his own considered judgment. A detailed assessment of Carnap’s attempt shows, nevertheless, that his approach is much less confused and hopeless than it has often been made out to be. By providing such a reassessment, the paper contributes to a reevaluation of Carnap’s contributions to the development of modern logic.

DOI: 10.1007/s11229-015-0877-z

Preprint on arXiv

John Baldwin on Model Theory and the Philosophy of Mathematical Practice

John T. Baldwin (Illinois-Chicago) has a draft of his book Formalism without Foundationalism: Model Theory and the Philosophy of Mathematical Practice. On, FOM he wrote:

Martin Davis posted a couple of days ago a message containing this sentence. “Gödel showed us that the wild infinite could not really be separated from the tame mathematical world where most mathematicians may prefer to pitch their tents.” This is an excuse for me to publicize my book in progress. Much of it is dedicated to the proposition that modern model theory provides a systematic way to separate the wild from the tame. More precisely, this book supports three main claims.
  1. Formalization of specific mathematical areas is a tool for studying mathematics itself as well as issues in the philosophy of mathematics (e.g. axiomatization, purity, categoricity and completeness).
  2. The systematic comparison of local formalizations of distinct areas is a tool for organizing and doing mathematics and the analysis of mathematical practice.
  3. The choice of vocabulary and logic appropriate to the particular topic are central to the success of a formalization. The logic which has been most important for the study of mathematical practice is first order logic

Contact him directly if you would like to see a draft.