Carnegie Mellon University

Summer School in Logic and Formal Epistemology

There is a long tradition of fruitful interaction between philosophy and the sciences.

Logic and statistics emerged, historically, from the combined philosophical and scientific inquiry into the nature of mathematical and scientific inference; and the modern conceptions of psychology, linguistics, and computer science are the results of sustained reflection on the nature of mind, language, and computation. In today's climate of disciplinary specialization, however, foundational reflection is becoming increasingly rare. As a result, developments in the sciences are often conceptually ill-founded, and philosophical debates often lack scientific substance.

The Department of Philosophy at Carnegie Mellon University hosts a summer school in logic and formal epistemology for promising undergraduates in philosophy, mathematics, computer science, linguistics, economics, and other sciences. The goals are to:

  • introduce promising students to cross-disciplinary fields of research at an early stage in their career; and
  • forge lasting links between the various disciplines.

The summer school is usually held in the first half of June, and includes morning and afternoon lectures and problem sessions.

The summer school is free: there is no tuition, and on-campus housing is provided at no cost.

The Summer School in Logic and Formal Epistemology is open to undergraduates, as well as to students who will have just completed their first year of graduate school. Applicants need not be US citizens. There are no grades, and the courses do not provide formal course credit. There is a $30 nonrefundable application fee.

Applications for this summer's program are now closed. An overview of topics and instructors can be found below. We are hoping and planning for an in-person event; however, should this prove to be impossible, the summer school will still take place remotely, compressed to a 3–4 day program. 


werner-tom.jpgThomas Werner, June 6–10
A Tour of Linguistics

Abstract: This course is an introduction to core topics in modern linguistics, from phonology to syntax to semantics and pragmatics. The material will be based on contemporary generative grammar as it informs compositional semantics and linguistic pragmatics, with a focus on the abstract principles by which phonetic sounds come to be vehicles for the transmission of information. In particular, we will be interested in how linguistic communication takes place within a shared field of experience, using physical events (speech) to expand that field.

Adam BjorndhalAdam Bjorndahl, June 13–17
Topology, Logic, and Epistemology

Abstract: This course is an introduction to epistemic logic, topology, and their relationship; no background in modal logic or topology is assumed. We'll begin by motivating and defining standard relational structure semantics for epistemic logic, and highlighting some classic correspondences between formulas in the language and properties of the structures. Next we'll introduce the notion of a topological space using a variety of metaphors and intuitions, and define topological semantics for the basic modal language. We'll examine the relationship between topological and relational semantics, establish the foundational result that S4 is “the logic of space” (i.e., sound and complete with respect to the class of all topological spaces), and discuss richer epistemic systems in which topology can be used to capture the distinction between the known and the knowable. This lays the groundwork to explore some more recent innovations in this area, such as topological models for evidence and justification, information update, and applications to the dynamics of program execution.

Kevin ZollmanKevin Zollman, June 20–24
Network Epistemology

Abstract: For a long time epistemology focused on the lone inquirer. Descartes worried about what he should believe given the evidence he had from his senses. However, much of our epistemic life is social: we learn from one another, we ask questions, we argue, we cajole. What's more, this social epistemic life takes place in a complex web of social interactions. We don't just learn from anyone, we tend to learn from our friends, relatives, and teachers. These observations have led to a new interdisciplinary field called "Network Epistemology" where we look at how the structure of our social world influences what we come to believe. Much of this work is done using mathematical or computer simulation models. In this course, we will look at a few examples from this field including models of misinformation, pluralistic ignorance, and the wisdom of the crowds.

2021 Summer School -- June 7-11

This year the sessions were held entirely remotely in compliance with COVID-related health and safety guidelines.

Monday, June 7: Mandy Simons
Natural Language Semantics

Tuesday, June 8: Francesca Zaffora Blando
Algorithmic randomness and learning

Wed/Thurs, June 9th/10th: Wilfried Sieg
Proofs as objects

Friday, June 11: Adam Bjorndahl
Epistemic logic and topology


2020 Summer School -- June 9-12

ss-virtual-annoucement-2020.png


2019 Summer School -- June 3-21

Week #1
(June 3-7)

Instructor: Professor Jeremy Avigad
Title: Logic and Interactive Theorem Proving

In computer science, "formal methods" are used to verify the correctness of hardware and software, as well as to verify the correctness of mathematical claims. During this week, we will explore the logical foundations that support formal verification, and you will learn how to use a contemporary theorem proving system known as Lean.

Week #2
(June 10-14)

Instructors: Professors Adam Bjorndahl and Teddy Seidenfeld
Title: Introduction to Epistemic Logic and the Probability of Consensus

The first part of the week will introduce epistemic logic, a branch of modal logic concerned with reasoning about knowledge and belief. No background in modal logic will be assumed. We'll motivate the development of the formal tools, survey some classic results in the field, and consider some extensions of the basic framework, such as: multi-agent systems and common knowledge, public announcements, and topological approaches. In the second part of the week, we will consider applications of the theory of probability to problems involving consensus among rational agents, both with respect to their degrees of belief and with respect to cooperative decision making.

Week #3
(June 17-21)

Instructors: Professors Clark Glymour and Kun Zhang
Title: Causation and Computation

The topic is how computational/statistical procedures and “big data” can discover causal relations. The course will be organized around lectures and computational projects.


2018 Summer School -- June 11-June 29

Our Summer School 2018 coordinates with the North American Summer School in Logic, Language and Information, NASSLLI, which constitutes the 3rd week of this year's Summer School, June 25-29, 2018. Weeks #1 and #2 are organized in order to prepare the Summer School participants for attending the NASSLLI.

Week #1
(June 11-15)

Instructor: Mandy Simons and other Linguistics Faculty
Title: Introduction to Linguistics for Philosophers and Logicians

Description: In the first week, we'll provide a whirlwind introduction to the fundamentals of formal linguistics, including phonology, syntax, semantics and pragmatics. The course will also include a brief introduction to the computational issues of Natural Language Processing. The goal is to provide the background necessary to understand the linguistic underpinnings of questions in formal semantics, computational linguistics and formal philosophy of language.

Week #2
(June 19-22)

Instructor: Adam Bjorndahl and other Formal Epistemology Faculty
Title: Introduction to Epistemic Logic and the Probability of Consensus

Description: The first part of the week will introduce epistemic logic, a branch of modal logic concerned with reasoning about knowledge and belief. No background in modal logic will be assumed. We'll motivate the development of the formal tools, survey some classic results in the field, and consider some extensions of the basic framework, such as: multi-agent systems and common knowledge, public announcements, and topological approaches. In the second part of the week we will consider applications of the theory of probability to problems involving consensus among rational agents, both with respect to their degrees of belief and with respect to cooperative decision making.

Week #3
(June 25-29)

Title: NASSLLI-2018

The North American Summer School in Logic, Language and Information has been providing outstanding interdisciplinary educational opportunities to graduate students and advanced undergraduates in logic, linguistics, computer science, cognitive science, and philosophy since it was launched as a biennial event in 2002. NASSLLI brings these disciplines together with the goal of producing excellence in the study of how minds and machines alike accomplish the tasks of representing, communicating, manipulating and reasoning with information.


2017 Summer School -- June 5-June 23

Week #1a
(June 5-9)

Instructor: Adam Bjorndahl

Title: Epistemic Logic and Topology 

Description: In this course we introduce epistemic logic and topology and explore the relationship between the two. No background in modal logic or topology is assumed.

We begin by motivating logics of knowledge and belief, and develop the formal tools that are typically used to study them; we then survey some classic results in this field. Next we turn to topology, building intuitions using a variety of metaphors and intuitions. In essence, by connecting the formal definition of a set's interior to the abstract concept of "robustness", we are able to co-opt the spatial notion of "nearness" as a means of representing uncertainty. To make this precise, we introduce topological semantics for the basic modal language, investigate its connection to the more standard relational semantics, and establish the foundational result that S4 is "the logic of space" (i.e., sound and complete with respect to the class of all topological spaces).

Viewing epistemology through the lens of topology highlights the distinction between the known and the knowable, between fact and measurement. To more fully incorporate this conceptual framework into our analysis, we introduce topological subset space semantics, which allows us to manipulate separately the state of the world and the epistemic state of the agent. We close with a look at some recent work that uses topology to improve our understanding of the dynamics of knowledge.

Week #1b
(June 9-10)

Center for Formal Epistemology Workshop

Title: Modality and Method

Speakers:
Franz Huber (University of Toronto)
Melissa Fusco (Columbia University)
Alexandru Baltag (Oxford)
Tamar Lando (Columbia)
Harvey Lederman (Pitt)
Dmitri Gallow (Pitt)

Week #2
(June 12-16)

Instructor: K.T. Kelly
Title: The Topology of Inquiry

Description: The standard mathematical frameworks for understanding reasoning are logic and computability for mathematical reasoning and probability theory for empirical reasoning. In this summer school session, we examine an alternative, topological viewpoint according to which computational and empirical undecidability can both be viewed as reflections of topological complexity. That may sound a bit odd, since topology is usually understood to be "rubber geometry", or the study geometrical relationships preserved under stretching operations that neither cut nor paste pieces together. In fact, topology is better understood as studying the mathematical structure of epistemic verifiability. Topological concepts and results will be applied to provide a unified, explanatory perspective on undecidability, on empirical underdetermination, on bounded rationality, and on the elusive connection between simplicity and empirical truth.

Background Reading:
1) "The Logic of Success"
British Journal for the Philosophy of Science, special millennium issue, 51, 2001, 639-666. 

2) Several overview papers are available on my web-site:
(with O. Schulte) "Church's Thesis and Hume's Problem," in Logic and Scientific Methods, M. L. Dalla Chiara, et al., eds. Dordrecht: Kluwer, 1997, pp. 383-398.

3) "Justification as Truth-finding Efficiency: How Ockham's Razor Works"Minds and Machines 14: 2004, pp. 485-505.

Week #3
(June 19 -23)

Instructor: Kevin Zollman
Title: The Economics of Science

Description: Science is a unique institution.  In most fields, people are rewarded for hard work with more money and promotions.  Scientists on the other hand are primarily paid in terms of credit for discoveries.  A scientists strives to be known as the person who discovered this thing or invented that theory.  What effect does this desire for credit have on the progress of science as a whole?  Is science benefited by this motivation or is it harmed?  In this course we will look at a number of mathematical and computer models of scientific behavior which strive to answer this question.