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; 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 and rigor.
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. During this three-week, intensive program, we introduce a small group of approximately 25 promising students to cross-disciplinary fields of research at an early stage in their career, forging lasting links between these disciplines along with friendships and professional contacts. Topics change from year to year, with daily sessions taught by CMU Philosophy faculty members and guest lectures sometimes offered by other professionals, grad students, and even summer school alumni.
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 $40 nonrefundable application fee.
Applications
- SSLFE application portal opens: December 14
- Portal closes: February 14
- Decisions released: March 14
Contact
The summer school is directed by Adam Bjorndahl. Inquiries may be directed to abjorn@cnlawyer18.com.
2025 Summer School Schedule
June 2–6, 2025
Aydin Mohseni
Bayesian Epistemology and Metascience
This course explores the foundational principles of Bayesian epistemology and their applications to metascience. Students will engage with topics including probabilistic reasoning, updating beliefs in light of evidence, and the use of formal models to analyze and improve scientific practices. Special emphasis will be placed on addressing contemporary challenges in science, including the replication crisis and recent methodological reforms.
June 9–13, 2025
Teddy Seidenfeld & Floris Persiau
Decision Theory, Imprecise Probabilities, and Algorithmic Randomness
The first half of this week will provide a decision-theoretic perspective for introducing selected topics in Imprecise Probabilities:
- B. de Finetti’s Coherence and personal probability
- The Fundamental Theorem and "weak-IP."
- On the Value of Information and IP theory
- Optimal sequential decisions and the disvalue of new information:
- Act/state dependence and game theory.
- IP sequential decision making and dilation.
- Optimal sequential decisions and the disvalue of new information:
- Multi-agent IP decision theory
- Pareto consensus and non-binary theories of choice.
- Axiomatizing IP decision making
- Three opportunities for IP DT.
- Forward induction in sequential games
- IP forecasting and de Finetti’s two senses of coherence
- Dominance principles: non-Archimedean theories, ...
The second half of the week will connect some of these ideas to the field of algorithmic randomness, which studies what it means for an infinite outcome sequence to be random. Consider for example infinite binary sequences that are generated by flipping a fair coin—which corresponds to probability 1/2: the infinite binary sequence 01010101... doesn’t seem random at all, whereas the sequence 10001011... seems more random. Algorithmic randomness notions try to formalise our intuition behind random sequences, by defining what it means for an infinite sequence to be random for an uncertainty model. Classically, these uncertainty models are probability measures. The field of imprecise probabilities, on the other hand, questions whether precise-probabilistic uncertainty models are always sufficient to capture one’s uncertainty, and puts forward alternative and (even) more general uncertainty models that allow for reasoning in an informative and conservative way. The following question then naturally pops up: can we allow for these more general uncertainty models in algorithmic randomness notions, and how does this change our understanding of algorithmically random sequences? Are there for example sequences whose randomness can only be described by an imprecise uncertainty model? This course will give an introduction to several basic concepts in the field of algorithmic randomness, and will provide answers to the above questions and more.
June 16–20, 2025
Clark Glymour & Peter Spirtes
The Logic of Discovery
The very idea that there is, or could be, a "Logic of Discovery" analogous to deductive logic but for empirical laws has been advocated and disputed for three centuries. In this century it was replaced by the development of algorithms that attempt to infer laws and causal relations from empirical data. This course will briefly review the history but focus on 21st century developments. We will describe algorithms, proofs of their correctness properties, and applications in finance, biology, neuroscience, and other areas.
Past Summer School Schedules
2024 Summer School Schedule
June 3–7, 2024
Chance and randomness
Francesca Zaffora Blando & Krzysztof Mierzewski
Abstract: Probability theory plays a crucial role in science, from inductive learning and statistical inference to information theory, to economics and decision theory, to physics, just to name a few. It also gives rise to some of the deepest and most captivating philosophical puzzles. Are probabilities in the world or in our heads? What, if anything, is the relationship between objective chances, frequencies, and subjective degrees of belief? Can there be non-trivial objective probabilities in a universe governed by deterministic physical laws? Should a theory of probability be grounded in a prior account of randomness or, vice-versa, should we think of randomness as requiring a prior understanding of probabilities? Can computational considerations shed light on our concepts of chance and randomness? In this course, we will explore these questions and more.
June 10–14, 2024
Categorical semantics and synthetic topology
Jonas Frey & Reid Barton
Abstract: Categorical semantics studies interpretations of logical systems using the language of category theory. This course will give an introduction to basic concepts including Lawvere theories and hyperdoctrines. The
logical systems we study might have nonclassical features: for example, the law of the excluded middle or the axiom of choice might not hold.
In the later parts of the course, we will study systems in which the basic objects have an "intrinsic" topological structure, with respect to which all functions are continuous. We will explain how this theory can be used to give synthetic accounts of topological concepts such as compactness.
No prior knowledge of category theory will be assumed.
June 17–21, 2024
The Logic of Discovery
Clark Glymour & Kun Zhang
Abstract: The very idea that there is, or could be, a "Logic of Discovery" analogous to deductive logic but for empirical laws has been advocated and disputed for three centuries. In this century it was replaced by the development of algorithms that attempt to infer laws and causal relations from empirical data. This course will briefly review the history but focus on 21st century developments. We will describe algorithms, proofs of their correctness properties, and applications in finance, biology, neuroscience, and other areas.
2023 Summer School
June 5–9, 2023
A tour of linguistics
Tom Werner & Mandy Simons
Abstract: This course introduces foundational topics in modern linguistics. We begin with speech sounds and look at how different languages organize sounds into abstract systems. Then we look at how larger linguistic units are built up, how meaning is grafted onto sounds, and how meaningful elements are combined into larger expressions. These investigations take us through major sub-disciplines of linguistics, from phonetics and phonology, to morphology and syntax, and onto semantics and pragmatics. Throughout, the focus is on language as a complex system of interlocking parts, and on the techniques and strategies by which linguists discover and analyze these parts.
June 12–16, 2023
Two approaches to knowing and believing: epistemic logic and imprecise probabilities
Adam Bjorndahl & Teddy Seidenfeld
Abstract: 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'll motivate and explore some uses of imprecise probability theory to model aspects of uncertainty that elude the framework of precise (subjective) probability theory. These include formal models of cooperative group decision making and formal models of robustness of inductive inference.
June 19–23, 2023
Chance and randomness
Francesca Zaffora Blando & Krzysztof Mierzewski
Abstract: Probability theory plays a crucial role in science, from inductive learning and statistical inference to information theory, to economics and decision theory, to physics, just to name a few. It also gives rise to some of the deepest and most captivating philosophical puzzles. Are probabilities in the world or in our heads? What, if anything, is the relationship between objective chances, frequencies, and subjective degrees of belief? Can there be non-trivial objective probabilities in a universe governed by deterministic physical laws? Should a theory of probability be grounded in a prior account of randomness or, vice-versa, should we think of randomness as requiring a prior understanding of probabilities? Can computational considerations shed light on our concepts of chance and randomness? In this course, we will explore these questions and more.
2022 Summer School
Thomas 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 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 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
2019 Summer School -- June 3-21
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Week #1 |
Instructor: Professor Jeremy Avigad 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 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 |
| Week #3 (June 17-21) |
Instructors: Professors Clark Glymour and Kun Zhang 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.
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Week #1 |
Instructor: Mandy Simons and other Linguistics Faculty Description: In the first week, we'll provide a whirlwind introduction to the fundamentals of formal linguistics, including phonology, syntax, semantics |
| Week #2 (June 19-22) |
Instructor: Adam Bjorndahl and other Formal Epistemology Faculty 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 |
| 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
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Week #1a |
Instructor: Adam Bjorndahl Title: Epistemic Logic and Topology Description: In this 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. 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. |
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Week #1b |
Center for Formal Epistemology Workshop Title: Modality and Method Speakers: |
| Week #2 (June 12-16) |
Instructor: K.T. Kelly 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 Background Reading: |
| Week #3 (June 19 -23) |
Instructor: Kevin Zollman Description: Science is a unique institution. In most fields, people are rewarded for hard work with more money and promotions. Scientists |