Formal Epistemology Meets Philosophy of AI

Idea & Motivation

The workshop aims at exploring novel topics in Formal Epistemology that might be of relevance to philosophical and/or foundational questions about AI, and novel topics in the foundations and/or the philosophy of AI that might be of relevance to questions in Formal Epistemology.

Speakers

• Javier Belastegui Lazcano (ILCLI)
• Cordelia Berz (MCMP)
• Tina Eliassi-Rad (Northeastern University)
• Branden Fitelson (Northeastern University)
• Levin Hornischer (MCMP)
• Simon Huttegger (UC Irvine)
• Hannes Leitgeb (MCMP)
• Alessandra Marra (MCMP)
• Silvia Milano (Exeter)
• Jan-Willem Romeijn (Groningen)
• Tom Sterkenburg (MCMP)

Program

Time	Event
July 5th
08:30 - 09:00	Welcome & Coffee
09:00 - 10:30	Branden Fitelson (Northeastern University)
10:45 - 12:15	Simon Huttegger (UC Irvine)
12:15 - 13:15	Lunch Break
13:15 - 14:45	Hannes Leitgeb (MCMP)
15:00 - 16:30	Alessandra Marra (MCMP) & Javier Belastegui Lazcano (ILCLI)
16:30 - 17:00	Coffee Break
17:00 - 18:30	Jan-Willem Romeijn (Groningen)
19:00	Dinner at Arabesk (https://www.arabesk.de/en/restaurant/), Kaulbachstraße 86, 80802 Munich.
July 6th
08:30 - 09:00	Welcome & Coffee
09:00 - 10:30	Tina Eliassi-Rad (Northeastern University)
10:45 - 12:15	Cordelia Berz (MCMP)
12:15 - 13:15	Lunch Break
13:15 - 14:45	Levin Hornischer (MCMP)
15:00 - 16:30	Tom Sterkenburg (MCMP)
16:30 - 17:00	Coffee Break
17:00 - 18:30	Silvia Milano (Exeter)

Abstracts

Branden Fitelson: Automated Reasoning Tools for Pedagogy & Research in Logic & Formal Epistemology

In this talk, I will discuss various computational tools that I have been using in both my teaching and research in Logic and Formal Epistemology. Some notable applications will include: the logic and meaning of sentential connectives (especially conditionals), probability, and inductive logic.

Simon Huttegger: An Inductive Logic for Exponential Smoothing

Carnapian inductive logic and most of its variants are based on symmetry principles that require order invariance at some level. However, there are plausible predictive systems that fail to be order invariant. One case in point is exponential smoothing, which exhibits a recency effect by assigning weights to observations that depend on when they were made. I will derive exponential smoothing from first principles that are quite different from order invariance and discuss their significance for inductive logic and predictive systems.

Hannes Leitgeb: The Additive Logic of Epistemic Reasons. An Axiomatic Account

My talk will argue for a system of axioms that is meant to capture the logic of epistemic reasons, that is, normative reasons for belief. The system concerns a primitive direct-reason relation, a defined doxastic-reason relation, an identity criterion for what I am going to call the epistemic forces of reasons, a primitive aggregation function for reasons, and a primitive function for the revision of belief by reasons. Reasons are assumed to speak for (belief in) propositions with numerical strengths, the aggregation of reasons involves intersections of propositions and sums of strengths, belief is reconstructed as subjective probability, and ratios of new-to-old-odds are postulated to be a function of the strengths of reason. The resulting theory avoids problems that have been ascribed to the additive aggregation of reasons, and it entails that the epistemic forces of reasons conform to a vector structure and that the impact of a reason on belief corresponds to a probabilistic Jeffrey/Field-update. Its upshot is a systematic bridge between the philosophical theory of epistemic reasons and Bayesian formal epistemology, with possible applications in the philosophy of AI.

Alessandra Marra & Javier Belastegui Lazcano: Reasons as Vectors meet Reasons Holism

Reasons Holism is a family of positions within moral philosophy, according to which reasons are context-dependent: a feature that is a reason in one context may be no reason at all, or an opposite reason in another context. In the talk we will defend a holistic interpretation of Leitgeb's recent framework of reasons as vectors. Roughly put, the idea will be that a feature x could be a reason that supports a given possible world with some positive weight, while supporting another possible world with a null or negative weight, where those weights are then represented as coordinates of a vector x. We will show that such interpretation not only brings the framework of reasons as vectors close to prominent views in moral philosophy, but also provides novel conceptual and formal insights on Leitgeb's original framework.

Jan-Willem Romeijn: Overfitting in statistics and machine learning

Based on joint work with Daniel Herrmann (University of Groningen) and Tom Sterkenburg (LMU Munich)
Machine learning (ML) methods seem to defy statistical lore on the risks of overfitting. They often have many more adjustable parameters than are needed for fitting the data perfectly but, after showing predictive loss in the realm of normal overfitting, highly overparameterized ML models show surprisingly good predictive performance. In my talk I will review several attempts by statisticians and computer scientists to explain this so-called "double descent phenomenon" and distill three philosophical lessons from them that each derive from seeking continuity between statistics and ML. One is that our conception of model capacity needs an update, as it harbors a variety of ideas about complexity. A further lesson is that we have to flip the script on the problem of underdetermination: the use of unidentified statistical models offers predictive advantages, and this invites a fresh look at our empiricist ideals. A final lesson relies on De Finetti's representation theorem and on basic insights into the problem of induction: understanding the success of machine learning requires that we delve into processes of model and data construction.

Tina Eliassi-Rad: The Trilemma of Truth: Assessing Truthfulness of Responses by Large Language Models

I will present sAwMIL, an approach to separating true, false, and unverifiable statements in large language models (LLMs). sAwMIL addresses flawed assumptions in previous works. I will also discuss criteria for validating approaches like sAwMIL that track the truthfulness of probes on LLMs. I will conclude with findings from a comprehensive study involving multiple LLMs and probe datasets. If time permits, I will outline my larger project on measuring epistemic instability in human-AI societies. This work was done jointly with Germans Savcisens.

Cordelia Berz: How Well Does ChatGPT Infer and Explain? A Study in Counterfactual Reasoning

This paper investigates the counterfactual reasoning capabilities of large language models (LLMs), a critical aspect as they are increasingly used in algorithmic decision-making. We replicate a psychological experiment to examine how LLMs (GPT models, from text-davinci-002 to gpt-4o and o1-mini) answer counterfactual questions about simple mechanical devices. We analyse their responses, confidence, and free-form explanations, comparing them to human judgements and two theoretical frameworks: Pearl's (2009) interventionist account and Hiddleston's (2005) minimal network theory. Our results show that newer GPT models exhibit more sophisticated reasoning, including sensitivity to linguistic framing and uncertainty, mirroring some human behaviours. However, no model fully replicates human reasoning or consistently aligns with either theoretical framework. These findings offer a benchmark for evaluating counterfactual reasoning in LLMs and highlight the need for more theory-informed approaches to aligning model behaviour with human-like inference.

Levin Hornischer: Explaining Neural Networks with Reasons

We propose a new interpretability method for neural networks, which is based on a novel mathematico-philosophical theory of reasons. Our method computes a vector for each neuron, called its reasons vector. We then can compute how strongly this reasons vector speaks for various propositions, e.g., the proposition that the input image depicts digit 2 or that the input prompt has a negative sentiment. This yields an interpretation of neurons, and groups thereof, that combines a logical and a Bayesian perspective, and accounts for polysemanticity (i.e., that a single neuron can figure in multiple concepts). We show, both theoretically and empirically, that this method is: (1) grounded in a philosophically established notion of explanation, (2) uniform, i.e., applies to the common neural network architectures and modalities, (3) scalable, since computing reason vectors only involves forward-passes in the neural network, (4) faithful, i.e., intervening on a neuron based on its reason vector leads to expected changes in model output, (5) correct in that the model's reasons structure matches that of the data source, (6) trainable, i.e., neural networks can be trained to improve their reason strengths, (7) useful, i.e., it delivers on the needs for interpretability by increasing, e.g., robustness and fairness. (This is joint work with Hannes Leitgeb; a preprint is available at https://philpapers.org/rec/HORENN.)

Tom Sterkenburg: Bayesian learning and Bayesian deep learning

Bayesian deep learning is an alternative to the standard approach in deep learning. Instead of using the data to optimize the parameters of a deep neural net towards a single predictive function, we put a prior over the parameters and use the data to approximate a posterior over predictive functions. Bayesian deep learning is inspired and motivated by the Bayesian philosophy, but at the same time departs in seemingly significant ways from the standard Bayesian picture.

In this talk, I consider the question whether Bayesian deep learning is Bayesian --- including why we would want to ask such a question. I discuss an analogous back-and-forth in the philosophy of statistics, and cast the question as a question about the justification for learning algorithms. I then draw from Simon Huttegger (The Probabilistic Foundations of Rational Learning, Cambridge, 2017) for an up-to-date and inclusive account of the philosophical foundations of rational or Bayesian learning, and present the use of so-called "cold posteriors" in Bayesian deep learning as an interesting case for the justificatory question of is-it-Bayesian-or-not.

 

 

Organizer

Hannes Leitgeb

Venue

IBZ, Amalienstr. 38, 80799 Munich.

Registration

Please register sending an email to Office.Leitgeb@lrz.uni-muenchen.de.