Academic Appointments

Honors & Awards

  • Dean's Award for Achievements in Teaching, School of Humanities and Sciences (2019-2020)

Program Affiliations

  • Symbolic Systems Program

2023-24 Courses

Stanford Advisees

All Publications

  • A Simple Logic of Concepts JOURNAL OF PHILOSOPHICAL LOGIC Icard, T. F., Moss, L. S. 2022
  • An interaction effect of norm violations on causal judgment. Cognition Gill, M., Kominsky, J. F., Icard, T. F., Knobe, J. 2022; 228: 105183


    Existing research has shown that norm violations influence causal judg- ments, and a number of different models have been developed to explain these effects. One such model, the necessity/sufficiency model, predicts an interac- tion pattern in people's judgments. Specifically, it predicts that when people are judging the degree to which a particular factor is a cause, there should be an interaction between (a) the degree to which that factor violates a norm and (b) the degree to which another factor in the situation violates norms. A study of moral norms (N=1000) and norms of proper functioning (N=3000) revealed robust evidence for the predicted interaction effect. The implications of these patterns for existing theories of causal judgments is discussed.

    View details for DOI 10.1016/j.cognition.2022.105183

    View details for PubMedID 35830782

  • Causal Distillation for Language Models Wu, Z., Geiger, A., Rozner, J., Kreiss, E., Lu, H., Icard, T., Potts, C., Goodman, N., ASSOC COMPUTAT LINGUIST ASSOC COMPUTATIONAL LINGUISTICS-ACL. 2022: 4288-4295
  • Inference From Explanation JOURNAL OF EXPERIMENTAL PSYCHOLOGY-GENERAL Kirfel, L., Icard, T., Gerstenberg, T. 2021


    What do we communicate with causal explanations? Upon being told, "E because C", a person might learn that C and E both occurred, and perhaps that there is a causal relationship between C and E. In fact, causal explanations systematically disclose much more than this basic information. Here, we offer a communication-theoretic account of explanation that makes specific predictions about the kinds of inferences people draw from others' explanations. We test these predictions in a case study involving the role of norms and causal structure. In Experiment 1, we demonstrate that people infer the normality of a cause from an explanation when they know the underlying causal structure. In Experiment 2, we show that people infer the causal structure from an explanation if they know the normality of the cited cause. We find these patterns both for scenarios that manipulate the statistical and prescriptive normality of events. Finally, we consider how the communicative function of explanations, as highlighted in this series of experiments, may help to elucidate the distinctive roles that normality and causal structure play in causal judgment, paving the way toward a more comprehensive account of causal explanation. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

    View details for DOI 10.1037/xge0001151

    View details for Web of Science ID 000733088000001

    View details for PubMedID 34928680

  • Expectations Affect Physical Causation Judgments JOURNAL OF EXPERIMENTAL PSYCHOLOGY-GENERAL Gerstenberg, T., Icard, T. 2020; 149 (3): 599–607


    When several causes contributed to an outcome, people often single out one as "the" cause. What explains this selection? Previous work has argued that people select abnormal events as causes, though recent work has shown that sometimes normal events are preferred over abnormal ones. Existing studies have relied on vignettes that commonly feature agents committing immoral acts. An important challenge to the thesis that norms permeate causal reasoning is that people's responses may merely reflect pragmatic or social reasoning rather than arising from causal cognition per se. We tested this hypothesis by asking whether the previously observed patterns of causal selection emerge in tasks that recruit participants' causal reasoning about physical systems. Strikingly, we found that the same patterns observed in vignette studies with intentional agents arise in visual animations of physical interactions. Our results demonstrate how deeply normative expectations affect causal cognition. (PsycINFO Database Record (c) 2020 APA, all rights reserved).

    View details for DOI 10.1037/xge0000670

    View details for Web of Science ID 000512302600015

    View details for PubMedID 31512904

  • Why Be Random? Mind Icard, T. 2020

    View details for DOI 10.1093/mind/fzz065

  • On Open-Universe Causal Reasoning Ibeling, D., Icard, T., Adams, R. P., Gogate JMLR-JOURNAL MACHINE LEARNING RESEARCH. 2020: 1233-1243
  • Probabilistic Reasoning Across the Causal Hierarchy Ibeling, D., Icard, T., Assoc Advancement Artificial Intelligence ASSOC ADVANCEMENT ARTIFICIAL INTELLIGENCE. 2020: 10170-10177
  • Calibrating Generative Models: The Probabilistic Chomsky-Schützenberger Hierarchy Journal of Mathematical Psychology Icard, T. 2020; 95
  • Bayes, Bounds, and Rational Analysis PHILOSOPHY OF SCIENCE Icard, T. F. 2018; 85 (1): 79–101

    View details for DOI 10.1086/694837

    View details for Web of Science ID 000419596500004

  • Inferring probability comparisons MATHEMATICAL SOCIAL SCIENCES Harrison-Trainor, M., Holliday, W. H., Icard, T. F. 2018; 91: 62–70
  • Normality and actual causal strength. Cognition Icard, T. F., Kominsky, J. F., Knobe, J. 2017; 161: 80-93


    Existing research suggests that people's judgments of actual causation can be influenced by the degree to which they regard certain events as normal. We develop an explanation for this phenomenon that draws on standard tools from the literature on graphical causal models and, in particular, on the idea of probabilistic sampling. Using these tools, we propose a new measure of actual causal strength. This measure accurately captures three effects of normality on causal judgment that have been observed in existing studies. More importantly, the measure predicts a new effect ("abnormal deflation"). Two studies show that people's judgments do, in fact, show this new effect. Taken together, the patterns of people's causal judgments thereby provide support for the proposed explanation.

    View details for DOI 10.1016/j.cognition.2017.01.010

    View details for PubMedID 28157584

  • Indicative Conditionals and Dynamic Epistemic Logic ELECTRONIC PROCEEDINGS IN THEORETICAL COMPUTER SCIENCE Holliday, W. H., Icard, T. F. 2017: 337–51
  • Pragmatic Considerations on Comparative Probability PHILOSOPHY OF SCIENCE Icard, T. F. 2016; 83 (3): 348-370
  • A note on cancellation axioms for comparative probability THEORY AND DECISION Harrison-Trainor, M., Holliday, W. H., Icard, T. F. 2016; 80 (1): 159-166
  • Iterating semantic automata LINGUISTICS AND PHILOSOPHY Steinert-Threlkeld, S., Icard, T. F. 2013; 36 (2): 151-173
  • Inclusion and Exclusion in Natural Language STUDIA LOGICA Icard, T. F. 2012; 100 (4): 705-725
  • Provability and Interpretability Logics with Restricted Realizations NOTRE DAME JOURNAL OF FORMAL LOGIC Icard, T. F., Joosten, J. J. 2012; 53 (2): 133-154
  • A Topological Study of the Closed Fragment of GLP JOURNAL OF LOGIC AND COMPUTATION Icard, T. 2011; 21 (4): 683-696