### Abstract

A widespread assumption in the contemporary discussion of probabilistic models of cognition, often attributed to the Bayesian program, is that inference is optimal when the observer's priors match the true priors in the world—the actual “statistics of the environment.” But in fact the idea of a “true” prior plays no role in traditional Bayesian philosophy, which regards probability as a quantification of belief, not an objective characteristic of the world. In this paper I discuss the significance of the traditional Bayesian epistemic view of probability and its mismatch with the more objectivist assumptions about probability that are widely held in contemporary cognitive science. I then introduce a novel mathematical framework, the observer lattice, that aims to clarify this issue while avoiding philosophically tendentious assumptions. The mathematical argument shows that even if we assume that “ground truth” probabilities actually do exist, there is no objective way to tell what they are. Different observers, conditioning on different information, will inevitably have different probability estimates, and there is no general procedure to determine which one is right. The argument sheds light on the use of probabilistic models in cognitive science, and in particular on what exactly it means for the mind to be “tuned” to its environment.

Original language | English (US) |
---|---|

Pages (from-to) | 1871-1903 |

Number of pages | 33 |

Journal | Cognitive Science |

Volume | 41 |

Issue number | 7 |

DOIs | |

State | Published - Sep 2017 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Experimental and Cognitive Psychology
- Cognitive Neuroscience
- Artificial Intelligence

### Keywords

- Bayesian inference
- Epistemology
- Probability
- Subjectivism

### Cite this

*Cognitive Science*,

*41*(7), 1871-1903. https://doi.org/10.1111/cogs.12444

}

*Cognitive Science*, vol. 41, no. 7, pp. 1871-1903. https://doi.org/10.1111/cogs.12444

**What Are the “True” Statistics of the Environment?** / Feldman, Jacob.

Research output: Contribution to journal › Article

TY - JOUR

T1 - What Are the “True” Statistics of the Environment?

AU - Feldman, Jacob

PY - 2017/9

Y1 - 2017/9

N2 - A widespread assumption in the contemporary discussion of probabilistic models of cognition, often attributed to the Bayesian program, is that inference is optimal when the observer's priors match the true priors in the world—the actual “statistics of the environment.” But in fact the idea of a “true” prior plays no role in traditional Bayesian philosophy, which regards probability as a quantification of belief, not an objective characteristic of the world. In this paper I discuss the significance of the traditional Bayesian epistemic view of probability and its mismatch with the more objectivist assumptions about probability that are widely held in contemporary cognitive science. I then introduce a novel mathematical framework, the observer lattice, that aims to clarify this issue while avoiding philosophically tendentious assumptions. The mathematical argument shows that even if we assume that “ground truth” probabilities actually do exist, there is no objective way to tell what they are. Different observers, conditioning on different information, will inevitably have different probability estimates, and there is no general procedure to determine which one is right. The argument sheds light on the use of probabilistic models in cognitive science, and in particular on what exactly it means for the mind to be “tuned” to its environment.

AB - A widespread assumption in the contemporary discussion of probabilistic models of cognition, often attributed to the Bayesian program, is that inference is optimal when the observer's priors match the true priors in the world—the actual “statistics of the environment.” But in fact the idea of a “true” prior plays no role in traditional Bayesian philosophy, which regards probability as a quantification of belief, not an objective characteristic of the world. In this paper I discuss the significance of the traditional Bayesian epistemic view of probability and its mismatch with the more objectivist assumptions about probability that are widely held in contemporary cognitive science. I then introduce a novel mathematical framework, the observer lattice, that aims to clarify this issue while avoiding philosophically tendentious assumptions. The mathematical argument shows that even if we assume that “ground truth” probabilities actually do exist, there is no objective way to tell what they are. Different observers, conditioning on different information, will inevitably have different probability estimates, and there is no general procedure to determine which one is right. The argument sheds light on the use of probabilistic models in cognitive science, and in particular on what exactly it means for the mind to be “tuned” to its environment.

KW - Bayesian inference

KW - Epistemology

KW - Probability

KW - Subjectivism

UR - http://www.scopus.com/inward/record.url?scp=85029458484&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85029458484&partnerID=8YFLogxK

U2 - 10.1111/cogs.12444

DO - 10.1111/cogs.12444

M3 - Article

C2 - 27859520

AN - SCOPUS:85029458484

VL - 41

SP - 1871

EP - 1903

JO - Cognitive Science

JF - Cognitive Science

SN - 0364-0213

IS - 7

ER -