Related papers: Dismantling the Surprise Test "Paradox"
In the histories formulation of quantum theory, sets of coarse-grained histories that are consistent obey the classical probability rules. It has been argued that these sets can describe the quasi-classical behaviour of closed quantum…
Consider a community of scientists whose labs are each capable of conducting a different set of experiments. The scientists want to work together to confirm a new hypothesis, but to ensure blindness, their labs generally prohibit the…
Zero factorial, defined to be one, is often counterintuitive to students but nonetheless an interesting concept to convey in a classroom environment. The challenge is to delineate the concept in a simple and effective way through the…
We study the problem of explaining observations about the probabilities of events, such as "it rains $20\%$ of the time", "rain and snow are equally likely", etc. We explain these statements with a probability distribution or a statement…
This paper shows that one cannot learn the probability of rare events without imposing further structural assumptions. The event of interest is that of obtaining an outcome outside the coverage of an i.i.d. sample from a discrete…
A central challenge in statistical inference is the presence of confounding variables that may distort observed associations between treatment and outcome. Conventional "causal" methods, grounded in assumptions such as ignorability, exclude…
Stories interest us not because they are a sequence of mundane and predictable events but because they have drama and tension. Crucial to creating dramatic and exciting stories are surprise and suspense. The thesis trains a series of deep…
This short note introduces a formal system of truth and paradoxicality, outlining the main motivation, and proving its $\omega$-consistency. The system is called TP, for 'Truth and Paradoxicality'.
We motivate and describe a theory of belief in this paper. This theory is developed with the following view of human belief in mind. Consider the belief that an event E will occur (or has occurred or is occurring). An agent either…
These lectures deal with the problem of inductive inference, that is, the problem of reasoning under conditions of incomplete information. Is there a general method for handling uncertainty? Or, at least, are there rules that could in…
In this paper, we argue that while the concept of a set-theoretic paradox (or paradoxical set) can be relatively well-defined within a formal setting, the concept of a set-theoretic hypodox (or hypodoxical set) remains significantly less…
Surprisal theory links human processing effort to the predictability of an upcoming linguistic unit, but empirical work often leaves the notion of a unit underspecified. In practice, experimental stimuli are segmented into linguistically…
When a teacher provides examples for a student to study, these examples must be informative, enabling a student to progress from their current state toward a target concept or skill. Good teachers must therefore simultaneously infer what…
Transformers have recently been shown to be capable of reliably performing logical reasoning over facts and rules expressed in natural language, but abductive reasoning - inference to the best explanation of an unexpected observation - has…
We present a case study in {\it experimental} yet {\it rigorous} mathematics by describing an algorithm, fully implemented in both Mathematica and Maple, that {\it automatically conjectures}, and then {\it automatically proves}, closed-form…
Ramsey Theorem [6] for pairs is intuitionistically but not classically provable: it is equivalent to a subclassical principle [2]. In this note we show that Ramsey may be restated in an intuitionistically provable form, which is informative…
An analysis using classical stochastic processes is used to construct a consistent system of quantum counterfactual reasoning. When applied to a counterfactual version of Hardy's paradox, it shows that the probabilistic character of quantum…
Among the many decisions to be made in their teaching practice, physics teachers must decide how to explain each particular phenomenon to students. This study explores student teachers' (STs) decision-making process when presented with…
Background. From information theory, surprisal is a measurement of how unexpected an event is. Statistical language models provide a probabilistic approximation of natural languages, and because surprisal is constructed with the probability…
In school districts where assignments are exclusively determined by a clearinghouse students can only appeal their assignment with a valid reason. An assignment is incontestable if it is appeal-proof. We study incontestability when students…