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I argue against the halfer response to the Sleeping Beauty case by presenting a new problem for halfers. When the original Sleeping Beauty case is generalized, it follows from the halfer’s key premise that Beauty must update her credence in a fair coin’s landing heads in such a way that it becomes arbitrarily close to certainty. This result is clearly absurd. I go on to argue that the halfer’s key premise must be rejected on pain of absurdity, leaving the halfer response to the original Sleeping Beauty case unsupported. I consider two ways that halfers might avoid the absurdity without giving up their key premise. Neither way succeeds. My argument lends support to the thirder response, and, in particular, to the idea that agents may be rationally compelled to update their beliefs despite not having learned any new evidence.

Qualitative knowledge is about types of things, and their excellences. There are many ways we humans produce qualitative knowledge about the world, and much of it is derived from non-quantitative sources (e.g., narratives, clinical experiences, intuitions). The purpose of my dissertation was to investigate the possibility of using Bayesian inferences to improve quantitative analysis in special education research with qualitative knowledge. It is impossible, however, to fully disentangle philosophy of inquiry, methodology, and methods. My evaluation of Bayesian estimators, thus, addresses each of these areas. Chapter Two offers a philosophical argument to substantiate the thesis that Bayesian inference is usually more applicable in education science than classical inference. I then moved on, in Chapter Three, to consider methodology. I used simulation procedures to show that even a minimum amount of qualitative information can suffice to improve Bayesian t-tests' frequency properties. Finally, in Chapter Four, I offered a practical demonstration of how Bayesian methods could be utilized in special education research to solve technical problems. In Chapter Five, I show how these three chapters, taken together, evidence that Bayesian analysis can promote a romantic science of special education - i.e., a non-positivistic science that invites teleological explanation. These explanations are often produced by researchers in the qualitative tradition, and Bayesian priors are formal mechanism for strengthening quantitative analysis with such qualitative bits of information. Researchers are also free to use their favorite qualitative methods to elicit such priors from experts.