Mathematical epistemology

When problems arise in model experiments for the above mentioned reasons, one cannot put the blame on an epistemologically and mathematically sound method. 

The present paper will put forward the point that a Bayesian framework may be viewed as rather natural for tackling issues (a) and (b) altogether. Indeed, beyond the forceful epistemological and decision-theory feamres of a Bayesian approach, it includes by definition a double-level probabilistic model separating epistemic and aleatory components and offers a traceable process to mix the encoding of engineering expertise inside priors and the observations inside an updated epistemic layer that proves mathematically consistent even when dealing with very low-size samples. 

Schommer Aikins, M., Duell, O. K., Hutter, R. (2005). Epistemological beliefs, mathematical problem-solving beliefs, and academic performance of middle school students. The Elementary School Journal, 105(3), 289-304. 

This paper analyses the path of experimental research that led Michael Faraday (1791-1867) to enunciate in 1834 the first law of electro-chemistry. The specific experiments that Faraday performed and his view of the results were influenced by a number of factors. This paper discusses these including his antipathy towards mathematics, his religious beliefs, his epistemology and the large number of other important experimental discoveries that he made between 1831 and 1834 which threatened to overwhelm him with empirical information which could not be quickly assimilated. This forms the context in which Faraday s new knowledge of electrochemistry was developed. 

PauUng and Slater justified the visual models of traditional chemists through skillful application of the mathematical language of quantum mechanics. Hiickel s model, on the contrary, imderpinned the organic chemist s classical visualizations while placing them at the same time on a new foundation that would ultimately articulate a new epistemological hamework. 

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