Coherence Preservation: A Threat to Probabilistic Measures of Coherence

This thesis proposes a new requirement that probabilistic measures of coherence should ideally satisfy. This requirement is called ‘coherence preservation’. Probabilistic measures of coherence build on the idea that coherence is the mutual support between elements of a set. Using the requirement of coherence preservation, one may reevaluate mainstream probabilistic coherence measures, and draw the conclusion that all these measures fail to capture certain aspects of our intuitive understanding of coherence. We begin with a review of different probabilistic coherence measures. Next, we extend our survey with a proof for the non-existence of a truth-conducive coherence measure, and we discuss various follow-up attempts of saving coherence. By presenting the requirement of coherence preservation, it can be shown that in some cases, the degree of coherence of a set decreases when the set is extended with a proposition which confirms every element of the set. Based on this observation, we can show that attempts of saving coherence leads to counterintuitive results. One should therefore look for a different way of characterizing coherence, which better captures the non-quantitative aspect of this notion.