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The problem is "your precise belief in $H$ becomes imprecise"; or rather, your precise belief in $H$ as represented by $P(H)$ becomes imprecise.
The Bayesian agent must have a precise belief about the coin's landing heads on the next toss.
So the alleged problem with dilation and reflection is not as simple as "your precise belief becomes imprecise".
Besides discord and non-specificity, which hide in a precise belief structure, we claim that fuzziness is also associated with an interval-valued belief structure.
Any other precise belief you might have in $X$ is such that $Y$ now affects your posterior belief in $H$. Figure 2 shows the situation for one particular belief about how likely $X$ is; for one particular $p\in P$.
Similar(55)
He notes that it is not the case that it is always unreasonable or impossible for you to have precise beliefs: in that case precision could serve as a regulative ideal.
But they do not dwell on the Rajneeshees' precise beliefs; their respectful silence, seemingly motivated by good faith, has the effect of enhancing the mystic's mystique.
By retaining the precise beliefs and attitudes of Austen's characters, Trollope alters our responses to them, now viewed through the distorting filter of the 21st century.
The project is complicated by the fact that vague partial beliefs interact with precise beliefs (MacFarlane 2010).
A high number of 0 and 100 responses probably reflects absence of precise beliefs and therefore some uncertainty.
Likewise, on the belief side, some contend (notably, Joyce 2010) that the evidence may be such that it does not commit a rational agent to precise beliefs measurable by a unique probability function.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com