Impossibility axioms

Probability values lie continuously in the range 0 to 1 inclusive, where the endpoints zero and unity are identified with impossibility and certainty, respectively. This follows immediately for the frequentist for the axiomatic approach it is adopted as an axiom, but one imbued with Laplace s commonsense. Any other range could be chosen at the cost of greater difficulty of interpretation. 

Insects provide another difficulty. One of the axioms of entomology is that in the Northern Hemisphere, insect populations are larger and more varied in the eastern parts of a continental mass. In addition to its other problems, eastern viticulture must do constant battle against numerous voracious insect pests. The rose chafer regularly appears just in time to nip off inflorescences as they are about to flower. The Japanese beetle turns every leaf of a grapevine into a piece of lace, if allowed to. In the Tidewater sections of the lower part, nematode infestation can be so severe as to make viticulture almost impossible. 

Show from our axiom S c > 0 that this process is indeed impossible. 

However, prior-data conflicts must be avoided or, at least, detected and explained before the inference. Such conflicts can appear when prior and data favour areas of the parameters space far from each other, or when the subjective source (expert) becomes largely predominant. Dedicated criteria have been recently proposed by Evans and Moshonov (2006) then Bous-quet (2008). Of course, many scientist do not feel at ease with the concept of prior distribution. Although its mathematical existence is grounded of five axioms of rational behavior (Savage, 1954), one can object that the man in the street does not obey this strict axiomatic corpus (Munier Parent, 1995) or that encoding expert knowledge into probability distribution looks like an impossible mission. 

Acquisition of empirical axioms , i.e. empirically true formulas, which it is impossible to infer from other true formulas. 

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