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Unlike the Probability Theory based on additivity, Statistical Inferenceseems to hesitate between "Additivity" and a so-called "Maxitivity" approach.After a brief overview of three types of principles for any (parametric)statistical theory and the proof that these principles are mutually exclusive,the paper shows that two kinds of support measures are conceivable, an additiveone and a maxitive one (based on maximization operators). Unfortunately, noneof them is able to cope with the ignorance part of the statistical experimentand, in the meantime, with the partial information given through the structureof the data. To conclude, the author promotes the combined use of bothapproaches, as an efficient middle-of-the-road position for the statistician.

"Additivity" versus "Maxitivity" at the heart of the paradoxical and efficient nature of Statistics