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Unlike a widespread opinion, the constitution of objectivity (in Kant's sense) does not require a strict, determinist, application of the category of causality to phenomena manifested in space-time. Some stochastic theories, using probabilities at their fundamental level, are just as able to constitute a domain of objects as determinist theories. In this paper, the conditions to be fulfilled for numbers to be considered as probabilities of intrinsic properties of an object of experience are displayed. These conditions, that synthesize George Boole's relations and John Bell's inequalities, are discussed in detail. Where they are not fulfilled, they make us suspect that it is impossible to achieve the detachment of an object from the instruments that give access to it. Copyright © 2012 ICPHS.