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We present the leading hypotheses of a work in progress aiming at testing and comparing neural activities in the case of a cognitive illusion (the bat-and-ball illusion) and in the case of a typical instance of framing effects. We focus on contrasted answers linked to Stanovich's system 1 vs system 2. We expect to see such a contrast in the case of the bat-and-ball illusions but not in the case of framing-effects which cannot be called 'cognitive illusions' in the same sense. Another focus of interest in our study is about a possible "sense of rationality" experienced by subjects giving intuitive erroneous answers to cognitive tasks after significant reaction times. We try to consider in which sense data pointing to the existence of such feelings of irrationality could be experimentally relevant to the classification of cognitive illusions and biases.
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