Mechanisms of undecidable temporal Reasoning

 The research presented here studies the inferential mechanisms of qualitative reasoning in adults applied to undecidable hypothetical statements about cinematic time.
Qualitative reasoning is different from quantitative reasoning in that it does not rely on numeric data. Inferences such as "more than..."  "less than..." or "the same..." are used. Cinematic times utilizes three concepts: time, speed, and space.

Qualitative cinematic judgements can consist of "more time," "the same time," "less time," "faster," "the same speed," "slower," "more space," "the same amout of space," "less space."  Hypothetical statements consist of giving two pieces of qualitative information out of three, for example, information on length of time, and space, and ask for a judgement on missing information (speed, in this case). Hypothetical undecidables are different from decidable statements because the three responses remain possible.

Two hundred adult subjects (one hundren "novices" and one hundred "experts" with 5 - 7 years of post physical mathematics) listened to two undecidable hypothetical statements on four types of information: relative to  the speed of two vehicles (the red car is going faster than the black car), in the order of departure (the red car leaves before the black car), in the order of arrival (the red car arrives before the black car), and one specifying that the two vehicles leave from the same spot. The subject is asked to respond on the length of the race and the distance covered.

Results show that: 1) The role of cinematic information does not modify the quality of temporal inferences. 2) Undecidable problems pose many difficulties even for "experts." 3) Two inferential mechanisms explain the majority of the experts' responses but only 5 for the novices.

These results illustrate the words of Piaget (1969): "Time poses terrifying problems to genetic epistemology."

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