ABSTRACT
We have constantly seen that the formation of propositional logic, which itself marks the appearance of formal thought, depends on the establishment of a combinatorial system. The structured whole depends on this combinatorial system which is manifested in the subjects’ potential ability to link a set of base associations or correspondences with each other in all possible ways so as to draw from them the relationships of implication, disjunction, exclusion, etc. Faced with an induction problem in which subjects at concrete stage II would be limited to classifications, serial ordering, equalizations, and correspondences, the substage III-B adolescents combine all of the known factors among themselves in terms of all of the possible links. But the problems given the subjects up to this point have involved factors which can be disassociated and combined at will or simply made to correspond without going beyond the level of observation or of “raw” experiment. One may wonder what would happen if we posed a problem that involved combinations directly—i.e., one that involved elements or factors whose combination is indispensable if variable results are to be obtained. Will subjects at substage II-B or even II-A discover a combinatorial system to meet the requirements of the experiment, one which would demonstrate the independence of this combinatorial system in relation to propositional logic? Must one await the formal stage for the establishment of this experimental combinatorial system, and will the stage II children accomplish nothing more than scattered empirical combinations without a total system such as we have seen elsewhere (in studying the formation of the mathematical operations of combinations, permutations, and arrangements)? 2
