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What, in effect are the conditions for the construction of formal
thought? The child must not only apply operations to objects - in
other words, mentally execute possible actions on them - he must
also 'reflect' those operations in the absence of the objects which
are replaced by pure propositions. Thus 'reflection' is thought
raised to the second power. Concrete thinking is the representation
of a possible action, and formal thinking is the representation of
a representation of possible action... It is not surprising,
therefore, that the system of concrete operations must be completed
during the last years of childhood before it can be 'reflected' by
formal operations. In terms of their function, formal operations do
not differ from concrete operations except that they are applied to
hypotheses or propositions whose logic is an abstract translation of
the system of 'inference' that governs concrete operations.
-- Jean Piaget
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