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Levels of knowing Piaget's constructivism included the principle that knowledge always [cf. "sans fin" in note 9 in 2009 below] develops through serial levels, where level n is "better" than level n - 1. This has the consequence that you rightly find puzzling, roughly how to get "more from less". Jan has reminded that this problem was known to Plato, and I guess your email is to the effect that it remains unresolved. I agree; though all the same, as Andre has noticed, we are not entirely without guidance about "ways ahead" here, both in adult science and in the psychology of development in infancy. 3 things though: - the history of science attests that in fact knowledge develops, for example Riemann's geometry is "more advanced" than Euclid's, and yet Riemann learned Euclidean geometry en route to his. - a standard alternative to construction through knowledge levels is realism [Plato, Frege, Popper] according to which reality is already there en bloc and available antecedently to be known. Under realism, Euclidean and Riemannian theorems are truths in virtue of their correspondence with abstract objects, such as platonic forms, fregean thoughts, popperian 3rd world objects. With all respect to Plato et al, realism strikes me as a "real slum" and untenable since it has to include objects corresponding to phlogiston theory and not merely to modern chemistry, objects that - in the final analysis - can never be known since [i] a representational theory of knowledge requires some way to check the fit between any representation and its object - which is impossible since under representationalism, the sole way to ascertain this is through "a" representation; and [ii] any such interpretation is thereby incomplete in principle and is ultimately dependent on an infinite regress, not a pleasant prospect surely, at least not if you are committed to objective knowledge. - hey: you have an example in the US in "we can do it, yes we can". That is ok, even if, right now, we don’t yet know how. But at least there are pointers, and I reckon Piaget's focus on necessitating reasons is a route worth taking (cf. my 2009 paper). Smith, L. (2009). Piaget's developmental epistemology. In U. Müller, J. Carpendale, & L. Smith (eds.). Cambridge companion to Piaget. [pp. 64-93]. Cambridge: Cambridge University Press. Necessary knowledge Two things. [i] Method is the under-labourer of theory, so though I am with you in supporting a method that depends on counter-arguments, all the same that alone is not enough to warrant conclusions about necessity. Counter-suggestions and counter-arguments have a valid role in contexts about truth-value [this sparkling wine - is it Champagne? Oh, you say it’s champagne - or is it Cava?]. Still, they are required, notably in studies of children's development of necessary knowledge - a basic argument is in my 1992 paper (cf.?sect 13 of my 1993 book), with an elaborated version in?chap 5 of my 2002 book. [ii] There are multiple criteria of necessity, and no doubt the choice is a hard one to make. Further, the operationalisation of any specific criterion is a critical issue in view of the persistent tendency in the literature to focus on psychological factors to the exclusion of epistemic modalities. Bon voyage! Smith, L. (1992). Judgments and justifications as criteria for the attribution of?children's knowledge. British Journal of Developmental Psychology, 10, 1-23. Smith, L. (1993). Necessary knowledge. Hove, UK: Erlbaum Associates. Smith, L. (2002). Reasoning by mathematical induction in children’s arithmetic. Oxford: Pergamon Press.