  In the present essay we attempt to reconstruct Newtonian mechanics under the
guidance of logical principles and of a constructive approach related to the
genetic epistemology of J. Piaget and R. Garc\'ia \citep{piag89}. Instead of
addressing Newton's equations as a set of axioms, ultimately given by the
revelation of a prodigious mind, we search for the fundamental knowledge,
beliefs and provisional assumptions that can produce classical mechanics. We
start by developing our main tool: the No Arbitrariness Principle, that we
present in a form that is apt for a mathematical theory as classical mechanics.
Subsequently, we introduce the presence of the observer, analysing then the
relation objective-subjective and seeking objectivity going across
subjectivity. We take special care of establishing the precedence among all
contributions to mechanics, something that can be better appreciated by
considering the consequences of removing them: (a) the consequence of
renouncing logic and the laws of understanding is not being able to understand
the world, (b) renouncing the early elaborations of primary concepts such as
time and space leads to a dissociation between everyday life and physics, the
latter becoming entirely pragmatic and justified \emph{a-posteriori} (because
it is convenient), (c) changing our temporary beliefs has no real cost other
than effort. Finally, we exemplify the present approach by reconsidering the
constancy of the velocity of light. It is shown that it is a result of
Newtonian mechanics, rather than being in contradiction with it. We also
indicate the hidden assumption that leads to the (apparent) contradiction.

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