There are two basic principles, or building blocks of Du Châtelet’s metaphysics of science, namely the principle of contradiction and the principle of sufficient reason. Du Châtelet also speaks about first principles, d.i. “certain principles whose truth is known without even reflecting on it, because they are self-evident.”

The principle of contradiction states that one cannot both affirm and deny something in the same sense at the same time:

Contradiction is called, which affirms and denies the same thing at the same time; This principle is the first Axiom, upon which all truths are founded.

On appelle Contradiction, ce qui affirme et nie la même chose en même tems; ce principe est le prémier Axiome, sur lequel toutes les vérités sont fondées.

On appelle Contradiction, ce qui affirme et nie la même chose en même tems; ce principe est le prémier Axiome, sur lequel toutes les vérités sont fondées.

Man nennet es einen Widerspruch, wenn man eben dieselbe Sache zugleich bekräftiget und verneinet. Dieser Grundsatz ist der erste, worauf alle Wahrheiten fussen.

In line with Aristotle, Du Châtelet defends the principle of contradiction as a first principle, or axiom. One cannot argue against this principle without using it, and this, in turn, is self-defeating. Thus, the principle of contradiction is the “foundation of all certainty in human knowledge” («fondement de toute certitude»). Even the Phyrrhonists, well known for their radical skepticism, never denied this principle, and even Descartes used it in his philosophy to prove that we exist.

The violation of the principle of contradiction would mean that anything can be proven, e.g., the sum of 2 and 2 would give 4 as well as 6. However, we all know that it is impossible for two and two to make six. Thus, some philosophers argue that the principle of contradiction defines what is possible and what is impossible:

It follows from this that the impossible is that which implies a contradiction; and the impossible does not imply it at all.

Il suit de ce que l’on vient de dire que l’Impossible est ce qui implique contradiction, & le possible ce qui ne l’implique point.

Il decoulé de ce que l’on vient de dire que l’Impossible est ce qui implique contradiction, & le possible ce qui ne l’implique point.

Aus dem itztgedachten fliesset, daß dasjenige unmöglich sey, was einen Widerspruch in sich hält, und möglich, was nichts widersprechendes in sich hält.

There is, however, an alternative definition of the possible and the impossible: impossible is that which does not give a clear and distinct idea; possible is that which one can conceive, and which corresponds to a clear idea. In any case, whenever it is claimed that something is impossible, we must be able to prove it. An absolute proof of consistency requires absolute certainty. Without this condition our ideas are more or less probable opinions. So long as we are not in the position of absolute certainty, it is indispensable to verify one’s ideas in order to preserve oneself from error, i.e., to demonstrate the reality of our ideas and not to admit any as incontestable, unless confirmed by experiment or demonstration («par l’expérience our par la démonstration»).

The principle of contradiction suffices for necessary truths («vérités nécessaires»), i.e., truths which can be only determined by a single way («ne sont déterminables que d’une seule manière«).  Concerning contingent truths («vérites contingents»), i.e. a thing can exist in various ways («différentes manieres») and non of its determinations is more necessary than another, one needs the principle of sufficient reason.

According to Du Châtelet the principle of sufficient reason is as fundamental and universal as the principle of contradiction. The negation of this principle would result in great absurdities. Firstly, things could exist only for an instant; one could no longer be sure that a thing is the same as it was a moment before. Secondly,