infinitesimal

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I believe the conclusion is inescapable that Leibniz is here declaring the impossibility of the existence of infinitesimals.
It is important to note that in general in the context of responding to Cartesians, Leibniz is less likely to underline the outright denial of the existence of infinitesimals for the reasons indicated above: to do so requires us to identify what we can conceive with what can be conceived simpliciter.
59) On the basis of such passages John Earman proposes that Leibniz is in fact speaking of two different sorts of infinitesimals, and that his denial of one sort is in fact a "cover" for his commitment to the other.
Bernoulli, on the other hand, is inclined to think that infinitesimals do exist, although he agrees with Leibniz that they have not been demonstrated to exist.
Leibniz was living in Paris and had just invented the infinitesimal calculus.
6) As this last remark indicates, the metaphysical outpourings of 1676 should in large part be understood as motivated by the antecedent success of the newly invented infinitesimal calculus, which had washed over Leibniz's metaphysics with the force of a tidal wave.
Despite Bernoulli being an accomplished practitioner of the infinitesimal calculus, it may perhaps be tempting to dismiss this as a quaint fallacy generated by an archaic understanding of the nature of the mathematical infinite.
there are an infinite number of terms there exists an infinitesimal.
As we have seen, in the correspondence with Bernoulli, there is a potentially competing candidate for the role played by the indefinite infinite in both the realms of the infinitely large and small: although he cannot demonstrate them Leibniz also cannot find a way to rule out the existence of infinitesimal (but not minimal) and infinitely large (but not maximal) magnitudes.
By 1703-5, the period during which Leibniz wrote the New Essays, Leibniz has moved to the position that any infinite or infinitesimal quantities are impossible.
Yet in doing so, he indicates just how weak a commitment to the infinite is required to work in the mathematical realm, even in the case of the infinitesimal calculus.