# Is Leibnizian calculus embeddable in first order logic?

We just published an article making what we feel is a plausible case in favor of an affirmative answer in Foundations of Science, see preprint here. The basic argument is that while such a requirement may seem very limitative, such an embedding seems possible with a small number of additional ingredients like a black box for returing the sum of a series, and I was curious how well-supported this appears and if there are aspects that may have been overlooked.

Crosslisted at MSE.

• Cross-posting creates problems for moderators and is discouraged meta.stackexchange.com/questions/64068/… This also looks like an invitation to discuss a paper more than an answerable question for SE. But this kind is sufficiently unusual, so I am not sure how people might feel. Perhaps you could change "how convincing" to something less opinion based, and "aspects that may have been overlooked" to something more specific. – Conifold May 19 '16 at 22:35
• @Conifold, I got rid of the "convincing" but I am not sure what to do about the aspects. If I knew which aspects we overlooked I wouldn't have overlooked them :-) Given Leibniz's vast oeuvre it is surely possible that we overlooked a relevant aspect that doesn't lend itself easily to first order formalisation. I am pretty sure nobody found a proof of the extreme value theorem there, though. – Mikhail Katz May 20 '16 at 7:53
• I don't see how this is really a question for a site on the History of Science and Mathematics. It is simply a technical math question, no more and no less. – KCd May 21 '16 at 3:04
• @KCd, the question requires a certain amount of expertise in the work of Leibniz, which not all technical mathematicians possess. – Mikhail Katz May 22 '16 at 6:58
• I'd argue that to do Leibnizian (and Eulerian, and Lagrangian etc.) calculus, the formalisation of "$y$ is a function of $x$" is required first. I asked about that here and although no one stated it explicitly, I think the answer is no, this is no directly formalisable in first order logic. – Michael Bächtold Jun 14 at 14:14