Related papers: Is pluralism in the history of mathematics possibl…
We examine some recent scholarship on Leibniz's philosophy of the infinitesimal calculus. We indicate difficulties that arise in articles by Bassler, Knobloch, and Arthur, due to a denial to Leibniz's infinitesimals of the status of…
Putnam and Finkelstein can be read as providing an answer to Kripke's skeptical argument by appealing to the way mathematics is commonly pursued. Nowadays, the debate surrounding pluralism has questioned the postulation of a unique way of…
An age-old controversy in mathematics concerns the necessity and the possibility of constructive proofs. The controversy has been rekindled by recent advances which demonstrate the feasibility of a fully constructive mathematics. This…
We describe a mainstream "universalist" approach to the understanding of mathematics. We then conduct a systematic (but not exhaustive) review of the academic literature on the decolonisation of mathematics and identify how this challenges…
We analyze the developments in mathematical rigor from the viewpoint of a Burgessian critique of nominalistic reconstructions. We apply such a critique to the reconstruction of infinitesimal analysis accomplished through the efforts of…
University level mathematics in a number of countries is under pressure to `decolonise the curriculum'. This paper considers, as a test case, a possible `decolonisation' of linear algebra. This is a representative case, since linear algebra…
Leibniz's mathematical texts are a perfect example of a type of historical document that is extremely difficult to deal with in the context of an editorial enterprise: the draft. The tables in Leibniz's mathematical manuscripts are a…
This essay considers ways that recent uses of computers in mathematics challenge contemporary views on the nature of mathematical understanding. It also puts these challenges in a historical perspective and offers speculation as to a…
We contribute to the lively debate in current scholarship on the Leibnizian calculus. In a recent text, Arthur and Rabouin argue that non-Archimedean continua are incompatible with Leibniz's concepts of number, quantity and magnitude. They…
We present a characterization of the completeness of the field of real numbers in the form of a \emph{collection of ten equivalent statements} borrowed from algebra, real analysis, general topology and non-standard analysis. We also discuss…
In this note some philosophical thoughts and observations about mathematics are expressed, arranged as challenges to some common claims.
It was conjectured that multiplicity of a singularity is bi-Lipschitz invariant. We disprove this conjecture, constructing examples of bi-Lipschitz equivalent complex algebraic singularities with different values of multiplicity.
One of the variants for systematizing the activities of the historian of mathematics is proposed, as well as a scheme for organizing research and search work in the preparation of scientific articles and reports on the history of science.
This paper provides an overview of recent historical research regarding scientifically-informed challenges to the idea that the stars are other suns orbited by other inhabited earths -- an idea that came to be known as "the Plurality of…
The way Leibniz applied his philosophy to mathematics has been the subject of longstanding debates. A key piece of evidence is his letter to Masson on bodies. We offer an interpretation of this often misunderstood text, dealing with the…
We explore Leibniz's understanding of the differential calculus, and argue that his methods were more coherent than is generally recognized. The foundations of the historical infinitesimal calculus of Newton and Leibniz have been a target…
Axiomatizing mathematical structures is a goal of Mathematical Logic. Axiomatizability of the theories of some structures have turned out to be quite difficult and challenging, and some remain open. However axiomatization of some…
This paper frames calculus as a global, centuries-long development rather than a subject that began only with Newton and Leibniz. Drawing on ideas from Greek, Indian, Islamic, and later European mathematics, it highlights how concepts like…
Aristotelian assertoric syllogistic, which is currently of growing interest, has attracted the attention of the founders of modern logic, who approached it in several (semantical and syntactical) ways. Further approaches were introduced…
This paper introduces and defends an account of model-based science that I dub model pluralism. I argue that despite a growing awareness in the philosophy of science literature of the multiplicity, diversity, and richness of models and…