-
8The Interrelations Between Mathematics and Philosophy in Leibniz’s ThoughtIn Douglas M. Jesseph (ed.), G.W. Leibniz, Interrelations Between Mathematics and Philosophy, Springer Verlag. pp. 3-21. 2015.This paper consists of three main sections. In the first section, we consider how early attempts at understanding the relationship between mathematics and philosophy in Leibniz’s thought were often made within the framework of grand reconstructions guided by intellectual trends such as the search for “the ideal of system”. In the second section, we proceed to recount Leibniz’s first encounter with contemporary mathematics during his four years of study in Paris presenting some of the earliest ma…Read more
-
42Confronting Ideals of Proof with the Ways of Proving of the Research MathematicianStudia Logica 96 (2): 273-288. 2010.In this paper, we discuss the prevailing view amongst philosophers and many mathematicians concerning mathematical proof. Following Cellucci, we call the prevailing view the “axiomatic conception” of proof. The conception includes the ideas that: a proof is finite, it proceeds from axioms and it is the final word on the matter of the conclusion. This received view can be traced back to Frege, Hilbert and Gentzen, amongst others, and is prevalent in both mathematical text books and logic text boo…Read more
-
EMILY R. GROSHOLZ: Representation and Productive Ambiguity in Mathematics and the SciencesStudia Leibnitiana 38 (2). 2006.
-
16How did Bertrand Russell make Leibniz into a ''Fellow Spirit''?*In Pauline Phemister & Stuart Brown (eds.), Leibniz and the English-Speaking World, Springer. pp. 195--205. 2007.
-
35Macbeth Danielle. Frege's logic. Harvard University Press, Cambridge, Massachusetts, 2005, xii+ 206 pp (review)Bulletin of Symbolic Logic 12 (3): 496-498. 2006.
-
30Revisiting the question about proof: philosophical theory, history, and mathematical practiceManuscrito 31 (1): 361-386. 2008.This paper revisits some of Chateaubriand’s critical considerations with regard to representing our reasoning practices in logic and mathematics by means of “idealized syntax”. I focus on the persistently critical side of these considerations which aim to prepare the ground for “an interesting epistemology of logic and mathematics” that ought to make room for understanding the pragmatic dimensions of proofs as explanatory rational displays. First, I discuss the 20th century “syntactic conception…Read more
-
18