Introduction

Carlos Álvarez, Marco Panza

1-2

Do mathematical constructions escape logic?

Jean-Louis Gardies

3-24

Mathematical reasoning vs. abductive reasoning

a structural approach

Atocha Aliseda

25-44

Intentional gaps in mathematical proofs

Don Fallis

45-69

Randomization, persuasiveness and rigor in proofs

Catherine Womach, Matrin Farach

71-84

Proofs and programs

Giuseppe Longo

85-117

Mathematical proofs

Marco Panza

119-158

Representational innovation and mathematical ontology

Madeline M. Muntersbjorn

159-180

Does mathematics have objects? in what sense?

Michael Otte

181-216

Physical-mathematical reasoning

Galileo on the extruding power of terrestrial rotation

Maurice A. Finocchiaro

217-244

Fréchet and the logic of the constitution of abstract spaces from concrete reality

Luis C. Arboleda, Luis C. Recalde

245-272

Styles of physical thinking versus mathematical ones

Jan Lacki

273-288

Two ways of reasoning and two ways of arguing in geometry

some remarks concerning the application of figures in euclidean geometry

Carlos Álvarez

289-323

Modern infinitesimals as a tool to match intuitive and formal reasoning in analysis

Robert Lutz

325-351