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INTRODUCTION
DO MATHEMATICAL CONSTRUCTIONS ESCAPE LOGIC?
MATHEMATICAL REASONING VS. ABDUCTIVE REASONING
INTENTIONAL GAPS IN MATHEMATICAL PROOFS
RANDOMIZATION, PERSUASIVENESS AND RIGOR IN PROOFS
PROOFS AND PROGRAMS
MATHEMATICAL PROOFS
REPRESENTATIONAL INNOVATION AND MATHEMATICAL ONTOLOGY*
DOES MATHEMATICS HAVE OBJECTS? IN WHAT SENSE?
PHYSICAL-MATHEMATICAL REASONING
FRÉCHET AND THE LOGIC OF THE CONSTITUTION OF ABSTRACT SPACES FROM CONCRETE REALITY
STYLES OF PHYSICAL THINKING VERSUS MATHEMATICAL ONES
TWO WAYS OF REASONING AND TWO WAYS OF ARGUING IN GEOMETRY. SOME REMARKS CONCERNING THE APPLICATION OF FIGURES IN EUCLIDEAN GEOMETRY
MODERN INFINITESIMALS AS A TOOL TO MATCH INTUITIVE AND FORMAL REASONING IN ANALYSIS