GABRIELE LOLLI

Ambiguity

A Journey through Literature and Mathematics

Despite the suspicion and distrust with which it is generally associated, ambiguity is in fact a useful, even valuable, quality in many fields. In mathematics – the science in which clearness and accuracy reign supreme – ambiguities provide the spark to finding solutions and shedding light on intuitive insights, and thus provide opportunities and incentives for progress. Something similar happens in literature and artistic creation, where ambiguity enhances beauty and aesthetic pleasure. The book explains the importance of this key concept, narrates episodes and events from the history of mathematics (such as: the Greeks’ bewilderment after having discovered incommensurability; non-Euclidean geometry; the infinite; and probability), examines a selection of literary examples drawn from Italo Calvino, Philip Roth and Herman Melville, and describes how literature and mathematics come together in the game of chess.

Gabriele Lolli teaches Philosophy of Mathematics at the Scuola Normale Superiore in Pisa, after having taught Mathematical Logic for many years at the University of Turin.

Introduzione
LETTERATURA
1. Ambiguità nella letteratura
2. Italo Calvino
3. Herman Melville
4. Memoria e invenzione
5. Philip Roth
6. Il doppio
7. Un romanzo matematico
MATEMATICA
8. Rifiuto del formalismo
9. Sulle tracce dell'ambiguità in matematica
1. La dimostrazione
2. Le logiche e l'esistenza
3. Geometrie non euclidee
4. Infinitesimi
5. Nuovi concetti
6. L'infinito
7. Reazioni
8. ε-δ infinitesimi
9. Inevitabile
10. Sette tipi di ambiguità in matematica
11. Le ambiguità produttive
12. Ambiguità ovunque
13. A scuola
GIOCHI, LINGUAGGIO E LOGICA
14. Ambiguità negli scacchi
15. Linguaggio e logica
1. Il linguaggio logico
2. Il ragionamento
3. Il dilemma del robot
4. Grammatiche ambigue
16. L'ambiguità tipica
Riferimenti bibliografici
Indice dei nomi
series "Intersezioni"
pp. 304, 978-88-15-27043-6
publication year 2017