Medieval Finitism (Elements in the Philosophy of Mathematics)

Zarepour, Mohammad Saleh

Cambridge University Press（2025/01発売）

• 製本 Hardcover:ハードカバー版／ページ数 80 p.
• 言語 ENG
• 商品コード 9781009618434
• DDC分類 111.60902

Full Description

Discussing various versions of two medieval arguments for the impossibility of infinity, this Element sheds light on early stages of the evolution of the notion of INFINITIES OF DIFFERENT SIZES. The first argument is called 'the Equality Argument' and relies on the premise that all infinities are equal. The second argument is called 'the Mapping Argument' and relies on the assumption that if one thing is mapped/ superposed upon another thing and neither exceeds the other, the two things are equal to each other. Although these arguments were initially proposed in the context of discussions against the possibility of infinities, they have played pivotal roles in the historical evolution of the notion of INFINITIES OF DIFFERENT SIZES.

Contents

1. Introduction; 2. Definition and characteristics of infinity; 3. The equality argument; 4. The mapping argument; 5. Conclusion; List of abbreviations; List of ancient and medieval thinkers discussed in this element; References.