Ontology and the Foundations of Mathematics

Erscheinungsjahr 2022
ISBN: 978-1-108-71693-2
Verlag: Cambridge University Press

Buch, Englisch, 75 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 95 g

Reihe: Elements in the Philosophy of Mathematics

This Element looks at the problem of inter-translation between mathematical realism and anti-realism and argues that so far as realism is inter-translatable with anti-realism, there is a burden on the realist to show how her posited reality differs from that of the anti-realist. It also argues that an effective defence of just such a difference needs a commitment to the independence of mathematical reality, which in turn involves a commitment to the ontological access problem – the problem of how knowable mathematical truths are identifiable with a reality independent of us as knowers. Specifically, if the only access problem acknowledged is the epistemological problem – i.e. the problem of how we come to know mathematical truths – then nothing is gained by the realist notion of an independent reality and in effect, nothing distinguishes realism from anti-realism in mathematics.

Autoren/Hrsg.

Rush, Penelope

Fachgebiete

• Geisteswissenschaften Philosophie Wissenschaftstheorie, Wissenschaftsphilosophie

Inhaltsverzeichnis

1. What are we Talking about?; 2. Inter-translatability; 3. Two Access Problems; 4. Independence; 5. Justification.