RT Dissertation/Thesis
T1 Objectivity with Objects. A Modal Explanation of the Infinite
A1 Ordóñez Miguéns, Ismael
K1 objectivity
K1 fictionalism
K1 multiversism
K1 abstraction principles
K1 potentialism
K1 set theory
AB The objectivity of mathematics has been questioned for two reasons: Benacerraf’s challengeand the emergence of several limitation theorems in mathematics. This has led to the searchfor new explanations of mathematical knowledge and alternatives to universist platonism.Mainly, mathematical knowledge has been reduced to logical knowledge. Against this,this dissertation argues that mathematical knowledge cannot be reduced to logical knowledge.The two best proposals defending this reduction, fictionalism and multiversism, runinto serious problems. Both will be challenged to explain how mathematical language acquiresits content. Then, it will be argued that they do not satisfy this test. Faced with thisproblem, an alternative explanation of mathematical language and mathematical knowledgewill be developed using abstraction principles. As a result, mathematical knowledge willbe explained through linguistic competence. Finally, the proposal will be applied to ZF settheory.
YR 2024
FD 2024
LK http://hdl.handle.net/10347/33900
UL http://hdl.handle.net/10347/33900
LA eng
DS Minerva
RD 24 abr 2026