Provider: Ingenta Connect
Database: Ingenta Connect
Content: application/x-research-info-systems
TY - ABST
AU - Wójtowicz, Krzysztof
TI - Independence and Justification in Mathematics
JO - Poznan Studies in the Philosophy of the Sciences and the Humanities
PY - 2006-11-01T00:00:00///
VL - 91
IS - 1
SP - 349
EP - 373
N2 - In the article the problem of independence in mathematics is discussed. The status of the continuum hypothesis, large cardinal axioms and the axiom of constructablility is presented in some detail. The problem whether incompleteness is really relevant for ordinary mathematics and for empirical science is investigated. Another aim of the article is to give some arguments for the thesis that the problem of reliability and justification of new axioms is well-posed and worthy of attention. In my opinion, investigations concerning the status of independent sentences give insight into our understanding of mathematical concepts, of mathematical knowledge and of the role of mathematics in empirical science.
UR - http://www.ingentaconnect.com/content/rodopi/pozs/2006/00000091/00000001/art00022
ER -