No one has ever seen an infinite set, ergo, they probably don’t exist, and at any rate I have no reason to believe in them.
Does this mean that infinite sets are not logical implications of some general beliefs you already have?
Many schools of math philosophy do without infinity:
http://en.wikipedia.org/wiki/Finitism
http://en.wikipedia.org/wiki/Ultrafinitism
http://en.wikipedia.org/wiki/Mathematical_constructivism
http://en.wikipedia.org/wiki/Intuitionism
Does this mean that infinite sets are not logical implications of some general beliefs you already have?
Many schools of math philosophy do without infinity:
http://en.wikipedia.org/wiki/Finitism
http://en.wikipedia.org/wiki/Ultrafinitism
http://en.wikipedia.org/wiki/Mathematical_constructivism
http://en.wikipedia.org/wiki/Intuitionism