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June 7th, 2014, 01:30 PM  #11 
Senior Member Joined: Dec 2013 From: Russia Posts: 327 Thanks: 108 
OK, but are there many interesting facts that require CH? Even if this is the case, CH then serves as as an axiom whose independence from other axioms and whose importance was realized in the 20th century. So we have AC and CH. Are there many more? I was saying that hunting for new axioms just to be able to justify interesting results is not a common occurrence. But even if it were, this does not change the concept of a formal proof (in the narrow sense). Or do you want to say that this concept of mathematics is deficient? For example, that we determine what's true intuitively rather than using formal derivations? Then how would you define a formal proof?

June 7th, 2014, 01:49 PM  #12  
Senior Member Joined: Apr 2014 From: zagreb, croatia Posts: 234 Thanks: 33 Math Focus: philosophy/found of math, metamath, logic, set/category/order/number theory, algebra, topology  Quote:
 

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