Georg Cantor and contemporary set theorists like Quine and Maddy have shown that denying the part-whole axiom for infinite sets yields a consistent, well-developed mathematics that maps onto physical theories.
?Rate how convincing each reason is below to see the overall strength.
No one has weighed in yet. Be the first to share reasons for or against this statement.
Sign in or register to share your perspective on this statement.
Part-whole axiom(as a mathematical principle being questioned)
A basic logical rule that says if something is part of a larger thing, then the larger thing should contain all its parts (sounds obvious, but it breaks down in strange ways with infinity).
Physical theories(as what the mathematics is being applied to)
Scientific explanations of how the natural world works, like Einstein's theory of relativity or quantum mechanics.
Quine(as a proper name referring to the philosopher whose theory is being discussed)
Willard Van Orman Quine was a 20th-century American philosopher who wrote about how we know things and how language works. In this statement, we're discussing one of his specific ideas about observation.
Set theorists(as the experts working with Cantor's ideas)
Mathematicians and philosophers who specialize in studying sets and the logical rules that govern them.
Set theory(as used in mathematics)
A branch of mathematics that studies collections of objects (called 'sets') and the rules for how they relate to each other.
consistent(Contrasted with the model-theoretic notion of satisfiability)
A proof-theoretic notion indicating that no contradiction is derivable from a set of sentences