Around page 300 of his book "Mathematical Thought and its Objects", Charles Parsons discusses the work of Edward Nelson, who believes that mathematical induction is impredicative, because it can be ...
At the end of the paper Division by three by Peter G. Doyle and John H. Conway, the authors say: Not that we believe there really are any such things as infinite sets, or that the Zermelo-Fraenkel ...
Mathematician Edward Nelson is known for his extreme views on the foundations of mathematics, variously described as "ultrafintism" or "strict finitism" (Nelson's preferred term), which came into the ...
Hilbert's program is popularly understood as an attempt to justify infinitary mathematics with a finitary consistency proof. Godel's Second Theorem is usually considered as showing this is not ...