Wed 13 Apr, 2016 02:46 pm - *Explain why the axiom of infinity and the axiom of choice are crucial for the construction of the real numbers within in a system of logic.
* What do the following axioms say? Axiom of... (view)
Wed 13 Apr, 2016 02:45 pm - *Why is Russell forced to introduce the axiom of reducibility into his type theory? A good answer will need to bring in the need for logicists to define the real numbers, and an explanation of why... (view)
Wed 13 Apr, 2016 02:43 pm - * What is an impredicative definition? How is this notion used by Russell to resolve Cantor's Paradox?
* What goes wrong when we try to figure out the cardinality of the set C which... (view)
Wed 13 Apr, 2016 02:42 pm - *Logicists suggest that the reals just are cuts. But somebody might worry that there might be more reals than there are cuts. Explain why we need not worry, that is, give reasons for thinking... (view)
Wed 13 Apr, 2016 02:41 pm - *Describe Russell's type theory. In what respects does his system differ from predicate logic (first order logic)?
* According to Russell, what is a number? Show how Russell might define... (view)
Wed 13 Apr, 2016 02:39 pm - 1. What is Logicism? How do Logicists, respond to Kant's claim that 7+5=12 could not possibly be analytic?
2. In order to succeed at the Logicist program, what must the Logicist... (view)
Wed 13 Apr, 2016 02:38 pm - Explain the Logicist, Formalist, Intuitionist, and Realist positions on the questions: "Why are mathematical claims true?" "What is Mathematics about?" "Is actual... (view)
Wed 13 Apr, 2016 02:33 pm - 1. It has been explained that to show that a set of items is countable, all you have to do is use the method of naming (digits), that is, name all members of the set, giving each member a unique... (view)
