Preintuitionism - Article Index

Encyclopedia - Preintuitionism: Encyclopedia Ii - Preintuitionism - The Principle Of Complete Induction
This sense of definition allowed Poincaré to argue with Bertrand Russell over Giuseppe Peano's axiomatic theory of natural numbers. Pean...   » Read the article

Encyclopedia - Controversy Over Cantor's Theory: Encyclopedia Ii - Controversy Over Cantor's Theory - Objections To Hume's Principle
As argued above, many naïve objections depend on implicitly denying Hume's principle, and are therefore question-begging. Wittgenstein e...   » Read the article

Encyclopedia - Controversy Over Cantor's Theory: Encyclopedia Ii - Controversy Over Cantor's Theory - Objection To The Axiom Of Infinity
One of the most common (and also the most respectable) objections to Cantor's theory of infinite number involves the axiom of infinity. I...   » Read the article

Encyclopedia - Controversy Over Cantor's Theory: Encyclopedia Ii - Controversy Over Cantor's Theory - Footnote
The quote "Later generations will regard set theory as a disease from which one has recovered" is from Kline[1982], and is apparently his...   » Read the article

Encyclopedia - Controversy Over Cantor's Theory: Encyclopedia Ii - Controversy Over Cantor's Theory - Preface
The pure mathematicians and applied mathematicians who object to Cantor's theory of sets claim that Cantor introduced into mathematics an...   » Read the article

Encyclopedia - Controversy Over Cantor's Theory: Encyclopedia Ii - Controversy Over Cantor's Theory - Objections To Cantor's Theorem
As shown above, most objections to Cantor's theorem (i.e. the theorem that no set can be correlated one-one with the set of all of its su...   » Read the article

Encyclopedia - Controversy Over Cantor's Theory: Encyclopedia Ii - Controversy Over Cantor's Theory - Introduction
Georg Cantor's argument that there are sets that have a cardinality (or "power" or "number") that is greater than the (already infinite) ...   » Read the article

Encyclopedia - Controversy Over Cantor's Theory: Encyclopedia Ii - Controversy Over Cantor's Theory - Naïve Objections
Objections to Cantor's proof (together with objections to Gödel's theorem) are a standard feature of mathematical Usenet discussions. Th...   » Read the article

Encyclopedia - Controversy Over Cantor's Theory: Encyclopedia Ii - Controversy Over Cantor's Theory - Cantor's Argument
Cantor's 1891 argument is that there exists an infinite set (which he identifies with the set of real numbers), which has a larger number...   » Read the article

Encyclopedia - Controversy Over Cantor's Theory: Encyclopedia Ii - Controversy Over Cantor's Theory - Reception Of The Argument
From the start, Cantor's Theory was controversial among mathematicians and (later) philosophers. I don't know what predominates in Cantor...   » Read the article

Encyclopedia - Preintuitionism: Encyclopedia Ii - Preintuitionism - Arguments Over The Excluded Middle
It was for this assertion, among others, that Poincaré was considered to be similar to the intuitionists. For Brouwer though, the Pre-In...   » Read the article

Encyclopedia - Preintuitionism: Encyclopedia Ii - Preintuitionism - The Introduction Of Natural Numbers
The Pre-Intuitionists, as defined by Brouwer, differed from the Formalist standpoint in several ways. In the introduction of natural numb...   » Read the article