17 ideas
8679 | We perceive the objects of set theory, just as we perceive with our senses [Gödel] |
9942 | Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam] |
10061 | The If-thenist view only seems to work for the axiomatised portions of mathematics [Musgrave] |
10065 | Perhaps If-thenism survives in mathematics if we stick to first-order logic [Musgrave] |
10049 | Logical truths may contain non-logical notions, as in 'all men are men' [Musgrave] |
10050 | A statement is logically true if it comes out true in all interpretations in all (non-empty) domains [Musgrave] |
18062 | Set-theory paradoxes are no worse than sense deception in physics [Gödel] |
10868 | The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg] |
13517 | If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD] |
10058 | No two numbers having the same successor relies on the Axiom of Infinity [Musgrave] |
10271 | Basic mathematics is related to abstract elements of our empirical ideas [Gödel] |
10062 | Formalism seems to exclude all creative, growing mathematics [Musgrave] |
10063 | Formalism is a bulwark of logical positivism [Musgrave] |
16659 | Relations do not add anything to reality, though they are real aspects of the world [Olivi] |
16673 | Quantity just adds union and location to the extension of parts [Olivi] |
10060 | Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave] |
16663 | Things are limited by the species to certain modes of being [Olivi] |