Do you agree... Ten Questions about Intuitionism

This website has as its goal to investigate the opinions of the mathematical community on intuitionism. To this end it presents ten slightly provocative questions and collects answers to these questions from as many people as possible.

If you want to participate in this investigation, send your answers to the ten questions to answers@intuitionism.org. The web site also contains an annotated version of these questions which for each question presents a short explanation of how you might look at it.

Each question should be answered by yes or no or mu (= "the question is meaningless", or "it depends", or maybe, as Bas put it: "explaining how you should look at this question takes so much text that there is no point in doing so"; also use this if you do not know your answer to a question, or do not want to think about it), together with a possibly empty motivation. Try to have as little mus as possible. For each person the answers will be summarized on the main page as a string of +s, -s or #s.

Questions

  1. Do you agree that it is impossible to define a total function from the reals to the reals which is not continuous?
  2. Do you agree that the intermediate value theorem does not hold the way that it is normally stated?
  3. Do you agree that there are only three infinite cardinalities?
  4. Do you agree that the continuum hypothesis is a meaningful statement that has a definite truth value, even if we do not know what it is?
  5. Do you agree that the axiom which states the existence of an inaccessible cardinal is a meaningful statement that has a definite truth value, even if we do not know what it is?
  6. Do you agree that for any mathematical question it is easy to build a machine with two lights, yes and no, where the light marked yes will be on if it is true and the light marked no will be on if it is false?
  7. Do you agree that for any two statements the first implies the second or the second implies the first?
  8. Do you agree that a constructive proof of a theorem gives more insight than a classical proof?
  9. Do you agree that mathematics can be done using different kinds of reasoning, and that depending on the situation different kinds of reasoning are appropriate?
  10. Do you agree that all mathematical truths are true, but that some mathematical truths are more true than other mathematical truths?

Answers

 

(last modification 2008-01-07)