The phil papers survey is a survey sent out to philosophers asking their views on various topics. Sadly, it doesn’t get sent out to philosophy bloggers, so what we philosophy bloggers think, in general, is a deep mystery, akin to which theory of quantum physics is right. But given that I like philosophy and it has a lot of questions, I thought it would be fun to walk through how I’d answer each question.
Great post. You should take this periodically to see how things change.
For the continuum hypothesis, my understanding is that it literally has no truth value because both it and its negation are consistent with standard mathematical set theory or seining. But I’m no expert.
People dispute whether the continuum hypothesis has a definite truth value because both the affirmation and negation of the hypothesis can be shown to be compatible with the basic set axioms out there. So some people who think there are no "further facts" about mathematics beyond the consequences of axioms say it has no truth value, whereas there are Platonists who take the opposite approach and argue ZFC's agnosticism here shows it doesn't fully capture the actual nature of sets. I'm personally undecided but I lean towards the latter view.
Anyway, this is a fun idea! I might try it tonight and see how far I get. I didn't even know they had all these extended questions!
Great post. You should take this periodically to see how things change.
For the continuum hypothesis, my understanding is that it literally has no truth value because both it and its negation are consistent with standard mathematical set theory or seining. But I’m no expert.
Did you just refer to Immanuel Kant (1724-1804) as an "ancient philosopher"?
People dispute whether the continuum hypothesis has a definite truth value because both the affirmation and negation of the hypothesis can be shown to be compatible with the basic set axioms out there. So some people who think there are no "further facts" about mathematics beyond the consequences of axioms say it has no truth value, whereas there are Platonists who take the opposite approach and argue ZFC's agnosticism here shows it doesn't fully capture the actual nature of sets. I'm personally undecided but I lean towards the latter view.
Anyway, this is a fun idea! I might try it tonight and see how far I get. I didn't even know they had all these extended questions!
Is 81 a joke I can’t tell?