18 ideas
22138 | Science rests on scholastic metaphysics, not on Hume, Kant or Carnap [Boulter] |
17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
13412 | Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf] |
13413 | We must explain how we know so many numbers, and recognise ones we haven't met before [Benacerraf] |
13411 | If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [Benacerraf] |
17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
13415 | An adequate account of a number must relate it to its series [Benacerraf] |
22134 | Thoughts are general, but the world isn't, so how can we think accurately? [Boulter] |
22150 | Logical possibility needs the concepts of the proposition to be adequate [Boulter] |
22139 | Experiments don't just observe; they look to see what interventions change the natural order [Boulter] |
22136 | Science begins with sufficient reason, de-animation, and the importance of nature [Boulter] |
22135 | Our concepts can never fully capture reality, but simplification does not falsify [Boulter] |
22152 | Aristotelians accept the analytic-synthetic distinction [Boulter] |
22156 | The facts about human health are the measure of the values in our lives [Boulter] |