19 ideas
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] |
12456 | I aim to establish certainty for mathematical methods [Hilbert] |
12461 | We believe all mathematical problems are solvable [Hilbert] |
9633 | No one shall drive us out of the paradise the Cantor has created for us [Hilbert] |
12460 | We extend finite statements with ideal ones, in order to preserve our logic [Hilbert] |
12462 | Only the finite can bring certainty to the infinite [Hilbert] |
12455 | The idea of an infinite totality is an illusion [Hilbert] |
17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
12457 | There is no continuum in reality to realise the infinitely small [Hilbert] |
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] |
12459 | The subject matter of mathematics is immediate and clear concrete symbols [Hilbert] |
18112 | Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert] |
4304 | Descartes says there are two substance, Spinoza one, and Leibniz infinitely many [Cottingham] |
9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
4303 | The notion of substance lies at the heart of rationalist metaphysics [Cottingham] |
4306 | For rationalists, it is necessary that effects be deducible from their causes [Cottingham] |