16 ideas
9540 | A 'value-assignment' (V) is when to each variable in the set V assigns either the value 1 or the value 0 [Hughes/Cresswell] |
9541 | The Law of Transposition says (P→Q) → (¬Q→¬P) [Hughes/Cresswell] |
9543 | The rules preserve validity from the axioms, so no thesis negates any other thesis [Hughes/Cresswell] |
17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
9544 | A system is 'weakly' complete if all wffs are derivable, and 'strongly' if theses are maximised [Hughes/Cresswell] |
17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
5500 | Biologists see many organic levels, 'abstract' if seen from below, 'structural' if seen from above [Lycan] |
5494 | 'Lightning is electric discharge' and 'Phosphorus is Venus' are synthetic a posteriori identities [Lycan] |
5496 | Functionalism has three linked levels: physical, functional, and mental [Lycan] |
5499 | A mental state is a functional realisation of a brain state when it serves the purpose of the organism [Lycan] |
5501 | People are trying to explain biological teleology in naturalistic causal terms [Lycan] |