1925 | The Foundations of Mathematics |
§1 | p.165 | 13425 | Formalism is hopeless, because it focuses on propositions and ignores concepts |
§1 | p.168 | 13426 | Formalists neglect content, but the logicists have focused on generalizations, and neglected form |
§1 | p.179 | 13427 | Either 'a = b' vacuously names the same thing, or absurdly names different things |
§2 | p.191 | 13428 | Reducibility: to every non-elementary function there is an equivalent elementary function |
§5 | p.222 | 13430 | Infinity: there is an infinity of distinguishable individuals |
p.171 | p.26 | 13334 | Contradictions are either purely logical or mathematical, or they involved thought and language |
1925 | Universals |
p.12 | p.12 | 8494 | Obviously 'Socrates is wise' and 'Socrates has wisdom' express the same fact |
p.13 | p.13 | 8495 | The distinction between particulars and universals is a mistake made because of language |
p.8 | p.8 | 8493 | We could make universals collections of particulars, or particulars collections of their qualities |
1926 | Truth and Probability |
p.32 | 19143 | Ramsey gave axioms for an uncertain agent to decide their preferences |
1927 | Facts and Propositions |
p.16 | 3750 | "It is true that x" means no more than x |
p.51 | p.102 | 18818 | Sentence meaning is given by the actions to which it would lead |
1928 | Law and Causality |
p.74 | 10993 | Ramsey's Test: believe the consequent if you believe the antecedent |
§A | p.143 | 9418 | All knowledge needs systematizing, and the axioms would be the laws of nature |
§B | p.150 | 9420 | Causal laws result from the simplest axioms of a complete deductive system |
B | p.396 | 13766 | 'If' is the same as 'given that', so the degrees of belief should conform to probability theory |
B 155 n | p.155 | 14279 | Asking 'If p, will q?' when p is uncertain, then first add p hypothetically to your knowledge |
1928 | works |
p.31 | 6409 | The 'simple theory of types' distinguishes levels among properties |
p.259 | 3212 | Beliefs are maps by which we steer |
1929 | Knowledge |
p.176 | 19724 | Belief is knowledge if it is true, certain, and obtained by a reliable process |