41 ideas
7823 | Lucretius was rediscovered in 1417 [Grayling] |
6420 | Only by analysing is progress possible in philosophy [Russell] |
6432 | Analysis gives new knowledge, without destroying what we already have [Russell] |
6437 | The theory of types makes 'Socrates and killing are two' illegitimate [Russell] |
6442 | Truth belongs to beliefs, not to propositions and sentences [Russell] |
10147 | The Axiom of Choice is consistent with the other axioms of set theory [Feferman/Feferman] |
10148 | Axiom of Choice: a set exists which chooses just one element each of any set of sets [Feferman/Feferman] |
10149 | Platonist will accept the Axiom of Choice, but others want criteria of selection or definition [Feferman/Feferman] |
10150 | The Trichotomy Principle is equivalent to the Axiom of Choice [Feferman/Feferman] |
10146 | Cantor's theories needed the Axiom of Choice, but it has led to great controversy [Feferman/Feferman] |
6436 | I gradually replaced classes with properties, and they ended as a symbolic convenience [Russell] |
7528 | Leibniz bases everything on subject/predicate and substance/property propositions [Russell] |
6439 | Names are meaningless unless there is an object which they designate [Russell] |
10158 | A structure is a 'model' when the axioms are true. So which of the structures are models? [Feferman/Feferman] |
10162 | Tarski and Vaught established the equivalence relations between first-order structures [Feferman/Feferman] |
10160 | Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman] |
10159 | Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman] |
10161 | If a sentence holds in every model of a theory, then it is logically derivable from the theory [Feferman/Feferman] |
10156 | 'Recursion theory' concerns what can be solved by computing machines [Feferman/Feferman] |
10155 | Both Principia Mathematica and Peano Arithmetic are undecidable [Feferman/Feferman] |
6423 | We tried to define all of pure maths using logical premisses and concepts [Russell] |
6424 | Formalists say maths is merely conventional marks on paper, like the arbitrary rules of chess [Russell] |
6425 | Formalism can't apply numbers to reality, so it is an evasion [Russell] |
6426 | Intuitionism says propositions are only true or false if there is a method of showing it [Russell] |
6419 | In 1899-1900 I adopted the philosophy of logical atomism [Russell] |
6438 | Complex things can be known, but not simple things [Russell] |
6434 | Facts are everything, except simples; they are either relations or qualities [Russell] |
6440 | Universals can't just be words, because words themselves are universals [Russell] |
6430 | In epistemology we should emphasis the continuity between animal and human minds [Russell] |
6441 | Pragmatism judges by effects, but I judge truth by causes [Russell] |
6431 | Empiricists seem unclear what they mean by 'experience' [Russell] |
6444 | True belief about the time is not knowledge if I luckily observe a stopped clock at the right moment [Russell] |
6433 | Behaviourists struggle to explain memory and imagination, because they won't admit images [Russell] |
6443 | Surprise is a criterion of error [Russell] |
6427 | Unverifiable propositions about the remote past are still either true or false [Russell] |
6435 | You can believe the meaning of a sentence without thinking of the words [Russell] |
7809 | In an honour code shame is the supreme punishment, and revenge is a duty [Grayling] |
7824 | If suicide is lawful, but assisting suicide is unlawful, powerless people are denied their rights [Grayling] |
7819 | Religion gives answers, comforts, creates social order, and panders to superstition [Grayling] |
7817 | To make an afterlife appealing, this life has to be denigrated [Grayling] |
7818 | In Greek mythology only heroes can go to heaven [Grayling] |