62 ideas
| 14888 | Wisdom prevents us from being ruled by the moment [Nietzsche] |
| 14863 | Unlike science, true wisdom involves good taste [Nietzsche] |
| 14890 | Suffering is the meaning of existence [Nietzsche] |
| 14861 | Philosophy ennobles the world, by producing an artistic conception of our knowledge [Nietzsche] |
| 14885 | The first aim of a philosopher is a life, not some works [Nietzsche] |
| 14887 | You should only develop a philosophy if you are willing to live by it [Nietzsche] |
| 14889 | Philosophy is pointless if it does not advocate, and live, a new way of life [Nietzsche] |
| 14862 | Philosophy is more valuable than much of science, because of its beauty [Nietzsche] |
| 14878 | It would better if there was no thought [Nietzsche] |
| 14881 | Why do people want philosophers? [Nietzsche] |
| 14876 | Philosophy is always secondary, because it cannot support a popular culture [Nietzsche] |
| 14860 | Kant has undermined our belief in metaphysics [Nietzsche] |
| 14859 | If philosophy controls science, then it has to determine its scope, and its value [Nietzsche] |
| 9724 | Until the 1960s the only semantics was truth-tables [Enderton] |
| 9703 | 'dom R' indicates the 'domain' of objects having a relation [Enderton] |
| 9705 | 'fld R' indicates the 'field' of all objects in the relation [Enderton] |
| 9704 | 'ran R' indicates the 'range' of objects being related to [Enderton] |
| 9710 | We write F:A→B to indicate that A maps into B (the output of F on A is in B) [Enderton] |
| 9707 | 'F(x)' is the unique value which F assumes for a value of x [Enderton] |
| 9712 | A relation is 'symmetric' on a set if every ordered pair has the relation in both directions [Enderton] |
| 9713 | A relation is 'transitive' if it can be carried over from two ordered pairs to a third [Enderton] |
| 9699 | The 'powerset' of a set is all the subsets of a given set [Enderton] |
| 9700 | Two sets are 'disjoint' iff their intersection is empty [Enderton] |
| 9702 | A 'domain' of a relation is the set of members of ordered pairs in the relation [Enderton] |
| 9701 | A 'relation' is a set of ordered pairs [Enderton] |
| 9706 | A 'function' is a relation in which each object is related to just one other object [Enderton] |
| 9708 | A function 'maps A into B' if the relating things are set A, and the things related to are all in B [Enderton] |
| 9709 | A function 'maps A onto B' if the relating things are set A, and the things related to are set B [Enderton] |
| 9711 | A relation is 'reflexive' on a set if every member bears the relation to itself [Enderton] |
| 9714 | A relation satisfies 'trichotomy' if all pairs are either relations, or contain identical objects [Enderton] |
| 9717 | A set is 'dominated' by another if a one-to-one function maps the first set into a subset of the second [Enderton] |
| 9715 | An 'equivalence relation' is a reflexive, symmetric and transitive binary relation [Enderton] |
| 9716 | We 'partition' a set into distinct subsets, according to each relation on its objects [Enderton] |
| 9722 | Inference not from content, but from the fact that it was said, is 'conversational implicature' [Enderton] |
| 14880 | Logic is just slavery to language [Nietzsche] |
| 9718 | Validity is either semantic (what preserves truth), or proof-theoretic (following procedures) [Enderton] |
| 9721 | A logical truth or tautology is a logical consequence of the empty set [Enderton] |
| 9994 | A truth assignment to the components of a wff 'satisfy' it if the wff is then True [Enderton] |
| 9719 | A proof theory is 'sound' if its valid inferences entail semantic validity [Enderton] |
| 9720 | A proof theory is 'complete' if semantically valid inferences entail proof-theoretic validity [Enderton] |
| 9995 | Proof in finite subsets is sufficient for proof in an infinite set [Enderton] |
| 9996 | Expressions are 'decidable' if inclusion in them (or not) can be proved [Enderton] |
| 9997 | For a reasonable language, the set of valid wff's can always be enumerated [Enderton] |
| 14869 | If some sort of experience is at the root of matter, then human knowledge is close to its essence [Nietzsche] |
| 579 | Cratylus said you couldn't even step into the same river once [Cratylus, by Aristotle] |
| 9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
| 14875 | Belief matters more than knowledge, and only begins when knowledge ceases [Nietzsche] |
| 14866 | It always remains possible that the world just is the way it appears [Nietzsche] |
| 578 | Cratylus decided speech was hopeless, and his only expression was the movement of a finger [Cratylus, by Aristotle] |
| 14872 | Our knowledge is illogical, because it rests on false identities between things [Nietzsche] |
| 14879 | The most extreme scepticism is when you even give up logic [Nietzsche] |
| 14873 | If we find a hypothesis that explains many things, we conclude that it explains everything [Nietzsche] |
| 14868 | Our primary faculty is perception of structure, as when looking in a mirror [Nietzsche] |
| 14870 | We experience causation between willing and acting, and thereby explain conjunctions of changes [Nietzsche] |
| 14867 | It is just madness to think that the mind is supernatural (or even divine!) [Nietzsche] |
| 14884 | The shortest path to happiness is forgetfulness, the path of animals (but of little value) [Nietzsche] |
| 14886 | Education is contrary to human nature [Nietzsche] |
| 14883 | We should evaluate the past morally [Nietzsche] |
| 14882 | Protest against vivisection - living things should not become objects of scientific investigation [Nietzsche] |
| 14865 | We do not know the nature of one single causality [Nietzsche] |
| 14871 | Laws of nature are merely complex networks of relations [Nietzsche] |
| 14864 | The Greeks lack a normative theology: each person has their own poetic view of things [Nietzsche] |