51 ideas
8013 | In the Reformation, morality became unconditional but irrational, individually autonomous, and secular [MacIntyre] |
8021 | The Levellers and the Diggers mark a turning point in the history of morality [MacIntyre] |
19579 | The history of philosophy is just experiments in how to do philosophy [Novalis] |
19583 | Philosophy only begins when it studies itself [Novalis] |
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] |
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] |
19581 | A problem is a solid mass, which the mind must break up [Novalis] |
19584 | Whoever first counted to two must have seen the possibility of infinite counting [Novalis] |
22025 | Novalis thought self-consciousness cannot disclose 'being', because we are temporal creatures [Novalis, by Pinkard] |
9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
22067 | Poetry is true idealism, and the self-consciousness of the universe [Novalis] |
8006 | When Aristotle speaks of soul he means something like personality [MacIntyre] |
19585 | Every person has his own language [Novalis] |
19582 | Morality and philosophy are mutually dependent [Novalis] |
8002 | Sophists don't distinguish a person outside one social order from someone outside all order [MacIntyre] |
8012 | The value/fact logical gulf is misleading, because social facts involve values [MacIntyre] |
8005 | 'Happiness' is a bad translation of 'eudaimonia', which includes both behaving and faring well [MacIntyre] |
8001 | 'Dikaiosune' is justice, but also fairness and personal integrity [MacIntyre] |
8023 | My duties depend on my identity, which depends on my social relations [MacIntyre] |
22027 | Life isn't given to us like a novel - we write the novel [Novalis] |
8022 | I am naturally free if I am not tied to anyone by a contract [MacIntyre] |
8031 | Fans of natural rights or laws can't agree on what the actual rights or laws are [MacIntyre] |
19580 | If the pupil really yearns for the truth, they only need a hint [Novalis] |
8008 | The Bible is a story about God in which humans are incidental characters [MacIntyre] |