51 ideas
21032 | Speak truth only to those who deserve the truth [Sandel] |
21033 | Careful evasions of truth at least show respect for it [Sandel] |
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] |
9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
21036 | Not all deals are fair deals [Sandel] |
21038 | Does consent create the obligation, or must there be some benefit? [Sandel] |
21039 | Moral contracts involve both consent and reciprocity; making the deal, and keeping it [Sandel] |
21030 | The categorical imperative is not the Golden Rule, which concerns contingent desires [Sandel] |
21031 | Man cannot dispose of himself, because he is not a thing to be owned [Sandel] |
21035 | Just visiting (and using roads) is hardly ratifying the Constitution [Sandel] |
21037 | A ratified constitution may not be a just constitution [Sandel] |
21034 | A just constitution harmonises the different freedoms [Sandel] |
21049 | Liberal freedom was a response to assigned destinies like caste and class [Sandel] |
21040 | Libertarians just want formal equality in a free market; the meritocratic view wants fair equality [Sandel] |
21028 | We can approach justice through welfare, or freedom, or virtue [Sandel] |
21027 | Justice concerns how a society distributes what it prizes - wealth, rights, power and honours [Sandel] |
21042 | Should we redress wrongs done by a previous generation? [Sandel] |
21043 | Distributive justice concern deserts, as well as who gets what [Sandel] |
21052 | Justice is about how we value things, and not just about distributions [Sandel] |
21048 | Work is not fair if it is negotiated, even in a fair situation, but if it suits the nature of the worker [Sandel] |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
21045 | Teleological thinking is essential for social and political issues [Sandel] |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |