78 ideas
6405 | Moore's 'The Nature of Judgement' (1898) marked the rejection (with Russell) of idealism [Moore,GE, by Grayling] |
1798 | He studied philosophy by suspending his judgement on everything [Pyrrho, by Diog. Laertius] |
17992 | The main aim of philosophy is to describe the whole Universe. [Moore,GE] |
7527 | Analysis for Moore and Russell is carving up the world, not investigating language [Moore,GE, by Monk] |
1800 | Sceptics say reason is only an instrument, because reason can only be attacked with reason [Pyrrho, by Diog. Laertius] |
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] |
13201 | ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [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] |
13204 | The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton] |
13206 | A 'linear or total ordering' must be transitive and satisfy trichotomy [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] |
13200 | Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton] |
13199 | The empty set may look pointless, but many sets can be constructed from it [Enderton] |
13203 | The singleton is defined using the pairing axiom (as {x,x}) [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] |
13202 | Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton] |
13205 | We can only define functions if Choice tells us which items are involved [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] |
21342 | A relation is internal if two things possessing the relation could not fail to be related [Moore,GE, by Heil] |
9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
6672 | Moore's Paradox: you can't assert 'I believe that p but p is false', but can assert 'You believe p but p is false' [Moore,GE, by Lowe] |
20147 | Arguments that my finger does not exist are less certain than your seeing my finger [Moore,GE] |
6349 | I can prove a hand exists, by holding one up, pointing to it, and saying 'here is one hand' [Moore,GE] |
6595 | If we need a criterion of truth, we need to know whether it is the correct criterion [Pyrrho, by Fogelin] |
6593 | The Pyrrhonians attacked the dogmas of professors, not ordinary people [Pyrrho, by Fogelin] |
6592 | Academics said that Pyrrhonians were guilty of 'negative dogmatism' [Pyrrho, by Fogelin] |
1805 | Judgements vary according to local culture and law (Mode 5) [Pyrrho, by Diog. Laertius] |
1803 | Objects vary according to which sense perceives them (Mode 3) [Pyrrho, by Diog. Laertius] |
1807 | Perception varies with viewing distance and angle (Mode 7) [Pyrrho, by Diog. Laertius] |
1810 | Perception and judgement depend on comparison (Mode 10) [Pyrrho, by Diog. Laertius] |
1802 | Individuals vary in responses and feelings (Mode 2) [Pyrrho, by Diog. Laertius] |
1801 | Animals vary in their feelings and judgements (Mode 1) [Pyrrho, by Diog. Laertius] |
1804 | Perception varies with madness or disease (Mode 4) [Pyrrho, by Diog. Laertius] |
1808 | Perception of things depends on their size or quantity (Mode 8) [Pyrrho, by Diog. Laertius] |
1806 | Perception of objects depends on surrounding conditions (Mode 6) [Pyrrho, by Diog. Laertius] |
1809 | Perception is affected by expectations (Mode 9) [Pyrrho, by Diog. Laertius] |
22302 | Moor bypassed problems of correspondence by saying true propositions ARE facts [Moore,GE, by Potter] |
7526 | Hegelians say propositions defy analysis, but Moore says they can be broken down [Moore,GE, by Monk] |
21233 | The beautiful is whatever it is intrinsically good to admire [Moore,GE] |
8039 | Moore tries to show that 'good' is indefinable, but doesn't understand what a definition is [MacIntyre on Moore,GE] |
22151 | The Open Question argument leads to anti-realism and the fact-value distinction [Boulter on Moore,GE] |
11056 | The naturalistic fallacy claims that natural qualties can define 'good' [Moore,GE] |
8033 | Moore cannot show why something being good gives us a reason for action [MacIntyre on Moore,GE] |
8032 | Can learning to recognise a good friend help us to recognise a good watch? [MacIntyre on Moore,GE] |
11050 | Moore's combination of antinaturalism with strong supervenience on the natural is incoherent [Hanna on Moore,GE] |
23726 | Despite Moore's caution, non-naturalists incline towards intuitionism [Moore,GE, by Smith,M] |
18676 | We should ask what we would judge to be good if it existed in absolute isolation [Moore,GE] |
11057 | It is always an open question whether anything that is natural is good [Moore,GE] |
5925 | The three main values are good, right and beauty [Moore,GE, by Ross] |
5902 | For Moore, 'right' is what produces good [Moore,GE, by Ross] |
5903 | 'Right' means 'cause of good result' (hence 'useful'), so the end does justify the means [Moore,GE] |
5907 | Relationships imply duties to people, not merely the obligation to benefit them [Ross on Moore,GE] |
3062 | There are no causes, because they are relative, and alike things can't cause one another [Pyrrho, by Diog. Laertius] |
3063 | Motion can't move where it is, and can't move where it isn't, so it can't exist [Pyrrho, by Diog. Laertius] |