31 ideas
10775 | The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp] |
10766 | Logic is either for demonstration, or for characterizing structures [Tharp] |
10767 | Elementary logic is complete, but cannot capture mathematics [Tharp] |
10769 | Second-order logic isn't provable, but will express set-theory and classic problems [Tharp] |
10762 | In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp] |
10776 | The main quantifiers extend 'and' and 'or' to infinite domains [Tharp] |
10774 | There are at least five unorthodox quantifiers that could be used [Tharp] |
10777 | Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp] |
10773 | The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp] |
10765 | Soundness would seem to be an essential requirement of a proof procedure [Tharp] |
10763 | Completeness and compactness together give axiomatizability [Tharp] |
10770 | If completeness fails there is no algorithm to list the valid formulas [Tharp] |
10771 | Compactness is important for major theories which have infinitely many axioms [Tharp] |
10772 | Compactness blocks infinite expansion, and admits non-standard models [Tharp] |
10764 | A complete logic has an effective enumeration of the valid formulas [Tharp] |
10768 | Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp] |
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] |
19739 | The maxim for suicide is committed to the value of life, and is thus contradictory [Kant] |