25 ideas
17892 | For clear questions posed by reason, reason can also find clear answers [Gödel] |
9188 | Gödel proved that first-order logic is complete, and second-order logic incomplete [Gödel, by Dummett] |
18739 | Three stages of philosophical logic: syntactic (1905-55), possible worlds (1963-85), widening (1990-) [Horsten/Pettigrew] |
18741 | Logical formalization makes concepts precise, and also shows their interrelation [Horsten/Pettigrew] |
10620 | Originally truth was viewed with total suspicion, and only demonstrability was accepted [Gödel] |
18744 | Models are sets with functions and relations, and truth built up from the components [Horsten/Pettigrew] |
17883 | Gödel's Theorems did not refute the claim that all good mathematical questions have answers [Gödel, by Koellner] |
17885 | Gödel eventually hoped for a generalised completeness theorem leaving nothing undecidable [Gödel, by Koellner] |
10614 | The real reason for Incompleteness in arithmetic is inability to define truth in a language [Gödel] |
18740 | If 'exist' doesn't express a property, we can hardly ask for its essence [Horsten/Pettigrew] |
18745 | A Tarskian model can be seen as a possible state of affairs [Horsten/Pettigrew] |
18747 | The 'spheres model' was added to possible worlds, to cope with counterfactuals [Horsten/Pettigrew] |
18748 | Epistemic logic introduced impossible worlds [Horsten/Pettigrew] |
18746 | Possible worlds models contain sets of possible worlds; this is a large metaphysical commitment [Horsten/Pettigrew] |
18750 | Using possible worlds for knowledge and morality may be a step too far [Horsten/Pettigrew] |
19682 | Internalists are much more interested in evidence than externalists are [McGrew] |
19684 | Does spotting a new possibility count as evidence? [McGrew] |
19687 | Absence of evidence proves nothing, and weird claims need special evidence [McGrew] |
19688 | Every event is highly unlikely (in detail), but may be perfectly plausible [McGrew] |
19686 | Criminal law needs two separate witnesses, but historians will accept one witness [McGrew] |
19680 | Maybe all evidence consists of beliefs, rather than of facts [McGrew] |
19681 | If all evidence is propositional, what is the evidence for the proposition? Do we face a regress? [McGrew] |
19689 | Several unreliable witnesses can give good support, if they all say the same thing [McGrew] |
19683 | Narrow evidentialism relies wholly on propositions; the wider form includes other items [McGrew] |
19685 | Falsificationism would be naive if even a slight discrepancy in evidence killed a theory [McGrew] |