22 ideas
17641 | Discoveries in mathematics can challenge philosophy, and offer it a new foundation [Russell] |
17638 | If one proposition is deduced from another, they are more certain together than alone [Russell] |
17632 | Non-contradiction was learned from instances, and then found to be indubitable [Russell] |
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] |
18744 | Models are sets with functions and relations, and truth built up from the components [Horsten/Pettigrew] |
17629 | Which premises are ultimate varies with context [Russell] |
17630 | The sources of a proof are the reasons why we believe its conclusion [Russell] |
17640 | Finding the axioms may be the only route to some new results [Russell] |
17627 | It seems absurd to prove 2+2=4, where the conclusion is more certain than premises [Russell] |
17628 | Arithmetic was probably inferred from relationships between physical objects [Russell] |
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] |
17637 | The most obvious beliefs are not infallible, as other obvious beliefs may conflict [Russell] |
17639 | Believing a whole science is more than believing each of its propositions [Russell] |
17631 | Induction is inferring premises from consequences [Russell] |
17633 | The law of gravity has many consequences beyond its grounding observations [Russell] |
16711 | Heretics should be eradicated like wolves [Aquinas] |