29 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] |
17640 | Finding the axioms may be the only route to some new results [Russell] |
17629 | Which premises are ultimate varies with context [Russell] |
17630 | The sources of a proof are the reasons why we believe its conclusion [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] |
8780 | Attributes are functions, not objects; this distinguishes 'square of 2' from 'double of 2' [Geach] |
11910 | Being 'the same' is meaningless, unless we specify 'the same X' [Geach] |
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] |
8775 | A big flea is a small animal, so 'big' and 'small' cannot be acquired by abstraction [Geach] |
8776 | We cannot learn relations by abstraction, because their converse must be learned too [Geach] |
2567 | You can't define real mental states in terms of behaviour that never happens [Geach] |
2568 | Beliefs aren't tied to particular behaviours [Geach] |
8781 | The mind does not lift concepts from experience; it creates them, and then applies them [Geach] |
8769 | If someone has aphasia but can still play chess, they clearly have concepts [Geach] |
8770 | 'Abstractionism' is acquiring a concept by picking out one experience amongst a group [Geach] |
8771 | 'Or' and 'not' are not to be found in the sensible world, or even in the world of inner experience [Geach] |
8772 | We can't acquire number-concepts by extracting the number from the things being counted [Geach] |
8773 | Abstractionists can't explain counting, because it must precede experience of objects [Geach] |
8774 | The numbers don't exist in nature, so they cannot have been abstracted from there into our languages [Geach] |
8778 | Blind people can use colour words like 'red' perfectly intelligently [Geach] |
8777 | If 'black' and 'cat' can be used in the absence of such objects, how can such usage be abstracted? [Geach] |
8779 | We can form two different abstract concepts that apply to a single unified experience [Geach] |
1590 | The just man does not harm his enemies, but benefits everyone [Plato] |
17633 | The law of gravity has many consequences beyond its grounding observations [Russell] |