23 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] |
4187 | 'There is nothing without a reason why it should be rather than not be' (a generalisation of 'Why?') [Schopenhauer] |
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] |
17630 | The sources of a proof are the reasons why we believe its conclusion [Russell] |
17629 | Which premises are ultimate varies with context [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] |
4192 | All necessity arises from causation, which is conditioned; there is no absolute or unconditioned necessity [Schopenhauer] |
4190 | All understanding is an immediate apprehension of the causal relation [Schopenhauer] |
17637 | The most obvious beliefs are not infallible, as other obvious beliefs may conflict [Russell] |
6871 | We can't only believe things if we are currently conscious of their justification - there are too many [Goldman] |
6872 | Internalism must cover Forgotten Evidence, which is no longer retrievable from memory [Goldman] |
6874 | Internal justification needs both mental stability and time to compute coherence [Goldman] |
17639 | Believing a whole science is more than believing each of its propositions [Russell] |
6873 | Coherent justification seems to require retrieving all our beliefs simultaneously [Goldman] |
6875 | Reliability involves truth, and truth is external [Goldman] |
17631 | Induction is inferring premises from consequences [Russell] |
4191 | What we know in ourselves is not a knower but a will [Schopenhauer] |
21368 | The knot of the world is the use of 'I' to refer to both willing and knowing [Schopenhauer] |
17633 | The law of gravity has many consequences beyond its grounding observations [Russell] |
4189 | Time may be defined as the possibility of mutually exclusive conditions of the same thing [Schopenhauer] |