16 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] |
| 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] |
| 17423 | The essence of natural numbers must reflect all the functions they perform [Sicha] |
| 17425 | To know how many, you need a numerical quantifier, as well as equinumerosity [Sicha] |
| 17424 | Counting puts an initial segment of a serial ordering 1-1 with some other entities [Sicha] |
| 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] |
| 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] |
| 20695 | God's eternal power and deity are clearly seen in what has been created [Paul] |