28 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] |
| 2098 | The principle of sufficient reason is needed if we are to proceed from maths to physics [Leibniz] |
| 3646 | There is always a reason why things are thus rather than otherwise [Leibniz] |
| 2104 | No reason could limit the quantity of matter, so there is no limit [Leibniz] |
| 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] |
| 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] |
| 8714 | Fictionalists say 2+2=4 is true in the way that 'Oliver Twist lived in London' is true [Field,H] |
| 19385 | All simply substances are in harmony, because they all represent the one universe [Leibniz] |
| 21346 | The ratio between two lines can't be a feature of one, and cannot be in both [Leibniz] |
| 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] |
| 2105 | Things are infinitely subdivisible and contain new worlds, which atoms would make impossible [Leibniz] |
| 2106 | The only simple things are monads, with no parts or extension [Leibniz] |
| 2102 | Atomism is irrational because it suggests that two atoms can be indistinguishable [Leibniz] |
| 17633 | The law of gravity has many consequences beyond its grounding observations [Russell] |
| 20965 | Leibniz upheld conservations of momentum and energy [Leibniz, by Papineau] |
| 2103 | The idea that the universe could be moved forward with no other change is just a fantasy [Leibniz] |
| 2100 | Space and time are purely relative [Leibniz] |
| 2107 | No time exists except instants, and instants are not even a part of time, so time does not exist [Leibniz] |
| 2101 | If everything in the universe happened a year earlier, there would be no discernible difference [Leibniz] |
| 22894 | If time were absolute that would make God's existence dependent on it [Leibniz, by Bardon] |
| 2099 | The existence of God, and all metaphysics, follows from the Principle of Sufficient Reason [Leibniz] |