25 ideas
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] |
6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
6304 | Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik] |
6300 | Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik] |
6303 | Sets are positions in patterns [Resnik] |
6302 | Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik] |
6295 | There are too many mathematical objects for them all to be mental or physical [Resnik] |
6296 | Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik] |
6301 | Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik] |
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] |
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] |
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] |
21798 | To universalise 'give everything to the poor' leads to absurdity [Hegel] |
21797 | Immortality does not come at a later time, but when pure knowing Spirit fully grasps the universal [Hegel] |