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Full Idea
If the ratio of two lines L and M is conceived as abstracted from them both, without considering which is the subject and which the object, which will then be the subject? We cannot say both, for then we should have an accident in two subjects.
Gist of Idea
The ratio between two lines can't be a feature of one, and cannot be in both
Source
Gottfried Leibniz (Letters to Samuel Clarke [1716], 5th Paper, §47), quoted by John Heil - Relations 'External'
Book Ref
'Routledge Companion to Metaphysics', ed/tr. Le Poidevin/Simons etc [Routledge 2012], p.315
A Reaction
[compressed] Leibniz is rejecting external relations as having any status in ontology. It looks like a mistake (originating in Aristotle) to try to shoehorn the ontology of relations into the substance-properties framework.
Related Idea
Idea 21345 Aristotle said relations are not substances, so (if they exist) they must be accidents [Aristotle, by Heil]
| 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] |
| 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] |
| 2100 | Space and time are purely relative [Leibniz] |
| 2101 | If everything in the universe happened a year earlier, there would be no discernible difference [Leibniz] |
| 2102 | Atomism is irrational because it suggests that two atoms can be indistinguishable [Leibniz] |
| 2103 | The idea that the universe could be moved forward with no other change is just a fantasy [Leibniz] |
| 2104 | No reason could limit the quantity of matter, so there is no limit [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] |
| 2107 | No time exists except instants, and instants are not even a part of time, so time does not exist [Leibniz] |
| 20965 | Leibniz upheld conservations of momentum and energy [Leibniz, by Papineau] |
| 21346 | The ratio between two lines can't be a feature of one, and cannot be in both [Leibniz] |
| 19385 | All simply substances are in harmony, because they all represent the one universe [Leibniz] |