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| 2098 | The principle of sufficient reason is needed if we are to proceed from maths to physics |
| Full Idea: In order to proceed from mathematics to physics the principle of sufficient reason is necessary, that nothing happens without there being a reason why it should be thus rather than otherwise. | |||
| From: Gottfried Leibniz (Letters to Samuel Clarke [1716], §2) |
| 3646 | There is always a reason why things are thus rather than otherwise |
| Full Idea: Nothing happens without a sufficient reason why it should be thus rather than otherwise. | |||
| From: Gottfried Leibniz (Letters to Samuel Clarke [1716], 3.2) |
| 2104 | No reason could limit the quantity of matter, so there is no limit |
| Full Idea: There is no possible reason which could limit the quantity of matter; therefore there cannot in fact be any such limitation. | |||
| From: Gottfried Leibniz (Letters to Samuel Clarke [1716], 4.21) |
| 19385 | All simply substances are in harmony, because they all represent the one universe |
| Full Idea: All simple substances will always have a harmony among themselves, because they always represent the same universe. | |||
| From: Gottfried Leibniz (Letters to Samuel Clarke [1716], V §91), quoted by Richard T.W. Arthur - Leibniz | |||
| A reaction: We can accept that the universe itself does not contain contradictions (how could it), but it is a leap of faith to say that all monads represent the universe well enough to avoid contradictions. Maps can contradict one another. |
| 21346 | The ratio between two lines can't be a feature of one, and cannot be in both |
| 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. | |||
| From: Gottfried Leibniz (Letters to Samuel Clarke [1716], 5th Paper, §47), quoted by John Heil - Relations 'External' | |||
| 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. |
| 2106 | The only simple things are monads, with no parts or extension |
| Full Idea: According to me there is nothing simple except true monads, which have no parts and no extensions. | |||
| From: Gottfried Leibniz (Letters to Samuel Clarke [1716], 5.24) |
| 2105 | Things are infinitely subdivisible and contain new worlds, which atoms would make impossible |
| Full Idea: The least corpuscle is actually subdivided ad infinitum and contains a world of new created things, which this universe would lack if this corpuscle were an atom. | |||
| From: Gottfried Leibniz (Letters to Samuel Clarke [1716], 4.PS) |
| 2102 | Atomism is irrational because it suggests that two atoms can be indistinguishable |
| Full Idea: There are no two individuals indiscernible from one another - leaves, or drops of water, for example. This is an argument against atoms, which, like the void, are opposed to the principles of a true metaphysic. | |||
| From: Gottfried Leibniz (Letters to Samuel Clarke [1716], 4.04) |
| 20965 | Leibniz upheld conservations of momentum and energy |
| Full Idea: In place of Descartes's conservation of 'quantity of motion', Leibniz upheld both the conservation of linear momentum and the conservation of kinetic energy. | |||
| From: report of Gottfried Leibniz (Letters to Samuel Clarke [1716], 5th paper) by David Papineau - Thinking about Consciousness App 2 | |||
| A reaction: The point is that momentum involves velocity (which includes direction) rather than speed. Leibniz more or less invented the concept of 'energy' ('vis viva'). Papineau says these two leave no room for causation by mental substance. |
| 2103 | The idea that the universe could be moved forward with no other change is just a fantasy |
| Full Idea: To say that God could cause the universe to move forward in a straight line or otherwise without changing it in any other way is another fanciful supposition. | |||
| From: Gottfried Leibniz (Letters to Samuel Clarke [1716], 4.14) |
| 2100 | Space and time are purely relative |
| Full Idea: I have more than once stated that I held space to be something purely relative, like time. | |||
| From: Gottfried Leibniz (Letters to Samuel Clarke [1716], 3.4) |
| 2107 | No time exists except instants, and instants are not even a part of time, so time does not exist |
| Full Idea: How could a thing exist, no part of which ever exists? In the case of time, nothing exists but instants, and an instant is not even a part of time. | |||
| From: Gottfried Leibniz (Letters to Samuel Clarke [1716], 5.49) |
| 2101 | If everything in the universe happened a year earlier, there would be no discernible difference |
| Full Idea: To ask why God did not make everything a year sooner would be reasonable if time were something apart from temporal things, but time is just the succession of things, which remains the same if the universe is created a year sooner. | |||
| From: Gottfried Leibniz (Letters to Samuel Clarke [1716], 3.6) |
| 22894 | If time were absolute that would make God's existence dependent on it |
| Full Idea: Leibniz argues that if time is a thing in itself, and God is 'in' time, then God would be dependent for His existence on the existence of time. | |||
| From: report of Gottfried Leibniz (Letters to Samuel Clarke [1716]) by Adrian Bardon - Brief History of the Philosophy of Time 3 'Newton' | |||
| A reaction: Hence Leibniz says time is merely relations between events. Not sure what he thinks an event is. What is God made of? Is there some divine matter upon which God's existence must depend? |
| 2099 | The existence of God, and all metaphysics, follows from the Principle of Sufficient Reason |
| Full Idea: By this principle alone, that there must be a sufficient reason why things are thus rather than otherwise, I prove the existence of the Divinity, and all the rest of metaphysics or natural theology. | |||
| From: Gottfried Leibniz (Letters to Samuel Clarke [1716], §2) |