24 ideas
| 2098 | The principle of sufficient reason is needed if we are to proceed from maths to physics [Leibniz] |
| 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 [Leibniz] |
| 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 [Leibniz] |
| 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) |
| 17824 | The master science is physical objects divided into sets [Maddy] |
| Full Idea: The master science can be thought of as the theory of sets with the entire range of physical objects as ur-elements. | |
| From: Penelope Maddy (Sets and Numbers [1981], II) | |
| A reaction: This sounds like Quine's view, since we have to add sets to our naturalistic ontology of objects. It seems to involve unrestricted mereology to create normal objects. |
| 17825 | Set theory (unlike the Peano postulates) can explain why multiplication is commutative [Maddy] |
| Full Idea: If you wonder why multiplication is commutative, you could prove it from the Peano postulates, but the proof offers little towards an answer. In set theory Cartesian products match 1-1, and n.m dots when turned on its side has m.n dots, which explains it. | |
| From: Penelope Maddy (Sets and Numbers [1981], II) | |
| A reaction: 'Turning on its side' sounds more fundamental than formal set theory. I'm a fan of explanation as taking you to the heart of the problem. I suspect the world, rather than set theory, explains the commutativity. |
| 17826 | Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy] |
| Full Idea: The standard account of the relationship between numbers and sets is that numbers simply are certain sets. This has the advantage of ontological economy, and allows numbers to be brought within the epistemology of sets. | |
| From: Penelope Maddy (Sets and Numbers [1981], III) | |
| A reaction: Maddy votes for numbers being properties of sets, rather than the sets themselves. See Yourgrau's critique. |
| 17828 | Numbers are properties of sets, just as lengths are properties of physical objects [Maddy] |
| Full Idea: I propose that ...numbers are properties of sets, analogous, for example, to lengths, which are properties of physical objects. | |
| From: Penelope Maddy (Sets and Numbers [1981], III) | |
| A reaction: Are lengths properties of physical objects? A hole in the ground can have a length. A gap can have a length. Pure space seems to contain lengths. A set seems much more abstract than its members. |
| 17827 | Sets exist where their elements are, but numbers are more like universals [Maddy] |
| Full Idea: A set of things is located where the aggregate of those things is located, ...but a number is simultaneously located at many different places (10 in my hand, and a baseball team) ...so numbers seem more like universals than particulars. | |
| From: Penelope Maddy (Sets and Numbers [1981], III) | |
| A reaction: My gut feeling is that Maddy's master idea (of naturalising sets by building them from ur-elements of natural objects) won't work. Sets can work fine in total abstraction from nature. |
| 17830 | Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy] |
| Full Idea: I am not suggesting a reduction of number theory to set theory ...There are only sets with number properties; number theory is part of the theory of finite sets. | |
| From: Penelope Maddy (Sets and Numbers [1981], V) |
| 17823 | If mathematical objects exist, how can we know them, and which objects are they? [Maddy] |
| Full Idea: The popular challenges to platonism in philosophy of mathematics are epistemological (how are we able to interact with these objects in appropriate ways) and ontological (if numbers are sets, which sets are they). | |
| From: Penelope Maddy (Sets and Numbers [1981], I) | |
| A reaction: These objections refer to Benacerraf's two famous papers - 1965 for the ontology, and 1973 for the epistemology. Though he relied too much on causal accounts of knowledge in 1973, I'm with him all the way. |
| 17829 | Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy] |
| Full Idea: Number words are not like normal adjectives. For example, number words don't occur in 'is (are)...' contexts except artificially, and they must appear before all other adjectives, and so on. | |
| From: Penelope Maddy (Sets and Numbers [1981], IV) | |
| A reaction: [She is citing Benacerraf's arguments] |
| 19385 | All simply substances are in harmony, because they all represent the one universe [Leibniz] |
| 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 [Leibniz] |
| 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. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |
| 2106 | The only simple things are monads, with no parts or extension [Leibniz] |
| 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) |
| 2102 | Atomism is irrational because it suggests that two atoms can be indistinguishable [Leibniz] |
| 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) |
| 2105 | Things are infinitely subdivisible and contain new worlds, which atoms would make impossible [Leibniz] |
| 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) |
| 20965 | Leibniz upheld conservations of momentum and energy [Leibniz, by Papineau] |
| 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 [Leibniz] |
| 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 [Leibniz] |
| 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 [Leibniz] |
| 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 [Leibniz] |
| 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 [Leibniz, by Bardon] |
| 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 [Leibniz] |
| 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) |