10 ideas
| 15897 | Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed [Zermelo, by Lavine] |
| Full Idea: Zermelo realised that the Axiom of Choice (based on arbitrary functions) could be used to 'count', in the Cantorian sense, those collections that had given Cantor so much trouble, which restored a certain unity to set theory. | |
| From: report of Ernst Zermelo (Proof that every set can be well-ordered [1904]) by Shaughan Lavine - Understanding the Infinite I |
| 15642 | If kinds depend only on what can be observed, many underlying essences might produce the same kind [Eagle] |
| Full Idea: If the kinds there are depend not on the essences of the objects but on their observed distinguishing particulars, ...then for any kind that we think there is, it is possible that there are many underlying essences which are observably indistinguishable. | |
| From: Antony Eagle (Locke on Essences and Kinds [2005], IV) | |
| A reaction: Eagle is commenting on Locke's reliance on nominal essences. This seems to be the genuine problem with jadeite and nephrite (both taken to be 'jade'), or with 'fool's gold'. This isn't an objection to Locke; it just explains the role of science. |
| 15645 | Nominal essence are the observable properties of things [Eagle] |
| Full Idea: It is clear the nominal essences really are the properties of the things which have them: they are (a subset of) the observable properties of the things. | |
| From: Antony Eagle (Locke on Essences and Kinds [2005], IV) | |
| A reaction: I think this is wrong. The surface characteristics are all that is available to us, so our classifications must be based on those, but it is on the ideas of them, not their intrinsic natures. That is empiricsm! What makes the properties 'essential'? |
| 15643 | Nominal essence mistakenly gives equal weight to all underlying properties that produce appearances [Eagle] |
| Full Idea: Nominal essence does not allow for gradations in significance for the underlying properties. Those are all essential for the object behaving as it observably does, and they must all be given equal weight when deciding what the object does. | |
| From: Antony Eagle (Locke on Essences and Kinds [2005], IV) | |
| A reaction: This is where 'scientific' essentialism comes in. If we take one object, or one kind of object, in isolation, Eagle is right. When we start to compare, and to set up controlled conditions tests, we can dig into the 'gradations' he cares about. |
| 13195 | To explain a house we must describe its use, as well as its parts [Leibniz] |
| Full Idea: A house would be badly explained if we were to describe only the arrangement of its parts, but not its use. | |
| From: Gottfried Leibniz (On Body and Force, Against the Cartesians [1702], p.255) | |
| A reaction: This must partly fall under pragmatics (i.e. what the enquirer is interested in). But function plays a genuine role in artefacts, and also in evolved biological organs. |
| 13193 | Active force is not just potential for action, since it involves a real effort or striving [Leibniz] |
| Full Idea: Active force should not be thought of as the simple and common potential [potentia] or receptivity to action of the schools. Rather, active force involves an effort [conatus] or striving [tendentia] toward action. | |
| From: Gottfried Leibniz (On Body and Force, Against the Cartesians [1702], p.252) | |
| A reaction: This is why Leibniz is lured into making his active forces more and more animistic, till they end up like proto-minds (though never, remember, conscious and willing minds). |
| 15641 | Kinds are fixed by the essential properties of things - the properties that make it that kind of thing [Eagle] |
| Full Idea: The natural thought is to think that real kinds are given only by classification on the basis of essential properties: properties that make an object the kind of thing that it is. | |
| From: Antony Eagle (Locke on Essences and Kinds [2005], II) | |
| A reaction: Circularity alert! Circularity alert! Essence gives a thing its kind - and hence we can see what the kind is? Test for a trivial property! Eagle is not unaware of these issues. Does he mean 'necessary' rather than 'essential'? |
| 13194 | God's laws would be meaningless without internal powers for following them [Leibniz] |
| Full Idea: To say that, in creation, God gave bodies a law for acting means nothing, unless, at the same time, he gave them something by means of which it could happen that the law is followed. | |
| From: Gottfried Leibniz (On Body and Force, Against the Cartesians [1702], p.253) | |
| A reaction: This is the beginning of the modern rebellion against the medieval view of laws as imposed from outside on passive matter. Unfortunately for Leibniz, once you have postulated active internal powers, the external laws become redundant. |
| 13196 | All qualities of bodies reduce to forces [Leibniz] |
| Full Idea: All qualities of bodies .....are in the end reduced [revoco] to forces. | |
| From: Gottfried Leibniz (On Body and Force, Against the Cartesians [1702], p.256) | |
| A reaction: The dots conceal a long qualification, but he is essentially standing by this simple remark. If you substitute the word 'powers' for 'forces', I think that is just about right. |
| 13192 | Power is passive force, which is mass, and active force, which is entelechy or form [Leibniz] |
| Full Idea: The dynamicon or power [potentia] in bodies is twofold, passive and active. Passive force [vis] constitutes matter or mass [massa], and active force constitutes entelechy or form. | |
| From: Gottfried Leibniz (On Body and Force, Against the Cartesians [1702], p.252) | |
| A reaction: This is explicitly equating the innate force understood in physics with Aristotelian form. The passive force is to explain the resistance of bodies. I like the equation of force with power. He says the entelechy is 'analogous' to a soul. |