13 ideas
| 10882 | Predicative definitions only refer to entities outside the defined collection [Horsten] |
| Full Idea: Definitions are called 'predicative', and are considered sound, if they only refer to entities which exist independently from the defined collection. | |
| From: Leon Horsten (Philosophy of Mathematics [2007], §2.4) |
| 10884 | A theory is 'categorical' if it has just one model up to isomorphism [Horsten] |
| Full Idea: If a theory has, up to isomorphism, exactly one model, then it is said to be 'categorical'. | |
| From: Leon Horsten (Philosophy of Mathematics [2007], §5.2) |
| 10885 | Computer proofs don't provide explanations [Horsten] |
| Full Idea: Mathematicians are uncomfortable with computerised proofs because a 'good' proof should do more than convince us that a certain statement is true. It should also explain why the statement in question holds. | |
| From: Leon Horsten (Philosophy of Mathematics [2007], §5.3) |
| 10881 | The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten] |
| Full Idea: The notion of an ordinal number is a set-theoretic, and hence non-arithmetical, concept. | |
| From: Leon Horsten (Philosophy of Mathematics [2007], §2.3) |
| 15797 | All structures are dispositional, objects are dispositions sets, and events manifest dispositions [Fetzer] |
| Full Idea: I propose a dispositional ontology for the physical world, according to which a) every structural property is a dispositional one, b) a physical object is an ordered set of dispositions, and c) every event manifests a dispositional property of the world. | |
| From: J.H. Fetzer (A World of Dispositions [1977], Intro) | |
| A reaction: Mumford says this is consistent with ontology as a way of describing the world, rather than being facts about the world. I like Fetzer's sketch, which sounds to have a lot in common with 'process philosophy'. |
| 15800 | All events and objects are dispositional, and hence all structural properties are dispositional [Fetzer] |
| Full Idea: Every atomic event in the world's history is a manifestation of some dispositional property of the world and every physical object is an instantiation of some set of dispositions; hence, every structural property is dispositional in kind. | |
| From: J.H. Fetzer (A World of Dispositions [1977], 5) | |
| A reaction: I quite like this drastic view, but there remains the intuition that there must always be something which has the disposition. That may be because I have not yet digested the lessons of modern physics. |
| 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). |
| 15798 | Kinds are arrangements of dispositions [Fetzer] |
| Full Idea: Kinds of things are specific arrangements of dispositions. | |
| From: J.H. Fetzer (A World of Dispositions [1977], 2) | |
| A reaction: A 'disposition' doesn't seem quite the right word for what is basic to the physical world, though Harré and Madden make a good case for the 'fields' of physic being understood in that way. I prefer 'power', though that doesn't solve anything. |
| 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. |
| 15799 | Lawlike sentences are general attributions of disposition to all members of some class [Fetzer] |
| Full Idea: Lawlike sentences are conceived as logically general dispositional statements attributing permanent dispositional properties to every member of a reference class. ...Their basic form is that of subjunctive generalizations. | |
| From: J.H. Fetzer (A World of Dispositions [1977], 3) | |
| A reaction: I much prefer talk of 'lawlike sentences' to talk of 'laws'. At least they imply that the true generalisations about nature are fairly fine-grained. Why not talk of 'generalisations' instead of 'laws'? Fetzer wants dispositions to explain everything. |
| 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. |