9 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) |
| 16655 | Different genera are delimited by modes of predication, which rest on modes of being [Aquinas] |
| Full Idea: Being is delimited into different genera in accord with different modes of predicating, which depend on different modes of being. | |
| From: Thomas Aquinas (On Aristotle's 'Metaphysics' [1266], V.9.890), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 12.3 | |
| A reaction: I like this. When people say that predication is the way we divide things up, and go all linguistic-relativist about things, they forget how closely language not only describes reality, but arises out of, or is even caused by, reality. 'Grue' is silly. |
| 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. |
| 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. |
| 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. |