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) |
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. |
22254 | Economic capitalist liberty naturally leads to democratic political liberty [Novak] |
Full Idea: The natural logic of capitalism leads to democracy. For economic liberties without political liberties are inherently unstable. | |
From: Michael Novak (The Spirit of Democratic Capitalism [1982], p.15), quoted by David Conway - Capitalism and Community II | |
A reaction: Not sure about 'inherently unstable'. Only in the sense that if you dish out economic liberties, people come to expect political liberties. China and Hong Kong are each currently facing this problem. Capitalist liberty can be highly restricted. |
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. |