11 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) |
| 8526 | We might treat both tropes and substances as fundamental, so we can't presume it is just tropes [Daly] |
| Full Idea: Since C.B. Martin accepts both tropes and substances as fundamental, the claim that tropes are the only fundamental constituents is a further, independent claim. | |
| From: Chris Daly (Tropes [1995], §4) | |
| A reaction: A dubious mode of argument. Martin may only make the claim because he is ignorant, of facts or of language. Why are some tropes perfectly similar? Is it the result of something more fundamental? |
| 8527 | More than one trope (even identical ones!) can occupy the same location [Daly] |
| Full Idea: More than one trope can occupy the same spatio-temporal location, and it even seems possible for a pair of exactly resembling tropes to occupy the same spatio-temporal location. | |
| From: Chris Daly (Tropes [1995], §6) | |
| A reaction: This may be the strongest objection to tropes. Being disc-shaped and red would occupy the same location. Aristotle's example of mixing white with white (Idea 557) would be the second case. Individuation of these 'particulars' is the problem. |
| 8528 | If tropes are linked by the existence of concurrence, a special relation is needed to link them all [Daly] |
| Full Idea: To explain how tropes form bundles, concurrence relations are invoked. But tropes F and G and a concurrence relation C don't ensure that F stands in C to G. So trope theory needs 'instantiation' relations (special relational tropes) after all. | |
| From: Chris Daly (Tropes [1995], §7) | |
| A reaction: Campbell presents relations as 'second-order' items dependent on tropes (Idea 8525), but that seems unclear. Daly's argument resembles Russell's (which he likes), that some sort of universal is inescapable. It also resembles Bradley's regress (7966). |
| 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. |