7 ideas
8920 | Equivalence relations are reflexive, symmetric and transitive, and classify similar objects [Lipschutz] |
Full Idea: A relation R on a non-empty set S is an equivalence relation if it is reflexive (for each member a, aRa), symmetric (if aRb, then bRa), and transitive (aRb and bRc, so aRc). It tries to classify objects that are in some way 'alike'. | |
From: Seymour Lipschutz (Set Theory and related topics (2nd ed) [1998], 3.9) | |
A reaction: So this is an attempt to formalise the common sense notion of seeing that two things have something in common. Presumably a 'way' of being alike is going to be a property or a part |
8568 | A property is merely a constituent of laws of nature; temperature is just part of thermodynamics [Mellor] |
Full Idea: Being a constituent of probabilistic laws of nature is all there is to being a property. There is no more to temperature than the thermodynamics and other laws they occur in. | |
From: D.H. Mellor (Properties and Predicates [1991], 'Props') | |
A reaction: How could thermodynamics be worked out without a prior concept of temperature? I think it is at least plausible to deny that there are any 'laws' of nature. But even Quine can't deny that some things are too hot to touch. |
8564 | There is obviously a possible predicate for every property [Mellor] |
Full Idea: To every property there obviously corresponds a possible predicate applying to all and only those particulars with that property. | |
From: D.H. Mellor (Properties and Predicates [1991], 'Intro') | |
A reaction: This doesn't strike me as at all obvious. If nature dictates the properties, there may be vastly more than any human language could cope with. It is daft to say that a property can only exist if humanity can come up with a predicate for it. |
8566 | We need universals for causation and laws of nature; the latter give them their identity [Mellor] |
Full Idea: I take the main reason for believing in contingent universals to be the roles they play in causation and in laws of nature, and those laws are what I take to give those universals their identity. | |
From: D.H. Mellor (Properties and Predicates [1991], 'Props') | |
A reaction: He agrees with Armstrong. Sounds a bit circular - laws are built on universals, and universals are identified by laws. It resembles a functionalist account of mental events. I think it is wrong. A different account of laws will be needed... |
8565 | If properties were just the meanings of predicates, they couldn't give predicates their meaning [Mellor] |
Full Idea: One reason for denying that properties just are the meanings of our predicates is that, if they were, they could not give our predicates their meanings. | |
From: D.H. Mellor (Properties and Predicates [1991], 'Props') | |
A reaction: Neither way round sounds quite right to me. Predicate nominalism is wrong, but what is meant by a property 'giving' a predicate its meaning? It doesn't seem to allow room for error in our attempts to name the properties. |
13128 | 'Ultimate sortals' cannot explain ontological categories [Westerhoff on Wiggins] |
Full Idea: 'Ultimate sortals' are said to be non-subordinated, disjoint from one another, and uniquely paired with each object. Because of this, the ultimate sortal cannot be a satisfactory explication of the notion of an ontological category. | |
From: comment on David Wiggins (Identity and Spatio-Temporal Continuity [1971], p.75) by Jan Westerhoff - Ontological Categories §26 | |
A reaction: My strong intuitions are that Wiggins is plain wrong, and Westerhoff gives the most promising reasons for my intuition. The simplest point is that objects can obviously belong to more than one category. |
8567 | Singular causation requires causes to raise the physical probability of their effects [Mellor] |
Full Idea: Singular causation entails physical probabilities or chances. ...Causal laws require causes to raise their effects' chances, as when fires have a greater chance of occurring when explosions do. | |
From: D.H. Mellor (Properties and Predicates [1991], 'Props') | |
A reaction: It seems fairly obvious that a probability can be increased without actually causing something. Just after a harmless explosion is a good moment for arsonists, especially if Mellor will be the investigating officer. |