8 ideas
| 9565 | Zermelo made 'set' and 'member' undefined axioms [Zermelo, by Chihara] |
| Full Idea: The terms 'set' and 'is a member of' are primitives of Zermelo's 1908 axiomatization of set theory. They are not given model-theoretic analyses or definitions. | |
| From: report of Ernst Zermelo (works [1920]) by Charles Chihara - A Structural Account of Mathematics 7.5 | |
| A reaction: This looks like good practice if you want to work with sets, but not so hot if you are interested in metaphysics. |
| 3339 | For Zermelo's set theory the empty set is zero and the successor of each number is its unit set [Zermelo, by Blackburn] |
| Full Idea: For Zermelo's set theory the empty set is zero and the successor of each number is its unit set. | |
| From: report of Ernst Zermelo (works [1920]) by Simon Blackburn - Oxford Dictionary of Philosophy p.280 |
| 8967 | Not all predicates can be properties - 'is non-self-exemplifying', for example [Lowe] |
| Full Idea: We cannot assume that every meaningful predicate necessarily expresses a property that some entity could possess. The predicate 'is non-self-exemplifying' is meaningful, yet it would be contradictory for there to be any such property. | |
| From: E.J. Lowe (Individuation [2003]) | |
| A reaction: This clinches what I would take to be a foregone conclusion - that you can't know what the world contains just by examining the predicates of the English language. However, I suppose predicates are needed to know properties. |
| 8965 | Neither mere matter nor pure form can individuate a sphere, so it must be a combination [Lowe] |
| Full Idea: A sphere's matter could not be what makes it one sphere, since matter lacks intrinsic unity, ..and the form cannot make it that very sphere, since an identical sphere may exemplify that universal. So it is a combination of form and matter. | |
| From: E.J. Lowe (Individuation [2003], 5) | |
| A reaction: But how do two aspects of the sphere, neither of which has the power to individuate, achieve individuation when they are combined? Like parents, I suppose. Two totally identical spheres can only be individuated by location. |
| 8968 | If the flagpole causally explains the shadow, the shadow cannot explain the flagpole [Lowe] |
| Full Idea: Two distinct entities cannot explain each other, in the same sense of 'explain'. If the height of the flagpole causally explains the length of the shadow, the shadow cannot explain the flagpole, though it may predict the latter. | |
| From: E.J. Lowe (Individuation [2003], 12) | |
| A reaction: This seems related to the question of the direction of time/causation. Some explanations can be benignly circular, as when a married couple have a passion for chinese food. [S.Bromberger 1966 invented the flagpole case]. |
| 8966 | Properties are facets of objects, only discussable separately by an act of abstraction [Lowe] |
| Full Idea: In no sense is a property a 'constituent' of an object: it is merely a 'facet' or 'aspect' of an object - something which we can talk about or think of separately from that object only by an act of abstraction. | |
| From: E.J. Lowe (Individuation [2003], 8) | |
| A reaction: This appears to be in tune with traditional abstractionism, even though Lowe is committed to the reality of universals. To what do I refer when I say 'I like your car, apart from its colour'? |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |