7 ideas
| 4037 | Ockham's Razor is the principle that we need reasons to believe in entities [Mellor/Oliver] |
| Full Idea: Ockham's Razor is the principle that we need reasons to believe in entities. | |
| From: DH Mellor / A Oliver (Introduction to 'Properties' [1997], §9) | |
| A reaction: This presumably follows from an assumption that all beliefs need reasons, but is that the case? The Principle of Sufficient Reason precedes Ockham's Razor. |
| 21554 | Sets always exceed terms, so all the sets must exceed all the sets [Lackey] |
| Full Idea: Cantor proved that the number of sets in a collection of terms is larger than the number of terms. Hence Cantor's Paradox says the number of sets in the collection of all sets must be larger than the number of sets in the collection of all sets. | |
| From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127) | |
| A reaction: The sets must count as terms in the next iteration, but that is a normal application of the Power Set axiom. |
| 21553 | It seems that the ordinal number of all the ordinals must be bigger than itself [Lackey] |
| Full Idea: The ordinal series is well-ordered and thus has an ordinal number, and a series of ordinals to a given ordinal exceeds that ordinal by 1. So the series of all ordinals has an ordinal number that exceeds its own ordinal number by 1. | |
| From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127) | |
| A reaction: Formulated by Burali-Forti in 1897. |
| 4027 | Properties are respects in which particular objects may be alike or differ [Mellor/Oliver] |
| Full Idea: Properties are respects in which particular objects may be alike or differ. | |
| From: DH Mellor / A Oliver (Introduction to 'Properties' [1997], §1) | |
| A reaction: Note that this definition does not mention a causal role for properties. |
| 4029 | Nominalists ask why we should postulate properties at all [Mellor/Oliver] |
| Full Idea: Nominalists ask why we should postulate properties at all. | |
| From: DH Mellor / A Oliver (Introduction to 'Properties' [1997], §3) | |
| A reaction: Objects might be grasped without language, but events cannot be understood, and explanations of events seem inconceivable without properties (implying that they are essentially causal). |
| 4039 | Abstractions lack causes, effects and spatio-temporal locations [Mellor/Oliver] |
| Full Idea: Abstract entities (such as sets) are usually understood as lacking causes, effects, and spatio-temporal location. | |
| From: DH Mellor / A Oliver (Introduction to 'Properties' [1997], §10) | |
| A reaction: This seems to beg some questions. Has the ideal of 'honour' never caused anything? Young men dream of pure velocity. |
| 7496 | Rules and duties are based on the will, as that is all we control [Montaigne] |
| Full Idea: Since actions and performances are not wholly in our power and since nothing is really in our power but our will - it is on the will that all the rules and duties of Man are based and established. | |
| From: Michel de Montaigne (I.7 Our deeds are judged by intention [1580], p.0028) | |
| A reaction: This is almost Kant's claim that the only truly good thing is a good will (e.g. Idea 3711). Aristotle disagrees, because a virtuous person should also have good desires. We may will to have good desires, but virtue requires actually having them. |