16 ideas
| 14092 | Philosophers are often too fussy about words, dismissing perfectly useful ordinary terms [Rosen] |
| Full Idea: Philosophers can sometimes be too fussy about the words they use, dismissing as 'unintelligible' or 'obscure' certain forms of language that are perfectly meaningful by ordinary standards, and which may be of some real use. | |
| From: Gideon Rosen (Metaphysical Dependence [2010], 01) | |
| A reaction: Analytic philosophers are inclined to drop terms they can't formalise, but there is more to every concept than its formalisation (Frege's 'direction' for example). I want to rescue 'abstraction' and 'essence'. Rosen says distinguish, don't formalise. |
| 14100 | Figuring in the definition of a thing doesn't make it a part of that thing [Rosen] |
| Full Idea: From the simple fact that '1' figures in the definition of '2', it does not follow that 1 is part of 2. | |
| From: Gideon Rosen (Metaphysical Dependence [2010], 10) | |
| A reaction: He observes that quite independent things can be mentioned on the two sides of a definition, with no parthood relation. You begin to wonder what a definition really is. A causal chain? |
| 14096 | Explanations fail to be monotonic [Rosen] |
| Full Idea: The failure of monotonicity is a general feature of explanatory relations. | |
| From: Gideon Rosen (Metaphysical Dependence [2010], 05) | |
| A reaction: In other words, explanations can always shift in the light of new evidence. In principle this is right, but some explanations just seem permanent, like plate-tectonics as explanation for earthquakes. |
| 13949 | All models of Peano axioms are isomorphic, so the models all seem equally good for natural numbers [Cartwright,R on Peano] |
| Full Idea: Peano's axioms are categorical (any two models are isomorphic). Some conclude that the concept of natural number is adequately represented by them, but we cannot identify natural numbers with one rather than another of the isomorphic models. | |
| From: comment on Giuseppe Peano (Principles of Arithmetic, by a new method [1889], 11) by Richard Cartwright - Propositions 11 | |
| A reaction: This is a striking anticipation of Benacerraf's famous point about different set theory accounts of numbers, where all models seem to work equally well. Cartwright is saying that others have pointed this out. |
| 18113 | PA concerns any entities which satisfy the axioms [Peano, by Bostock] |
| Full Idea: Peano Arithmetic is about any system of entities that satisfies the Peano axioms. | |
| From: report of Giuseppe Peano (Principles of Arithmetic, by a new method [1889], 6.3) by David Bostock - Philosophy of Mathematics 6.3 | |
| A reaction: This doesn't sound like numbers in the fullest sense, since those should facilitate counting objects. '3' should mean that number of rose petals, and not just a position in a well-ordered series. |
| 17634 | Peano axioms not only support arithmetic, but are also fairly obvious [Peano, by Russell] |
| Full Idea: Peano's premises are recommended not only by the fact that arithmetic follows from them, but also by their inherent obviousness. | |
| From: report of Giuseppe Peano (Principles of Arithmetic, by a new method [1889], p.276) by Bertrand Russell - Regressive Method for Premises in Mathematics p.276 |
| 15653 | We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness [Halbach on Peano] |
| Full Idea: Peano Arithmetic cannot derive its own consistency from within itself. But it can be strengthened by adding this consistency statement or by stronger axioms (particularly ones partially expressing soundness). These are known as Reflexion Principles. | |
| From: comment on Giuseppe Peano (Principles of Arithmetic, by a new method [1889], 1.2) by Volker Halbach - Axiomatic Theories of Truth (2005 ver) 1.2 |
| 17635 | Arithmetic can have even simpler logical premises than the Peano Axioms [Russell on Peano] |
| Full Idea: Peano's premises are not the ultimate logical premises of arithmetic. Simpler premises and simpler primitive ideas are to be had by carrying our analysis on into symbolic logic. | |
| From: comment on Giuseppe Peano (Principles of Arithmetic, by a new method [1889], p.276) by Bertrand Russell - Regressive Method for Premises in Mathematics p.276 |
| 14097 | Things could be true 'in virtue of' others as relations between truths, or between truths and items [Rosen] |
| Full Idea: Our relation of 'in virtue of' is among facts or truths, whereas Fine's relation (if it is a relation at all) is a relation between a given truth and items whose natures ground that truth. | |
| From: Gideon Rosen (Metaphysical Dependence [2010], 07 n10) | |
| A reaction: This disagreement between two key players in the current debate on grounding looks rather significant. I think I favour Fine's view, as it seems more naturalistic, and less likely to succumb to conventionalism. |
| 14095 | Facts are structures of worldly items, rather like sentences, individuated by their ingredients [Rosen] |
| Full Idea: Facts are structured entities built up from worldly items rather as sentences are built up from words. They might be identified with Russellian propositions. They are individuated by their constituents and composition, and are fine-grained. | |
| From: Gideon Rosen (Metaphysical Dependence [2010], 04) | |
| A reaction: I'm a little cautious about the emphasis on being sentence-like. We have Russell's continual warnings against imposing subject-predicate structure on things. I think we should happily talk about 'facts' in metaphysics. |
| 14093 | An 'intrinsic' property is one that depends on a thing and its parts, and not on its relations [Rosen] |
| Full Idea: One intuitive gloss on 'intrinsic' property is that a property is intrinsic iff whether or not a thing has it depends entirely on how things stand with it and its parts, and not on its relation to some distinct thing. | |
| From: Gideon Rosen (Metaphysical Dependence [2010], 02) | |
| A reaction: He offers this as a useful reward for reviving 'depends on' in metaphysical talk. The problem here would be to explain the 'thing' and its 'parts' without mentioning the target property. The thing certainly can't be a bundle of tropes. |
| 14094 | The excellent notion of metaphysical 'necessity' cannot be defined [Rosen] |
| Full Idea: Many of our best words in philosophy do not admit of definition, the notion of metaphysical 'necessity' being one pertinent example. | |
| From: Gideon Rosen (Metaphysical Dependence [2010], 03) | |
| A reaction: Rosen is busy defending words in metaphysics which cannot be pinned down with logical rigour. We are allowed to write □ for 'necessary', and it is accepted by logicians as being stable in a language. |
| 14101 | Are necessary truths rooted in essences, or also in basic grounding laws? [Rosen] |
| Full Idea: Fine says a truth is necessary when it is a logical consequence of the essential truths, but maybe it is a consequence of the essential truths together with the basic grounding laws (the 'Moorean connections'). | |
| From: Gideon Rosen (Metaphysical Dependence [2010], 13) | |
| A reaction: I'm with Fine all the way here, as we really don't need to clog nature up with things called 'grounding laws', which are both obscure and inexplicable. Fine's story is the one for naturalistically inclined philosophers. |
| 1556 | By nature people are close to one another, but culture drives them apart [Hippias] |
| Full Idea: I regard you all as relatives - by nature, not by convention. By nature like is akin to like, but convention is a tyrant over humankind and often constrains people to act contrary to nature. | |
| From: Hippias (fragments/reports [c.430 BCE]), quoted by Plato - Protagoras 337c8 |
| 14099 | 'Bachelor' consists in or reduces to 'unmarried' male, but not the other way around [Rosen] |
| Full Idea: It sounds right to say that Fred's being a bachelor consists in (reduces to) being an unmarried male, but slightly off to say that Fred's being an unmarried male consists in (or reduces to) being a bachelor. There is a corresponding explanatory asymmetry. | |
| From: Gideon Rosen (Metaphysical Dependence [2010], 10) | |
| A reaction: This emerging understanding of the asymmetry of the idea shows that we are not just dealing with a simple semantic identity. Our concepts are richer than our language. He adds that a ball could be blue in virtue of being cerulean. |
| 14098 | An acid is just a proton donor [Rosen] |
| Full Idea: To be an acid just is to be a proton donor. | |
| From: Gideon Rosen (Metaphysical Dependence [2010], 10) | |
| A reaction: My interest here is in whether we can say that we have found the 'essence' of an acid - so we want to know whether something 'deeper' explains the proton-donation. I suspect not. Being a proton donor happens to have a group of related consequences. |