18 ideas
| 13917 | Metaphysics aims to identify categories of being, and show their interdependency [Lowe] |
| Full Idea: The central task of metaphysics is to chart the possibilities of existence by identifying the categories of being and the relations of ontological dependency in which beings of different categories stand to one another. | |
| From: E.J. Lowe (Two Notions of Being: Entity and Essence [2008], Intro) | |
| A reaction: I am beginning to think that he is right about the second one, and that dependency and grounding relations are the name of the game. I don't have Lowe's confidence that philosophers can parcel up reality in neat and true ways. |
| 13919 | Philosophy aims not at the 'analysis of concepts', but at understanding the essences of things [Lowe] |
| Full Idea: The central task of philosophy is the cultivation of insights into natures or essences, and not the 'analysis of concepts', with which it is apt to be confused. | |
| From: E.J. Lowe (Two Notions of Being: Entity and Essence [2008], 1) | |
| A reaction: This immediately strikes me as a false dichotomy. I like the idea of trying to understand the true natures of things, but how are we going to do it in our armchairs? |
| 21560 | Any linguistic expression may lack meaning when taken out of context [Russell] |
| Full Idea: Any sentence, a single word, or a single component phrase, may often be quite devoid of meaning when separated from its context. | |
| From: Bertrand Russell (Substitutional Classes and Relations [1906], p.165) | |
| A reaction: Contextualism is now extremely fashionable, in philosophy of language and in epistemology. Here Russell is looking for a contextual way to define classes [so says Lackey, the editor]. |
| 21561 | 'The number one is bald' or 'the number one is fond of cream cheese' are meaningless [Russell] |
| Full Idea: 'The number one is bald' or 'the number one is fond of cream cheese' are, I maintain, not merely silly remarks, but totally devoid of meaning. | |
| From: Bertrand Russell (Substitutional Classes and Relations [1906], p.166) | |
| A reaction: He connects this to paradoxes in set theory, such as the assertion that 'the class of human beings is a human being' (which is the fallacy of composition). |
| 18130 | Axiom of Reducibility: there is always a function of the lowest possible order in a given level [Russell, by Bostock] |
| Full Idea: Russell's Axiom of Reducibility states that to any propositional function of any order in a given level, there corresponds another which is of the lowest possible order in the level. There corresponds what he calls a 'predicative' function of that level. | |
| From: report of Bertrand Russell (Substitutional Classes and Relations [1906]) by David Bostock - Philosophy of Mathematics 8.2 |
| 13373 | Typically, paradoxes are dealt with by dividing them into two groups, but the division is wrong [Priest,G] |
| Full Idea: A natural principle is the same kind of paradox will have the same kind of solution. Standardly Ramsey's first group are solved by denying the existence of some totality, and the second group are less clear. But denial of the groups sink both. | |
| From: Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §5) | |
| A reaction: [compressed] This sums up the argument of Priest's paper, which is that it is Ramsey's division into two kinds (see Idea 13334) which is preventing us from getting to grips with the paradoxes. Priest, notoriously, just lives with them. |
| 13368 | The 'least indefinable ordinal' is defined by that very phrase [Priest,G] |
| Full Idea: König: there are indefinable ordinals, and the least indefinable ordinal has just been defined in that very phrase. (Recall that something is definable iff there is a (non-indexical) noun-phrase that refers to it). | |
| From: Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §3) | |
| A reaction: Priest makes great subsequent use of this one, but it feels like a card trick. 'Everything indefinable has now been defined' (by the subject of this sentence)? König, of course, does manage to pick out one particular object. |
| 13370 | 'x is a natural number definable in less than 19 words' leads to contradiction [Priest,G] |
| Full Idea: Berry: if we take 'x is a natural number definable in less than 19 words', we can generate a number which is and is not one of these numbers. | |
| From: Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §3) | |
| A reaction: [not enough space to spell this one out in full] |
| 13369 | By diagonalization we can define a real number that isn't in the definable set of reals [Priest,G] |
| Full Idea: Richard: φ(x) is 'x is a definable real number between 0 and 1' and ψ(x) is 'x is definable'. We can define a real by diagonalization so that it is not in x. It is and isn't in the set of reals. | |
| From: Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §3) | |
| A reaction: [this isn't fully clear here because it is compressed] |
| 13366 | The least ordinal greater than the set of all ordinals is both one of them and not one of them [Priest,G] |
| Full Idea: Burali-Forti: φ(x) is 'x is an ordinal', and so w is the set of all ordinals, On; δ(x) is the least ordinal greater than every member of x (abbreviation: log(x)). The contradiction is that log(On)∈On and log(On)∉On. | |
| From: Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §2) |
| 13367 | The next set up in the hierarchy of sets seems to be both a member and not a member of it [Priest,G] |
| Full Idea: Mirimanoff: φ(x) is 'x is well founded', so that w is the cumulative hierarchy of sets, V; &delta(x) is just the power set of x, P(x). If x⊆V, then V∈V and V∉V, since δ(V) is just V itself. | |
| From: Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §2) |
| 13371 | If you know that a sentence is not one of the known sentences, you know its truth [Priest,G] |
| Full Idea: In the family of the Liar is the Knower Paradox, where φ(x) is 'x is known to be true', and there is a set of known things, Kn. By knowing a sentence is not in the known sentences, you know its truth. | |
| From: Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §4) | |
| A reaction: [mostly my wording] |
| 13372 | There are Liar Pairs, and Liar Chains, which fit the same pattern as the basic Liar [Priest,G] |
| Full Idea: There are liar chains which fit the pattern of Transcendence and Closure, as can be seen with the simplest case of the Liar Pair. | |
| From: Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §4) | |
| A reaction: [Priest gives full details] Priest's idea is that Closure is when a set is announced as complete, and Transcendence is when the set is forced to expand. He claims that the two keep coming into conflict. |
| 21562 | There is no complexity without relations, so no propositions, and no truth [Russell] |
| Full Idea: Relations in intension are of the utmost importance to philosophy and philosophical logic, since they are essential to complexity, and thence to propositions, and thence to the possibility of truth and falsehood. | |
| From: Bertrand Russell (Substitutional Classes and Relations [1906], p.174) | |
| A reaction: Should we able to specify the whole of reality, if we have available to us objects, properties and relations? There remains indeterminate 'stuff', when it does not compose objects. There are relations between pure ideas. |
| 13918 | Holes, shadows and spots of light can coincide without being identical [Lowe] |
| Full Idea: Holes are things of such a kind that they can coincide without being identical - as are, for example, shadows and spots of light. | |
| From: E.J. Lowe (Two Notions of Being: Entity and Essence [2008], 1) | |
| A reaction: His point is that they thereby fail one of the standard tests for being an 'object'. |
| 13921 | All things must have an essence (a 'what it is'), or we would be unable to think about them [Lowe] |
| Full Idea: Things must have an essence, in the sense of 'what it is to be the individual of that kind', or it would make no sense to say we can talk or think comprehendingly about things at all. If we don't know what it is, how can we think about it? | |
| From: E.J. Lowe (Two Notions of Being: Entity and Essence [2008], 2) | |
| A reaction: Lowe presents this as a sort of Master Argument for essences. I think he is working with the wrong notion of essence. All he means is that things must have identities to be objects of thought. Why equate identity with essence, and waste a good concept? |
| 13922 | Knowing an essence is just knowing what the thing is, not knowing some further thing [Lowe] |
| Full Idea: To know something's essence is not to be acquainted with some further thing of a special kind, but simply to understand what exactly that thing is. | |
| From: E.J. Lowe (Two Notions of Being: Entity and Essence [2008], 2) | |
| A reaction: I think he is wrong about this, or at least is working with an unhelpful notion of essence. Identity is one thing, and essence is another. I take essences to be certain selected features of things, which explain their nature. |
| 13920 | Each thing has to be of a general kind, because it belongs to some category [Lowe] |
| Full Idea: Any individual thing must be a thing of some general kind - because, at the very least, it must belong to some ontological category. | |
| From: E.J. Lowe (Two Notions of Being: Entity and Essence [2008], 2) | |
| A reaction: Where does the law that 'everything must have a category' come from? I'm baffled by remarks of this kind. Where do we get the categories from? From observing the individuals. So which has priority? Not the categories. Is God a kind? |