21 ideas
| 21829 | Philosophy aims to understand how things (broadly understood) hang together (broadly understood) [Sellars] |
| Full Idea: The aim of philosophy, abstractly formulated, is to understand how things in the broadest possible sense of the term hang together in the broadest possible sense of the term. | |
| From: Wilfrid Sellars (Philosophy and Scientific Image of Man [1962], p.3), quoted by Owen Flanagan - The Really Hard Problem 1 'Vocation' | |
| A reaction: I'm happier with broad things than broad hanging together, but to me this sounds about right. |
| 14240 | The empty set is something, not nothing! [Oliver/Smiley] |
| Full Idea: Some authors need to be told loud and clear: if there is an empty set, it is something, not nothing. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 1.2) | |
| A reaction: I'm inclined to think of a null set as a pair of brackets, so maybe that puts it into a metalanguage. |
| 14241 | We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley] |
| Full Idea: The empty set is said to be useful to express non-existence, but saying 'there are no Us', or ¬∃xUx are no less concise, and certainly less roundabout. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 1.2) |
| 14239 | The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley] |
| Full Idea: The empty set is usually derived via Zermelo's axiom of separation. But the axiom of separation is conditional: it requires the existence of a set in order to generate others as subsets of it. The original set has to come from the axiom of infinity. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 1.2) | |
| A reaction: They charge that this leads to circularity, as Infinity depends on the empty set. |
| 14242 | Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley] |
| Full Idea: Suppose we introduce Ω not as a term standing for a supposed empty set, but as a paradigm of an empty term, not standing for anything. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 1.2) | |
| A reaction: This proposal, which they go on to explore, seems to mean that Ω (i.e. the traditional empty set symbol) is no longer part of set theory but is part of semantics. |
| 14243 | The unit set may be needed to express intersections that leave a single member [Oliver/Smiley] |
| Full Idea: Thomason says with no unit sets we couldn't call {1,2}∩{2,3} a set - but so what? Why shouldn't the intersection be the number 2? However, we then have to distinguish three different cases of intersection (common subset or member, or disjoint). | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 2.2) |
| 14234 | If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley] |
| Full Idea: A 'singularist', who refers to objects one at a time, must resort to the language of sets in order to replace plural reference to members ('Henry VIII's wives') by singular reference to a set ('the set of Henry VIII's wives'). | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], Intro) | |
| A reaction: A simple and illuminating point about the motivation for plural reference. Null sets and singletons give me the creeps, so I would personally prefer to avoid set theory when dealing with ontology. |
| 14237 | We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley] |
| Full Idea: Plurals earn their keep in set theory, to answer Skolem's remark that 'in order to treat of 'sets', we must begin with 'domains' that are constituted in a certain way'. We can speak in the plural of 'the objects', not a 'domain' of objects. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], Intro) | |
| A reaction: [Skolem 1922:291 in van Heijenoort] Zermelo has said that the domain cannot be a set, because every set belongs to it. |
| 14245 | Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley] |
| Full Idea: Logical truths should be true no matter what exists, so true even if nothing exists. The classical predicate calculus, however, makes it logically true that something exists. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 5.1) |
| 14246 | If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley] |
| Full Idea: If mathematics was purely concerned with mathematical objects, there would be no room for applied mathematics. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 5.1) | |
| A reaction: Love it! Of course, they are using 'objects' in the rather Fregean sense of genuine abstract entities. I don't see why fictionalism shouldn't allow maths to be wholly 'pure', although we have invented fictions which actually have application. |
| 14247 | Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley] |
| Full Idea: Identifying numbers with sets may mean one of three quite different things: 1) the sets represent the numbers, or ii) they are the numbers, or iii) they replace the numbers. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 5.2) | |
| A reaction: Option one sounds the most plausible to me. I will take numbers to be patterns embedded in nature, and sets are one way of presenting them in shorthand form, in order to bring out what is repeated. |
| 6550 | Reduction requires that an object's properties consist of its constituents' properties and relations [Sellars] |
| Full Idea: The 'Principle of Reducibility' says if an object is a system of objects, then every property of the object must consist in the fact that its constituents have such and such qualities and such and such relations | |
| From: Wilfrid Sellars (Philosophy and Scientific Image of Man [1962], p.27), quoted by William Lycan - Consciousness | |
| A reaction: This sounds to me a more promising attitude to reduction than all this talk of Ernest Nagel's 'Bridge Laws'. If we ask HOW a higher level property arises because of a lower level property, we can describe a mechanism rather than a law. |
| 10496 | Monothetic categories have fixed defining features, and polythetic categories do not [Ellen] |
| Full Idea: Many categories are 'monothetic' (the defining set of features is always unique), and others are 'polythetic' (single features being neither essential to group membership nor sufficient to allocate an item to a group). | |
| From: Roy Ellen (Anthropological Studies of Classification [1996], p.33) | |
| A reaction: This seems a rather important distinction which hasn't made its way into philosophy, where there is a horrible tendency to oversimplify, with the dream of a neat and unified picture. But see Goodman's 'Imperfect Community' problem (Idea 7957). |
| 10497 | In symbolic classification, the categories are linked to rules [Ellen] |
| Full Idea: Symbolic classification occurs when we use some things as a means of saying something about other things. ..They enhance the significance of some categories, so that categories imply rules and rules imply categories. | |
| From: Roy Ellen (Anthropological Studies of Classification [1996], p.35) | |
| A reaction: I'm afraid the anthropologists seem to have more of interest to say about categories than philosophers do. Though maybe we couldn't do anthropology if philosophers had made us more self-conscious about categories. Teamwork! |
| 10494 | Several words may label a category; one word can name several categories; some categories lack words [Ellen] |
| Full Idea: Words are not always a good guide to the existence of categories: there may be several words which label the same categories (synonyms). and the same word can be used for quite different ideas. Some categories may exist without being labelled. | |
| From: Roy Ellen (Categories, Classification, Cogn. Anthropology [2006], I) | |
| A reaction: This is the sort of point which seems obvious to anyone outside philosophy, but which philosophers seem to find difficult to accept. Philosophers should pay much more attention to animals, and to illiterate peoples. Varieties of rice can lack labels. |
| 10495 | Continuous experience sometimes needs imposition of boundaries to create categories [Ellen] |
| Full Idea: Because parts of our experience of the world are complexly continuous, it is occasionally necessary to impose boundaries to produce categories at all. | |
| From: Roy Ellen (Anthropological Studies of Classification [1996], p.33) | |
| A reaction: I like it. Ellen says that people tend to universally cut nature somewhere around the joints, but we can't cope with large things, so the sea tends to be labelled in sections, even though most of the world's seas are continuous. |
| 8793 | If observation is knowledge, it is not just an experience; it is a justification in the space of reasons [Sellars] |
| Full Idea: In characterizing an observational episode or state as 'knowing', we are not giving an empirical description of it; we are placing it in the logical space of reasons, of justifying and being able to justify what one says. | |
| From: Wilfrid Sellars (Does Emp.Knowledge have Foundation? [1956], p.123) | |
| A reaction: McDowell has made the Kantian phrase 'the logical space of reasons' very popular. This is a very nice statement of the internalist view of justification, with which I sympathise more and more. It is a rationalist coherentist view. It needn't be mystical! |
| 8792 | Observations like 'this is green' presuppose truths about what is a reliable symptom of what [Sellars] |
| Full Idea: Observational knowledge of any particular fact, e.g. that this is green, presupposes that one knows general facts of the form 'X is a reliable symptom of Y'. | |
| From: Wilfrid Sellars (Does Emp.Knowledge have Foundation? [1956], p.123) | |
| A reaction: This is a nicely observed version of the regress problem with justification. I would guess that foundationalists would simply deny that this further knowledge is required; 'this is green' arises out of the experience, but it is not an inference. |
| 10498 | Classification is no longer held to be rooted in social institutions [Ellen] |
| Full Idea: The view that all classification finds its roots in social institutions is now generally considered untenable. | |
| From: Roy Ellen (Anthropological Studies of Classification [1996], p.36) | |
| A reaction: And about time too. Ellen (an anthropologist) inevitably emphasises the complexity of the situation, but endorses the idea that people everywhere largely cut nature at the joints. |
| 6382 | The 'grain problem' says physical objects are granular, where sensations appear not to be [Sellars, by Polger] |
| Full Idea: Sellars' Grain Problem contended that it was a problem for materialism that physical objects have a granularity whereas sensations are homogeneous and without grain. | |
| From: report of Wilfrid Sellars (Empiricism and the Philosophy of Mind [1956], Ch. n22) by Thomas W. Polger - Natural Minds Ch.1 n22 | |
| A reaction: This doesn't strike me as a serious problem. I assume that my sensations are granular, but at a level too fine for me to introspect. There are three hundred trillion connections in the brain (Idea 2952), a lot of them involved in sensations. |
| 8791 | The concept of 'green' involves a battery of other concepts [Sellars] |
| Full Idea: One can only have the concept of green by having a whole battery of concepts of which it is one element. | |
| From: Wilfrid Sellars (Does Emp.Knowledge have Foundation? [1956], p.120) | |
| A reaction: This points in the direction of holism about language and thought, but need not imply it. It might be that concepts have to be learned in small families. It is not clear, though, what is absolutely essential to 'green', except that it indicates colour. |