29 ideas
| 8956 | What is a singleton set, if a set is meant to be a collection of objects? [Szabó] |
| Full Idea: The relationship between an object and its singleton is puzzling. Our intuitive conception of a set is a collection of objects - what are we to make of a collection of a single object? | |
| From: Zoltán Gendler Szabó (Nominalism [2003], 4.1) | |
| A reaction: The ontological problem seems to be the same as that of the empty set, and indeed the claim that a pair of entities is three things. For logicians the empty set is as real as a pet dog, but not for me. |
| 10405 | In the iterative conception of sets, they form a natural hierarchy [Swoyer] |
| Full Idea: In the iterative conception of sets, they form a natural hierarchy. | |
| From: Chris Swoyer (Properties [2000], 4.1) |
| 10407 | Logical Form explains differing logical behaviour of similar sentences [Swoyer] |
| Full Idea: 'Logical Form' is a technical notion motivated by the observation that sentences with a similar surface structure may exhibit quite different logical behaviour. | |
| From: Chris Swoyer (Properties [2000], 4.2) | |
| A reaction: [Swoyer goes on to give some nice examples] The tricky question is whether each sentence has ONE logical form. Pragmatics warns us of the dangers. One needs to check numerous inferences from a given sentences, not just one. |
| 18085 | Values that approach zero, becoming less than any quantity, are 'infinitesimals' [Cauchy] |
| Full Idea: When the successive absolute values of a variable decrease indefinitely in such a way as to become less than any given quantity, that variable becomes what is called an 'infinitesimal'. Such a variable has zero as its limit. | |
| From: Augustin-Louis Cauchy (Cours d'Analyse [1821], p.19), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.4 | |
| A reaction: The creator of the important idea of the limit still talked in terms of infinitesimals. In the next generation the limit took over completely. |
| 18084 | When successive variable values approach a fixed value, that is its 'limit' [Cauchy] |
| Full Idea: When the values successively attributed to the same variable approach indefinitely a fixed value, eventually differing from it by as little as one could wish, that fixed value is called the 'limit' of all the others. | |
| From: Augustin-Louis Cauchy (Cours d'Analyse [1821], p.19), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.4 | |
| A reaction: This seems to be a highly significan proposal, because you can now treat that limit as a number, and adds things to it. It opens the door to Cantor's infinities. Is the 'limit' just a fiction? |
| 14592 | Some abstract things have a beginning and end, so may exist in time (though not space) [Swoyer] |
| Full Idea: Many things that seem to be abstract also seem to have a beginning (and ending) in time, such as a language like Urdu. It may be tempting to say that such things exist in time but not in space, but where exactly? | |
| From: Chris Swoyer (Abstract Entities [2008], 1.1) | |
| A reaction: A few distinctions might be needed. Urdu-speaking is an ability of certain people. We abstract from that their 'language'. There is nothing there apart from that ability. It has no more abstract existence than the 'weather'. |
| 10421 | Supervenience is nowadays seen as between properties, rather than linguistic [Swoyer] |
| Full Idea: Supervenience is sometimes taken to be a relationship between two fragments of language, but it is increasingly taken to be a relationship between pairs of families of properties. | |
| From: Chris Swoyer (Properties [2000], 7.17) | |
| A reaction: If supervenience is a feature of the world, rather than of our descriptions, then it cries out for explanation, just as any other regularities do. Personally I would have thought the best explanation of the supervenience of mind and body was obvious. |
| 8953 | Abstract entities don't depend on their concrete entities ...but maybe on the totality of concrete things [Szabó] |
| Full Idea: It is better not to include in the definition of abstract entities that they ontologically depend on their concrete correlates. Note: ..but they may depend on the totality of concreta; maybe 'the supervenience of the abstract' is part of ordinary thought. | |
| From: Zoltán Gendler Szabó (Nominalism [2003], 2.2) | |
| A reaction: [the quoted phrase is from Gideon Rosen] It certainly seems unlikely that the concept of the perfect hexagon depends on a perfect hexagon having existed. Human minds have intervened between the concrete and the abstract. |
| 14594 | Ontologists seek existence and identity conditions, and modal and epistemic status for a thing [Swoyer] |
| Full Idea: Four things philosophers often want to know about a given sort of entity are: its existence conditions, its identity conditions, its modal status, and its epistemic status. | |
| From: Chris Swoyer (Abstract Entities [2008], 3) | |
| A reaction: I prefer 'modal profile' to 'modal status'. The 'existence conditions' sound rather epistemic. Why does the existence of anything require 'conditions' other than just existing? I suspect identity is irrelevant if humans aren't around. |
| 10410 | Anti-realists can't explain different methods to measure distance [Swoyer] |
| Full Idea: Anti-realists theories of measurement (like operationalism) cannot explain how we can use different methods to measure the same thing (e.g. lengths and distances in cosmology, geology, histology and atomic physics). | |
| From: Chris Swoyer (Properties [2000], 4.2) | |
| A reaction: Swoyer says that the explanation is that measurement aims at objective properties, the same in each of these areas. Quite good. |
| 10399 | If a property such as self-identity can only be in one thing, it can't be a universal [Swoyer] |
| Full Idea: Some properties may not be universals, if they can only be exemplified by one thing, such as 'being identical with Socrates'. | |
| From: Chris Swoyer (Properties [2000]) | |
| A reaction: I think it is absurd to think that self-identity is an intrinsic 'property', possessed by everything. That a=a is a convenience for logicians, meaning nothing in the world. And it is relational. The sharing of properties is indeed what needs explanation. |
| 10416 | Can properties have parts? [Swoyer] |
| Full Idea: Can properties have parts? | |
| From: Chris Swoyer (Properties [2000], 6.4) | |
| A reaction: If powers are more fundamental than properties, with the latter often being complexes of the underlying powers, then yes they do. But powers don't. Presumably whatever is fundamental shouldn't have parts. Why? |
| 14595 | Can properties exemplify other properties? [Swoyer] |
| Full Idea: Can properties themselves exemplify properties? | |
| From: Chris Swoyer (Abstract Entities [2008], 3) | |
| A reaction: Since I espouse a rather strict causal view of true properties, and lump the rest into the category of 'predicates', I am inclined to answer 'no' to this. Most people would disagree. 'Bright red' seems to be an example. But it isn't. |
| 10417 | There are only first-order properties ('red'), and none of higher-order ('coloured') [Swoyer] |
| Full Idea: 'Elementarism' is the view that there are first-order properties, but that there are no properties of any higher-order. There are first-order properties like various shades of red, but there is no higher-order property, like 'being a colour'. | |
| From: Chris Swoyer (Properties [2000], 7.1) | |
| A reaction: [He cites Bergmann 1968] Interesting. Presumably the programme is naturalistic (and hence congenial to me), and generalisations about properties are conceptual, while the properties themselves are natural. |
| 10413 | The best-known candidate for an identity condition for properties is necessary coextensiveness [Swoyer] |
| Full Idea: The best-known candidate for an identity condition for properties is necessary coextensiveness. | |
| From: Chris Swoyer (Properties [2000], 6) | |
| A reaction: The necessity (in all possible worlds) covers renates and cordates. It is hard to see how one could assert the necessity without some deeper explanation. What makes us deny that actually coextensive renates and cordates have different properties? |
| 10402 | Various attempts are made to evade universals being wholly present in different places [Swoyer] |
| Full Idea: The worry that a single thing could be wholly present in widely separated locations has led to trope theory, to the claim that properties are not located in their instances, or to the view that this treats universals as if they were individuals. | |
| From: Chris Swoyer (Properties [2000], 2.2) | |
| A reaction: I find it dispiriting to come to philosophy in the late twentieth century and have to inherit such a ridiculous view as that there are things that are 'wholly present' in many places. |
| 10400 | Conceptualism says words like 'honesty' refer to concepts, not to properties [Swoyer] |
| Full Idea: Conceptualists urge that words like 'honesty', which might seem to refer to properties, really refer to concepts. A few contemporary philosophers have defended conceptualism, and recent empirical work bears on it, but the view is no longer common. | |
| From: Chris Swoyer (Properties [2000], 1.1) | |
| A reaction: ..and that's all Swoyer says about this very interesting view! He only cites Cocchiarella 1986 Ch.3. The view leaves a lot of work to be done in explaining how nature is, and how our concepts connect to it, and arise in response to it. |
| 10403 | If properties are abstract objects, then their being abstract exemplifies being abstract [Swoyer] |
| Full Idea: If properties are abstract objects, then the property of being abstract should itself exemplify the property of being abstract. | |
| From: Chris Swoyer (Properties [2000], 2.2) | |
| A reaction: Swoyer links this observation with Plato's views on self-predication, and his Third Man Argument (which I bet originated with Aristotle in the Academy!). Do we have a regress of objects, as well as a regress of properties? |
| 14593 | Quantum field theory suggests that there are, fundamentally, no individual things [Swoyer] |
| Full Idea: Quantum field theory strongly suggests that there are (at the fundamental level) no individual, particular things. | |
| From: Chris Swoyer (Abstract Entities [2008], 2.1) | |
| A reaction: When people introduce quantum theory into ontological discussions I reach for my shotgun, but it does rather look as if things turn to mush at the bottom level. |
| 10406 | One might hope to reduce possible worlds to properties [Swoyer] |
| Full Idea: One might hope to reduce possible worlds to properties. | |
| From: Chris Swoyer (Properties [2000], 4.1) | |
| A reaction: [He cites Zalta 1983 4.2, and Forrest 1986] I think we are dealing with nothing more than imagined possibilities, which are inferred from our understanding of the underlying 'powers' of the actual world (expressed as 'properties'). |
| 10404 | Extreme empiricists can hardly explain anything [Swoyer] |
| Full Idea: Extreme empiricists wind up unable to explain much of anything. | |
| From: Chris Swoyer (Properties [2000], 2.3) | |
| A reaction: This seems to be the major problem for empiricism, but I am not sure why inference to the best explanation should not be part of a sensible empirical approach. Thinking laws are just 'descriptions of regularities' illustrates the difficulty. |
| 8954 | Geometrical circles cannot identify a circular paint patch, presumably because they lack something [Szabó] |
| Full Idea: The vocabulary of geometry is sufficient to identify the circle, but could not be used to identify any circular paint patch. The reason must be that the circle lacks certain properties that can distinguish paint patches from one another. | |
| From: Zoltán Gendler Szabó (Nominalism [2003], 2.2) | |
| A reaction: I take this to be support for the traditional view, that abstractions are created by omitting some of the properties of physical objects. I take them to be fictional creations, reified by language, and not actual hidden entities that have been observed. |
| 10408 | Intensions are functions which map possible worlds to sets of things denoted by an expression [Swoyer] |
| Full Idea: Intensions are functions that assign a set to the expression at each possible world, ..so the semantic value of 'red' is the function that maps each possible world to the set of things in that world that are red. | |
| From: Chris Swoyer (Properties [2000], 4.2) | |
| A reaction: I am suddenly deeply alienated from this mathematical logicians' way of talking about what 'red' means! We need more psychology, not less. We call things red if we imagine them as looking red. Is imagination a taboo in analytical philosophy? |
| 10409 | Research suggests that concepts rely on typical examples [Swoyer] |
| Full Idea: Recent empirical work on concepts says that many concepts have graded membership, and stress the importance of phenomena like typicality, prototypes, and exemplars. | |
| From: Chris Swoyer (Properties [2000], 4.2) | |
| A reaction: [He cites Rorsch 1978 as the start of this] I say the mind is a database, exactly corresponding to tables, fields etc. Prototypes sound good as the way we identify a given category. Universals are the 'typical' examples labelling areas (e.g. goat). |
| 8955 | Abstractions are imperceptible, non-causal, and non-spatiotemporal (the third explaining the others) [Szabó] |
| Full Idea: In current discussions, abstract entities are usually distinguished as 1) in principle imperceptible, 2) incapable of causal interaction, 3) not located in space-time. The first is often explained by the second, which is in turn explained by the third. | |
| From: Zoltán Gendler Szabó (Nominalism [2003], 2.2) | |
| A reaction: Szabó concludes by offering 3 as the sole criterion of abstraction. As Lewis points out, the Way of Negation for defining abstracta doesn't tell us very much. Courage may be non-spatiotemporal, but what about Alexander the Great's courage? |
| 10401 | The F and G of logic cover a huge range of natural language combinations [Swoyer] |
| Full Idea: All sorts of combinations of copulas ('is') with verbs, adverbs, adjectives, determiners, common nouns, noun phrases and prepositional phrases go over into the familiar Fs and Gs of standard logical notation. | |
| From: Chris Swoyer (Properties [2000], 1.2) | |
| A reaction: This is a nice warning of how misleading logic can be when trying to understand how we think about reality. Montague semantics is an attempt to tackle the problem. Numbers as adjectives are a clear symptom of the difficulties. |
| 10420 | Maybe a proposition is just a property with all its places filled [Swoyer] |
| Full Idea: Some say we can think of a proposition as a limiting case of a property, as when the two-place property '___ loves ___' can become the zero-placed property, or proposition 'that Sam loves Darla'. | |
| From: Chris Swoyer (Properties [2000], 7.6) | |
| A reaction: If you had a prior commitment to the idea that reality largely consists of bundles of properties, I suppose you might find this tempting. |
| 10412 | If laws are mere regularities, they give no grounds for future prediction [Swoyer] |
| Full Idea: If laws were mere regularities, then the fact that observed Fs have been Gs would give us no reason to conclude that those Fs we haven't encountered will also be Gs. | |
| From: Chris Swoyer (Properties [2000], 4.2) | |
| A reaction: I take this simple point to be very powerful. No amount of regularity gives grounds for asserting future patterns - one only has Humean habits. Causal mechanisms are what we are after. |
| 10411 | Two properties can have one power, and one property can have two powers [Swoyer] |
| Full Idea: If properties are identical when they confer the same capacities on their instances, different properties seem able to bestow the same powers (e.g. force), and one property can bestow different powers (attraction or repulsion). | |
| From: Chris Swoyer (Properties [2000], 4.2) | |
| A reaction: Interesting, but possibly a misunderstanding. Powers are basic, and properties are combinations of powers. A 'force' isn't a basic power, it is a consequence of various properties. Relational behaviours are also not basic powers, which are the source. |