17 ideas
| 12797 | If plural variables have 'some values', then non-count variables have 'some value' [Laycock] |
| Full Idea: If a plural variable is said to have not a single value but some values (some clothes), then a non-count variable may have, more quirkier still, some value (some clothing, for instance) in ranging arbitrarily over the scattered stuff. | |
| From: Henry Laycock (Words without Objects [2006], 4.4) | |
| A reaction: We seem to need the notion of a sample, or an archetype, to fit the bill. I hereby name them 'sample variables'. Damn - Laycock got there first, on p.137. |
| 12794 | Plurals are semantical but not ontological [Laycock] |
| Full Idea: Plurality is a semantical but not also an ontological construction. | |
| From: Henry Laycock (Words without Objects [2006], Intro 4) | |
| A reaction: I love it when philososphers make simple and illuminating remarks like this. You could read 500 pages of technical verbiage about plural reference without grasping that this is the underlying issue. Sounds right to me. |
| 17963 | The facts of geometry, arithmetic or statics order themselves into theories [Hilbert] |
| Full Idea: The facts of geometry order themselves into a geometry, the facts of arithmetic into a theory of numbers, the facts of statics, electrodynamics into a theory of statics, electrodynamics, or the facts of the physics of gases into a theory of gases. | |
| From: David Hilbert (Axiomatic Thought [1918], [03]) | |
| A reaction: This is the confident (I would say 'essentialist') view of axioms, which received a bit of a setback with Gödel's Theorems. I certainly agree that the world proposes an order to us - we don't just randomly invent one that suits us. |
| 17966 | Axioms must reveal their dependence (or not), and must be consistent [Hilbert] |
| Full Idea: If a theory is to serve its purpose of orienting and ordering, it must first give us an overview of the independence and dependence of its propositions, and second give a guarantee of the consistency of all of the propositions. | |
| From: David Hilbert (Axiomatic Thought [1918], [09]) | |
| A reaction: Gödel's Second theorem showed that the theory can never prove its own consistency, which made the second Hilbert requirement more difficult. It is generally assumed that each of the axioms must be independent of the others. |
| 17694 | Some non-count nouns can be used for counting, as in 'several wines' or 'fewer cheeses' [Laycock] |
| Full Idea: The very words we class as non-count nouns may themselves be used for counting, of kinds or types, and phrases like 'several wines' are perfectly in order. ...Not only do we have 'less cheese', but we also have the non-generic 'fewer cheeses'. | |
| From: Henry Laycock (Words without Objects [2006], Intro 4 n23) | |
| A reaction: [compressed] Laycock generally endorses the thought that what can be counted is not simply distinguished by a precise class of applied vocabulary. He offers lots of borderline or ambiguous cases in his footnotes. |
| 17695 | Some apparent non-count words can take plural forms, such as 'snows' or 'waters' [Laycock] |
| Full Idea: Some words that seem to be semantically non-count can take syntactically plural forms: 'snows', 'sands', 'waters' and the like. | |
| From: Henry Laycock (Words without Objects [2006], Intro 4 n24) | |
| A reaction: This seems to involve parcels of the stuff. The 'snows of yesteryear' occur at different times. 'Taking the waters' probably involves occasions. The 'Arabian sands' presumably occur in different areas. Semantics won't fix what is countable. |
| 17967 | To decide some questions, we must study the essence of mathematical proof itself [Hilbert] |
| Full Idea: It is necessary to study the essence of mathematical proof itself if one wishes to answer such questions as the one about decidability in a finite number of operations. | |
| From: David Hilbert (Axiomatic Thought [1918], [53]) |
| 17965 | The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert] |
| Full Idea: The linearity of the equation of the plane and of the orthogonal transformation of point-coordinates is completely adequate to produce the whole broad science of spatial Euclidean geometry purely by means of analysis. | |
| From: David Hilbert (Axiomatic Thought [1918], [05]) | |
| A reaction: This remark comes from the man who succeeded in producing modern axioms for geometry (in 1897), so he knows what he is talking about. We should not be wholly pessimistic about Hilbert's ambitious projects. He had to dig deeper than this idea... |
| 17964 | Number theory just needs calculation laws and rules for integers [Hilbert] |
| Full Idea: The laws of calculation and the rules of integers suffice for the construction of number theory. | |
| From: David Hilbert (Axiomatic Thought [1918], [05]) | |
| A reaction: This is the confident Hilbert view that the whole system can be fully spelled out. Gödel made this optimism more difficult. |
| 12792 | The category of stuff does not suit reference [Laycock] |
| Full Idea: The central fact about the category of stuff or matter is that it is profoundly antithetical to reference. | |
| From: Henry Laycock (Words without Objects [2006], Pref) | |
| A reaction: This is taking 'reference' in the strictly singular classical sense, but clearly we refer to water in various ways. Laycock's challenge is very helpful. We have been in the grips of a terrible orthodoxy. |
| 12799 | Descriptions of stuff are neither singular aggregates nor plural collections [Laycock] |
| Full Idea: The definite descriptions of stuff like water are neither singular descriptions denoting individual mereological aggregates, nor plural descriptions denoting multitudes of discrete units or semantically determined atoms. | |
| From: Henry Laycock (Words without Objects [2006], 5.3) | |
| A reaction: Laycock makes an excellent case for this claim, and seems to invite a considerable rethink of our basic ontology to match it, one which he ultimately hints at calling 'romantic'. Nice. Conservatives try to force stuff into classical moulds. |
| 12818 | We shouldn't think some water retains its identity when it is mixed with air [Laycock] |
| Full Idea: Suppose that water, qua vapour, mixes with the atmosphere. Is there any abstract metaphysical principle, other than that of atomism, which implies that water must, in any such process, retain its identity? That claim seems indefensible. | |
| From: Henry Laycock (Words without Objects [2006], 1.2 n22) | |
| A reaction: It can't be right that some stuff always loses its identity in a mixture, if the mixture was in a closed vessel, and then separated again. Dispersion is what destroys the identity, not mixing. |
| 12795 | Parts must be of the same very general type as the wholes [Laycock] |
| Full Idea: The notion of a part is such that parts must be of the same very general type - concrete, material or physical, for instance - as the wholes of which they are (said to be) parts. | |
| From: Henry Laycock (Words without Objects [2006], 2.9) | |
| A reaction: The phrase 'same very general type' cries out for investigation. Can an army contain someone who isn't much of a soldier? Can the Treasury contain a fear of inflation? |
| 17696 | 'Humility is a virtue' has an abstract noun, but 'water is a liquid' has a generic concrete noun [Laycock] |
| Full Idea: Work is needed to distinguish abstract nouns ...from the generic uses of what are otherwise concrete nouns. The contrast is that of 'humility is a virtue' and 'water is a liquid'. | |
| From: Henry Laycock (Words without Objects [2006], Intro 4 n25) | |
| A reaction: 'Work is needed' implies 'let me through, I'm an analytic philosopher', but I don't think they will separate very easily. What does 'watery' mean? Does water have concrete virtues? |
| 12791 | It is said that proper reference is our intellectual link with the world [Laycock] |
| Full Idea: Some people hold that it is reference, in some more or less full-blooded sense, which constitutes our basic intellectual or psychological connection with the world. | |
| From: Henry Laycock (Words without Objects [2006], Pref) | |
| A reaction: This is the view which Laycock sets out to challenge, by showing that we talk about stuff like water without any singular reference occurring at all. I think he is probably right. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |
| 17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |
| Full Idea: By pushing ahead to ever deeper layers of axioms ...we also win ever-deeper insights into the essence of scientific thought itself, and become ever more conscious of the unity of our knowledge. | |
| From: David Hilbert (Axiomatic Thought [1918], [56]) | |
| A reaction: This is the less fashionable idea that scientific essentialism can also be applicable in the mathematic sciences, centring on the project of axiomatisation for logic, arithmetic, sets etc. |