28 ideas
| 18806 | Frege thought traditional categories had psychological and linguistic impurities [Frege, by Rumfitt] |
| Full Idea: Frege rejected the traditional categories as importing psychological and linguistic impurities into logic. | |
| From: report of Gottlob Frege (Function and Concept [1891]) by Ian Rumfitt - The Boundary Stones of Thought 1.2 | |
| A reaction: Resisting such impurities is the main motivation for making logic entirely symbolic, but it doesn't follow that the traditional categories have to be dropped. |
| 12219 | Whether a modal claim is true depends on how the object is described [Quine, by Fine,K] |
| Full Idea: Quine says if ∃x□(x>7) makes sense, then for which object x is the condition rendered true? Specify it as '9' and it is apparently rendered true, specify it as 'the number of planets' and it is apparently rendered false. | |
| From: report of Willard Quine (Three Grades of Modal Involvement [1953]) by Kit Fine - Quine on Quantifying In p.105 | |
| A reaction: This is normally characterised as Quine saying that only de dicto involvement is possible, and not de re involvement. Or that that all essences are nominal, and cannot be real. |
| 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. |
| 8490 | First-level functions have objects as arguments; second-level functions take functions as arguments [Frege] |
| Full Idea: Just as functions are fundamentally different from objects, so also functions whose arguments are and must be functions are fundamentally different from functions whose arguments are objects. The latter are first-level, the former second-level, functions. | |
| From: Gottlob Frege (Function and Concept [1891], p.38) | |
| A reaction: In 1884 he called it 'second-order'. This is the standard distinction between first- and second-order logic. The first quantifies over objects, the second over intensional entities such as properties and propositions. |
| 8492 | Relations are functions with two arguments [Frege] |
| Full Idea: Functions of one argument are concepts; functions of two arguments are relations. | |
| From: Gottlob Frege (Function and Concept [1891], p.39) | |
| A reaction: Nowadays we would say 'two or more'. Another interesting move in the aim of analytic philosophy to reduce the puzzling features of the world to mathematical logic. There is, of course, rather more to some relations than being two-argument functions. |
| 10922 | Objects are the values of variables, so a referentially opaque context cannot be quantified into [Quine] |
| Full Idea: The objects of a theory are not properly describable as the things named by the singular terms; they are the values, rather, of the variables of quantification. ..So a referentially opaque context is one that cannot properly be quantified into. | |
| From: Willard Quine (Three Grades of Modal Involvement [1953], p.174) | |
| A reaction: The point being that you cannot accurately pick out the objects in the domain |
| 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. |
| 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. |
| 8487 | Arithmetic is a development of logic, so arithmetical symbolism must expand into logical symbolism [Frege] |
| Full Idea: I am of the opinion that arithmetic is a further development of logic, which leads to the requirement that the symbolic language of arithmetic must be expanded into a logical symbolism. | |
| From: Gottlob Frege (Function and Concept [1891], p.30) | |
| A reaction: This may the the one key idea at the heart of modern analytic philosophy (even though logicism may be a total mistake!). Logic and arithmetical foundations become the master of ontology, instead of the servant. The jury is out on the whole enterprise. |
| 18899 | Frege takes the existence of horses to be part of their concept [Frege, by Sommers] |
| Full Idea: Frege regarded the existence of horses as a property of the concept 'horse'. | |
| From: report of Gottlob Frege (Function and Concept [1891]) by Fred Sommers - Intellectual Autobiography 'Realism' |
| 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. |
| 4028 | Frege allows either too few properties (as extensions) or too many (as predicates) [Mellor/Oliver on Frege] |
| Full Idea: Frege's theory of properties (which he calls 'concepts') yields too few properties, by identifying coextensive properties, and also too many, by letting every predicate express a property. | |
| From: comment on Gottlob Frege (Function and Concept [1891]) by DH Mellor / A Oliver - Introduction to 'Properties' §2 | |
| A reaction: Seems right; one extension may have two properties (have heart/kidneys), two predicates might express the same property. 'Cutting nature at the joints' covers properties as well as objects. |
| 8489 | The concept 'object' is too simple for analysis; unlike a function, it is an expression with no empty place [Frege] |
| Full Idea: I regard a regular definition of 'object' as impossible, since it is too simple to admit of logical analysis. Briefly: an object is anything that is not a function, so that an expression for it does not contain any empty place. | |
| From: Gottlob Frege (Function and Concept [1891], p.32) | |
| A reaction: Here is the core of the programme for deriving our ontology from our logic and language, followed through by Russell and Quine. Once we extend objects beyond the physical, it becomes incredibly hard to individuate them. |
| 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? |
| 10923 | Aristotelian essentialism says a thing has some necessary and some non-necessary properties [Quine] |
| Full Idea: What Aristotelian essentialism says is that you can have open sentences Fx and Gx, such that ∃x(nec Fx.Gx.Źnec Gx). For example, ∃x(nec(x>5). there are just x planets. Źnec(there are just x planets)). | |
| From: Willard Quine (Three Grades of Modal Involvement [1953], p.176) | |
| A reaction: This is a denial of 'maximal essentialism', that all of a things properties might be essential. Quine is thus denying necessity, except under a description. He may be equivocating over the reference of 'there are just 9 planets'. |
| 10921 | Necessity can attach to statement-names, to statements, and to open sentences [Quine] |
| Full Idea: Three degrees necessity in logic or semantics: first and least is attaching a semantical predicate to the names of statements (as Nec '9>5'); second and more drastic attaches to statements themselves; third and gravest attaches to open sentences. | |
| From: Willard Quine (Three Grades of Modal Involvement [1953], p.158) |
| 10924 | Necessity is in the way in which we say things, and not things themselves [Quine] |
| Full Idea: Necessity resides in the way in which we say things, and not in the things we talk about. | |
| From: Willard Quine (Three Grades of Modal Involvement [1953], p.176) | |
| A reaction: This is a culminating idea of Quine's thoroughgoing empiricism, as filtered through logical positivism. I would hardly dare to accuse Quine of a use/mention confusion (his own bęte noir), but one seems to me to be lurking here. |
| 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? |
| 9947 | Concepts are the ontological counterparts of predicative expressions [Frege, by George/Velleman] |
| Full Idea: Concepts, for Frege, are the ontological counterparts of predicative expressions. | |
| From: report of Gottlob Frege (Function and Concept [1891]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2 | |
| A reaction: That sounds awfully like what many philosophers call 'universals'. Frege, as a platonist (at least about numbers), I would take to be in sympathy with that. At least we can say that concepts seem to be properties. |
| 10319 | An assertion about the concept 'horse' must indirectly speak of an object [Frege, by Hale] |
| Full Idea: Frege had a notorious difficulty over the concept 'horse', when he suggests that if we wish to assert something about a concept, we are obliged to proceed indirectly by speaking of an object that represents it. | |
| From: report of Gottlob Frege (Function and Concept [1891], Ch.2.II) by Bob Hale - Abstract Objects | |
| A reaction: This sounds like the thin end of a wedge. The great champion of objects is forced to accept them here as a façon de parler, when elsewhere they have ontological status. |
| 8488 | A concept is a function whose value is always a truth-value [Frege] |
| Full Idea: A concept in logic is closely connected with what we call a function. Indeed, we may say at once: a concept is a function whose value is always a truth-value. ..I give the name 'function' to what is meant by the 'unsaturated' part. | |
| From: Gottlob Frege (Function and Concept [1891], p.30) | |
| A reaction: So a function becomes a concept when the variable takes a value. Problems arise when the value is vague, or the truth-value is indeterminable. |
| 9948 | Unlike objects, concepts are inherently incomplete [Frege, by George/Velleman] |
| Full Idea: For Frege, concepts differ from objects in being inherently incomplete in nature. | |
| From: report of Gottlob Frege (Function and Concept [1891]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2 | |
| A reaction: This is because they are 'unsaturated', needing a quantified variable to complete the sentence. This could be a pointer towards Quine's view of properties, as simply an intrinsic feature of predication about objects, with no separate identity. |
| 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. |
| 4972 | I may regard a thought about Phosphorus as true, and the same thought about Hesperus as false [Frege] |
| Full Idea: From sameness of meaning there does not follow sameness of thought expressed. A fact about the Morning Star may express something different from a fact about the Evening Star, as someone may regard one as true and the other false. | |
| From: Gottlob Frege (Function and Concept [1891], p.14) | |
| A reaction: This all gets clearer if we distinguish internalist and externalist theories of content. Why take sides on this? Why not just ask 'what is in the speaker's head?', 'what does the sentence mean in the community?', and 'what is the corresponding situation?' |
| 8491 | The Ontological Argument fallaciously treats existence as a first-level concept [Frege] |
| Full Idea: The ontological proof of God's existence suffers from the fallacy of treating existence as a first-level concept. | |
| From: Gottlob Frege (Function and Concept [1891], p.38 n) | |
| A reaction: [See Idea 8490 for first- and second-order functions] This is usually summarised as the idea that existence is a quantifier rather than a predicate. |