16 ideas
10528 | Definitions concern how we should speak, not how things are [Fine,K] |
Full Idea: Our concern in giving a definition is not to say how things are by to say how we wish to speak | |
From: Kit Fine (Precis of 'Limits of Abstraction' [2005], p.310) | |
A reaction: This sounds like an acceptable piece of wisdom which arises out of analytical and linguistic philosophy. It puts a damper on the Socratic dream of using definition of reveal the nature of reality. |
4975 | A thought can be split in many ways, so that different parts appear as subject or predicate [Frege] |
Full Idea: A thought can be split up in many ways, so that now one thing, now another, appears as subject or predicate | |
From: Gottlob Frege (On Concept and Object [1892], p.199) | |
A reaction: Thus 'the mouse is in the box', and 'the box contains the mouse'. A simple point, but important when we are trying to distinguish thought from language. |
21597 | Logical connectives have the highest precision, yet are infected by the vagueness of true and false [Russell, by Williamson] |
Full Idea: Russell says the best chance of avoiding vagueness are the logical connectives. ...But the vagueness of 'true' and 'false' infects the logical connectives too. All words are vague. Russell concludes that all language is vague. | |
From: report of Bertrand Russell (Vagueness [1923]) by Timothy Williamson - Vagueness 2.4 | |
A reaction: This relies on the logical connectives being defined semantically, in terms of T and F, but that is standard. Presumably the formal uninterpreted syntax is not vague. |
9949 | There is the concept, the object falling under it, and the extension (a set, which is also an object) [Frege, by George/Velleman] |
Full Idea: For Frege, the extension of the concept F is an object, as revealed by the fact that we use a name to refer to it. ..We must distinguish the concept, the object that falls under it, and the extension of the concept, which is the set containing the object. | |
From: report of Gottlob Frege (On Concept and Object [1892]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2 | |
A reaction: This I take to be the key distinction needed if one is to grasp Frege's account of what a number is. When we say that Frege is a platonist about numbers, it is because he is committed to the notion that the extension is an object. |
10529 | If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K] |
Full Idea: Neo-Fregeans have thought that Hume's Principle, and the like, might be definitive of number and therefore not subject to the usual epistemological worries over its truth. | |
From: Kit Fine (Precis of 'Limits of Abstraction' [2005], p.310) | |
A reaction: This seems to be the underlying dream of logicism - that arithmetic is actually brought into existence by definitions, rather than by truths derived from elsewhere. But we must be able to count physical objects, as well as just counting numbers. |
10530 | Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K] |
Full Idea: The fundamental difficulty facing the neo-Fregean is to either adopt the predicative reading of Hume's Principle, defining numbers, but inadequate, or the impredicative reading, which is adequate, but not really a definition. | |
From: Kit Fine (Precis of 'Limits of Abstraction' [2005], p.312) | |
A reaction: I'm not sure I understand this, but the general drift is the difficulty of building a system which has been brought into existence just by definition. |
18995 | Frege mistakenly takes existence to be a property of concepts, instead of being about things [Frege, by Yablo] |
Full Idea: Frege's theory treats existence as a property, not of things we call existent, but of concepts instantiated by those things. 'Biden exists' says our Biden-concept has instances. That is certainly not how it feels! We speak of the thing, not of concepts. | |
From: report of Gottlob Frege (On Concept and Object [1892]) by Stephen Yablo - Aboutness 01.4 | |
A reaction: Yablo's point is that you must ask what the sentence is 'about', and then the truth will refer to those things. Frege gets into a tangle because he thinks remarks using concepts are about the concepts. |
9051 | Since natural language is not precise it cannot be in the province of logic [Russell, by Keefe/Smith] |
Full Idea: Russell takes it that logic assumes precision, and since natural language is not precise it cannot be in the province of logic at all. | |
From: report of Bertrand Russell (Vagueness [1923]) by R Keefe / P Smith - Intro: Theories of Vagueness §1 | |
A reaction: I find this view congenial. It seems to me that the necessary prelude to logic is to do everything you can to eliminate ambiguity and vagueness from the sentences at issue. We want the proposition, or logical form. If there isn't one, forget it? |
9054 | Vagueness is only a characteristic of representations, such as language [Russell] |
Full Idea: Vagueness and precision alike are characteristics which can only belong to a representation, of which language is an example. | |
From: Bertrand Russell (Vagueness [1923], p.62) | |
A reaction: Russell was the first to tackle the question of vagueness, and he may have got it right. If we are unable to decide which set an object belongs in (red or orange) that is a problem for our conceptual/linguistic scheme. The object still has a colour! |
10317 | It is unclear whether Frege included qualities among his abstract objects [Frege, by Hale] |
Full Idea: Expositors of Frege's views have disagreed over whether abstract qualities are to be reckoned among his objects. | |
From: report of Gottlob Frege (On Concept and Object [1892]) by Bob Hale - Abstract Objects Ch.2.II | |
A reaction: [he cites Dummett 1973:70-80, and Wright 1983:25-8] There seems to be a danger here of a collision between Fregean verbal approaches to ontological commitment and the traditional views about universals. No wonder they can't decide. |
10535 | Frege's 'objects' are both the referents of proper names, and what predicates are true or false of [Frege, by Dummett] |
Full Idea: Frege's notion of an object plays two roles in his semantics. Objects are the referents of proper names, and they are equally what predicates are true and false of. | |
From: report of Gottlob Frege (On Concept and Object [1892]) by Michael Dummett - Frege Philosophy of Language (2nd ed) Ch.4 | |
A reaction: Frege is the source of a desperate desire to turn everything into an object (see Idea 8858!), and he has the irritating authority of the man who invented quantificational logic. Nothing but trouble, that man. |
9839 | Frege equated the concepts under which an object falls with its properties [Frege, by Dummett] |
Full Idea: Frege equated the concepts under which an object falls with its properties. | |
From: report of Gottlob Frege (On Concept and Object [1892], p.201) by Michael Dummett - Frege philosophy of mathematics Ch.8 | |
A reaction: I take this to be false, as objects can fall under far more concepts than they have properties. I don't even think 'being a pencil' is a property of pencils, never mind 'being my favourite pencil', or 'not being Alexander the Great'. |
4973 | As I understand it, a concept is the meaning of a grammatical predicate [Frege] |
Full Idea: As I understand it, a concept is the meaning of a grammatical predicate. | |
From: Gottlob Frege (On Concept and Object [1892], p.193) | |
A reaction: All the ills of twentieth century philosophy reside here, because it makes a concept an entirely linguistic thing, so that animals can't have concepts, and language is cut off from reality, leading to relativism, pragmatism, and other nonsense. |
10527 | An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K] |
Full Idea: If an abstraction principle is going to be acceptable, then it should not 'inflate', i.e. it should not result in there being more abstracts than there are objects. By this mark Hume's Principle will be acceptable, but Frege's Law V will not. | |
From: Kit Fine (Precis of 'Limits of Abstraction' [2005], p.307) | |
A reaction: I take this to be motivated by my own intuition that abstract concepts had better be rooted in the world, or they are not worth the paper they are written on. The underlying idea this sort of abstraction is that it is 'shared' between objects. |
9167 | Frege felt that meanings must be public, so they are abstractions rather than mental entities [Frege, by Putnam] |
Full Idea: Frege felt that meanings are public property, and identified concepts (and hence 'intensions' or meanings) with abstract entities rather than mental entities. | |
From: report of Gottlob Frege (On Concept and Object [1892]) by Hilary Putnam - Meaning and Reference p.150 | |
A reaction: This is the germ of Wittgenstein's private language argument. I am inclined to feel that Frege approached language strictly as a logician, and didn't really care that he got himself into implausible platonist ontological commitments. |
4974 | For all the multiplicity of languages, mankind has a common stock of thoughts [Frege] |
Full Idea: For all the multiplicity of languages, mankind has a common stock of thoughts. | |
From: Gottlob Frege (On Concept and Object [1892], p.196n) | |
A reaction: Given the acknowledgement here that two very different sentences in different languages can express the same thought, he should recognise that at least some aspects of a thought are non-linguistic. |