20 ideas
| 6859 | Analytic philosophy has much higher standards of thinking than continental philosophy [Williamson] |
| Full Idea: Certain advances in philosophical standards have been made within analytic philosophy, and there would be a serious loss of integrity involved in abandoning them in the way required to participate in current continental philosophy. | |
| From: Timothy Williamson (Interview with Baggini and Stangroom [2001], p.151) | |
| A reaction: The reply might be to concede the point, but say that the precision and rigour achieved are precisely what debar analytical philosophy from thinking about the really interesting problems. One might as well switch to maths and have done with it. |
| 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. |
| 17751 | Gödel proved the completeness of first order predicate logic in 1930 [Gödel, by Walicki] |
| Full Idea: Gödel proved the completeness of first order predicate logic in his doctoral dissertation of 1930. | |
| From: report of Kurt Gödel (Completeness of Axioms of Logic [1930]) by Michal Walicki - Introduction to Mathematical Logic History E.2.2 |
| 6862 | Fuzzy logic uses a continuum of truth, but it implies contradictions [Williamson] |
| Full Idea: Fuzzy logic is based on a continuum of degrees of truth, but it is committed to the idea that it is half-true that one identical twin is tall and the other twin is not, even though they are the same height. | |
| From: Timothy Williamson (Interview with Baggini and Stangroom [2001], p.154) | |
| A reaction: Maybe to be shocked by a contradiction is missing the point of fuzzy logic? Half full is the same as half empty. The logic does not say the twins are different, because it is half-true that they are both tall, and half-true that they both aren't. |
| 6858 | Formal logic struck me as exactly the language I wanted to think in [Williamson] |
| Full Idea: As soon as I started learning formal logic, that struck me as exactly the language that I wanted to think in. | |
| From: Timothy Williamson (Interview with Baggini and Stangroom [2001]) | |
| A reaction: It takes all sorts It is interesting that formal logic might be seen as having the capacity to live up to such an aspiration. I don't think the dream of an ideal formal language is dead, though it will never encompass all of reality. Poetic truth. |
| 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. |
| 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' |
| 6863 | Close to conceptual boundaries judgement is too unreliable to give knowledge [Williamson] |
| Full Idea: If one is very close to a conceptual boundary, then one's judgement will be too unreliable to constitute knowledge, and therefore one will be ignorant. | |
| From: Timothy Williamson (Interview with Baggini and Stangroom [2001], p.156) | |
| A reaction: This is the epistemological rather than ontological interpretation of vagueness. It sounds very persuasive, but I am reluctant to accept that reality is full of very precise boundaries which we cannot quite discriminate. |
| 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. |
| 6861 | What sort of logic is needed for vague concepts, and what sort of concept of truth? [Williamson] |
| Full Idea: The problem of vagueness is the problem of what logic is correct for vague concepts, and correspondingly what notions of truth and falsity are applicable to vague statements (does one need a continuum of degrees of truth, for example?). | |
| From: Timothy Williamson (Interview with Baggini and Stangroom [2001], p.153) | |
| A reaction: This certainly makes vagueness sound like one of the most interesting problems in all of philosophy, though also one of the most difficult. Williamson's solution is that we may be vague, but the world isn't. |
| 6860 | How can one discriminate yellow from red, but not the colours in between? [Williamson] |
| Full Idea: If one takes a spectrum of colours from yellow to red, it might be that given a series of colour samples along that spectrum, each sample is indiscriminable by the naked eye from the next one, though samples at either end are blatantly different. | |
| From: Timothy Williamson (Interview with Baggini and Stangroom [2001], p.151) | |
| A reaction: This seems like a nice variant of the Sorites paradox (Idea 6008). One could demonstrate it with just three samples, where A and C seemed different from each other, but other comparisons didn't. |
| 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. |
| 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. |