23 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. |
| 19053 | Logic would be more natural if negation only referred to predicates [Dummett] |
| Full Idea: A better proposal for a formal logic closer to natural language would be one that had a negation-operator only for (simple) predicates. | |
| From: Michael Dummett (Presupposition [1960], p.27) | |
| A reaction: Dummett observes that classical formal logic was never intended to be close to natural language. Term logic does have that aim, but the meta-question is whether that end is desirable, and why. |
| 22246 | A train of reasoning must be treated as all happening simultaneously [Recanati] |
| Full Idea: For logic purposes, a train of reasoning has to be construed as synchronic. | |
| From: François Recanati (Mental Files in Flux [2016], 5.2) | |
| A reaction: If we are looking for a gulf between logic and the real world this is a factor to be considered, along with Nietzsche's observation about necessary simplification. [ref to Kaplan 'Afterthoughts' 1989, 584-5] |
| 19052 | Natural language 'not' doesn't apply to sentences [Dummett] |
| Full Idea: Natural language does not possess a sentential negation-operator. | |
| From: Michael Dummett (Presupposition [1960], p.27) | |
| A reaction: This is a criticism of Strawson, who criticises logic for not following natural language, but does it himself with negation. In the question of how language and logic connect, this idea seems important. Term Logic aims to get closer to natural language. |
| 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' |
| 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. |
| 22247 | Indexicality is not just a feature of language; examples show it also occurs in thought [Recanati] |
| Full Idea: People once took indexicality to be exclusively a property of language, ....but a series of examples seemed to establish that the thought expressed by uttering an indexical sentence is itself indexical (and is thus 'essential'). | |
| From: François Recanati (Mental Files in Flux [2016], 6.1) | |
| A reaction: Perry's example of not realising it is him leaking the sugar in a supermarket is the best known example. Was this a key moment for realising that philosophy of thought is (pace Dummett) more important than philosophy of language? |
| 22248 | How can we communicate indexical thoughts to people not in the right context? [Recanati] |
| Full Idea: Indexical thoughts create an obvious problem with regard to communication. How can we manage to communicate such thoughts to those who are not in the right context? | |
| From: François Recanati (Mental Files in Flux [2016], 7.1) | |
| A reaction: One answer is that you often cannot communicate them. If I write on a wall 'I am here now', that doesn't tell the next passer-by very much. But 'it's raining here' said in a telephone call works fine - if you know the location of the caller. |
| 22242 | Mental files are concepts, which are either collections or (better) containers [Recanati] |
| Full Idea: Mental files are entries in the mental encyclopedia, that is, concepts. Some, following Grice, say they are information collections, but I think of them as containers. Collections are determined by their elements, but containers have independent identity. | |
| From: François Recanati (Mental Files in Flux [2016], Pref) | |
| A reaction: [compressed] [Grice reference is 'Vacuous Names' (1969)] I agree with Recanati. The point is that you can invoke a file by a label, even when you don't know what the content is. |
| 22243 | The Frege case of believing a thing is both F and not-F is explained by separate mental files [Recanati] |
| Full Idea: Frege's Constraint says if a subject believes an object is both F and not-F (as in 'Frege cases'), then the subject thinks of that object under distinct modes of presentation. Having distinct mental files of the object is sufficient to generate this. | |
| From: François Recanati (Mental Files in Flux [2016], Pref) | |
| A reaction: [compressed] When you look at how many semantic puzzles (notably from Frege and Kripke) are solved by the existence of labelled mental files, the case for them is overwhelming. |
| 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. |
| 22245 | A linguistic expression refers to what its associated mental file refers to [Recanati] |
| Full Idea: Mental files determine the reference of linguistic expressions: an expression refers to what the mental file associated with it refers to (at the time of tokening). | |
| From: François Recanati (Mental Files in Flux [2016], 5) | |
| A reaction: Invites the question of how mental files manage to refer, prior to the arrival of a linguistic expression. A mental file is usually fully of descriptions, but it might be no more than a label. |
| 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?' |
| 22250 | There are speakers' thoughts and hearers' thoughts, but no further thought attached to the utterance [Recanati] |
| Full Idea: There is the speaker's thought and the thought formed by the hearer. That is all there is. We don't need an additional entity, the thought expressed by the utterance. | |
| From: François Recanati (Mental Files in Flux [2016], 7.2) | |
| A reaction: This fits my view of propositions nicely. They are the two 'thoughts'. The notion of some further abstract 'proposition' with its own mode of independent existence strikes me as ontologically absurd. |
| 22249 | The Naive view of communication is that hearers acquire exactly the thoughts of the speaker [Recanati] |
| Full Idea: The Naive Conception of Communication rests on the idea that communication is the replication of thoughts: the thought the hearer entertains when he understands what the speaker is saying is the very thought which the speaker expressed. | |
| From: François Recanati (Mental Files in Flux [2016], 7.1) | |
| A reaction: It is hard to believe that any modern thinker would believe such a view, given holistic views of language etc. |
| 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. |