25 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. |
| 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. |
| 16405 | To understand a name (unlike a description) picking the thing out is sufficient? [Stalnaker] |
| Full Idea: If we ask 'what must you know to understand a name?', the naïve answer is that one must know who or what it names - nothing more. (But no one would give this answer about what is needed to understand a definite description). | |
| From: Robert C. Stalnaker (Reference and Necessity [1997], 4) | |
| A reaction: Presumably this is naive because names can be full of meaning ('the Empress'), or description and reference together ('there's the man who robbed me') and so on. It's a nice starting point though. A number can serve as a name. |
| 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. |
| 16407 | Possible worlds allow separating all the properties, without hitting a bare particular [Stalnaker] |
| Full Idea: The possible worlds framework suggests a way to express the idea that a particular is conceptually separable from its properties without relying on the rejected picture of a bare particular. | |
| From: Robert C. Stalnaker (Reference and Necessity [1997], 5) | |
| A reaction: As I read him, Stalnaker's proposal just comes down to replacing each property in turn with a different one. 'Strip away' red by making it green. It being green in w1 doesn't throw extra light. Can it be a bare particular in w37? |
| 16397 | If it might be true, it might be true in particular ways, and possible worlds describe such ways [Stalnaker] |
| Full Idea: A clarifying assumption is that if something might be true, then it might be true in some particular way. …Possible worlds begin from this, and the assumption that what might be true can be described as how a possibility might be realised. | |
| From: Robert C. Stalnaker (Reference and Necessity [1997], 2) | |
| A reaction: This is a leading practitioner giving his best shot at explaining the rationale of the possible worlds approach, addressed to many sceptics. Most sceptics, I think, don't understand the qualifications the practitioners apply to their game. |
| 16399 | Possible worlds are ontologically neutral, but a commitment to possibilities remains [Stalnaker] |
| Full Idea: I argue for the metaphysical neutrality of the possible worlds framework, but I do not suggest that its use is free of ontological commitment to possibilities (ways things might be, counterfactual situations, possible states of worlds). | |
| From: Robert C. Stalnaker (Reference and Necessity [1997], 2) | |
| A reaction: Glad to hear this, as I have always been puzzled at possible aspirations to eliminate modality (such as possibility) by introducing 'possible' worlds. Commitment to possibilities I take to be basic and unavoidable. |
| 16398 | Possible worlds allow discussion of modality without controversial modal auxiliaries [Stalnaker] |
| Full Idea: The main benefit of the possible worlds move is to permit one to paraphrase modal claims in an extensional language that has quantifiers, but no modal auxiliaries, so the semantic stucture of modal discourse can be discussed without the controversies. | |
| From: Robert C. Stalnaker (Reference and Necessity [1997], 2) | |
| A reaction: The strategy introduces the controversy of possible worlds instead, but since they just boil down to collections of objects with properties, classical logic can reign. Possible worlds are one strategy alongside many others. |
| 16396 | Kripke's possible worlds are methodological, not metaphysical [Stalnaker] |
| Full Idea: The possible worlds framework that Kripke introduces should be understood not as a metaphysical theory, but as a methodological framework. | |
| From: Robert C. Stalnaker (Reference and Necessity [1997], Intro) | |
| A reaction: That's certainly how I see possible worlds. I lose no sleep over whether they exist. I just take a set of possible worlds to be like cells in a spreadsheet, or records in a database. |
| 16408 | Rigid designation seems to presuppose that differing worlds contain the same individuals [Stalnaker] |
| Full Idea: A rigid designator is a designator that denotes the same individual in all possible worlds; doesn't this presuppose that the same individuals can be found in differing possible worlds? | |
| From: Robert C. Stalnaker (Reference and Necessity [1997], 5) | |
| A reaction: This is part of Stalnaker's claim that Kripke already has a metaphysics in place when he starts on his semantics and his theory of reference. Kripke needs a global domain, not a variable domain. Possibilities suggest variable domains to me. |
| 19261 | Understanding is seeing coherent relationships in the relevant information [Kvanvig] |
| Full Idea: What is distinctive about understanding (after truth is satisfied) is the internal seeing or appreciating of explanatory and other coherence-inducing relationships in a body of information that is crucial for understanding. | |
| From: Jonathan Kvanvig (The Value of Knowledge and the Pursuit of Understanding [2003], 198), quoted by Anand Vaidya - Understanding and Essence 'Distinction' | |
| A reaction: For me this ticks exactly the right boxes. Coherent explanations are what we want. The hardest part is the ensure their truth. Kvanvig claims this is internal, so we can understand even if, Gettier-style, our external connections are lucky. |
| 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. |
| 16406 | If you don't know what you say you can't mean it; what people say usually fits what they mean [Stalnaker] |
| Full Idea: If you don't know what you are saying then you don't mean what you say, and also speakers generally mean what they say (in that what they say coincides with what they mean). | |
| From: Robert C. Stalnaker (Reference and Necessity [1997], 4) | |
| A reaction: Both these thoughts seem completely acceptable and correct, but rely on something called 'meaning' that is distinct from saying. I would express this in terms of propositions, which I take to be mental events. |
| 16404 | In the use of a name, many individuals are causally involved, but they aren't all the referent [Stalnaker] |
| Full Idea: The causal theory of reference is criticised for vagueness. Causal connections are ubiquitous, and there are obviously many individuals that are causally implicated in the speaker's use of a name, but they aren't all plausible candidates for the referent. | |
| From: Robert C. Stalnaker (Reference and Necessity [1997], 4) | |
| A reaction: This seems to be a very good objection. Among all the causal links back to some baptised object, we have to pick out the referential link, which needs a criterion. |
| 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?' |
| 16403 | 'Descriptive' semantics gives a system for a language; 'foundational' semantics give underlying facts [Stalnaker] |
| Full Idea: 'Descriptive' semantics gives a semantics for the language without saying how practice explains why the semantics is right; …'foundational' semantics concerns the facts that give expressions their semantic values. | |
| From: Robert C. Stalnaker (Reference and Necessity [1997], §1) | |
| A reaction: [compressed] Sounds parallel to the syntax/semantics distinction, or proof-theoretical and semantic validity. Or the sense/reference distinction! Or object language/metalanguage. Shall I go on? |
| 16401 | To understand an utterance, you must understand what the world would be like if it is true [Stalnaker] |
| Full Idea: To understand what is said in an utterance of 'The first dog born at sea was a basset hound', one needs to know what the world would have been like in order for what was said in that utterance to be true. | |
| From: Robert C. Stalnaker (Reference and Necessity [1997], 3) | |
| A reaction: Put like that, the idea is undeniable. Understanding involves truth conditions. Does mean involve the understanding of the meaning. What do you understand when you understand a sentence? Just facts about dogs? Or something in the sentence? |
| 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. |