23 ideas
| 18274 | Analysis complicates a statement, but only as far as the complexity of its meaning [Wittgenstein] |
| Full Idea: Analysis makes the statement more complicated than it was; but it cannot and ought not to make it more complicated than its meaning (Bedeutung) was to begin with. When the statement is as complex as its meaning, then it is completely analysed. | |
| From: Ludwig Wittgenstein (Notebooks 1914-1916 [1915], 46e) | |
| A reaction: But how do you assess how complex the 'Bedeutung' was before you started? |
| 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. |
| 16908 | We can dispense with self-evidence, if language itself prevents logical mistakes [Jeshion on Wittgenstein] |
| Full Idea: The 'self-evidence' of which Russell talks so much can only be dispensed with in logic if language itself prevents any logical mistake. | |
| From: comment on Ludwig Wittgenstein (Notebooks 1914-1916 [1915], 4) by Robin Jeshion - Frege's Notion of Self-Evidence 4 | |
| A reaction: Jeshion presents this as a key idea, turning against Frege, and is the real source of the 'linguistic turn' in philosophy. If self-evidence is abandoned, then language itself is the guide to truth, so study language. I think I prefer Frege. See Quine? |
| 18276 | A statement's logical form derives entirely from its constituents [Wittgenstein] |
| Full Idea: The logical form of the statement must already be given in the forms of its constituents. | |
| From: Ludwig Wittgenstein (Notebooks 1914-1916 [1915], 23e) | |
| A reaction: This would evidently require each constituent to have a 'logical form'. It is hard to see what that could beyond its part of speech. Do two common nouns have the same logical form? |
| 6563 | 'And' and 'not' are non-referring terms, which do not represent anything [Wittgenstein, by Fogelin] |
| Full Idea: Wittgenstein's 'fundamental idea' is that the 'and' and 'not' which guarantee the truth of "not p and not-p" are meaningful, but do not get their meaning by representing or standing for or referring to some kind of entity; they are non-referring terms. | |
| From: report of Ludwig Wittgenstein (Notebooks 1914-1916 [1915], §37) by Robert Fogelin - Walking the Tightrope of Reason Ch.1 | |
| A reaction: Wittgenstein then defines the terms using truth tables, to show what they do, rather than what they stand for. This seems to me to be a candidate for the single most important idea in the history of the philosophy of logic. |
| 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' |
| 23472 | The sense of propositions relies on the world's basic logical structure [Wittgenstein] |
| Full Idea: In order for a proposition to be CAPABLE of making sense, the world must already have the logical structure it has. The logic of the world is prior to all truth and falsehood. | |
| From: Ludwig Wittgenstein (Notebooks 1914-1916 [1915], p.14c) | |
| A reaction: It seems that in Tractatus it is propositions about facts which are true or false, but prior to the facts are substance and the objects, and it is there that we find the logical structure of the world. I see this view as modern stoicism. |
| 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. |
| 23500 | My main problem is the order of the world, and whether it is knowable a priori [Wittgenstein] |
| Full Idea: The great problem around which everything turns that I write is: is there an order in the world a priori, and if so what does it consist in? | |
| From: Ludwig Wittgenstein (Notebooks 1914-1916 [1915], 15.06.01) | |
| A reaction: Morris identifies this as a 'Kantian question'. I trace it back to stoicism. This question has never bothered me. It just seems weird to think that you can infer reality from the examination of your own thinking. Perhaps I should take it more seriously? |
| 22323 | The philosophical I is the metaphysical subject, the limit - not a part of the world [Wittgenstein] |
| Full Idea: The philosophical I is not the man, not the human body, or the human soul of wh9ch psychology treats, but the metaphysical subject, the limit - not a part of the world. | |
| From: Ludwig Wittgenstein (Notebooks 1914-1916 [1915], 1916. 2 Sep), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 58 Intro | |
| A reaction: This is to treat the self as a phenomenon of thought, rather than of a human being. So if a machine could think, would it hence necessarily have a metaphysical self? |
| 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. |
| 23481 | Propositions assemble a world experimentally, like the model of a road accident [Wittgenstein] |
| Full Idea: In the proposition a world is as it were put together experimentally. (As when in the law court in Paris a motor-car accident is represented by means of dolls, etc). | |
| From: Ludwig Wittgenstein (Notebooks 1914-1916 [1915], 14.09.29) | |
| A reaction: [see Tractatus 4.031] This is the first appearance of LW's picture (or model) theory of meaning. It may well be the best theory of meaning anyone has come up with, since meaning being out in the world strikes me as absurd. |
| 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?' |
| 4678 | Absolute prohibitions are the essence of ethics, and suicide is the most obvious example [Wittgenstein] |
| Full Idea: If suicide is allowed, then everything is allowed. If anything is not allowed, then suicide is not allowed. This throws a light on the nature of ethics, for suicide is, so to speak, the elementary sin. | |
| From: Ludwig Wittgenstein (Notebooks 1914-1916 [1915], end), quoted by Jonathan Glover - Causing Death and Saving Lives §13 | |
| A reaction: This reveals the religious streak in Wittgenstein. I am reluctant to judge suicide, but this seems wrong. Should a 'jumper' worry if they land on someone else and kill them? Of course they should. |
| 16697 | Time is independent of motion, because God could stop everything for a short or long time [Crathorn, by Pasnau] |
| Full Idea: Suppose God annihilates everything, and then creates something new. The vacant interval could last a shorter or longer time, so there are facts about time independent of facts about motion. | |
| From: report of William Crathorn (Sentences [1335], I.16, concl.2) by Robert Pasnau - Metaphysical Themes 1274-1671 18.2 | |
| A reaction: Not very persuasive if God is in some way 'timeless'. Crathorn would have loved Shoemaker's argument, where motionless time is the best explanation, rather than a possible explanation. |
| 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. |