20 ideas
| 1749 | If all laws were abolished, philosophers would still live as they do now [Aristippus elder] |
| Full Idea: If all laws were abolished, philosophers would still live as they do now. | |
| From: Aristippus the elder (fragments/reports [c.395 BCE]), quoted by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.4 | |
| A reaction: Presumably philosophers develop inner laws which other people lack. |
| 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. |
| 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. |
| 4921 | Quantum states in microtubules could bind brain activity to produce consciousness [Penrose] |
| Full Idea: I propose that microtubules in nerve cells could give rise to a stable quantum state that would bind the activity of brain cells throughout the cerebrum and in doing so give rise to consciousness. | |
| From: Roger Penrose (Could a computer ever understand? [1998], p.329) | |
| A reaction: This seems to offer a physical theory to account for the 'unity' of the mind (which so impressed Descartes), but I don't quite see why being aware of things would ensue from some 'quantum binding'. I daresay 'quantum binding' occurs in the Sun. |
| 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?' |
| 3558 | Only the Cyrenaics reject the idea of a final moral end [Aristippus elder, by Annas] |
| Full Idea: The Cyrenaics are the most radical ancient moral philosophers, since they are the only school explicitly to reject the importance of achieving an overall final end. | |
| From: report of Aristippus the elder (fragments/reports [c.395 BCE]) by Julia Annas - The Morality of Happiness 11.1 | |
| A reaction: This looks like dropping out, but it could also be Keats's 'negative capability', of simply participating in existence without needing to do anything about it. |
| 5835 | The road of freedom is the surest route to happiness [Aristippus elder, by Xenophon] |
| Full Idea: The surest road to happiness is not the path through rule nor through servitude, but through liberty. | |
| From: report of Aristippus the elder (fragments/reports [c.395 BCE]) by Xenophon - Memorabilia of Socrates 2.1.9 | |
| A reaction: The great anarchist slogan. Personally I don't believe it, because I agree a little with Hobbes that authority is required to make cooperation flourish, and that is essential for full happiness. If I were a slave, I would agree with Aristippus. |
| 3018 | People who object to extravagant pleasures just love money [Aristippus elder, by Diog. Laertius] |
| Full Idea: When blamed for buying expensive food he asked "Would you have bought it for just three obols?" When the person said yes, he said,"Then it is not that I am fond of pleasure, but that you are fond of money". | |
| From: report of Aristippus the elder (fragments/reports [c.395 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.7.4 |
| 1751 | Pleasure is the good, because we always seek it, it satisfies us, and its opposite is the most avoidable thing [Aristippus elder, by Diog. Laertius] |
| Full Idea: Pleasure is the good because we desire it from childhood, when we have it we seek nothing further, and the most avoidable thing is its opposite, pain. | |
| From: report of Aristippus the elder (fragments/reports [c.395 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.8 |
| 1755 | Errors result from external influence, and should be corrected, not hated [Aristippus elder, by Diog. Laertius] |
| Full Idea: Errors ought to meet with pardon, for a man does not err intentionally, but influenced by some external circumstances. We should not hate someone who has erred, but teach him better. | |
| From: report of Aristippus the elder (fragments/reports [c.395 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.9 |
| 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. |