22 ideas
| 22396 | We take courage, temperance, wisdom and justice as moral, but Aristotle takes wisdom as intellectual [Foot] |
| Full Idea: For us there are four cardinal moral virtues: courage, temperance, wisdom and justice. But Aristotle and Aquinas call only three of these virtues moral virtues; practical wisdom (phronesis, prudentia) they class with the intellectual virtues. | |
| From: Philippa Foot (Virtues and Vices [1978], p.2) | |
| A reaction: I'm not sure about 'for us'. How many of us rank temperance as a supreme virtue? Aristotle ranks phronesis (which I think of as 'common sense') as the key enabler of the moral virtues, making it unlike the other intellectual virtues. |
| 22397 | Wisdom is open to all, and not just to the clever or well trained [Foot] |
| Full Idea: Knowledge that can be acquired only by someone who is clever or who has access to special training is not counted as part of wisdom. | |
| From: Philippa Foot (Virtues and Vices [1978], p.6) | |
| A reaction: Consider Pierre's peasant friend Platon Karatayev in 'War and Peace'. I assume 'special training' rules out anyone with a philosophy degree. |
| 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. |
| 17783 | A number is not a multitude, but a unified ratio between quantities [Newton] |
| Full Idea: By a Number we understand not so much a Multitude of Unities, as the abstracted Ratio of any Quantity to another Quantity of the same Kind, which we take for unity. | |
| From: Isaac Newton (Universal Arithmetick [1669]), quoted by John Mayberry - What Required for Foundation for Maths? p.407-2 | |
| A reaction: This needs a metaphysics of 'kinds' (since lines can't have ratios with solids). Presumably Newton wants the real numbers to be more basic than the natural numbers. This is the transition from Greek to modern. |
| 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. |
| 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?' |
| 22402 | Most people think virtues can be displayed in bad actions [Foot] |
| Full Idea: Hardly anyone sees any difficulty in the thought that virtues may sometimes be displayed in bad actions. The courage of the villain can be spoken of as quite unproblematic. | |
| From: Philippa Foot (Virtues and Vices [1978], III) | |
| A reaction: She cites Peter Geach as a sole opponent of this view. The courage of the entire German army in WWII seems to fall into this category. The boldness of villains has to impress the virtuous but timid. |
| 23145 | Virtues are intended to correct design flaws in human beings [Foot, by Driver] |
| Full Idea: A popular view (expressed by Philippa Foot) is that the virtues work to 'correct' for the baser human impulses and motives. …Virtues are solutions to design flaws in human beings. | |
| From: report of Philippa Foot (Virtues and Vices [1978]) by Julia Driver - The Virtues and Human Nature 1 | |
| A reaction: Quite a plausible thought. Not so much design flaws, though, as natural traits of character that suited hunter gatherers but not modern cosmopolitan capitalists. Driver disagrees. |
| 22401 | Actions can be in accordance with virtue, but without actually being virtuous [Foot] |
| Full Idea: Some actions are in accordance with virtue without requiring virtue for their performance, whereas others are both in accordance with virtue and such as to show possession of a virtue. | |
| From: Philippa Foot (Virtues and Vices [1978], p.13) | |
| A reaction: She cites the case of an honest trader, who is honest because of self-interest. She is disentangling Kant from his daft idea that only dutiful (and reluctant) actions are virtuous. Kant was only thinking of 'in accordance' cases. |
| 22398 | Virtues are corrective, to resist temptation or strengthen motivation [Foot] |
| Full Idea: The virtues are corrective, each one standing at a point at which there is some temptation to be resisted or deficiency of motivation to be made good. | |
| From: Philippa Foot (Virtues and Vices [1978], II) | |
| A reaction: A beautifully simple and accurate observation, which I don't remember meeting in Aristotle (...though she cites him as saying that virtues concern what is difficult for us). Justice and charity are given as examples of inadequate motivation. |
| 22403 | Temperance is not a virtue if it results from timidity or excessive puritanism [Foot] |
| Full Idea: In some people temperance is not a virtue, but is rather connected with timidity or with a grudging attitude to the acceptance of good things. | |
| From: Philippa Foot (Virtues and Vices [1978], III) | |
| A reaction: Timidity seems right. The grudging attitude may result from some larger doubts about pleasure, which could be plausible. |
| 22400 | Courage overcomes the fears which should be overcome, and doesn't overvalue personal safety [Foot] |
| Full Idea: The fears that count against a man's courage are those that we think he should overcome, and among them, in a special class, those that reflect the fact that he values his safety too much. | |
| From: Philippa Foot (Virtues and Vices [1978], II) | |
| A reaction: I think that sentence tells us more accurately what courage is than anything in Aristotle's discussion. Ask yourself which of your fears really ought to be overcome, and particularly beware of over-valuing your own safety. But stay safe if you can! |
| 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. |