41 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. |
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. |
9224 | Proceduralism offers a version of logicism with no axioms, or objects, or ontological commitment [Fine,K] |
Full Idea: My Proceduralism offers axiom-free foundations for mathematics. Axioms give way to the stipulation of procedures. We obtain a form of logicism, but with a procedural twist, and with a logic which is ontologically neutral, and no assumption of objects. | |
From: Kit Fine (Our Knowledge of Mathematical Objects [2005], 1) | |
A reaction: [See Ideas 9222 and 9223 for his Proceduralism] Sounds like philosophical heaven. We get to take charge of mathematics, without the embarrassment of declaring ourselves to be platonists. Someone, not me, should evaluate this. |
9222 | The objects and truths of mathematics are imperative procedures for their construction [Fine,K] |
Full Idea: I call my new approach to mathematics 'proceduralism'. It agrees with Hilbert and Poincaré that the objects and truths are postulations, but takes them to be imperatival rather than indicative in form; not propositions, but procedures for construction. | |
From: Kit Fine (Our Knowledge of Mathematical Objects [2005], Intro) | |
A reaction: I'm not sure how an object or a truth can be a procedure, any more than a house can be a procedure. If a procedure doesn't have a product then it is an idle way to pass the time. The view seems to be related to fictionalism. |
9223 | My Proceduralism has one simple rule, and four complex rules [Fine,K] |
Full Idea: My Proceduralism has one simple rule (introduce an object), and four complex rules: Composition (combining two procedures), Conditionality (if A, do B), Universality (do a procedure for every x), and Iteration (rule to keep doing B). | |
From: Kit Fine (Our Knowledge of Mathematical Objects [2005], 1) | |
A reaction: It sounds like a highly artificial and private game which Fine has invented, but he claims that this is the sort of thing that practising mathematicians have always done. |
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?' |
7222 | It is a crime for someone with a violent disposition to get drunk [Mill] |
Full Idea: The making himself drunk, in a person whom drunkenness excites to do harm to others, is a crime against others. | |
From: John Stuart Mill (On Liberty [1857], Ch.5) | |
A reaction: This principle (based on knowing your own dispositions) is a very good account of the ethics drunkenness. We have a moral duty to know and remember our own dispositions. Violent people should avoid arguments as well as alcohol. |
7214 | Ethics rests on utility, which is the permanent progressive interests of people [Mill] |
Full Idea: I regard utility as the ultimate appeal on all ethical questions; but it must be utility in the largest sense, grounded on the permanent interests of a man as a progressive being. | |
From: John Stuart Mill (On Liberty [1857], Ch.1) | |
A reaction: Mill, writing in praise of personal liberty, is desperate to introduce a paternalistic element into his politics, and the 'maximisation of happiness' will justify such paternalism, while his basic liberal principle (Idea 7211) won't. Mill's Dilemma. |
7212 | Individuals have sovereignty over their own bodies and minds [Mill] |
Full Idea: Over himself, over his own body and mind, the individual is sovereign. | |
From: John Stuart Mill (On Liberty [1857], Ch.1) | |
A reaction: If I should not even think about evil deeds, then neither should you. I would prevent you if I could. I would prevent you from drinking yourself to death, if I could. It is just that intrusions into private lives leads to greater trouble. |
7210 | The will of the people is that of the largest or most active part of the people [Mill] |
Full Idea: The will of the people practically means the will of the most numerous or the most active part of the people. | |
From: John Stuart Mill (On Liberty [1857], Ch.1) | |
A reaction: Hence the nicely coined modern phrase 'the silent majority', on whose behalf certain politicians, usually conservative, offer to speak. It is unlikely that the silent majority are actually deeply opposed to the views of the very active part. |
7227 | It is evil to give a government any more power than is necessary [Mill] |
Full Idea: Government interference should be restricted because of the great evil of adding unnecessarily to its power. | |
From: John Stuart Mill (On Liberty [1857], Ch.5) | |
A reaction: This would need justification, because it might be replied that individuals should not have unnecessary power either. The main problem is that governments have armies, police and money. |
7228 | Individuals often do things better than governments [Mill] |
Full Idea: Government power should be restricted because things are often done better by individuals. | |
From: John Stuart Mill (On Liberty [1857], Ch.5) | |
A reaction: This contains some truth, but it is obvious that innumerable things can be done better by governments, and also (and more importantly) that innumerable other good things might be done by governments which individuals can't be bothered to do. |
7230 | Aim for the maximum dissemination of power consistent with efficiency [Mill] |
Full Idea: The safest practical ideal is to aim for the greatest dissemination of power consistent with efficiency. | |
From: John Stuart Mill (On Liberty [1857], Ch.5) | |
A reaction: This is a very nice principle, which I would think desirable within an institution as well as on the scale of the state. I am becoming a fan of Mill's politics. I still say that freedom is an overrated virtue, so efficiency must be underrated. |
20515 | Maximise happiness by an area of strict privacy, and an area of utilitarian interventions [Mill, by Wolff,J] |
Full Idea: For Mill the greatest happiness will be achieved by giving people a private sphere of interests where no intervention is permitted, while allowing a public sphere where intervention is possible, but only on utilitarian grounds. | |
From: report of John Stuart Mill (On Liberty [1857]) by Jonathan Wolff - An Introduction to Political Philosophy (Rev) 4 'Liberty' | |
A reaction: This is probably standard liberal practice nowadays. Freely consenting adult sexual activity is agreed to be wholly private. At least some lip-service is paid to increasing happiness when government intervenes. |
7229 | People who transact their own business will also have the initiative to control their government [Mill] |
Full Idea: A people accustomed to transacting their own business is certain to be free; it will never let itself be enslaved by any man or body of men because these are able to seize and pull the reins of the central administration. | |
From: John Stuart Mill (On Liberty [1857], Ch.5) | |
A reaction: He makes reference to Americans. This is an important idea, because it shows that democratic control is not just a matter of elections (which can be abolished or suborned), but is also a characteristic of a certain way of life. |
7211 | Prevention of harm to others is the only justification for exercising power over people [Mill] |
Full Idea: The only purpose for which power can be rightfully exercised over any member of a civilised community, against his will, is to prevent harm to others; his own good, either physical or moral, is not a sufficient warrant. | |
From: John Stuart Mill (On Liberty [1857], Ch.1) | |
A reaction: This is the key idea in Mill's liberalism, though he goes on to offer some qualifications of this absolute prohibition. I don't disagree with this principle, but there may be a lot more indirect harm than we realise (eg. in allowing liberal sex or drugs). |
7231 | The worth of a State, in the long run, is the worth of the individuals composing it [Mill] |
Full Idea: The worth of a State, in the long run, is the worth of the individuals composing it. | |
From: John Stuart Mill (On Liberty [1857], Ch.5) | |
A reaction: This is a key idea of liberalism, opposed to any idea that we should abandon our own value to that of our state. I agree, but communitarians can subscribe to this too, while disagreeing that maximum freedom is the strategy to follow. |
7217 | The main argument for freedom is that interference with it is usually misguided [Mill] |
Full Idea: The strongest of all the arguments against the interference of the public with purely personal conduct is that, when it does interfere, the odds are that it interferes wrongly, and in the wrong place. | |
From: John Stuart Mill (On Liberty [1857], Ch.4) | |
A reaction: This is also a well known objection to capital punishment. Generalised, well established, legal interferences are perhaps more likely to get it right than ad hoc decisions about individuals by individual officials. |
7213 | Liberty arises at the point where people can freely and equally discuss things [Mill] |
Full Idea: Liberty, as a principle, has no application to any state of things anterior to the time when mankind have become capable of being improved by free and equal discussion. | |
From: John Stuart Mill (On Liberty [1857], Ch.1) | |
A reaction: There is a Victorian (and Enlightenment) optimism here which a glimpse of the freedoms of the early twenty-first century might dampen. I doubt if Mill expected British tabloid newspapers, or porn on cable TV. Education and freedom connect. |
20516 | Mill defends freedom as increasing happiness, but maybe it is an intrinsic good [Wolff,J on Mill] |
Full Idea: Mill has presented liberty as instrumentally valuable, as a way of achieving the greatest possible happiness in society. But perhaps he should have argued that liberty is an intrinsic good, good in itself. | |
From: comment on John Stuart Mill (On Liberty [1857]) by Jonathan Wolff - An Introduction to Political Philosophy (Rev) 4 'Intrinsic' | |
A reaction: If freedom is intrinsically good, does this leave us (as Wolff warned earlier) unable to defend its value? Freedom isn't an intrinsic good for infants, so why should it be so for adults? Good because it brings happiness, or fulfils our nature? |
20517 | Utilitarianism values liberty, but guides us on which ones we should have or not have [Mill, by Wolff,J] |
Full Idea: Utilitarianism provides an account of what liberties we should and should not have. Mill argues we should be free to compete in trade, but not to use another's property without consent. Thus he sets limits to liberty, while paying it great respect. | |
From: report of John Stuart Mill (On Liberty [1857]) by Jonathan Wolff - An Introduction to Political Philosophy (Rev) 4 'Intrinsic' |
7215 | True freedom is pursuing our own good, while not impeding others [Mill] |
Full Idea: The only freedom which deserves the name, is that of pursuing our own good in our own way, so long as we do not attempt to deprive others of theirs, or impede their efforts to obtain it. | |
From: John Stuart Mill (On Liberty [1857], Ch.1) | |
A reaction: This principle will probably lead up a Prisoner's Dilemma cul-de-sac. The only freedom which deserves the name is the collective agreed freedom of a whole community to live well, when citizens volunteer to restrict their individual freedoms. |
7220 | Restraint for its own sake is an evil [Mill] |
Full Idea: All restraint, qua restraint, is an evil. | |
From: John Stuart Mill (On Liberty [1857], Ch.5) | |
A reaction: The ultimate justification for this is (presumably) utilitarian, but that would mean that there was nothing wrong with restraint if the person did not mind, or was not aware of the restraint. What is intrinsically wrong with restraint? |
7218 | Individuals are not accountable for actions which only concern themselves [Mill] |
Full Idea: My first maxim is that the individual is not accountable to society for his actions, in so far as these concern the interests of no person but himself. | |
From: John Stuart Mill (On Liberty [1857], Ch.5) | |
A reaction: This is a key idea of liberalism, and one which communitarians have doubts about (because it is almost impossible to perform an action which is of no interest, in the short or long term, to others). I share these doubts. |
7221 | Blocking entry to an unsafe bridge does not infringe liberty, since no one wants unsafe bridges [Mill] |
Full Idea: An official could turn a person back from an unsafe bridge without infringeing their liberty; for liberty consists in doing what one desires, and he does not desire to fall into the river. | |
From: John Stuart Mill (On Liberty [1857], Ch.5) | |
A reaction: Seems fair enough, but it justifies paternalist interference. The tricky one is where the official and the citizen disagree over what the citizen 'truly' desires. Asking people may involve too much time, but it could also involve too much effort. |
7223 | Pimping and running a gambling-house are on the border between toleration and restraint [Mill] |
Full Idea: A person being free to be a pimp, or to keep a gambling-house, lies on the exact boundary line between two principles, of toleration and of restraint. | |
From: John Stuart Mill (On Liberty [1857], Ch.5) | |
A reaction: Nothing illuminates a philosopher's principles more than for them to specify cases that lie on their borderlines. Both professions seem, unfortunately, to lead people into worse activities, such as violent bullying, or theft. Tricky.. |
7219 | Society can punish actions which it believes to be prejudicial to others [Mill] |
Full Idea: My second maxim is that for actions that are prejudicial to the interests of others, the individual is accountable, and subject to social or legal punishment, if society believes that this is requisite for its protection. | |
From: John Stuart Mill (On Liberty [1857], Ch.5) | |
A reaction: (wording compressed). The trouble with this would seem to be the possible disagreement between the individual and the society over whether the actions actually are prejudicial to others. It would justify a conservative society in being repressive. |
7226 | Benefits performed by individuals, not by government, help also to educate them [Mill] |
Full Idea: It is often desirable that beneficial things should be done by individuals, rather than by the government, as a means to their own mental education. | |
From: John Stuart Mill (On Liberty [1857], Ch.5) | |
A reaction: This raises the important danger, which even those on the political left must acknowledge, of the 'nanny state'. It offers a nicely paternalistic, and even patronising reason for giving people freedom, just as a parent might to a child. |
7224 | We need individual opinions and conduct, and State education is a means to prevent that [Mill] |
Full Idea: Individuality of character, and diversity in opinions and modes of conduct, involves diversity of education; a general State education is a mere contrivance for moulding people to be exactly like one another. | |
From: John Stuart Mill (On Liberty [1857], Ch.5) | |
A reaction: This strikes me as being particularly true with the advent in Britain of the National Curriculum in the early 1990s. However, if there is a pressure towards conformity in state education, private education is dominated by class and money. |
7225 | It is a crime to create a being who lacks the ordinary chances of a desirable existence [Mill] |
Full Idea: To bestow a life on someone which may be either a curse or a blessing, unless the being on whom it is to be bestowed will have at least the ordinary chances of a desirable existence, is a crime against that being. | |
From: John Stuart Mill (On Liberty [1857], Ch.5) | |
A reaction: This is the standard utilitarian attitude to engendering people. I think I have to agree. It is no argument against this to say that we value people with poor life prospects, once they have arrived. Altruism towards children may disguise selfish parents. |
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. |
7216 | The ethics of the Gospel has been supplemented by barbarous Old Testament values [Mill] |
Full Idea: To extract from the Gospel a body of ethical doctrine, has never been possible withouth eking it out from the Old Testament, that is, from a system elaborate indeed, but in many respects barbarous, and intended only for a barbarous people. | |
From: John Stuart Mill (On Liberty [1857], Ch.2) | |
A reaction: 'Barbarous' has a quaint Victorian ring to it, but his point is that the surviving teachings of Jesus are very thin and generalised. Christians would do better to expand their implications, than to borrow from the Old Testament. |