50 ideas
| 13252 | Some truths have true negations [Beall/Restall] |
| Full Idea: Dialetheism is the view that some truths have true negations. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 7.4) | |
| A reaction: The important thing to remember is that they are truths. Thus 'Are you feeling happy?' might be answered 'Yes and no'. |
| 13247 | A truthmaker is an object which entails a sentence [Beall/Restall] |
| Full Idea: The truthmaker thesis is that an object is a truthmaker for a sentence if and only if its existence entails the sentence. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.5.3) | |
| A reaction: The use of the word 'object' here is even odder than usual, and invites many questions. And the 'only if' seems peculiar, since all sorts of things can make a sentence true. 'There is someone in the house' for example. |
| 13249 | (∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically [Beall/Restall] |
| Full Idea: The inference of 'distribution' (∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically. It is straightforward to construct a 'stage' at which the LHS is true but the RHS is not. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 6.1.2) | |
| A reaction: This seems to parallel the iterative notion in set theory, that you must construct your hierarchy. All part of the general 'constructivist' approach to things. Is some kind of mad platonism the only alternative? |
| 13242 | It's 'relevantly' valid if all those situations make it true [Beall/Restall] |
| Full Idea: The argument from P to A is 'relevantly' valid if and only if, for every situation in which each premise in P is true, so is A. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.2) | |
| A reaction: I like the idea that proper inference should have an element of relevance to it. A falsehood may allow all sorts of things, without actually implying them. 'Situations' sound promising here. |
| 13243 | Excluded middle must be true for some situation, not for all situations [Beall/Restall] |
| Full Idea: Relevant logic endorses excluded middle, ..but says instances of the law may fail. Bv¬B is true in every situation that settles the matter of B. It is necessary that there is some such situation. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.2) | |
| A reaction: See next idea for the unusual view of necessity on which this rests. It seems easier to assert something about all situations than just about 'some' situation. |
| 13245 | Relevant consequence says invalidity is the conclusion not being 'in' the premises [Beall/Restall] |
| Full Idea: Relevant consequence says the conclusion of a relevantly invalid argument is not 'carried in' the premises - it does not follow from the premises. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.3.3) | |
| A reaction: I find this appealing. It need not invalidate classical logic. It is just a tougher criterion which is introduced when you want to do 'proper' reasoning, instead of just playing games with formal systems. |
| 13246 | Relevant logic does not abandon classical logic [Beall/Restall] |
| Full Idea: We have not abandoned classical logic in our acceptance of relevant logic. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.4) | |
| A reaction: It appears that classical logic is straightforwardly accepted, but there is a difference of opinion over when it is applicable. |
| 13254 | A doesn't imply A - that would be circular [Beall/Restall] |
| Full Idea: We could reject the inference from A to itself (on grounds of circularity). | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 8) | |
| A reaction: [Martin-Meyer System] 'It's raining today'. 'Are you implying that it is raining today?' 'No, I'm SAYING it's raining today'. Logicians don't seem to understand the word 'implication'. Logic should capture how we reason. Nice proposal. |
| 13255 | Relevant logic may reject transitivity [Beall/Restall] |
| Full Idea: Some relevant logics reject transitivity, but we defend the classical view. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 8) | |
| A reaction: [they cite Neil Tennant for this view] To reject transitivity (A?B ? B?C ? A?C) certainly seems a long way from classical logic. But in everyday inference Tennant's idea seems good. The first premise may be irrelevant to the final conclusion. |
| 13250 | Free logic terms aren't existential; classical is non-empty, with referring names [Beall/Restall] |
| Full Idea: A logic is 'free' to the degree it refrains from existential import of its singular and general terms. Classical logic must have non-empty domain, and each name must denote in the domain. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 7.1) | |
| A reaction: My intuition is that logic should have no ontology at all, so I like the sound of 'free' logic. We can't say 'Pegasus does not exist', and then reason about Pegasus just like any other horse. |
| 13235 | Logic studies consequence; logical truths are consequences of everything, or nothing [Beall/Restall] |
| Full Idea: Nowadays we think of the consequence relation itself as the primary subject of logic, and view logical truths as degenerate instances of this relation. Logical truths follow from any set of assumptions, or from no assumptions at all. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.2) | |
| A reaction: This seems exactly right; the alternative is the study of necessities, but that may not involve logic. |
| 13238 | Syllogisms are only logic when they use variables, and not concrete terms [Beall/Restall] |
| Full Idea: According to the Peripatetics (Aristotelians), only syllogistic laws stated in variables belong to logic, and not their applications to concrete terms. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.5) | |
| A reaction: [from Lukasiewicz] Seems wrong. I take it there are logical relations between concrete things, and the variables are merely used to describe these relations. Variables lack the internal powers to drive logical necessities. Variables lack essence! |
| 13234 | The view of logic as knowing a body of truths looks out-of-date [Beall/Restall] |
| Full Idea: Through much of the 20th century the conception of logic was inherited from Frege and Russell, as knowledge of a body of logical truths, as arithmetic or geometry was a knowledge of truths. This is odd, and a historical anomaly. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.2) | |
| A reaction: Interesting. I have always taken this idea to be false. I presume logic has minimal subject matter and truths, and preferably none at all. |
| 13232 | Logic studies arguments, not formal languages; this involves interpretations [Beall/Restall] |
| Full Idea: Logic does not study formal languages for their own sake, which is formal grammar. Logic evaluates arguments, and primarily considers formal languages as interpreted. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.1) | |
| A reaction: Hodges seems to think logic just studies formal languages. The current idea strikes me as a much more sensible view. |
| 13241 | The model theory of classical predicate logic is mathematics [Beall/Restall] |
| Full Idea: The model theory of classical predicate logic is mathematics if anything is. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 4.2.1) | |
| A reaction: This is an interesting contrast to the claim of logicism, that mathematics reduces to logic. This idea explains why students of logic are surprised to find themselves involved in mathematics. |
| 13253 | There are several different consequence relations [Beall/Restall] |
| Full Idea: We are pluralists about logical consequence because we take there to be a number of different consequence relations, each reflecting different precisifications of the pre-theoretic notion of deductive logical consequence. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 8) | |
| A reaction: I don't see how you avoid the slippery slope that leads to daft logical rules like Prior's 'tonk' (from which you can infer anything you like). I say that nature imposes logical conquence on us - but don't ask me to prove it. |
| 13240 | A sentence follows from others if they always model it [Beall/Restall] |
| Full Idea: The sentence X follows logically from the sentences of the class K if and only if every model of the class K is also a model of the sentence X. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 3.2) | |
| A reaction: This why the symbol |= is often referred to as 'models'. |
| 13236 | Logical truth is much more important if mathematics rests on it, as logicism claims [Beall/Restall] |
| Full Idea: If mathematical truth reduces to logical truth then it is important what counts as logically true, …but if logicism is not a going concern, then the body of purely logical truths will be less interesting. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.2) | |
| A reaction: Logicism would only be one motivation for pursuing logical truths. Maybe my new 'Necessitism' will derive the Peano Axioms from broad necessary truths, rather than from logic. |
| 13237 | Preface Paradox affirms and denies the conjunction of propositions in the book [Beall/Restall] |
| Full Idea: The Paradox of the Preface is an apology, that you are committed to each proposition in the book, but admit that collectively they probably contain a mistake. There is a contradiction, of affirming and denying the conjunction of propositions. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.4) | |
| A reaction: This seems similar to the Lottery Paradox - its inverse perhaps. Affirm all and then deny one, or deny all and then affirm one? |
| 594 | Speusippus suggested underlying principles for every substance, and ended with a huge list [Speussipus, by Aristotle] |
| Full Idea: Speusippus suggested principles for each substance, including principles for numbers, magnitude and the soul. He thus arrived at no mean list of substances. | |
| From: report of Speussipus (thirty titles (lost) [c.367 BCE]) by Aristotle - Metaphysics 1028b |
| 13244 | Relevant necessity is always true for some situation (not all situations) [Beall/Restall] |
| Full Idea: In relevant logic, the necessary truths are not those which are true in every situation; rather, they are those for which it is necessary that there is a situation making them true. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.2) | |
| A reaction: This seems to rest on the truthmaker view of such things, which I find quite attractive (despite Merricks's assault). Always ask what is making some truth necessary. This leads you to essences. |
| 13239 | Judgement is always predicating a property of a subject [Beall/Restall] |
| Full Idea: All judgement, for Kant, is essentially the predication of some property to some subject. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.5) | |
| A reaction: Presumably the denial of a predicate could be a judgement, or the affirmation of ambiguous predicates? |
| 13248 | We can rest truth-conditions on situations, rather than on possible worlds [Beall/Restall] |
| Full Idea: Situation semantics is a variation of the truth-conditional approach, taking the salient unit of analysis not to be the possible world, or some complete consistent index, but rather the more modest 'situation'. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.5.4) | |
| A reaction: When I read Davidson (and implicitly Frege) this is what I always assumed was meant. The idea that worlds are meant has crept in to give truth conditions for modal statements. Hence situation semantics must cover modality. |
| 13233 | Propositions commit to content, and not to any way of spelling it out [Beall/Restall] |
| Full Idea: Our talk of propositions expresses commitment to the general notion of content, without a commitment to any particular way of spelling this out. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.1) | |
| A reaction: As a fan of propositions I like this. It leaves open the question of whether the content belongs to the mind or the language. Animals entertain propositions, say I. |
| 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. |
| 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? |
| 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' |
| 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? |
| 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. |
| 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. |
| 2632 | Speusippus said things were governed by some animal force rather than the gods [Speussipus, by Cicero] |
| Full Idea: Speusippus, following his uncle Plato, held that all things were governed by some kind of animal force, and tried to eradicate from our minds any notion of the gods. | |
| From: report of Speussipus (thirty titles (lost) [c.367 BCE]) by M. Tullius Cicero - On the Nature of the Gods ('De natura deorum') I.33 |
| 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. |