28 ideas
9065 | S5 collapses iterated modalities (◊□P→□P, and ◊◊P→◊P) [Keefe/Smith] |
Full Idea: S5 collapses iterated modalities (so ◊□P → □P, and ◊◊P → ◊P). | |
From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §5) | |
A reaction: It is obvious why this might be controversial, and there seems to be a general preference for S4. There may be confusions of epistemic and ontic (and even semantic?) possibilities within a single string of modalities. |
3340 | Von Neumann defines each number as the set of all smaller numbers [Neumann, by Blackburn] |
Full Idea: Von Neumann defines each number as the set of all smaller numbers. | |
From: report of John von Neumann (works [1935]) by Simon Blackburn - Oxford Dictionary of Philosophy p.280 |
3355 | Von Neumann wanted mathematical functions to replace sets [Neumann, by Benardete,JA] |
Full Idea: Von Neumann suggested that functions be pressed into service to replace sets. | |
From: report of John von Neumann (works [1935]) by José A. Benardete - Metaphysics: the logical approach Ch.23 |
22716 | Von Neumann defined ordinals as the set of all smaller ordinals [Neumann, by Poundstone] |
Full Idea: At age twenty, Von Neumann devised the formal definition of ordinal numbers that is used today: an ordinal number is the set of all smaller ordinal numbers. | |
From: report of John von Neumann (works [1935]) by William Poundstone - Prisoner's Dilemma 02 'Sturm' | |
A reaction: I take this to be an example of an impredicative definition (not predicating something new), because it uses 'ordinal number' in the definition of ordinal number. I'm guessing the null set gets us started. |
9064 | Objects such as a cloud or Mount Everest seem to have fuzzy boundaries in nature [Keefe/Smith] |
Full Idea: A common intuition is that a vague object has indeterminate or fuzzy spatio-temporal boundaries, such as a cloud. Mount Everest can only have arbitrary boundaries placed around it, so in nature it must have fuzzy boundaries. | |
From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §5) | |
A reaction: We would have to respond by questioning whether Everest counts precisely as an 'object'. At the microscopic or subatomic level it seems that virtually everything has fuzzy boundaries. Maybe boundaries don't really exist. |
9044 | If someone is borderline tall, no further information is likely to resolve the question [Keefe/Smith] |
Full Idea: If Tek is borderline tall, the unclarity does not seem to be epistemic, because no amount of further information about his exact height (or the heights of others) could help us decide whether he is tall. | |
From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §1) | |
A reaction: One should add also that information about social conventions or conventions about the usage of the word 'tall' will not help either. It seems fairly obvious that God would not know whether Tek is tall, so the epistemic view is certainly counterintuitive. |
9048 | The simplest approach, that vagueness is just ignorance, retains classical logic and semantics [Keefe/Smith] |
Full Idea: The simplest approach to vagueness is to retain classical logic and semantics. Borderline cases are either true or false, but we don't know which, and, despite appearances, vague predicates have well-defined extensions. Vagueness is ignorance. | |
From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §1) | |
A reaction: It seems to me that you must have a rather unhealthy attachment to the logicians' view of the world to take this line. It is the passion of the stamp collector, to want everything in sets, with neatly labelled properties, and inference lines marked out. |
9055 | The epistemic view of vagueness must explain why we don't know the predicate boundary [Keefe/Smith] |
Full Idea: A key question for the epistemic view of vagueness is: why are we ignorant of the facts about where the boundaries of vague predicates lie? | |
From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §2) | |
A reaction: Presumably there is a range of answers, from laziness, to inability to afford the instruments, to limitations on human perception. At the limit, with physical objects, how do we tell whether it is us or the object which is afflicted with vagueness? |
9049 | Supervaluationism keeps true-or-false where precision can be produced, but not otherwise [Keefe/Smith] |
Full Idea: The supervaluationist view of vagueness is that 'tall' comes out true or false on all the ways in which we can make 'tall' precise. There is a gap for borderline cases, but 'tall or not-tall' is still true wherever you draw a boundary. | |
From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §1) | |
A reaction: [Kit Fine is the spokesperson for this; it preserves classical logic, but not semantics] This doesn't seem to solve the problem of vagueness, but it does (sort of) save the principle of excluded middle. |
9056 | Vague statements lack truth value if attempts to make them precise fail [Keefe/Smith] |
Full Idea: The supervaluationist view of vagueness proposes that a sentence is true iff it is true on all precisifications, false iff false on all precisifications, and neither true nor false otherwise. | |
From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §3) | |
A reaction: This seems to be just a footnote to the Russell/Unger view, that logic works if the proposition is precise, but otherwise it is either just the mess of ordinary life, or the predicate doesn't apply at all. |
9058 | Some of the principles of classical logic still fail with supervaluationism [Keefe/Smith] |
Full Idea: Supervaluationist logic (now with a 'definite' operator D) fails to preserve certain classical principles about consequence and rules of inference. For example, reduction ad absurdum, contraposition, the deduction theorem and argument by cases. | |
From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §3) | |
A reaction: The aim of supervaluationism was to try to preserve some classical logic, especially the law of excluded middle, in the face of problems of vagueness. More drastic views, like treating vagueness as irrelevant to logic, or the epistemic view, do better. |
9059 | The semantics of supervaluation (e.g. disjunction and quantification) is not classical [Keefe/Smith] |
Full Idea: The semantics of supervaluational views is not classical. A disjunction can be true without either of its disjuncts being true, and an existential quantification can be true without any of its substitution instances being true. | |
From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §3) | |
A reaction: There is a vaguely plausible story here (either red or orange, but not definitely one nor tother; there exists an x, but which x it is is undecidable), but I think I will vote for this all being very very wrong. |
9060 | Supervaluation misunderstands vagueness, treating it as a failure to make things precise [Keefe/Smith] |
Full Idea: Why should we think vague language is explained away by how things would be if it were made precise? Supervaluationism misrepresents vague expressions, as vague only because we have not bothered to make them precise. | |
From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §3) | |
A reaction: The theory still leaves a gap where vagueness is ineradicable, so the charge doesn't seem quite fair. Logicians always yearn for precision, but common speech enjoys wallowing in a sea of easy-going vagueness, which works fine. |
9050 | A third truth-value at borderlines might be 'indeterminate', or a value somewhere between 0 and 1 [Keefe/Smith] |
Full Idea: One approach to predications in borderline cases is to say that they have a third truth value - 'neutral', 'indeterminate' or 'indefinite', leading to a three-valued logic. Or a degree theory, such as fuzzy logic, with infinite values between 0 and 1. | |
From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §1) | |
A reaction: This looks more like a strategy for computer programmers than for metaphysicians, as it doesn't seem to solve the difficulty of things to which no one can quite assign any value at all. Sometimes you can't be sure if an entity is vague. |
9061 | People can't be placed in a precise order according to how 'nice' they are [Keefe/Smith] |
Full Idea: There is no complete ordering of people by niceness, and two people could be both fairly nice, nice to intermediate degrees, while there is no fact of the matter about who is the nicer. | |
From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §4) | |
A reaction: This is a difficulty if you are trying to decide vague predicates by awarding them degrees of truth. Attempts to place a precise value on 'nice' seem to miss the point, even more than utilitarian attempts to score happiness. |
9062 | If truth-values for vagueness range from 0 to 1, there must be someone who is 'completely tall' [Keefe/Smith] |
Full Idea: Many-valued theories still seem to have a sharp boundary between sentences taking truth-value 1 and those taking value less than 1. So there is a last man in our sorites series who counts as 'completely tall'. | |
From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §4) | |
A reaction: Lovely. Completely nice, totally red, perfectly childlike, an utter mountain, one hundred per cent amused. The enterprise seems to have the same implausibility found in Bayesian approaches to assessing evidence. |
9063 | How do we decide if my coat is red to degree 0.322 or 0.321? [Keefe/Smith] |
Full Idea: What could determine which is the correct function, settling that my coat is red to degree 0.322 rather than 0.321? | |
From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §4) | |
A reaction: It is not just the uncertainty of placing the coat on the scale. The two ends of the scale have all the indeterminacy of being red rather than orange (or, indeed, pink). You are struggling to find a spot on the ruler, when the ruler is placed vaguely. |
9045 | Vague predicates involve uncertain properties, uncertain objects, and paradoxes of gradual change [Keefe/Smith] |
Full Idea: Three interrelated features of vague predicates such as 'tall', 'red', 'heap', 'child' are that they have borderline cases (application is uncertain), they lack well-defined extensions (objects are uncertain), and they're susceptible to sorites paradoxes. | |
From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §1) | |
A reaction: The issue will partly depend on what you think an object is: choose from bundles of properties, total denial, essential substance, or featureless substance with properties. The fungal infection of vagueness could creep in at any point, even the words. |
9047 | Many vague predicates are multi-dimensional; 'big' involves height and volume; heaps include arrangement [Keefe/Smith] |
Full Idea: Many vague predicates are multi-dimensional. 'Big' of people depends on both height and volume; 'nice' does not even have clear dimensions; whether something is a 'heap' depends both the number of grains and their arrangement. | |
From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §1) | |
A reaction: Anyone who was hoping for a nice tidy theory for this problem should abandon hope at this point. Huge numbers of philosophical problems can be simplified by asking 'what exactly do you mean here?' (e.g. tall or bulky?). |
9053 | If there is a precise borderline area, that is not a case of vagueness [Keefe/Smith] |
Full Idea: If a predicate G has a sharply-bounded set of cases falling in between the positive and negative, this shows that merely having borderline cases is not sufficient for vagueness. | |
From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §1) | |
A reaction: Thus you might have 'pass', 'fail' and 'take the test again'. But there seem to be two cases in the border area: will decide later, and decision seems impossible. And the sharp boundaries may be quite arbitrary. |
7590 | Consequentialism emphasises value rather than obligation in morality [Scruton] |
Full Idea: According to consequentialism, the fundamental concept of morality is not obligation (deontological ethics) but value (axiological ethics). | |
From: Roger Scruton (A Dictionary of Political Thought [1982], 'consequentialism') | |
A reaction: These two views could come dramatically apart, in wartime, or in big ecological crises, or in a family breakup, or in religious disputes. Having identified the pair so clearly, why can we not aim for a civilised (virtuous) balance between the two? |
7589 | Altruism is either emotional (where your interests are mine) or moral (where they are reasons for me) [Scruton] |
Full Idea: Two distinct motives go by the name of altruism: the emotions of liking, love and friendship, making another's interest automatically mine; and the moral motive of respect or considerateness, where another's interests become reasons for me, but not mine. | |
From: Roger Scruton (A Dictionary of Political Thought [1982], 'altruism') | |
A reaction: The second one has a strongly Kantian flavour, with its notion of impersonal duty. Virtue theorists will aspire to achieve the first state rather than the second, because good actions are then actively desired, and give pleasure to the doer. |
7595 | The idea of a right seems fairly basic; justice may be the disposition to accord rights to people [Scruton] |
Full Idea: The idea of a right seems to be as basic as any other; we might even define justice in terms of it, as the disposition to accord to every person his rights. | |
From: Roger Scruton (A Dictionary of Political Thought [1982], 'rights') | |
A reaction: I am inclined to think that a set of fairly pure values (such as equality, kindness, sympathy, respect) must be in place before the idea of a right would occur to anyone. Aristotle has a powerful moral sense, but rights for slaves don't cross his mind. |
7588 | Allegiance is fundamental to the conservative view of society [Scruton] |
Full Idea: Conservatives have made the concept of allegiance, conceived as a power, fundamental to their description of the experience of society | |
From: Roger Scruton (A Dictionary of Political Thought [1982], 'allegiance') | |
A reaction: This provokes the famous slogan of "My country - right or wrong!" However, the issue here is not going to be decided by a consequentialist analysis, but by a view a of human nature. I think I would want to carefully prise allegiance apart from loyalty. |
7594 | Democrats are committed to a belief and to its opposite, if the majority prefer the latter [Scruton] |
Full Idea: The paradox of democracy (emphasised by Rousseau) is that I am compelled by my belief in democracy to embrace conflicting - perhaps even contradictory - opinions. If I believe A, and the majority vote for B, I am committed to enacting them both. | |
From: Roger Scruton (A Dictionary of Political Thought [1982], 'paradox of democracy') | |
A reaction: The paradox would have to be resolved by qualifying what exactly one is committed to by being a democrat. I would say I am committed to the right of my opponents to enact a policy with which I disagree. |
7593 | Liberals focus on universal human freedom, natural rights, and tolerance [Scruton, by PG] |
Full Idea: Liberalism believes (roughly) in the supremacy of the individual, who has freedom and natural rights; it focuses on human, not divine affairs; it claims rights and duties are universal; and it advocates tolerance in religion and morality. | |
From: report of Roger Scruton (A Dictionary of Political Thought [1982], 'liberalism') by PG - Db (ideas) | |
A reaction: I find it hard to disagree with these principles, but the upshot in practice is often an excessive commitment to freedom and tolerance, because people fail to realise the subtle long-term erosions of society that can result. |
7592 | For positivists law is a matter of form, for naturalists it is a matter of content [Scruton] |
Full Idea: For the positivist, law is law by virtue of its form; for the naturalist, by virtue of its content. | |
From: Roger Scruton (A Dictionary of Political Thought [1982], 'law') | |
A reaction: Clearly a perverse and 'unnatural' social rule (backed by government and implied force) is a 'law' in some sense of the word. It is hard to see how you could gain social consensus for a law if it didn't appear in some way to be 'natural justice'. |
7587 | The issue of abortion seems insoluble, because there is nothing with which to compare it [Scruton] |
Full Idea: The issue of abortion is intractable, partly because of the absence of any other case to which it can be assimilated. | |
From: Roger Scruton (A Dictionary of Political Thought [1982], 'abortion') | |
A reaction: This is the legalistic approach to the problem, which always looks for precedents and comparisons. All problems must hav solutions, though (mustn't they?). The problem, though, is not the value of the foetus, but the unique form of 'ownership'. |