48 ideas
| 9136 | The paradox of analysis says that any conceptual analysis must be either trivial or false [Sorensen] |
| Full Idea: The paradox of analysis says if a conceptual analysis states exactly what the original statement says, then the analysis is trivial; if it says something different from the original, then the analysis is mistaken. All analyses are trivial or false. | |
| From: Roy Sorensen (Vagueness and Contradiction [2001], 8.5) | |
| A reaction: [source is G.E. Moore] Good analyses typically give explanations, or necessary and sufficient conditions, or inferential relations. At their most trivial they at least produce a more profound dictionary than your usual lexicographer. Not guilty. |
| 9131 | Two long understandable sentences can have an unintelligible conjunction [Sorensen] |
| Full Idea: If there is an upper bound on the length of understandable sentences, then two understandable sentences can have an unintelligible conjunction. | |
| From: Roy Sorensen (Vagueness and Contradiction [2001], 6.4) | |
| A reaction: Not a huge paradox about the use of the word 'and', perhaps, but a nice little warning to be clear about what is being claimed before you cheerfully assert a screamingly obvious law of thought, such as conjunction. |
| 9139 | If nothing exists, no truthmakers could make 'Nothing exists' true [Sorensen] |
| Full Idea: If nothing exists, then there are no truthmakers that could make 'Nothing exists' true. | |
| From: Roy Sorensen (Vagueness and Contradiction [2001], 11.2) | |
| A reaction: [He cites David Lewis] We may be confusing truth with facts. I take facts to be independent of minds, but truth only makes sense as a concept in the presence of minds which are endeavouring to think well. |
| 9140 | Which toothbrush is the truthmaker for 'buy one, get one free'? [Sorensen] |
| Full Idea: If I buy two toothbrushes on a 'buy one, get one free' offer, which one did I buy and which one did I get free? Those who believe that each contingent truth has a truthmaker are forced to believe that 'buy one, get one free' is false. | |
| From: Roy Sorensen (Vagueness and Contradiction [2001], 11.6) | |
| A reaction: Nice. There really is no fact of which toothbrush is the free one. The underlying proposition must presumably be 'two for the price of one'. But you could hardly fault the first slogan under the Trades Descriptions Act. |
| 7785 | The use of plurals doesn't commit us to sets; there do not exist individuals and collections [Boolos] |
| Full Idea: We should abandon the idea that the use of plural forms commits us to the existence of sets/classes… Entities are not to be multiplied beyond necessity. There are not two sorts of things in the world, individuals and collections. | |
| From: George Boolos (To be is to be the value of a variable.. [1984]), quoted by Henry Laycock - Object | |
| A reaction: The problem of quantifying over sets is notoriously difficult. Try http://plato.stanford.edu/entries/object/index.html. |
| 10699 | Does a bowl of Cheerios contain all its sets and subsets? [Boolos] |
| Full Idea: Is there, in addition to the 200 Cheerios in a bowl, also a set of them all? And what about the vast number of subsets of Cheerios? It is haywire to think that when you have some Cheerios you are eating a set. What you are doing is: eating the Cheerios. | |
| From: George Boolos (To be is to be the value of a variable.. [1984], p.72) | |
| A reaction: In my case Boolos is preaching to the converted. I am particularly bewildered by someone (i.e. Quine) who believes that innumerable sets exist while 'having a taste for desert landscapes' in their ontology. |
| 10225 | Monadic second-order logic might be understood in terms of plural quantifiers [Boolos, by Shapiro] |
| Full Idea: Boolos has proposed an alternative understanding of monadic, second-order logic, in terms of plural quantifiers, which many philosophers have found attractive. | |
| From: report of George Boolos (To be is to be the value of a variable.. [1984]) by Stewart Shapiro - Philosophy of Mathematics 3.5 |
| 10736 | Boolos showed how plural quantifiers can interpret monadic second-order logic [Boolos, by Linnebo] |
| Full Idea: In an indisputable technical result, Boolos showed how plural quantifiers can be used to interpret monadic second-order logic. | |
| From: report of George Boolos (To be is to be the value of a variable.. [1984], Intro) by Øystein Linnebo - Plural Quantification Exposed Intro |
| 10780 | Any sentence of monadic second-order logic can be translated into plural first-order logic [Boolos, by Linnebo] |
| Full Idea: Boolos discovered that any sentence of monadic second-order logic can be translated into plural first-order logic. | |
| From: report of George Boolos (To be is to be the value of a variable.. [1984], §1) by Øystein Linnebo - Plural Quantification Exposed p.74 |
| 9119 | No attempt to deny bivalence has ever been accepted [Sorensen] |
| Full Idea: The history of deviant logics is without a single success. Bivalence has been denied at least since Aristotle, yet no anti-bivalent theory has ever left the philosophical nursery. | |
| From: Roy Sorensen (Vagueness and Contradiction [2001], Intro) | |
| A reaction: This is part of a claim that nothing in reality is vague - it is just our ignorance of the truth or falsity of some propositions. Personally I don't see why 'Grandad is bald' has to have a determinate truth value. |
| 10697 | Identity is clearly a logical concept, and greatly enhances predicate calculus [Boolos] |
| Full Idea: Indispensable to cross-reference, lacking distinctive content, and pervading thought and discourse, 'identity' is without question a logical concept. Adding it to predicate calculus significantly increases the number and variety of inferences possible. | |
| From: George Boolos (To be is to be the value of a variable.. [1984], p.54) | |
| A reaction: It is not at all clear to me that identity is a logical concept. Is 'existence' a logical concept? It seems to fit all of Boolos's criteria? I say that all he really means is that it is basic to thought, but I'm not sure it drives the reasoning process. |
| 9135 | We now see that generalizations use variables rather than abstract entities [Sorensen] |
| Full Idea: As philosophers gradually freed themselves from the assumption that all words are names, ..they realised that generalizations really use variables rather than names of abstract entities. | |
| From: Roy Sorensen (Vagueness and Contradiction [2001], 8.4) | |
| A reaction: This looks like a key thought in trying to understand abstraction - though I don't think you can shake it off that easily. (For all x)(x-is-a-bird then x-has-wings) seems to require a generalised concept of a bird to give a value to the variable. |
| 13671 | Second-order quantifiers are just like plural quantifiers in ordinary language, with no extra ontology [Boolos, by Shapiro] |
| Full Idea: Boolos proposes that second-order quantifiers be regarded as 'plural quantifiers' are in ordinary language, and has developed a semantics along those lines. In this way they introduce no new ontology. | |
| From: report of George Boolos (To be is to be the value of a variable.. [1984]) by Stewart Shapiro - Foundations without Foundationalism 7 n32 | |
| A reaction: This presumably has to treat simple predicates and relations as simply groups of objects, rather than having platonic existence, or something. |
| 10267 | We should understand second-order existential quantifiers as plural quantifiers [Boolos, by Shapiro] |
| Full Idea: Standard second-order existential quantifiers pick out a class or a property, but Boolos suggests that they be understood as a plural quantifier, like 'there are objects' or 'there are people'. | |
| From: report of George Boolos (To be is to be the value of a variable.. [1984]) by Stewart Shapiro - Philosophy of Mathematics 7.4 | |
| A reaction: This idea has potential application to mathematics, and Lewis (1991, 1993) 'invokes it to develop an eliminative structuralism' (Shapiro). |
| 10698 | Plural forms have no more ontological commitment than to first-order objects [Boolos] |
| Full Idea: Abandon the idea that use of plural forms must always be understood to commit one to the existence of sets of those things to which the corresponding singular forms apply. | |
| From: George Boolos (To be is to be the value of a variable.. [1984], p.66) | |
| A reaction: It seems to be an open question whether plural quantification is first- or second-order, but it looks as if it is a rewriting of the first-order. |
| 7806 | Boolos invented plural quantification [Boolos, by Benardete,JA] |
| Full Idea: Boolos virtually patented the new device of plural quantification. | |
| From: report of George Boolos (To be is to be the value of a variable.. [1984]) by José A. Benardete - Logic and Ontology | |
| A reaction: This would be 'there are some things such that...' |
| 9125 | Denying problems, or being romantically defeated by them, won't make them go away [Sorensen] |
| Full Idea: An unsolvable problem is still a problem, despite Wittgenstein's view that there are no genuine philosophical problems, and Kant's romantic defeatism in his treatment of the antinomies of pure reason. | |
| From: Roy Sorensen (Vagueness and Contradiction [2001], 4.3) | |
| A reaction: I like the spin put on Kant, that he is a romantic in his defeatism. He certainly seems reluctant to slash at the Gordian knot, e.g. by being a bit more drastically sceptical about free will. |
| 9137 | Banning self-reference would outlaw 'This very sentence is in English' [Sorensen] |
| Full Idea: The old objection to the ban on self-reference is that it is too broad; it bans innocent sentences such as 'This very sentence is in English'. | |
| From: Roy Sorensen (Vagueness and Contradiction [2001], 11.1) | |
| A reaction: Tricky. What is the sigificant difference between 'this sentence is in English' and 'this sentence is a lie'? The first concerns context and is partly metalinguistic. The second concerns semantics and truth. Concept and content.. |
| 9116 | Vague words have hidden boundaries [Sorensen] |
| Full Idea: Vague words have hidden boundaries. The subtraction of a single grain of sand might turn a heap into a non-heap. | |
| From: Roy Sorensen (Vagueness and Contradiction [2001], Intro) | |
| A reaction: The first sentence could be the slogan for the epistemic view of vagueness. The opposite view is Sainsbury's - that vague words are those which do not have any boundaries. Sorensen admits his view is highly counterintuitive. I think I prefer Sainsbury. |
| 10700 | First- and second-order quantifiers are two ways of referring to the same things [Boolos] |
| Full Idea: Ontological commitment is carried by first-order quantifiers; a second-order quantifier needn't be taken to be a first-order quantifier in disguise, having special items, collections, as its range. They are two ways of referring to the same things. | |
| From: George Boolos (To be is to be the value of a variable.. [1984], p.72) | |
| A reaction: If second-order quantifiers are just a way of referring, then we can see first-order quantifiers that way too, so we could deny 'objects'. |
| 16185 | Causality indicates which properties are real [Cartwright,N] |
| Full Idea: Causality is a clue to what properties are real. | |
| From: Nancy Cartwright (How the Laws of Physics Lie [1983], 9.3) | |
| A reaction: An interesting variant on the Shoemaker proposal that properties actually are causal. I'm not sure that there is anything more to causality that the expression in action of properties, which I take to be powers. Structures are not properties. |
| 9132 | An offer of 'free coffee or juice' could slowly shift from exclusive 'or' to inclusive 'or' [Sorensen] |
| Full Idea: Sometimes an exclusive 'or' gradually develops into an inclusive 'or'. A restaurant offers 'free coffee or juice'. The customers ask for both, and gradually they are given it, first as a courtesy, and eventually as an expectation. | |
| From: Roy Sorensen (Vagueness and Contradiction [2001], 7.2) | |
| A reaction: [compressed] A very nice example - of the rot of vagueness even seeping into the basic logical connectives. We don't have to accept it, though. Each instance of usage of 'or', by manager or customer, might be clearly one or the other. |
| 9128 | It is propositional attitudes which can be a priori, not the propositions themselves [Sorensen] |
| Full Idea: The primary bearer of apriority is the propositional attitude (believing, knowing, guessing and so on) rather than the proposition itself. A proposition could be a priori to homo sapiens but a posteriori to Neandethals. | |
| From: Roy Sorensen (Vagueness and Contradiction [2001], 6.3) | |
| A reaction: A putative supreme being is quite useful here, who might even see the necessity of Arsenal beating Manchester United next Saturday. Unlike infants, adults know a priori that square pegs won't fit round holes. |
| 9130 | Attributing apriority to a proposition is attributing a cognitive ability to someone [Sorensen] |
| Full Idea: Every attribution of apriority to a proposition is tacitly an attribution of a cognitive ability to some thinker. | |
| From: Roy Sorensen (Vagueness and Contradiction [2001], 6.3) | |
| A reaction: The ability would include a range of background knowledge, as well as a sheer power of intellect. If you know all of Euclid's theorems, you will spot facts about geometrical figues quicker than me. His point is important. |
| 9118 | The colour bands of the spectrum arise from our biology; they do not exist in the physics [Sorensen] |
| Full Idea: The bands of colour in a colour spectrum do not correspond to objective discontinuities in light wavelengths. These apparently external bands arise from our biology rather than simple physics. | |
| From: Roy Sorensen (Vagueness and Contradiction [2001], Intro) | |
| A reaction: If any more arguments are needed to endorse the fact that some qualities are clearly secondary (and, to my amazement, such arguments seem to be very much needed), I would take this to be one of the final conclusive pieces of evidence. |
| 9124 | We are unable to perceive a nose (on the back of a mask) as concave [Sorensen] |
| Full Idea: The human perceptual system appears unable to represent a nose as concave rather than convex. If you look at the concave side of a mask, you see the features as convex. | |
| From: Roy Sorensen (Vagueness and Contradiction [2001], 4.3) | |
| A reaction: I don't think that is quite true. You wouldn't put a mask on if you thought it was convex. It is usually when seen at a distance with strong cross-lighting that the effect emerges. Nevertheless, it is an important point. |
| 9126 | Bayesians build near-certainty from lots of reasonably probable beliefs [Sorensen] |
| Full Idea: Bayesians demonstrate that a self-correcting agent can build an imposing edifice of near-certain knowledge from numerous beliefs that are only slightly more probable than not. | |
| From: Roy Sorensen (Vagueness and Contradiction [2001], 6.1) | |
| A reaction: This strikes me as highly significant for the coherence account of justification, even if one is sceptical about the arithmetical approach to belief of Bayesianism. It seems obvious that lots of quite likely facts build towards certainty, Watson. |
| 9121 | Illusions are not a reason for skepticism, but a source of interesting scientific information [Sorensen] |
| Full Idea: Philosophers tend to associate illusions with skepticism. But since illusions are signs of modular construction, they are actually reason for scientific hope. Illusions have been very useful in helping us to understand vision. | |
| From: Roy Sorensen (Vagueness and Contradiction [2001], 1.4) | |
| A reaction: This is a nice reversal of the usual view. If I see double, it reveals to me that my eyes are not aligned properly. Anyone led to scepticism by illusions should pay more attention to themselves, and less to the reality they hope to know directly. |
| 16182 | Two main types of explanation are by causes, or by citing a theoretical framework [Cartwright,N] |
| Full Idea: In explaining a phenomenon one can cite the causes of that phenomenon; or one can set the phenomenon in a general theoretical framework. | |
| From: Nancy Cartwright (How the Laws of Physics Lie [1983], 4.1) | |
| A reaction: The thing is, you need to root an explanation in something taken as basic, and theoretical frameworks need further explanation, whereas causes seem to be basic. |
| 16184 | An explanation is a model that fits a theory and predicts the phenomenological laws [Cartwright,N] |
| Full Idea: To explain a phenomenon is to find a model that fits it into the basic framework of the theory and that thus allows us to derive analogues for the messy and complicated phenomenological laws that are true of it. | |
| From: Nancy Cartwright (How the Laws of Physics Lie [1983], 8.3) | |
| A reaction: This summarises the core of her view in this book. She is after models rather than laws, and the models are based on causes. |
| 16167 | Laws get the facts wrong, and explanation rests on improvements and qualifications of laws [Cartwright,N] |
| Full Idea: We explain by ceteris paribus laws, by composition of causes, and by approximations that improve on what the fundamental laws dictate. In all of these cases the fundamental laws patently do not get the facts right. | |
| From: Nancy Cartwright (How the Laws of Physics Lie [1983], Intro) | |
| A reaction: It is rather headline-grabbing to say in this case that laws do not get the facts right. If they were actually 'wrong' and 'lied', there wouldn't be much point in building explanations on them. |
| 16169 | Laws apply to separate domains, but real explanations apply to intersecting domains [Cartwright,N] |
| Full Idea: When different kinds of causes compose, we want to explain what happens in the intersection of different domains. But the laws we use are designed only to tell truly what happens in each domain separately. | |
| From: Nancy Cartwright (How the Laws of Physics Lie [1983], Intro) | |
| A reaction: Since presumably the laws are discovered through experiments which try to separate out a single domain, in those circumstances they actually are true, so they don't 'lie'. |
| 16176 | Covering-law explanation lets us explain storms by falling barometers [Cartwright,N] |
| Full Idea: Much criticism of the original covering-law model objects that it lets in too much. It seems we can explain Henry's failure to get pregnant by his taking birth control pills, and we can explain the storm by the falling barometer. | |
| From: Nancy Cartwright (How the Laws of Physics Lie [1983], 2.0) | |
| A reaction: I take these examples to show that true explanations must be largely causal in character. The physicality of causation is what matters, not 'laws'. I'd say the same of attempts to account for causation through counterfactuals. |
| 16177 | I disagree with the covering-law view that there is a law to cover every single case [Cartwright,N] |
| Full Idea: Covering-law theorists tend to think that nature is well-regulated; in the extreme, that there is a law to cover every case. I do not. | |
| From: Nancy Cartwright (How the Laws of Physics Lie [1983], 2.2) | |
| A reaction: The problem of coincidence is somewhere at the back of this thought. Innumerable events have their own explanations, but it is hard to explain their coincidence (see Aristotle's case of bumping into a friend in the market). |
| 16180 | You can't explain one quail's behaviour by just saying that all quails do it [Cartwright,N] |
| Full Idea: 'Why does that quail in the garden bob its head up and down in that funny way whenever it walks?' …'Because they all do'. | |
| From: Nancy Cartwright (How the Laws of Physics Lie [1983], 3.5) | |
| A reaction: She cites this as an old complaint against the covering-law model of explanation. It captures beautifully the basic error of the approach. We want to know 'why', rather than just have a description of the pattern. 'They all do' is useful information. |
| 16171 | The covering law view assumes that each phenomenon has a 'right' explanation [Cartwright,N] |
| Full Idea: The covering-law account supposes that there is, in principle, one 'right' explanation for each phenomenon. | |
| From: Nancy Cartwright (How the Laws of Physics Lie [1983], Intro) | |
| A reaction: Presumably the law is held to be 'right', but there must be a bit of flexibility in describing the initial conditions, and the explanandum itself. |
| 16183 | In science, best explanations have regularly turned out to be false [Cartwright,N] |
| Full Idea: There are a huge number of cases in the history of science where we now know our best explanations were false. | |
| From: Nancy Cartwright (How the Laws of Physics Lie [1983], 5.3) | |
| A reaction: [She cites Laudan 1981 for this] The Ptolemaic system and aether are the standard example cited for this. I believe strongly in the importance of best explanation. Only a fool would just accept the best explanation available. Coherence is needed. |
| 9134 | The negation of a meaningful sentence must itself be meaningful [Sorensen] |
| Full Idea: The negation of any meaningful sentence must itself be meaningful. | |
| From: Roy Sorensen (Vagueness and Contradiction [2001], 8.1) | |
| A reaction: Nice. Compare 'there is another prime number beyond the highest one we have found' with its negation. The first seems verifiable in principle, but the second one doesn't. So the verificationist must deny Sorensen's idea? |
| 9133 | Propositions are what settle problems of ambiguity in sentences [Sorensen] |
| Full Idea: Propositions play the role of dis-ambiguators; they are the things between which utterances are ambiguous. | |
| From: Roy Sorensen (Vagueness and Contradiction [2001], 7.7) | |
| A reaction: I have become a great fan of propositions, and I think this is one of the key reasons for believing in them. The proposition is what we attempt to pin down when asked 'what exactly did you mean by what you just said?' |
| 9129 | I can buy any litre of water, but not every litre of water [Sorensen] |
| Full Idea: I am entitled to buy any litre of water, but I am not entitled to buy every litre of water. | |
| From: Roy Sorensen (Vagueness and Contradiction [2001], 6.3) | |
| A reaction: A decent social system must somehow draw a line between buying up all the water and buying up all the paintings of Vermeer. Even the latter seems wicked, but it is hard to pin down the reason. |
| 16175 | A cause won't increase the effect frequency if other causes keep interfering [Cartwright,N] |
| Full Idea: A cause ought to increase the frequency of the effect, but this fact may not show up in the probabilities if other causes are at work. | |
| From: Nancy Cartwright (How the Laws of Physics Lie [1983], 1.1) | |
| A reaction: [She cites Patrick Suppes for this one] Presumably in experimental situations you can weed out the interference, but that threatens to eliminate mere 'probability' entirely. |
| 6781 | There are fundamental explanatory laws (false!), and phenomenological laws (regularities) [Cartwright,N, by Bird] |
| Full Idea: Nancy Cartwright distinguishes between 'fundamental explanatory laws', which we should not believe, and 'phenomenological laws', which are regularities established on the basis of observation. | |
| From: report of Nancy Cartwright (How the Laws of Physics Lie [1983]) by Alexander Bird - Philosophy of Science Ch.4 | |
| A reaction: The distinction is helpful, so that we can be clearer about what everyone is claiming. We can probably all agree on the phenomenological laws, which are epistemological. Personally I claim truth for the best fundamental explanatory laws. |
| 16166 | Laws of appearances are 'phenomenological'; laws of reality are 'theoretical' [Cartwright,N] |
| Full Idea: Philosophers distinguish phenomenological from theoretical laws. Phenomenological laws are about appearances; theoretical ones are about the reality behind the appearances. | |
| From: Nancy Cartwright (How the Laws of Physics Lie [1983], Intro) | |
| A reaction: I'm suspecting that Humeans only really believe in the phenomenological kind. I'm only interested in the theoretical kind, and I take inference to the best explanation to be the bridge between the two. Cartwright rejects the theoretical laws. |
| 16179 | Good organisation may not be true, and the truth may not organise very much [Cartwright,N] |
| Full Idea: There is no reason to think that the principles that best organise will be true, nor that the principles that are true will organise much. | |
| From: Nancy Cartwright (How the Laws of Physics Lie [1983], 2.5) | |
| A reaction: This is aimed at the Mill-Ramsey-Lewis account of laws, as axiomatisations of the observed patterns in nature. |
| 16170 | To get from facts to equations, we need a prepared descriptions suited to mathematics [Cartwright,N] |
| Full Idea: To get from a detailed factual knowledge of a situation to an equation, we must prepare the description of the situation to meet the mathematical needs of the theory. | |
| From: Nancy Cartwright (How the Laws of Physics Lie [1983], Intro) | |
| A reaction: She is clearly on to something here, as Galileo is blatantly wrong in his claim that the book of nature is written in mathematics. Mathematics is the best we can manage in getting a grip on the chaos. |
| 16181 | Simple laws have quite different outcomes when they act in combinations [Cartwright,N] |
| Full Idea: For explanation simple laws must have the same form when they act together as when they act singly. ..But then what the law states cannot literally be true, for the consequences that occur if it acts alone are not what occurs when they act in combination. | |
| From: Nancy Cartwright (How the Laws of Physics Lie [1983], 3.6) | |
| A reaction: This is Cartwright's basic thesis. Her point is that the laws 'lie', because they claim to predict a particular outcome which never ever actually occurs. She says we could know all the laws, and still not be able to explain anything. |
| 16178 | There are few laws for when one theory meets another [Cartwright,N] |
| Full Idea: Where theories intersect, laws are usually hard to come by. | |
| From: Nancy Cartwright (How the Laws of Physics Lie [1983], 2.3) | |
| A reaction: There are attempts at so-called 'bridge laws', to get from complex theories to simple ones, but her point is well made about theories on the same 'level'. |
| 9122 | God cannot experience unwanted pain, so God cannot understand human beings [Sorensen] |
| Full Idea: Theologians worry that God may be an alien being. God cannot feel pain since pain is endured against one's will. God is all powerful and suffers nothing against His Will. To understand pain, one must experience pain. So God's power walls him off from us. | |
| From: Roy Sorensen (Vagueness and Contradiction [2001], 3.2) | |
| A reaction: I can't think of a good theological reply to this. God, and Jesus too (presumably), can only experience pain if they volunteer for it. It is inconceivable that they could be desperate for it to stop, but were unable to achieve that. |