25 ideas
| 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. |
| 11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
| Full Idea: If a designated conclusion follows from the premisses, but the argument involves two howlers which cancel each other out, then the moral is that the path an argument takes from premisses to conclusion does matter to its logical evaluation. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], II) | |
| A reaction: The drift of this is that our view of logic should be a little closer to the reasoning of ordinary language, and we should rely a little less on purely formal accounts. |
| 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 |
| 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. |
| 11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
| Full Idea: A connective will possess the sense that it has by virtue of its competent users' finding certain rules of inference involving it to be primitively obvious. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], III) | |
| A reaction: Rumfitt cites Peacocke as endorsing this view, which characterises the logical connectives by their rules of usage rather than by their pure semantic value. |
| 11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
| Full Idea: If 'and' and 'but' really are alike in sense, in what might that likeness consist? Some philosophers of classical logic will reply that they share a sense by virtue of sharing a truth table. | |
| From: Ian Rumfitt ("Yes" and "No" [2000]) | |
| A reaction: This is the standard view which Rumfitt sets out to challenge. |
| 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...' |
| 7508 | Good reductionism connects fields of knowledge, but doesn't replace one with another [Pinker] |
| Full Idea: Good reductionism (also called 'hierarchical reductionism') consists not of replacing one field of knowledge with another, but of connecting or unifying them. | |
| From: Steven Pinker (The Blank Slate [2002], Ch.4) | |
| A reaction: A nice simple clarification. In this sense I am definitely a reductionist about mind (indeed, about everything). There is nothing threatening to even 'spiritual' understanding by saying that it is connected to the brain. |
| 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'. |
| 7510 | Connectionists say the mind is a general purpose learning device [Pinker] |
| Full Idea: Connectionists do not, of course, believe that the mind is a blank slate, but they do believe in the closest mechanistic equivalent, a general purpose learning device. | |
| From: Steven Pinker (The Blank Slate [2002], Ch.5) | |
| A reaction: This shows the closeness of connectionism to Hume's associationism (Idea 2189), which was just a minimal step away from Locke's mind as 'white paper' (Idea 7507). Pinker is defending 'human nature', but connectionism has a point. |
| 7513 | Is memory stored in protein sequences, neurons, synapses, or synapse-strengths? [Pinker] |
| Full Idea: Are memories stored in protein sequences, in new neurons or synapses, or in changes in the strength of existing synapses? | |
| From: Steven Pinker (The Blank Slate [2002], Ch.5) | |
| A reaction: This seems to be a neat summary of current neuroscientific thinking about memory. If you are thinking that memory couldn't possibly be so physical, don't forget the mind-boggling number of events involved in each tiny memory. See Idea 6668. |
| 7509 | Roundworms live successfully with 302 neurons, so human freedom comes from our trillions [Pinker] |
| Full Idea: The roundworm only has 959 cells, and 302 neurons in a fixed wiring diagram; it eats, mates, approaches and avoids certain smells, and that's about it. This makes it obvious that human 'free' behaviour comes from our complex biological makeup. | |
| From: Steven Pinker (The Blank Slate [2002], Ch.5) | |
| A reaction: I find this a persuasive example. Three hundred trillion neurons cannot possibly produce behaviour which is more than broadly predictable, and then it is the environment and culture that make it predictable, not the biology. |
| 7511 | Neural networks can generalise their training, e.g. truths about tigers apply mostly to lions [Pinker] |
| Full Idea: The appeal of neural networks is that they automatically generalize their training to similar new items. If one has been trained to think tigers eat frosted flakes, it will generalise that lions do too, because it knows tigers as sets of features. | |
| From: Steven Pinker (The Blank Slate [2002], Ch.5) | |
| A reaction: This certainly is appealing, because it offers a mechanistic account of abstraction and universals, which everyone agrees are central to proper thinking. |
| 7512 | There are five types of reasoning that seem beyond connectionist systems [Pinker, by PG] |
| Full Idea: Connectionist networks have difficulty with the kind/individual distinction (ducks/this duck), with compositionality (relations), with quantification (reference of 'all'), with recursion (embedded thoughts), and the categorical reasoning (exceptions). | |
| From: report of Steven Pinker (The Blank Slate [2002], Ch.5) by PG - Db (ideas) | |
| A reaction: [Read Pinker p.80!] These are essentially all the more sophisticated aspects of logical reasoning that Pinker can think of. Personally I would be reluctant to say a priori that connectionism couldn't cope with these things, just because they seem tough. |
| 11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |
| Full Idea: The standard view is that affirming not-A is more complex than affirming the atomic sentence A itself, with the latter determining its sense. But we could learn 'not' directly, by learning at once how to either affirm A or reject A. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], IV) | |
| A reaction: [compressed] This seems fairly anti-Fregean in spirit, because it looks at the psychology of how we learn 'not' as a way of clarifying what we mean by it, rather than just looking at its logical behaviour (and thus giving it a secondary role). |
| 7505 | Many think that accepting human nature is to accept innumerable evils [Pinker] |
| Full Idea: To acknowledge human nature, many think, is to endorse racism, sexism, war, greed, genocide, nihilism, reactionary politics, and neglect of children and the disadvantaged. | |
| From: Steven Pinker (The Blank Slate [2002], Pref) | |
| A reaction: The point is that modern liberal thinking says everything is nurture (which can be changed), not nature (which can't). Virtue theory, of which I am a fan, requires a concept of human nature, as the thing which can attain excellence in its function. |
| 7516 | In 1828, the stuff of life was shown to be ordinary chemistry, not a magic gel [Pinker] |
| Full Idea: In 1828 Friedrich Wöhler showed [by synthesising urea in the laboratory] that the stuff of life is not a magical, pulsating gel, but ordinary compounds following the laws of chemistry. | |
| From: Steven Pinker (The Blank Slate [2002], Ch.3) | |
| A reaction: Wöhler synthesised urea in the laboratory. |
| 7515 | All the evidence says evolution is cruel and wasteful, not intelligent [Pinker] |
| Full Idea: The overwhelming evidence is that the process of evolution, far from being intelligent and purposeful, is wasteful and cruel. | |
| From: Steven Pinker (The Blank Slate [2002], Ch.7) | |
| A reaction: This is why opponents should reject evolution totally, rather than compromise with it. Stick to a 6000-year-old world, fossils sent to test our faith, and species created in a flash (with no pain or waste). |
| 7514 | Intelligent Design says that every unexplained phenomenon must be design, by default [Pinker] |
| Full Idea: The originator of 'intelligent design' (the biochemist Michael Behe) takes every phenomenon whose evolutionary history has not yet been figured out, and chalks it up to design by default. | |
| From: Steven Pinker (The Blank Slate [2002], Ch.7) | |
| A reaction: This seems to summarise the strategy very nicely. The theory essentially exploits the 'wow!' factor. The bigger the wow! the more likely it is that it was created by God. But research has been eroding our wows steadily for four hundred years. |