19 ideas
| 18755 | Validity is explained as truth in all models, because that relies on the logical terms [McGee] |
| Full Idea: A model of a language assigns values to non-logical terms. If a sentence is true in every model, its truth doesn't depend on those non-logical terms. Hence the validity of an argument comes from its logical form. Thus models explain logical validity. | |
| From: Vann McGee (Logical Consequence [2014], 4) | |
| A reaction: [compressed] Thus you get a rigorous account of logical validity by only allowing the rigorous input of model theory. This is the modern strategy of analytic philosophy. But is 'it's red so it's coloured' logically valid? |
| 18751 | Natural language includes connectives like 'because' which are not truth-functional [McGee] |
| Full Idea: Natural language includes connectives that are not truth-functional. In order for 'p because q' to be true, both p and q have to be true, but knowing the simpler sentences are true doesn't determine whether the larger sentence is true. | |
| From: Vann McGee (Logical Consequence [2014], 2) |
| 18761 | Second-order variables need to range over more than collections of first-order objects [McGee] |
| Full Idea: To get any advantage from moving to second-order logic, we need to assign to second-order variables a role different from merely ranging over collections made up of things the first-order variables range over. | |
| From: Vann McGee (Logical Consequence [2014], 7) | |
| A reaction: Thus it is exciting if they range over genuine properties, but not so exciting if you merely characterise those properties as sets of first-order objects. This idea leads into a discussion of plural quantification. |
| 18753 | An ontologically secure semantics for predicate calculus relies on sets [McGee] |
| Full Idea: We can get a less ontologically perilous presentation of the semantics of the predicate calculus by using sets instead of concepts. | |
| From: Vann McGee (Logical Consequence [2014], 4) | |
| A reaction: The perilous versions rely on Fregean concepts, and notably Russell's 'concept that does not fall under itself'. The sets, of course, have to be ontologically secure, and so will involve the iterative conception, rather than naive set theory. |
| 18754 | Logically valid sentences are analytic truths which are just true because of their logical words [McGee] |
| Full Idea: Logically valid sentences are a species of analytic sentence, being true not just in virtue of the meanings of their words, but true in virtue of the meanings of their logical words. | |
| From: Vann McGee (Logical Consequence [2014], 4) | |
| A reaction: A helpful link between logical truths and analytic truths, which had not struck me before. |
| 18757 | Soundness theorems are uninformative, because they rely on soundness in their proofs [McGee] |
| Full Idea: Soundness theorems are seldom very informative, since typically we use informally, in proving the theorem, the very same rules whose soundness we are attempting to establish. | |
| From: Vann McGee (Logical Consequence [2014], 5) | |
| A reaction: [He cites Quine 1935] |
| 18760 | The culmination of Euclidean geometry was axioms that made all models isomorphic [McGee] |
| Full Idea: One of the culminating achievements of Euclidean geometry was categorical axiomatisations, that describe the geometric structure so completely that any two models of the axioms are isomorphic. The axioms are second-order. | |
| From: Vann McGee (Logical Consequence [2014], 7) | |
| A reaction: [He cites Veblen 1904 and Hilbert 1903] For most mathematicians, categorical axiomatisation is the best you can ever dream of (rather than a single true axiomatisation). |
| 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. |
| 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. |
| 18762 | A maxim claims that if we are allowed to assert a sentence, that means it must be true [McGee] |
| Full Idea: If our linguistic conventions entitle us to assert a sentence, they thereby make it true, because of the maxim that 'truth is the norm of assertion'. | |
| From: Vann McGee (Logical Consequence [2014], 8) | |
| A reaction: You could only really deny that maxim if you had no belief at all in truth, but then you can assert anything you like (with full entitlement). Maybe you can assert anything you like as long as it doesn't upset anyone? Etc. |
| 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. |
| 6005 | Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley] |
| Full Idea: Hermarchus said that animal killing is justified by considerations of human safety and nourishment and by animals' inability to form contractual relations of justice with us. | |
| From: report of Hermarchus (fragments/reports [c.270 BCE]) by David A. Sedley - Hermarchus | |
| A reaction: Could the last argument be used to justify torturing animals? Or could we eat a human who was too brain-damaged to form contracts? |
| 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. |