16 ideas
17879 | Axiomatising set theory makes it all relative [Skolem] |
Full Idea: Axiomatising set theory leads to a relativity of set-theoretic notions, and this relativity is inseparably bound up with every thoroughgoing axiomatisation. | |
From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.296) |
13536 | Skolem did not believe in the existence of uncountable sets [Skolem] |
Full Idea: Skolem did not believe in the existence of uncountable sets. | |
From: Thoralf Skolem (works [1920], 5.3) | |
A reaction: Kit Fine refers somewhere to 'unrepentent Skolemites' who still hold this view. |
17878 | If a 1st-order proposition is satisfied, it is satisfied in a denumerably infinite domain [Skolem] |
Full Idea: Löwenheim's theorem reads as follows: If a first-order proposition is satisfied in any domain at all, it is already satisfied in a denumerably infinite domain. | |
From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.293) |
17880 | Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem] |
Full Idea: The initial foundations should be immediately clear, natural and not open to question. This is satisfied by the notion of integer and by inductive inference, by it is not satisfied by the axioms of Zermelo, or anything else of that kind. | |
From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.299) | |
A reaction: This is a plea (endorsed by Almog) that the integers themselves should be taken as primitive and foundational. I would say that the idea of successor is more primitive than the integers. |
17881 | Mathematician want performable operations, not propositions about objects [Skolem] |
Full Idea: Most mathematicians want mathematics to deal, ultimately, with performable computing operations, and not to consist of formal propositions about objects called this or that. | |
From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.300) |
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. |
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. |