21 ideas
17750 | The first clear proof of the consistency of the first order predicate logic was in 1928 [Hilbert/Ackermann, by Walicki] |
14239 | The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley] |
14240 | The empty set is something, not nothing! [Oliver/Smiley] |
14241 | We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley] |
14242 | Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley] |
14243 | The unit set may be needed to express intersections that leave a single member [Oliver/Smiley] |
14234 | If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley] |
14237 | We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley] |
14245 | Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley] |
14246 | If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley] |
14247 | Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley] |
7508 | Good reductionism connects fields of knowledge, but doesn't replace one with another [Pinker] |
7510 | Connectionists say the mind is a general purpose learning device [Pinker] |
7513 | Is memory stored in protein sequences, neurons, synapses, or synapse-strengths? [Pinker] |
7509 | Roundworms live successfully with 302 neurons, so human freedom comes from our trillions [Pinker] |
7511 | Neural networks can generalise their training, e.g. truths about tigers apply mostly to lions [Pinker] |
7512 | There are five types of reasoning that seem beyond connectionist systems [Pinker, by PG] |
7505 | Many think that accepting human nature is to accept innumerable evils [Pinker] |
7516 | In 1828, the stuff of life was shown to be ordinary chemistry, not a magic gel [Pinker] |
7515 | All the evidence says evolution is cruel and wasteful, not intelligent [Pinker] |
7514 | Intelligent Design says that every unexplained phenomenon must be design, by default [Pinker] |