82 ideas
7490 | Because of Darwin, wisdom as a definite attainable state has faded [Watson] |
7461 | The three key ideas are the soul, Europe, and the experiment [Watson] |
7464 | The big idea: imitation, the soul, experiments, God, heliocentric universe, evolution? [Watson] |
7465 | Babylonian thinking used analogy, rather than deduction or induction [Watson] |
10987 | Three traditional names of rules are 'Simplification', 'Addition' and 'Disjunctive Syllogism' [Read] |
11004 | Necessity is provability in S4, and true in all worlds in S5 [Read] |
11018 | There are fuzzy predicates (and sets), and fuzzy quantifiers and modifiers [Read] |
11011 | Same say there are positive, negative and neuter free logics [Read] |
11020 | Realisms like the full Comprehension Principle, that all good concepts determine sets [Read] |
14187 | If logic is topic-neutral that means it delves into all subjects, rather than having a pure subject matter [Read] |
10986 | Not all validity is captured in first-order logic [Read] |
10972 | The non-emptiness of the domain is characteristic of classical logic [Read] |
11024 | Semantics must precede proof in higher-order logics, since they are incomplete [Read] |
10985 | We should exclude second-order logic, precisely because it captures arithmetic [Read] |
14188 | Not all arguments are valid because of form; validity is just true premises and false conclusion being impossible [Read] |
14182 | If the logic of 'taller of' rests just on meaning, then logic may be the study of merely formal consequence [Read] |
14183 | Maybe arguments are only valid when suppressed premises are all stated - but why? [Read] |
10970 | A theory of logical consequence is a conceptual analysis, and a set of validity techniques [Read] |
10984 | Logical consequence isn't just a matter of form; it depends on connections like round-square [Read] |
14184 | In modus ponens the 'if-then' premise contributes nothing if the conclusion follows anyway [Read] |
3299 | In logic identity involves reflexivity (x=x), symmetry (if x=y, then y=x) and transitivity (if x=y and y=z, then x=z) [Baillie] |
14186 | Logical connectives contain no information, but just record combination relations between facts [Read] |
10973 | A theory is logically closed, which means infinite premisses [Read] |
11007 | Quantifiers are second-order predicates [Read] |
10978 | In second-order logic the higher-order variables range over all the properties of the objects [Read] |
10971 | A logical truth is the conclusion of a valid inference with no premisses [Read] |
10988 | Any first-order theory of sets is inadequate [Read] |
10974 | Compactness is when any consequence of infinite propositions is the consequence of a finite subset [Read] |
10975 | Compactness does not deny that an inference can have infinitely many premisses [Read] |
10977 | Compactness blocks the proof of 'for every n, A(n)' (as the proof would be infinite) [Read] |
10976 | Compactness makes consequence manageable, but restricts expressive power [Read] |
11014 | Self-reference paradoxes seem to arise only when falsity is involved [Read] |
7466 | Mesopotamian numbers applied to specific things, and then became abstract [Watson] |
11025 | Infinite cuts and successors seems to suggest an actual infinity there waiting for us [Read] |
10979 | Although second-order arithmetic is incomplete, it can fully model normal arithmetic [Read] |
10980 | Second-order arithmetic covers all properties, ensuring categoricity [Read] |
10997 | Von Neumann numbers are helpful, but don't correctly describe numbers [Read] |
11016 | Would a language without vagueness be usable at all? [Read] |
11019 | Supervaluations say there is a cut-off somewhere, but at no particular place [Read] |
11012 | A 'supervaluation' gives a proposition consistent truth-value for classical assignments [Read] |
11013 | Identities and the Indiscernibility of Identicals don't work with supervaluations [Read] |
10995 | A haecceity is a set of individual properties, essential to each thing [Read] |
11001 | Equating necessity with truth in every possible world is the S5 conception of necessity [Read] |
10992 | The point of conditionals is to show that one will accept modus ponens [Read] |
10989 | The standard view of conditionals is that they are truth-functional [Read] |
11017 | Some people even claim that conditionals do not express propositions [Read] |
14185 | Conditionals are just a shorthand for some proof, leaving out the details [Read] |
10983 | Knowledge of possible worlds is not causal, but is an ontology entailed by semantics [Read] |
10982 | How can modal Platonists know the truth of a modal proposition? [Read] |
10996 | Actualism is reductionist (to parts of actuality), or moderate realist (accepting real abstractions) [Read] |
10981 | A possible world is a determination of the truth-values of all propositions of a domain [Read] |
11000 | If worlds are concrete, objects can't be present in more than one, and can only have counterparts [Read] |
20657 | There are 23 core brain functions, with known circuit, transmitters, genes and behaviour [Watson] |
10998 | The mind abstracts ways things might be, which are nonetheless real [Read] |
20656 | Traditional ideas of the mind were weakened in the 1950s by mind-influencing drugs [Watson] |
11005 | Negative existentials with compositionality make the whole sentence meaningless [Read] |
10966 | A proposition objectifies what a sentence says, as indicative, with secure references [Read] |
20655 | Humans have been hunter-gatherers for 99.5% of their existence [Watson] |
7477 | Modern democracy is actually elective oligarchy [Watson] |
7478 | Greek philosophers invented the concept of 'nature' as their special subject [Watson] |
20650 | The Uncertainty Principle implies that cause and effect can't be measured [Watson] |
20649 | The interference of light through two slits confirmed that it is waves [Watson] |
20661 | Electrons rotate in hyrogen atoms 10^13 times per second [Watson] |
20647 | Quantum theory explains why nature is made up of units, such as elements [Watson] |
20654 | Only four particles are needed for matter: up and down quark, electron, electron-neutrino [Watson] |
20651 | The shape of molecules is important, as well as the atoms and their bonds [Watson] |
20652 | In 1828 the animal substance urea was manufactured from inorganic ingredients [Watson] |
20658 | Information is physical, and living can be seen as replicating and preserving information [Watson] |
7462 | DNA mutation suggests humans and chimpanzees diverged 6.6 million years ago [Watson] |
7470 | During the rise of civilizations, the main gods changed from female to male [Watson] |
7474 | Hinduism has no founder, or prophet, or creed, or ecclesiastical structure [Watson] |
7479 | Modern Judaism became stabilised in 200 CE [Watson] |
7481 | The Israelites may have asserted the uniqueness of Yahweh to justify land claims [Watson] |
7480 | Monotheism was a uniquely Israelite creation within the Middle East [Watson] |
7471 | The Gathas (hymns) of Zoroastrianism date from about 1000 BCE [Watson] |
7473 | Zoroaster conceived the afterlife, judgement, heaven and hell, and the devil [Watson] |
7484 | Jesus never intended to start a new religion [Watson] |
7483 | Paul's early writings mention few striking episodes from Jesus' life [Watson] |
7475 | Confucius revered the spiritual world, but not the supernatural, or a personal god, or the afterlife [Watson] |
7476 | Taoism aims at freedom from the world, the body, the mind, and nature [Watson] |
7463 | The three basic ingredients of religion are: the soul, seers or priests, and ritual [Watson] |
7468 | In ancient Athens the souls of the dead are received by the 'upper air' [Watson] |