55 ideas
2956 | There is nothing so obvious that a philosopher cannot be found to deny it [Lockwood] |
2963 | There may only be necessary and sufficient conditions (and counterfactuals) because we intervene in the world [Lockwood] |
2958 | No one has ever succeeded in producing an acceptable non-trivial analysis of anything [Lockwood] |
9641 | Definitions should be replaceable by primitives, and should not be creative [Brown,JR] |
2959 | If something is described in two different ways, is that two facts, or one fact presented in two ways? [Lockwood] |
9634 | Set theory says that natural numbers are an actual infinity (to accommodate their powerset) [Brown,JR] |
9613 | Naïve set theory assumed that there is a set for every condition [Brown,JR] |
9615 | Nowadays conditions are only defined on existing sets [Brown,JR] |
9617 | The 'iterative' view says sets start with the empty set and build up [Brown,JR] |
9642 | A flock of birds is not a set, because a set cannot go anywhere [Brown,JR] |
9605 | If a proposition is false, then its negation is true [Brown,JR] |
9649 | Axioms are either self-evident, or stipulations, or fallible attempts [Brown,JR] |
9638 | Berry's Paradox finds a contradiction in the naming of huge numbers [Brown,JR] |
9604 | Mathematics is the only place where we are sure we are right [Brown,JR] |
9622 | 'There are two apples' can be expressed logically, with no mention of numbers [Brown,JR] |
9648 | π is a 'transcendental' number, because it is not the solution of an equation [Brown,JR] |
9621 | Mathematics represents the world through structurally similar models. [Brown,JR] |
9646 | There is no limit to how many ways something can be proved in mathematics [Brown,JR] |
9647 | Computers played an essential role in proving the four-colour theorem of maps [Brown,JR] |
9643 | Set theory may represent all of mathematics, without actually being mathematics [Brown,JR] |
9644 | When graphs are defined set-theoretically, that won't cover unlabelled graphs [Brown,JR] |
9625 | To see a structure in something, we must already have the idea of the structure [Brown,JR] |
9628 | Sets seem basic to mathematics, but they don't suit structuralism [Brown,JR] |
9606 | The irrationality of root-2 was achieved by intellect, not experience [Brown,JR] |
9612 | There is an infinity of mathematical objects, so they can't be physical [Brown,JR] |
9610 | Numbers are not abstracted from particulars, because each number is a particular [Brown,JR] |
9620 | Empiricists base numbers on objects, Platonists base them on properties [Brown,JR] |
9639 | Does some mathematics depend entirely on notation? [Brown,JR] |
9629 | For nomalists there are no numbers, only numerals [Brown,JR] |
9630 | The most brilliant formalist was Hilbert [Brown,JR] |
9608 | There are no constructions for many highly desirable results in mathematics [Brown,JR] |
9645 | Constructivists say p has no value, if the value depends on Goldbach's Conjecture [Brown,JR] |
9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
2969 | How does a direct realist distinguish a building from Buckingham Palace? [Lockwood] |
2970 | Dogs seem to have beliefs, and beliefs require concepts [Lockwood] |
2961 | Empiricism is a theory of meaning as well as of knowledge [Lockwood] |
2960 | Commonsense realism must account for the similarity of genuine perceptions and known illusions [Lockwood] |
2952 | A 1988 estimate gave the brain 3 x 10-to-the-14 synaptic junctions [Lockwood] |
2964 | How come unconscious states also cause behaviour? [Lockwood] |
2951 | Could there be unconscious beliefs and desires? [Lockwood] |
2953 | Fish may operate by blindsight [Lockwood] |
2967 | We might even learn some fundamental physics from introspection [Lockwood] |
2966 | Can phenomenal qualities exist unsensed? [Lockwood] |
2955 | If mental events occur in time, then relativity says they are in space [Lockwood] |
2950 | Only logical positivists ever believed behaviourism [Lockwood] |
2954 | Identity theory likes the identity of lightning and electrical discharges [Lockwood] |
9611 | 'Abstract' nowadays means outside space and time, not concrete, not physical [Brown,JR] |
9609 | The older sense of 'abstract' is where 'redness' or 'group' is abstracted from particulars [Brown,JR] |
2971 | Perhaps logical positivism showed that there is no dividing line between science and metaphysics [Lockwood] |
9640 | A term can have not only a sense and a reference, but also a 'computational role' [Brown,JR] |
9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
2962 | Maybe causation is a form of rational explanation, not an observation or a state of mind [Lockwood] |
2949 | We have the confused idea that time is a process of change [Lockwood] |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |