60 ideas
14027 | If we are to use words in enquiry, we need their main, unambiguous and uncontested meanings [Epicurus] |
9641 | Definitions should be replaceable by primitives, and should not be creative [Brown,JR] |
14040 | Observation and applied thought are always true [Epicurus] |
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] |
14028 | Nothing comes to be from what doesn't exist [Epicurus] |
14029 | If disappearing things went to nothingness, nothing could return, and it would all be gone by now [Epicurus] |
14030 | The totality is complete, so there is no room for it to change, and nothing extraneous to change it [Epicurus] |
9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
14048 | Astronomical movements are blessed, but they don't need the help of the gods [Epicurus] |
14044 | The perceived accidental properties of bodies cannot be conceived of as independent natures [Epicurus] |
14045 | Accidental properties give a body its nature, but are not themselves bodies or parts of bodies [Epicurus] |
14046 | A 'body' is a conception of an aggregate, with properties defined by application conditions [Epicurus] |
14047 | Bodies have impermanent properties, and permanent ones which define its conceived nature [Epicurus] |
14039 | Above and below us will never appear to be the same, because it is inconceivable [Epicurus] |
14050 | We aim to dissolve our fears, by understanding their causes [Epicurus] |
14037 | Atoms only have shape, weight and size, and the properties which accompany shape [Epicurus] |
6010 | Illusions are not false perceptions, as we accurately perceive the pattern of atoms [Epicurus, by Modrak] |
14041 | The soul is fine parts distributed through the body, resembling hot breath [Epicurus] |
14042 | The soul cannot be incorporeal, because then it could neither act nor be acted upon [Epicurus] |
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] |
9640 | A term can have not only a sense and a reference, but also a 'computational role' [Brown,JR] |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |
14032 | Totality has no edge; an edge implies a contrast beyond the edge, and there can't be one [Epicurus] |
14033 | Bodies are unlimited as well as void, since the two necessarily go together [Epicurus] |
14034 | There exists an infinity of each shape of atom, but the number of shapes is beyond our knowledge [Epicurus] |
14035 | Atoms just have shape, size and weight; colour results from their arrangement [Epicurus] |
14038 | There cannot be unlimited division, because it would reduce things to non-existence [Epicurus] |
14049 | We aim to know the natures which are observed in natural phenomena [Epicurus] |
14043 | The void cannot interact, but just gives the possibility of motion [Epicurus] |
14031 | Space must exist, since movement is obvious, and there must be somewhere to move in [Epicurus] |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
14036 | There are endless cosmoi, some like and some unlike this one [Epicurus] |