58 ideas
162 | Can we understand an individual soul without knowing the soul in general? [Plato] |
160 | The highest ability in man is the ability to discuss unity and plurality in the nature of things [Plato] |
22140 | The greatest philosophers are methodical; it is what makes them great [Grice] |
166 | A speaker should be able to divide a subject, right down to the limits of divisibility [Plato] |
9641 | Definitions should be replaceable by primitives, and should not be creative [Brown,JR] |
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] |
7953 | Reasoning needs to cut nature accurately at the joints [Plato] |
16121 | I revere anyone who can discern a single thing that encompasses many things [Plato] |
153 | It takes a person to understand, by using universals, and by using reason to create a unity out of sense-impressions [Plato] |
154 | We would have an overpowering love of knowledge if we had a pure idea of it - as with the other Forms [Plato] |
151 | True knowledge is of the reality behind sense experience [Plato] |
165 | If the apparent facts strongly conflict with probability, it is in everyone's interests to suppress the facts [Plato] |
9296 | The soul is self-motion [Plato] |
23997 | Plato saw emotions and appetites as wild horses, in need of taming [Plato, by Goldie] |
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] |
159 | Only a good philosopher can be a good speaker [Plato] |
5946 | 'Phaedrus' pioneers the notion of philosophical rhetoric [Lawson-Tancred on Plato] |
158 | An excellent speech seems to imply a knowledge of the truth in the mind of the speaker [Plato] |
155 | Beauty is the clearest and most lovely of the Forms [Plato] |
143 | The two ruling human principles are the natural desire for pleasure, and an acquired love of virtue [Plato] |
157 | Most pleasure is release from pain, and is therefore not worthwhile [Plato] |
144 | Reason impels us towards excellence, which teaches us self-control [Plato] |
156 | Bad people are never really friends with one another [Plato] |
9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |
148 | If the prime origin is destroyed, it will not come into being again out of anything [Plato] |
152 | The mind of God is fully satisfied and happy with a vision of reality and truth [Plato] |
150 | We cannot conceive of God, so we have to think of Him as an immortal version of ourselves [Plato] |
149 | There isn't a single reason for positing the existence of immortal beings [Plato] |
146 | Soul is always in motion, so it must be self-moving and immortal [Plato] |