61 ideas
| 192 | Only one thing can be contrary to something [Plato] |
| 9641 | Definitions should be replaceable by primitives, and should not be creative [Brown,JR] |
| 18335 | There are five problems which the truth-maker theory might solve [Rami] |
| 18334 | The truth-maker idea is usually justified by its explanatory power, or intuitive appeal [Rami] |
| 18339 | The truth-making relation can be one-to-one, or many-to-many [Rami] |
| 18333 | Central idea: truths need truthmakers; and possibly all truths have them, and makers entail truths [Rami] |
| 18342 | Most theorists say that truth-makers necessitate their truths [Rami] |
| 18340 | It seems best to assume different kinds of truth-maker, such as objects, facts, tropes, or events [Rami] |
| 18341 | Truth-makers seem to be states of affairs (plus optional individuals), or individuals and properties [Rami] |
| 18346 | 'Truth supervenes on being' only gives necessary (not sufficient) conditions for contingent truths [Rami] |
| 18345 | 'Truth supervenes on being' avoids entities as truth-makers for negative truths [Rami] |
| 18343 | Maybe a truth-maker also works for the entailments of the given truth [Rami] |
| 18338 | Truth-making is usually internalist, but the correspondence theory is externalist [Rami] |
| 18337 | Correspondence theories assume that truth is a representation relation [Rami] |
| 18347 | Deflationist truth is an infinitely disjunctive property [Rami] |
| 18350 | Truth-maker theorists should probably reject the converse Barcan formula [Rami] |
| 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] |
| 18336 | Internal relations depend either on the existence of the relata, or on their properties [Rami] |
| 190 | If asked whether justice itself is just or unjust, you would have to say that it is just [Plato] |
| 20184 | The only real evil is loss of knowledge [Plato] |
| 20185 | The most important things in life are wisdom and knowledge [Plato] |
| 191 | Everything resembles everything else up to a point [Plato] |
| 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] |
| 203 | Courage is knowing what should or shouldn't be feared [Plato] |
| 202 | No one willingly and knowingly embraces evil [Plato] |
| 193 | Some things are good even though they are not beneficial to men [Plato] |
| 197 | Some pleasures are not good, and some pains are not evil [Plato] |
| 200 | People tend only to disapprove of pleasure if it leads to pain, or prevents future pleasure [Plato] |
| 188 | Socrates did not believe that virtue could be taught [Plato] |
| 204 | Socrates is contradicting himself in claiming virtue can't be taught, but that it is knowledge [Plato] |
| 189 | If we punish wrong-doers, it shows that we believe virtue can be taught [Plato] |
| 9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |