64 ideas
125 | Is a gifted philosopher unmanly if he avoids the strife of the communal world? [Plato] |
1654 | In "Gorgias" Socrates is confident that his 'elenchus' will decide moral truth [Vlastos on Plato] |
4321 | We should test one another, by asking and answering questions [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] |
10779 | A comprehension axiom is 'predicative' if the formula has no bound second-order variables [Linnebo] |
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] |
10781 | A 'pure logic' must be ontologically innocent, universal, and without presuppositions [Linnebo] |
9605 | If a proposition is false, then its negation is true [Brown,JR] |
10778 | Can second-order logic be ontologically first-order, with all the benefits of second-order? [Linnebo] |
10783 | Plural quantification depends too heavily on combinatorial and set-theoretic considerations [Linnebo] |
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] |
10782 | The modern concept of an object is rooted in quantificational logic [Linnebo] |
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] |
114 | Rhetoric can produce conviction, but not educate people about right and wrong [Plato] |
116 | Rhetoric is irrational about its means and its ends [Plato] |
135 | All activity aims at the good [Plato] |
122 | Moral rules are made by the weak members of humanity [Plato] |
139 | A good person is bound to act well, and this brings happiness [Plato] |
128 | Is it natural to simply indulge our selfish desires? [Plato] |
4322 | In slaking our thirst the goodness of the action and the pleasure are clearly separate [Plato] |
136 | Good should be the aim of pleasant activity, not the other way round [Plato] |
134 | Good and bad people seem to experience equal amounts of pleasure and pain [Plato] |
132 | If happiness is the satisfaction of desires, then a life of scratching itches should be happiness [Plato] |
4319 | In a fool's mind desire is like a leaky jar, insatiable in its desires, and order and contentment are better [Plato] |
130 | Is the happiest state one of sensual, self-indulgent freedom? [Plato] |
120 | Should we avoid evil because it will bring us bad consequences? [Plato] |
118 | I would rather be a victim of crime than a criminal [Plato] |
140 | Self-indulgent desire makes friendship impossible, because it makes a person incapable of co-operation [Plato] |
131 | If absence of desire is happiness, then nothing is happier than a stone or a corpse [Plato] |
119 | A criminal is worse off if he avoids punishment [Plato] |
129 | Do most people praise self-discipline and justice because they are too timid to gain their own pleasure? [Plato] |
4320 | The popular view is that health is first, good looks second, and honest wealth third [Plato] |
137 | As with other things, a good state is organised and orderly [Plato] |
141 | A good citizen won't be passive, but will redirect the needs of the state [Plato] |
123 | Do most people like equality because they are second-rate? [Plato] |
124 | Does nature imply that it is right for better people to have greater benefits? [Plato] |
9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |