32 ideas
19115 | You can 'rebut' an argument's conclusion, or 'undercut' its premises [Antonelli] |
8623 | Proof reveals the interdependence of truths, as well as showing their certainty [Euclid, by Frege] |
13907 | If you pick an arbitrary triangle, things proved of it are true of all triangles [Euclid, by Lemmon] |
19119 | We infer that other objects are like some exceptional object, if they share some of its properties [Antonelli] |
19111 | Reasoning may be defeated by new premises, or by finding out more about the given ones [Antonelli] |
19114 | Should we accept Floating Conclusions, derived from two arguments in conflict? [Antonelli] |
19113 | Weakest Link Principle: prefer the argument whose weakest link is the stronger [Antonelli] |
19116 | Non-monotonic core: Reflexivity, Cut, Cautious Monotonicity, Left Logical Equivalence, Right Weakening [Antonelli] |
19117 | We can rank a formula by the level of surprise if it were to hold [Antonelli] |
19118 | People don't actually use classical logic, but may actually use non-monotonic logic [Antonelli] |
19110 | In classical logic the relation |= has Monotony built into its definition [Antonelli] |
19112 | Cautious Monotony ignores proved additions; Rational Monotony fails if the addition's negation is proved [Antonelli] |
6297 | Euclid's geometry is synthetic, but Descartes produced an analytic version of it [Euclid, by Resnik] |
9603 | An assumption that there is a largest prime leads to a contradiction [Euclid, by Brown,JR] |
9894 | A unit is that according to which each existing thing is said to be one [Euclid] |
8738 | Postulate 2 says a line can be extended continuously [Euclid, by Shapiro] |
22278 | Euclid relied on obvious properties in diagrams, as well as on his axioms [Potter on Euclid] |
8673 | Euclid's parallel postulate defines unique non-intersecting parallel lines [Euclid, by Friend] |
10250 | Euclid needs a principle of continuity, saying some lines must intersect [Shapiro on Euclid] |
10302 | Euclid says we can 'join' two points, but Hilbert says the straight line 'exists' [Euclid, by Bernays] |
14157 | Modern geometries only accept various parts of the Euclid propositions [Russell on Euclid] |
1600 | Euclid's common notions or axioms are what we must have if we are to learn anything at all [Euclid, by Roochnik] |
20086 | Nowadays sovereignty (once the basis of a state) has become relative [Reybrouck] |
20090 | Today it seems almost impossible to learn the will of the people [Reybrouck] |
20087 | There are no united monolothic 'peoples', and no 'national gut feelings' [Reybrouck] |
20089 | Technocrats may be efficient, but they lose legitimacy as soon as they do unpopular things [Reybrouck] |
20088 | Technocrats are expert managers, who replace politicians, and can be long-term and unpopular [Reybrouck] |
20085 | Democracy is the best compromise between legitimacy and efficiency [Reybrouck] |
20095 | A referendum result arises largely from ignorance [Reybrouck] |
20094 | You don't really govern people if you don't involve them [Reybrouck] |
20093 | In the 18th century democratic lots lost out to elections, that gave us a non-hereditary aristocracy [Reybrouck] |
20091 | Representative elections were developed in order to avoid democracy [Reybrouck] |