65 ideas
7278 | Words of wisdom are precise and clear [Zhuangzi (Chuang Tzu)] |
13860 | We can only learn from philosophers of the past if we accept the risk of major misrepresentation [Wright,C] |
7281 | Don't even start, let's just stay put [Zhuangzi (Chuang Tzu)] |
7282 | Disagreement means you do not understand at all [Zhuangzi (Chuang Tzu)] |
13883 | The best way to understand a philosophical idea is to defend it [Wright,C] |
7284 | If you beat me in argument, does that mean you are right? [Zhuangzi (Chuang Tzu)] |
10142 | The attempt to define numbers by contextual definition has been revived [Wright,C, by Fine,K] |
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] |
9868 | An expression refers if it is a singular term in some true sentences [Wright,C, by Dummett] |
6297 | Euclid's geometry is synthetic, but Descartes produced an analytic version of it [Euclid, by Resnik] |
13861 | Number theory aims at the essence of natural numbers, giving their nature, and the epistemology [Wright,C] |
9603 | An assumption that there is a largest prime leads to a contradiction [Euclid, by Brown,JR] |
13892 | One could grasp numbers, and name sizes with them, without grasping ordering [Wright,C] |
9894 | A unit is that according to which each existing thing is said to be one [Euclid] |
13867 | Instances of a non-sortal concept can only be counted relative to a sortal concept [Wright,C] |
8738 | Postulate 2 says a line can be extended continuously [Euclid, by Shapiro] |
10302 | Euclid says we can 'join' two points, but Hilbert says the straight line 'exists' [Euclid, by Bernays] |
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] |
14157 | Modern geometries only accept various parts of the Euclid propositions [Russell on Euclid] |
17441 | Wright thinks Hume's Principle is more fundamental to cardinals than the Peano Axioms are [Wright,C, by Heck] |
13862 | There are five Peano axioms, which can be expressed informally [Wright,C] |
17853 | Number truths are said to be the consequence of PA - but it needs semantic consequence [Wright,C] |
17854 | What facts underpin the truths of the Peano axioms? [Wright,C] |
1600 | Euclid's common notions or axioms are what we must have if we are to learn anything at all [Euclid, by Roochnik] |
13894 | Sameness of number is fundamental, not counting, despite children learning that first [Wright,C] |
10140 | We derive Hume's Law from Law V, then discard the latter in deriving arithmetic [Wright,C, by Fine,K] |
8692 | Frege has a good system if his 'number principle' replaces his basic law V [Wright,C, by Friend] |
17440 | Wright says Hume's Principle is analytic of cardinal numbers, like a definition [Wright,C, by Heck] |
13893 | It is 1-1 correlation of concepts, and not progression, which distinguishes natural number [Wright,C] |
13888 | If numbers are extensions, Frege must first solve the Caesar problem for extensions [Wright,C] |
13869 | Number platonism says that natural number is a sortal concept [Wright,C] |
13870 | We can't use empiricism to dismiss numbers, if numbers are our main evidence against empiricism [Wright,C] |
13873 | Treating numbers adjectivally is treating them as quantifiers [Wright,C] |
13899 | The Peano Axioms, and infinity of cardinal numbers, are logical consequences of how we explain cardinals [Wright,C] |
13896 | The aim is to follow Frege's strategy to derive the Peano Axioms, but without invoking classes [Wright,C] |
7804 | Wright has revived Frege's discredited logicism [Wright,C, by Benardete,JA] |
13863 | Logicism seemed to fail by Russell's paradox, Gödel's theorems, and non-logical axioms [Wright,C] |
13895 | The standard objections are Russell's Paradox, non-logical axioms, and Gödel's theorems [Wright,C] |
13884 | The idea that 'exist' has multiple senses is not coherent [Wright,C] |
13877 | Singular terms in true sentences must refer to objects; there is no further question about their existence [Wright,C] |
9878 | Contextually defined abstract terms genuinely refer to objects [Wright,C, by Dummett] |
13868 | Sortal concepts cannot require that things don't survive their loss, because of phase sortals [Wright,C] |
12189 | Logical necessity involves a decision about usage, and is non-realist and non-cognitive [Wright,C, by McFetridge] |
7289 | Do not try to do things, or to master knowledge; just be empty [Zhuangzi (Chuang Tzu)] |
23403 | You know you were dreaming when you wake, but there might then be a greater awakening from that [Zhuangzi (Chuang Tzu)] |
7285 | Did Chuang Tzu dream he was a butterfly, or a butterfly dream he was Chuang Tzu? [Zhuangzi (Chuang Tzu)] |
7277 | The perfect man has no self [Zhuangzi (Chuang Tzu)] |
7286 | To see with true clarity, your self must be irrelevant [Zhuangzi (Chuang Tzu)] |
13865 | 'Sortal' concepts show kinds, use indefinite articles, and require grasping identities [Wright,C] |
13866 | A concept is only a sortal if it gives genuine identity [Wright,C] |
13890 | Entities fall under a sortal concept if they can be used to explain identity statements concerning them [Wright,C] |
13898 | If we can establish directions from lines and parallelism, we were already committed to directions [Wright,C] |
13882 | A milder claim is that understanding requires some evidence of that understanding [Wright,C] |
7320 | Holism cannot give a coherent account of scientific methodology [Wright,C, by Miller,A] |
7279 | If words can't be defined, they may just be the chirruping of chicks [Zhuangzi (Chuang Tzu)] |
13885 | If apparent reference can mislead, then so can apparent lack of reference [Wright,C] |
17857 | We can accept Frege's idea of object without assuming that predicates have a reference [Wright,C] |
23404 | Words are for meaning, and once you have that you can forget the words [Zhuangzi (Chuang Tzu)] |
7283 | Great courage is not violent [Zhuangzi (Chuang Tzu)] |
7280 | As all life is one, what need is there for words? [Zhuangzi (Chuang Tzu)] |
7288 | Go with the flow, and be one with the void of Heaven [Zhuangzi (Chuang Tzu)] |
7287 | Fish forget about each other in the pond and forget each other in the Tao [Zhuangzi (Chuang Tzu)] |