45 ideas
6961 | An analogy begins to break down as soon as the two cases differ [Hume] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
8764 | Categories are the best foundation for mathematics [Shapiro] |
8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
21285 | Events are baffling before experience, and obvious after experience [Hume] |
22252 | Capitalism may actually be the best way to foster community [Conway,D] |
22253 | Capitalism is just the market, with optional limited government, and perhaps democracy [Conway,D] |
22256 | Capitalism prefers representative democracy, which avoids community decision-making [Conway,D] |
22255 | Capitalism breaks up extended families, and must then provide welfare for the lonely people [Conway,D] |
22257 | Capitalism is anti-community, by only valuing individuals, and breaking up families [Conway,D] |
6959 | We can't assume God's perfections are like our ideas or like human attributes [Hume] |
6957 | The objects of theological reasoning are too big for our minds [Hume] |
21255 | No being's non-existence can imply a contradiction, so its existence cannot be proved a priori [Hume] |
21254 | A chain of events requires a cause for the whole as well as the parts, yet the chain is just a sum of parts [Hume] |
1435 | If something must be necessary so that something exists rather than nothing, why can't the universe be necessary? [Hume] |
6962 | The thing which contains order must be God, so see God where you see order [Hume] |
21282 | Design cannot prove a unified Deity. Many men make a city, so why not many gods for a world? [Hume] |
21280 | From a ship you would judge its creator a genius, not a mere humble workman [Hume] |
21281 | This excellent world may be the result of a huge sequence of trial-and-error [Hume] |
21283 | Humans renew their species sexually. If there are many gods, would they not do the same? [Hume] |
6966 | Creation is more like vegetation than human art, so it won't come from reason [Hume] |
21284 | This Creator god might be an infant or incompetent or senile [Hume] |
21286 | Motion often begins in matter, with no sign of a controlling agent [Hume] |
21287 | The universe could settle into superficial order, without a designer [Hume] |
21288 | Ideas arise from objects, not vice versa; ideas only influence matter if they are linked [Hume] |
21256 | A surprise feature of all products of 9 looks like design, but is actually a necessity [Hume] |
6964 | From our limited view, we cannot tell if the universe is faulty [Hume] |
21279 | If the divine cause is proportional to its effects, the effects are finite, so the Deity cannot be infinite [Hume] |
6958 | How can we pronounce on a whole after a brief look at a very small part? [Hume] |
6963 | Why would we infer an infinite creator from a finite creation? [Hume] |
6960 | Analogy suggests that God has a very great human mind [Hume] |
6965 | The universe may be the result of trial-and-error [Hume] |
6967 | Order may come from an irrational source as well as a rational one [Hume] |