38 ideas
| 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] |
| 23154 | We divide mankind into friend and foe, and cooperate with one and compete with the other [Russell] |
| 23153 | Gradually loyalty to a creed increased, which could even outweigh nationality [Russell] |
| 23152 | Increasingly war expands communities, and unifies them through fear [Russell] |
| 23155 | In early societies the leaders needed cohesion, but the rest just had to obey [Russell] |
| 23156 | The economic and political advantages of great size seem to have no upper limit [Russell] |
| 23157 | Government has a negative purpose, to prevent trouble, and a positive aim of realising our desires [Russell] |
| 23151 | A monarch is known to everyone in the group, and can thus unite large groups [Russell] |
| 23167 | Power should be with smaller bodies, as long as it doesn't restrict central powers [Russell] |
| 23163 | In an anarchy universities, research, books, and even seaside holidays, would be impossible [Russell] |
| 23168 | A state is essential, to control greedy or predatory impulses [Russell] |
| 23166 | In democracy we are more aware of being governed than of our tiny share in government [Russell] |
| 23162 | Managers are just as remote from workers under nationalisation as under capitalism [Russell] |
| 23165 | Socialists say economic justice needs some state control of industries, and of foreign trade [Russell] |
| 23160 | Being a slave of society is hardly better than being a slave of a despot [Russell] |
| 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] |
| 23158 | Slavery began the divorce between the work and the purposes of the worker [Russell] |
| 23161 | Slaves can be just as equal as free people [Russell] |
| 23159 | Scarce goods may be denied entirely, to avoid their unequal distribution [Russell] |
| 23164 | Modern justice is seen as equality, apart from modest extra rewards for exceptional desert [Russell] |