50 ideas
| 21021 | Keep premises as weak as possible, to avoid controversial difficulties [Nussbaum] |
| 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] |
| 21812 | Being is the product of pure intellect [Plotinus] |
| 21817 | The One does not exist, but is the source of all existence [Plotinus] |
| 21824 | The One is a principle which transcends Being [Plotinus] |
| 21813 | Number determines individual being [Plotinus] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 5506 | If soul was like body, its parts would be separate, without communication [Plotinus] |
| 21827 | The movement of Soul is continuous, but we are only aware of the parts of it that are sensed [Plotinus] |
| 21828 | A person is the whole of their soul [Plotinus] |
| 21809 | Our soul has the same ideal nature as the oldest god, and is honourable above the body [Plotinus] |
| 21825 | The soul is outside of all of space, and has no connection to the bodily order [Plotinus] |
| 21007 | Storytelling is never neutral; some features of the world must be emphasised [Nussbaum] |
| 21826 | The Soul reasons about the Right, so there must be some permanent Right about which it reasons [Plotinus] |
| 6922 | Ecstasy is for the neo-Platonist the highest psychological state of man [Plotinus, by Feuerbach] |
| 21025 | Particularism gives no guidance for the future [Nussbaum] |
| 21026 | Compassion is unreliable, because it favours people close to us [Nussbaum] |
| 21019 | Social contracts assume equal powers among the participants [Nussbaum] |
| 21011 | We shouldn't focus on actual preferences, which may be distorted by injustices [Nussbaum] |
| 21008 | Liberalism does not need a comprehensive account of value [Nussbaum] |
| 21012 | Women are often treated like children, and not respected for their choices [Nussbaum] |
| 21015 | Negative liberty is incoherent; all liberties, to do and to be, require the prevention of interference [Nussbaum] |
| 21017 | Political freedom is an incoherent project, because some freedoms limit other freedoms [Nussbaum] |
| 21016 | Political and civil rights are not separate from economic and social rights [Nussbaum] |
| 21009 | Capabilities: Life, Health, Safety, Mental life, Love, Planning, Joining in, Nature, Play, Control [Nussbaum, by PG] |
| 21010 | Justice requires that the ten main capabilities of people are reasonably enabled [Nussbaum] |
| 21013 | Capabilities are grounded in bare humanity and agency; qualifying as rational is not needed [Nussbaum] |
| 21014 | Rights are not just barriers against state interference; governments must affirm capabilities of citizens [Nussbaum] |
| 21020 | Any establishment belief system is incompatible with full respect for all citizens [Nussbaum] |
| 21023 | We should respect animals in the way that we respect the animal nature in humans [Nussbaum] |
| 21024 | It may be no harm to kill an animal which cannot plan for its future [Nussbaum] |
| 21022 | The Capabilities Approach sees animals as agents, not just as having feelings [Nussbaum] |
| 21816 | Soul is the logos of Nous, just as Nous is the logos of the One [Plotinus] |
| 21815 | Because the One is immobile, it must create by radiation, light the sun producing light [Plotinus] |
| 21814 | How can multiple existence arise from the unified One? [Plotinus] |
| 21808 | Soul is author of all of life, and of the stars, and it gives them law and movement [Plotinus] |
| 21811 | Even the soul is secondary to the Intellectual-Principle [Nous], of which soul is an utterance [Plotinus] |