30 ideas
| 10147 | The Axiom of Choice is consistent with the other axioms of set theory [Feferman/Feferman] |
| 10148 | Axiom of Choice: a set exists which chooses just one element each of any set of sets [Feferman/Feferman] |
| 10149 | Platonist will accept the Axiom of Choice, but others want criteria of selection or definition [Feferman/Feferman] |
| 10150 | The Trichotomy Principle is equivalent to the Axiom of Choice [Feferman/Feferman] |
| 10146 | Cantor's theories needed the Axiom of Choice, but it has led to great controversy [Feferman/Feferman] |
| 10158 | A structure is a 'model' when the axioms are true. So which of the structures are models? [Feferman/Feferman] |
| 10162 | Tarski and Vaught established the equivalence relations between first-order structures [Feferman/Feferman] |
| 10160 | Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman] |
| 10159 | Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman] |
| 10161 | If a sentence holds in every model of a theory, then it is logically derivable from the theory [Feferman/Feferman] |
| 10156 | 'Recursion theory' concerns what can be solved by computing machines [Feferman/Feferman] |
| 10155 | Both Principia Mathematica and Peano Arithmetic are undecidable [Feferman/Feferman] |
| 6493 | We are not conscious of pure liquidity, but of the liquidity of water [Firth] |
| 4020 | The modern self has disengaged reason, self-exploration, and personal commitment [Taylor,C] |
| 4002 | My aim is to map the connections between our sense of self and our moral understanding [Taylor,C] |
| 4006 | I can only be aware of myself as a person who changes by means of my personal history [Taylor,C] |
| 4003 | Selfhood and moral values are inextricably intertwined [Taylor,C] |
| 4021 | Willingness to risk life was the constitutive quality of the man of honour [Taylor,C] |
| 4005 | To have respect for people, you must feel their claims, or their injustices, or hold them in awe [Taylor,C] |
| 4004 | Consistency presupposes intrinsic description [Taylor,C] |
| 4010 | In later utilitarianism the modern stress on freedom leads to the rejection of paternalism [Taylor,C] |
| 22809 | The social contract sees society as constituted by and for individuals [Taylor,C] |
| 22811 | Assigning a right based on a human capacity implies that the capacity should be developed [Taylor,C] |
| 22815 | If freedom depends on society and culture, the greatest freedom is in shaping them [Taylor,C] |
| 22814 | Our reliance on other people close to us does not imply any political obligations [Taylor,C] |
| 22812 | For most people the primacy of rights mainly concerns freedom [Taylor,C] |
| 22810 | A right is not just a rule, but also asserts certain ideas of moral worth [Taylor,C] |
| 22813 | Property is not essential for life, but it may be essential for independence [Taylor,C] |
| 23417 | If the state is neutral, there won't be sufficient community to support a welfare state [Taylor,C, by Kymlicka] |
| 4009 | Nominalists defended the sovereignty of God against the idea of natural existing good and evil [Taylor,C] |